# Complex antenna pattern measurements using infrared imaging and microwave holography

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Will B.A., Physics, State University of New York a t Geneseo, 1983 B.S.E.E., Clarkson College of Technology, 1983 M.S.E.E., Syracuse University, 1990 A Thesis subm itted to the Faculty of the Graduate School of the University of Colorado in p artial fulfillment of the requirem ents for the degree of Doctor of Philosophy Department of Electrical and Computer Engineering 1996 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9623704 Copyright 1996 by Will, John E. All rights reserved. UMI Microform 9623704 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © Copyright by John E. Will 1996 All Rights Reserved Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i This Dissertation for the Doctor of Philosophy degree by John E. Will has been approved for the Departm ent of Electrical and Computer Engineering by / / J /'Z r z .^ John D. Nor^ard Ronald M. Sega / M ark Robinson MaVek Grabowski Alan Mickelson Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Will, John E. (Ph.D., Electrical and Computer Engineering) Complex A ntenna P attern M easurem ents using Infrared Imaging and Microwave Holography Thesis directed by Professor John D. Norgard Infrared (IR) thermographic m easurem ents of microwave fields have been previously developed for the purpose of mapping radiating field intensity patterns and for mapping surface currents induced in conductors by radiating fields. A single therm al image provides a rapid m easurem ent of the field m agnitude over a surface, with the effective num ber of probe locations lim ited only by the pixel resolution of the imaging camera. This thesis research focused on investigating some methods of also determ in in gthe relative phase of the field by thermographic measurements. One method of determining the relative phase of the field a t each thermographic pixel location is a “Plane-to-Plane” (PTP) Fourier iterative technique. Field m agnitude m easurem ents are made over two planes, both in the radiating near-field of the antenna under test, and separated by only a few wavelengths. Starting with an estim ate of the field phase, Fourier processing techniques are used to iteratively “propagate” between the planes to determine the unique phase distribution a t each plane. The PTP processing technique is described and comparisons are then made between the sim ulated results and results from m easured IR thermograms of the field Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of a 36 element patch array antenna operating at 4 GHz using the UCCS Therm al Camera. Agreement between the simulations and m easured data results is very good, with the simulations indicating th a t a therm al m easurem ent dynamic range of about 30 dB is necessary to accurately reconstruct the field phase information. A second, completely independent, method related to classical optical holography is also described. This holographic technique uses the known m agnitude and phase of a second, reference source, field to back out the m agnitude and phase of the desired field from the interference patterns between the fields. Simulation results of this technique are shown which indicate excellent phase reconstruction from thermographic measurements having only a 20 dB dynamic range, given well known reference field data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS There are several individuals th a t I wish to thank for their support during this thesis research. Foremost of these is my wife, Barbara, and my sons David and Daniel (10 and 8). Barbara h ad to suffer with my gloomy moods, put up with periodically stressful times, and let prepared dinners go un-eaten, without truly understanding my joy found in a well-solved equation or a well-executed subroutine. My sons were great, constantly asking if I had "gotten my Doctor yet," wishing me well, offering to help, and being very empathetic about the stress surrounding each of the various exams and presentations. I wish to than k the National Institute of Standards and Technology (NIST) in Boulder, CO. Their interest and support in my thesis research topic allowed me to stay focused and committed to my research. Katie MacReynolds provided me with desperately needed near-field antenna calibration data from which I could compare my results with confidence. Dr. Carl Stubenrauch was my catalyst. We shared and discussed ideas on all aspects of my research, he cross-checked my codes and proof-read my reports, and we have become good friends. I could not have asked for a better research partner. I would also like to thank Dr. A.T. Adams, now retired, from Syracuse University, who was my M aster's thesis advisor and instructor for many of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. my EM classes in my M aster's program a t Syracuse. Because of his support and enthusiasm towards me, my M aster's program experience was very enjoyable; thus, encouraging me to continue with a Ph.D. There is also one individual th a t I wish to th an k th a t I have never met, Dr. G. Junkin of the University of Sheffield. After seeing a reference to a paper by Dr. Junkin related to my research, I sent him an email asking for more information. He responded back w ithin ju st a few hours, attaching a complete paper (text and figures) to his message. A few days later he sent some additional related papers of his th a t were about to be published th at were very helpful in my research. I sincerely appreciate his help, and hope th a t one day I will be able to m eet him to th an k him in person. I would also like to th an k my advisor, Dr. John Norgard, for suggesting this topic and introducing me to the people at NIST. His support and encouragement throughout my entire Ph.D. program have been very valuable. 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TABLE OF CONTENTS CHAPTER 1: INTRODUCTION.................................................................... 1 1.1 E x te n sio n of H a rd w ire T ech n iq u e s to T h erm o g ra p h ic M e a s u re m e n ts ..........................................................................................................2 1.2 S p e c ia l T h erm o g ra p h ic S c r e e n s ................................................................. 4 1.3 H o lo g ra p h ic T e c h n iq u e s................................................................................ 5 CHAPTER 2: IR MAGNITUDE MEASUREMENTS OF RADIATING FIELDS..............................................................................................................7 2.1 In tro d u c tio n to IR M a g n itu d e M e a s u re m e n ts.........................................7 2.2 T h e rm a l C o n v e c tio n ......................................................................................10 2.3 T h e rm a l C o n d u ctio n .....................................................................................13 2.4 T h e rm a l R a d ia tio n ........................................................................................13 2.5 T h e rm a l P a p e r T em p era tu re fro m In c id e n t F ie ld s.............................14 2.6 UCCS C a m e ra ................................................................................................. 19 CHAPTER 3: MEASUREMENT SETUP AND PROCEDURE................22 3.1 B a sic M ea su re m e n t S e tu p ............................................................................22 3.2 M ea su re m e n t P ro c e d u re ..............................................................................26 3.3 C onversion o f A G A 780 O u tp u t to E -F ield D a t a ...................................28 3.4 O ff-A xis Illu m in a tio n ................................................................................... 30 CHAPTER 4: PLANE-TO-PLANE (PTP) PHASE RETRIEVAL 32 4.1 In tro d u c tio n o f P T P T e c h n iq u e ...............................................................32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2 P la n a r N ear-F ield to F ar-F ield T ra n sfo rm a tio n s...............................35 4.3 P lane-to-P lane (PTP) P h a se R e trie v a l R e s u lts .................................... 41 4.3.1 Sim ulations................................................................................................. 41 4.3.2 IR Thermogram Results............................................................................. 45 4.4 F u tu re W o r k .....................................................................................................48 CHAPTER 5: HOLOGRAPHY..................................................................... 50 5.1 In tro d u c tio n to H o lo g ra p h ic T e c h n iq u e ................................................ 50 5.2 D e te rm in in g th e R eferen ce A n te n n a F ie ld .............................................55 5.3 C lassical H o lo g ra p h ic Im a g e R e c o n s tr u c tio n ..................................... 60 5.3.1 Theory o f Classical Holographic Image Reconstruction........................60 5.3.2 Sim ulation o f Classical Holographic Image Reconstruction............... 62 5.4 Im p ro ved H olo g ra p h ic Im a g e R e c o n stru c tio n ..................................... 64 5.4.1 Theory o f Improved Holographic Image Reconstruction.......................64 5.4.2 Sim ulation o f Improved Holographic Image Reconstruction............... 66 5.5 F u tu re H o lo g ra p h ic W o rk ...........................................................................68 CHAPTER 6: SUMMARY............................................................................. 70 BIBLIOGRAPHY...........................................................................................72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF FIGURES Figure 1 - Geometry of E-Field Incident on a M aterial....................................... 8 Figure 2 - Close-up IR Image of an Array Showing the Distortion from Rising Warmed A ir.......................................................................................................12 Figure 3 - Tem perature Rise in Teledeltos Paper v.s. Einc............................... 16 Figure 4 - Comparison of Normalized E-Field D ata Using Sm ith's E quationl8 Figure 5 - Comparison of Normalized E-Field D ata Using Polynomial Fit (Equation 13).................................................................................................... 19 Figure 6 - Photograph of IR M easurement Setup...............................................23 Figure 7 - Close up of Thermal Camera with Aiming Laser and M irrors...... 25 Figure 8 - Comparison of IR M easured E-Field to Expected Levels................30 Figure 9 - Schematic of PTP Measurement S etup..............................................33 Figure 10 - Plane-to-Plane (PTP) Phase Retrieval Process...............................34 Figure 11 - Exterior Field Regions of a Radiating A n te n n a.............................37 Figure 12 - PTP Generated Far-Field from NIST M agnitude D a ta ................42 Figure 13 - PTP Results Using NIST Magnitude D ata Truncated to 20 dB Dynamic R ange................................................................................................43 Figure 14 - PTP Results from Simulated 30 dB Dynamic Range D a ta .......... 45 Figure 15 - PTP Results for AGA 780 Therm ogram s........................................ 46 Figure 16 - Overlay of Convergence Error Metrics for Various PTP Runs ....48 Figure 17 - Typical Setup to Produce a Classical Optical Hologram...............51 Reproduced with permission of the copyright owner. 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Figure 18 - Setup to Produce a Microwave Hologram...................................... 52 Figure 19 - Schematic of the Setup for the Holographic M easurem ents 53 Figure 20 - Example of the Construction of a Microwave Hologram..............55 Figure 21 - Setup for Determining Tilted Plane Configuration...................... 57 Figure 22 - Contour Plots of the Magnitude of the Field of the Reference Antenna, (a) Computed horn NIST Near-Field Data, (b) From IR Thermogram M easurem ents...........................................................................59 Figure 23- Sim ulated Classical Hologram Reconstruction Comparison with True F a r Field for 36 by 36 Element A rray ................................................. 63 Figure 24 - Sim ulated Classical Hologram Reconstruction Comparison with True F ar Field for 6 by 6 Element A rray ..................................................... 64 Figure 25 - AUT Far-Field Computed from Sim ulated Hologram s................. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 CHAPTER 1: INTRODUCTION There continues to be significant interest in the development of new near-field m easurem ent techniques for the purpose of determ ining the farfield radiation patterns of antennas. The current practice today is to carefully position a hard-w ired field probe to several well known locations about a surface around the antenna-under-test (AUT) while recording the m agnitude and relative phase of each measurement [1]. Many different techniques have been developed for accurate probe positioning and minimization of the num ber of probe location m easurem ents required; however, all these techniques are time intensive due to the large num ber of probe m easurem ent locations required [2], Thermographic m easurem ents of microwave fields have been developed for the purpose of m apping radiating field intensity patterns [3, 4, 5, 6, 7, 8, 9, 10] and m apping surface currents induced in conductors by radiating fields [11, 12, 13, 14, 15]. A resistive sheet positioned in a radiating field will absorb energy in proportion to the strength of the radiating field, resulting in a tem perature rise in the sheet. A therm al 'picture' is then taken of the h eat p attern on the resistive sheet. Each pixel of this therm al picture then represents a m easurem ent of the intensity (magnitude) of the field at the pixel location on the resistive sheet. A single Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 therm al image, therefore, provides a rapid m easurem ent of the field magnitude over a surface; with the effective num ber of probe locations limited only by the pixel resolution of the imaging camera. The problem with this previous thermographic m easurem ent technique is th a t only the m agnitude of the field is measured. In order to obtain a far-field p attern from near-field antenna measurements, relative phase information is also required [1,2]. The m ain purpose of this work is to develop and evaluate several techniques for obtaining the necessary phase information from thermographic measurements. Several potential methods of obtaining phase from magnitude only thermographic m easurements are considered. These methods are grouped into those th a t were developed originally for hardw ired measurements, the development of special thermographic screens, and microwave holographic techniques. These are discussed separately below. 1.1 E x ten sio n of H a rd w ire T ech n iq u es to T h erm o g ra p h ic M ea su rem en ts Direct m easurement of phase information in standard hard-wired near-field antenna m easurem ent ranges requires the use of expensive vector m easurem ent equipment and suffers from inaccurate measurements, particularly at the higher frequencies, due to errors such as mechanical positioning of the probe antenna and tem perature induced cable length Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 changes. As a result, several algorithms have been proposed in recent years to retrieve phase measurements. information from phase-less (magnitude only) Comparison of some of the practical algorithms and an overview of the m athem atical basis of phase retrieval can be found in [16, 17]. Two closely related error-reduction type techniques, known as the Gerchberg-Saxton [18] and the Input-O utput [17] methods, require magnitude m easurem ents in both the near field and in the far field; thus, they are not practical for the therm al imaging technique (which requires high power levels), and, therefore, were not further investigated in this thesis research. An iterative Fourier technique known as the Miseli algorithm [19] requires two far-field m easurem ents with the antenna beam "defocused". This technique, therefore, is also impractical for consideration with a therm al imaging technique. Another technique, known as Plane-to-Plane (PTP) Phase Retrieval [20, 21, 22] was specifically developed for near-field measurements of antennas. A closely related phase retrieval algorithm [23] has been successfully implemented by Yaccarino and Rahmat-Samii a t the University of California at Los Angeles (UCLA) with a bi-polar planar hard-wired near field m easurem ent system using magnitude only data m easured over two planes separated by only 2.560 a. [24]. Further modifications and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 improvements to this technique have been carried out by Rahmat-Samii, et. al. [25] and Junkin et. al. at the University of Sheffield, UK. [26, 27, 28]. The question of the uniqueness of the solution obtained via a plane-to-plane phase retrieval algorithm has been addressed by several authors, most notably Isem ia, Leone, and Pierri [22, 29, 30 ]. One form of this Plane-to-Plane phase retrieval technique was applied to a set of therm ally acquired m agnitude data as p art of this research work, and is discussed in more detail in Chapter 3. 1.2 S p e c ia l T h erm o g ra p h ic Screens The concept of using a special therm al screen with built-in tuned dipoles to determine the m agnitude and phase of a radiating field was also reviewed as p a rt of this thesis research. The idea behind this concept, which is being pursued by Mission Research Corporation (MRC), is th a t a m atrix of dipoles, tuned to the frequency of measurement, is built into the resistive sheet used to therm ally measure the radiating field at each location for which m easured data is desired [31]. Typically, in near-field m easurements, the m easurem ent spacing is slightly less th an 0.5 X, and the planar area to be m easured is a few 10's cf X; thus, literally thousands of dipoles built into the screen would be required. The m agnitude and phase of the radiating field of the AUT is then determined from a series of m agnitude only therm al Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 m easurem ents made with the dipoles radiating at a known power level and relative phase. This technique was not pursued under this thesis research for two reasons. First, another group (MRC) is currently pursuing this technique, and, second, it appears th a t the required therm al screen(s) would be very difficult and expensive to build and would also have lim ited utility. 1.3 H olo g ra p h ic T echniques Microwave holography techniques appear well suited to the determination of the complete (complex) field data from thermographic measurements. In general, the term hologram m eans an interference pattern. In particular, hologram means a very special interference pattern from which it is possible to reconstruct the complete complex image. Holography was first introduced in 1948 at optical frequencies by Gabor [32]; while at microwave frequencies, holography was first demonstrated by Dooley in 1965 [33]. In microwave holography, as applied in this thesis research to therm al imaging of radiating RF fields, two antennas are set up to irradiate a resistive sheet from which the therm al image is to be recorded. One antenna is the antenna under test (AUT) and the second antenna is a well known reference (REF) antenna. The two Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 antennas are set to radiate at the same frequency, so th at a static interference pattern is generated on the therm al paper. The relative phase difference of the fields from the two antennas a t each location over the therm al paper produces either constructive or destructive interference. Two options for reconstructing the complex field data from this microwave hologram were considered in this thesis research. The first method is analogous to an optical hologram read-out. In this method, the hologram is processed by direct multiplication of each d ata point by a normalized reference wave, which is sim ilar to re-illum inating an optical hologram with its reference wave. The result is then three "images", viz. an amplitude modulated version of the reference wave, the desired complex image, and a phase-shifted complex conjugate of the desired image. Viewing of this image is then lim ited to the region of the desired image only. A second processing method results from the realization th a t the hologram can be processed exactly, th a t is, with the additional knowledge of the m agnitude of the field of the AUT, the other images can be removed in the final data. The m agnitude and phase of the field of the reference antenna are well known and the magnitude of the field of the AUT can be m easured by the IR imaging technique directly; thus, the hologram data can be presented as an equation with a single unknown, the phase of the AUT field. These two holographic processing methods and th eir results are discussed in detail in C hapter 4. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 CHAPTER 2: IR MAGNITUDE MEASUREMENTS OF RADIATING FIELDS 2.1 In tro d u c tio n to IR M a g n itu d e M ea su rem en ts The quality of the results of phase retrieval and holographic techniques depends a great deal on the quality of the magnitude data m easurements. This chapter discusses the background and process used to collect the IR therm al m easurem ents of the m agnitude of a radiating field. The basic principle involved in IR m easurem ents of the magnitude of a radiating field is th a t a lossy m aterial positioned in the field will heat as it absorbs power from the field. Since the absorbed power is related to the strength of the field, the tem perature rise in the m aterial can be m easured and then related to the field strength. For a thin, low-loss m aterial, the fields in the m aterial can be approximated as constant; thus, the power absorbed per square m eter in the m aterial is adequately described by [34]: P abs = + W where h is a vector normal to the surface of the lossy m aterial, d is the thickness of the lossy m aterial, co is the radian frequency, a is the real p art of the m aterial conductivity, s" is the im aginary p a rt of the complex permitivity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the material, |i" is the im aginary p art of the complex perm iability of the m aterial, and the t subscripts on the field quantities imply the tangential components. In this thesis research, Teledeltos paper was used as the lossy m aterial. The m aterial properties of this paper are d = 80 pm, o'' = 8 siemens/m, e" = 0, and p" = 0. Thus, for the Teledeltos paper, the absorbed power can be described by: )[% ¥* (2> Z 0 Consider the illustration of a propagating electric field incident on a sheet of therm al paper shown in Figure 1. As a result of the discontinuity between the wave impedance in the m aterial to the wave impedance in the surrounding air, there are reflecting waves at both boundaries of the m aterial in addition to the transm itted waves. The total electric field in the inc absorbing m aterial can be described as the summation of the positive inc z=0 z=d traveling wave transm itted from the incident wave through the m aterial Figure 1 - Geometry of E-Field Incident on a M aterial boundary and the negative traveling wave resulting from a reflection of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the transm itted wave off the back side of the absorbing material. Mathematically, this is represented as: E2 = EXe~r* +EZe~r'-z where y 2 = h +_ 2 _ =a V jo e 2 (3) 2 +jp 2. The square of this electric field is therefore: E \ = \E; |V2c- + \E2\2e2a'-: + 2 R e{£;£; (4) Using this result in equation 2 and integrating, the total absorbed power per square m eter in the Teledeltos paper is: Pabs = — 4 ] 5 l ( e^ _ - l)+A Re{£*£2--^ -W -l)} (5) Through the application of boundary conditions, E~_ and E2 can be determined from the original tangential incident electric field, E~rc as: e; e; r +i i - r 2p2 + -rp2(r + i) =e . i - r 2p2 =e , where, for norm al incidence, P = e~r'-d, T = (j]2 —770)/(772 + 77o)’ (6) "H2 intrinsic wave impedance in the material. V=. 'G JW + jCO S Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (7) 10 Due to energy conservation, in equilibrium, this absorbed power m ust be balanced by the power lost through therm al convection and therm al radiation as described below. 2.2 T h e rm a l C onvection Convection is the loss of h eat to the m aterial surrounding the therm al paper. Previous therm al imaging work [5, 6, 7, 14, 34, 35] has shown that convection is adequately described by Newton’s law of cooling: q = M(Ts - T a) (8) where q is the heat in W atts, h is the convection h e at transfer coefficient in W/m2K, A is the surface area in m2, Ts is the surface tem perature in K, and Ta is the am bient tem perature in K. In general, this convective h eat loss occurs on all six sides of a block of m aterial. The edges of the thin resistive paper used for these tests, however, have a negligible surface area; thus, convective losses from the edges of the paper were ignored. Additionally, the therm al paper was mounted on two layers of artist's poster board (total thickness of 1.0 cm). The poster board, therefore, represents a thick, EM transparent, therm ally insulative layer (low convection h eat transfer coefficient) between the paper and the radiating antenna. Thus, convection off the back side of the resistive paper was reduced to a negligible value. Convective h e at loss was then essentially lim ited to the front side of the therm al paper. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 The h eat transfer coefficient, h, is dependent on environmental factors such as the movement of air around the therm al paper (the capacity of the surrounding air to remove heat from the therm al paper); however, in this thesis research, since all therm al m easurem ents were performed in the enclosed anechoic chamber, a fixed value of h=0.93 as determined by Metzger [34] was used. In future work it may be possible to m easure certain environm ental factors to determine an accurate value of h a t the time of the therm al m easurement, and then use this value to balance the therm al paper heating equation. It is anticipated th a t some form of real-time determination of h such as this will be required in order to transfer the therm al m easurem ent technology from the (controlled) laboratory to a field m easurem ent system. A second problem with therm al convection is that, as the heat in the therm al paper is transferred to the surrounding air, the air decreases in density and, therefore, begins to rise. With the therm al paper oriented vertically, the rising, warmed, air tends to convect heat back into cooler areas of the therm al paper; thus, distorting the upper portion of the therm al image. This distortion can be clearly seen in Figure 2, which shows a close up therm al image of the radiating field from an array. The contour lines around the perim eter of the array in this image should be fairly rectangular, but as can be seen, the contour lines are deformed on the upper edge of the image. It may be possible to reduce or remove the effects of this distortion by data Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 processing. In addition, a modification of the screen with cells or baffles to reduce or eliminate air currents along the face of the screen may be possible. This is an area also left for future research. In this thesis work, distortion from rising, warmed air was eliminated by orienting the therm al screen horizontally as described in the test set-up section (Section 3.1). 10 20 PWlMBMni 30 40 50 60 Figure 2 - Close-up IR Image of an A rray Showing the D istortion from Rising W armed Air Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 2.3 T h e rm a l C onduction Conduction is the flow of h eat within a m aterial from hotter regions to cooler regions resulting in a "defocusing" of the therm al picture. The effect of conduction can be seen in the comparison of therm al m easurements to either hard-w ired m easurements or calculations as warmer than expected minimums (nulls) and cooler th an expected maximums [10, 36]. Thermal conduction is described mathem atically by Fourier's law of h eat conduction: qx = -kA ^ ex (9) where qx is the heat flow in the x direction in W atts, k is the therm al conductivity of the m aterial in W/mK, A is the cross-sectional surface area in m2 and T is the tem perature in K. Metzger [34] mentions th a t it may be possible to use therm al transport finite differencing methods to remove the therm al conduction distortions from the m easurement data. Other work, however, has shown that, in general, for low electrical conductivity therm al paper such as used in the measurements in this research, the therm al conductivity, k, is also low [11]. 2.4 T h e rm a l R a d ia tio n The Stefan-Boltzman law states th a t the total hemispherical emissive power of a blackbody is related to the tem perature of the blackbody by [37]: q = (JbA T Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (10) 14 where q is in watts, cn> is the Stefan-Boltzman constant (5.669E-8 W/m2K4), A is the surface area in m2, and T is the surface tem perature in K. The net power radiated by a gray body surrounded by several other gray bodies at different tem peratures is extremely complicated and, therefore, difficult to accurately compute for a test set-up like th a t used during this thesis research. A reasonably accurate first order approximation can be made, however, for a gray body with emissivity Sir (the Teledeltos paper), radiating into a larger body (the anechoic chamber) m aintained at a uniform ambient tem perature, Ta. Using this approximation, the net radiated power is given by: q = e,r<rbA ( T ; - T ; ) ( 11) 2.5 T h e rm a l P a p e r T em p era tu re fro m In c id e n t F ields The final (therm al equilibrium) tem perature of a sheet of Teledeltos paper in an EM field is then the result of a balance between the EM power absorbed by the paper and the power lost due to therm al convection and therm al radiation. Equations 8 and 11 therefore, can be combined as: ^ - £ ) +Mjr. - T.) 02 ) where Pabs is given by equations 5 and 6. R ather than attem pting to find a closed form solution to the above equations for Einc in terms of the therm al paper surface tem perature, a three Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 step process was performed. First, the above equations and constants were programmed into MATLAB and using the built in MAPLE symbolic solver, an array of surface tem perature values were then calculated for an array of Einc values. This data was then fit (via a built in least squares type polynomial fit function) to a 2nd order polynomial in surface tem perature. The MATLAB code MET2.M listed in Appendix A was used to perform these steps. Using this code, the best least-squares 2nd order polynomial fit for the Teledeltos paper is: 3.1x10~5(£,“.) + 3.5x1CT3(£ mc) - 0.302 = AT (13) where AT = Ts - Ta is the tem perature rise in Kelvins above ambient. Figure 3 shows a comparison of this polynomial (equation 13) to the computation of equation 12 (including equations 5 and 6). As shown in this figure, the fit is quite good with the exception of the lowest tem perature values. The disagreement in the curves at the low tem perature values is, however, partially offset by the lim itations of the UCCS AGA 780 therm al camera when set to the 10 degree therm al range (discussed in the next section). If the AGA 780 were used on a sm aller therm al range setting, such as 2 degrees, or a therm al camera with a greater dynamic range were used, then a different process of converting tem perature rise to incident E-field values would be necessary. For example, equations 5, 6, and 12 could be programed into an iterative minimization routine th a t uses the polynominal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 derived values (equation 13) as a starting point to provide a more accurate computation of tlie incident E-field from a m easured tem perature rise. Overlay o f M etzger's Equation (solid) with Polynom ial Fit (d ash ed ) 4 - Q. 100 300 200 400 500 600 F igure 3 - T em perature Rise in Teledeltos P aper v.s. Einc It should be stated that, at the sta rt of this thesis research, the following 2nd order polynomial taken from Sm ith’s M asters Thesis [38] was used to convert tem perature rise to E-field values: b + (b2 +4aAT)V2' 2a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (14) where a=3.703E-7, b=2.192E-4, AT is the difference in the pixel tem perature from the ambient background tem perature in Kelvins, and S is a scaling constant. The results from this equation do not agree very well with the expected results derived above. This, by itself, would not necessarily be serious; however, another problem was discovered. Two sets of thermograms were taken of an antenna radiating a t two different power levels; one a t a power level such th a t the maximum tem perature was near the full scale reading of the therm al camera (about 10 degrees above ambient), and one at a power level such th a t the maximum tem perature was at only about one th ird of the full scale reading of the therm al camera. When these thermograms were processed into incident E-field levels using equation 14 and then normalized, the agreement between them was very poor, except near the maximum value, as illustrated in Figure 4. This clearly illustrates th a t equation 14 is a poor representation of the tem perature rise from an incident field for the range of field values used during this thesis research. When these same thermograms were re-processed using the roots of equation 13, however, the agreement was quite good (given the differences in the m easurem ent dynamic range between the two thermograms) as shown in Figure 5. Equation 13, therefore, was used to convert thermogram tem peratures to E-field values throughout this thesis research work. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 Comparison of Normalized E-Field Data Using Smith's Equation 0.9 0.8 T3 - 0.7 0.6 1 0.5 U- £ 0.4 0.3 0.2 0.1 40 50 60 70 x-pixels Figure 4 - Com parison of Normalized E-Field D ata Using Sm ith's Equation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 Comparison of Normalized E-Field Data Using New Polynomial 1 0.9 0.8 -o 0.7 0.6 0.5 =5 0.4 2 0.3 0.2 0.1 0 10 20 30 40 50 60 70 80 x-pixels Figure 5 - Com parison o f N orm alized E-Field D ata Using Polynomial Fit (Equation 13) 2.6 UCCS C am era The current UCCS therm al camera is an AGA Thermovision® 780. This particular therm al camera provides an analog output to an external 8 bit digitizer to produce a m atrix of therm al intensity pixels [39]. These therm al intensity levels are in Isotherm al Units (IU) which are related to a blackbody tem perature by the non-linear relationship: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 where I is the Isotherm al U nit Value, T is the absolute tem perature in degrees K, and A, B, and C are constants associated with the sensor type and lens aperture setting. For example, for the long wave sensor (8-12 pm): A = 552855, B= 2994, and C=0.975 with an aperture setting of f=1.8 [40]. The controls of the therm al camera allow full scale therm al range to be set as either 2, 5, 10, 20, 50, 100, 200, 500, or 1000 IUs with an analog vernier adjustm ent for the setting of the IU of the center of the therm al range. From the 8 bit digitizer, there are 256 linear intensity levels across the full scale of the cam era output in IUs. For sm all changes in IUs (<10), near room tem perature, the conversion to blackbody tem perature (equation 15) is nearly linear. The conversion from blackbody tem perature to the strength of the square of the electric field is also approximately a linear conversion for small tem perature changes as discussed in the section above. There are, therefore, roughly 256 linear levels in the m easurem ent of the magnitude of the electric field using the UCCS therm al camera. Assuming the best of circumstances, i.e., a barely saturated therm al image, this results in 101ogio(256), or about 24 dB of dynamic range [measured as the difference in the full scale level (256 levels) to the sm allest detectable change (1 level)]. In addition, m easurem ents made with the UCCS therm al camera on a therm ally stable object indicate variations of about ± 2 intensity levels for m easurements of identical tem peratures after using a 15 fram e average. The actual, realizable, dynamic range for therm al m easurem ents of the electric Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 field strength, therefore, were reduced to about 20 dB of dynamic range and S/N for most measurements. An IBM/XT personal computer is interfaced to the external digitizer connected to the AGA 780 therm al camera and is used to retrieve and store the digital pixel intensity levels. An existing compiled PASCAL program called GETDAT.EXE w as used to collect IR images from the external digitizer and store them on a PC disk. This program perm itted a maximum of 15 frames of IR data to be captured at one time. The full 15 frames of data capture was used for each scene of data collected in this thesis research. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 CHAPTER 3: MEASUREMENT SETUP AND PROCEDURE 3.1 B a sic M ea su rem en t S e tu p A photograph of the setup used in this thesis research for both the Plane-to-Plane (PTP) and holographic m easurements (to be discussed in detail below) is shown in Figure 6. The 36 element patch array antenna used as the AUT is shown at the top of the photograph. This antenna was supplied by the N ational Institue of Standards and Technology (NIST), Boulder, CO. Complete calibration data in the form of standard planar near field scan data was also supplied by NIST. Centered, directly below the array antenna is the therm al paper, with its backing of therm al insulator (poster board), oriented horizontally and sitting on a wooden perim eter frame. Also, above the therm al paper near the top right h an d side of the photograph, is shown the 4 GHz Standard Gain Horn used as a reference antenna during the holographic data measurements. This reference horn, and complete calibration data for the horn, were also supplied by NIST. Well below the therm al paper (almost 3 meters below) is the AGA 780 therm al imaging camera. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 Figure 6 - Photograph o f IR M easurem ent Setup Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 The AGA 780 therm al imaging camera requires liquid nitrogen to cool the therm al detector; thus, the camera m ust be positioned within ju st a few degrees of level. In order to view the therm al paper hanging above the camera, an IR m irror was used to re-direct the camera view in the vertical direction. The m irror used was a 127 mm by 102 mm gold coated first- surface m irror obtained from Edm und Scientific. In addition, a second, lower quality, first-surface mirror of the same size was mounted adjacent to the first m irror such th a t the total mirror surface was 254 mm by 102 mm. This second m irror was only used to aid in the alignm ent and aiming of the therm al camera. A leveling laser was attached to the top of the camera and aimed into the second mirror with the laser beam parallel to the camera optical path. A bubble level built into the leveling laser was used to level the therm al camera. Then, a small patch of reflective m aterial was temporarily attached to the therm al paper at the location of the laser spot. The mirror tilt angle was then adjusted such th at the laser fight reflecting off of the patch on the therm al paper returned into the laser aperture. In this way, a nearly perfect perpendicular view of the therm al paper was ensured. Figure 7 is a photograph showing a close-up view of the therm al camera with the mirrors and laser attached. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 Figure 7 - Close up of Therm al Cam era w ith Aiming Laser and M irrors In plan ar near-field antenna measurements, it is desirable to measure the m agnitude and phase of the field over a planar m atrix with spacings of slightly less th an one h a lf wavelength, and to cover the entire region of non zero field amplitude. Obviously, the size of this region varies with antenna design; however, a good rule-of-thumb estim ate for many antennas is twice the size of the antenna aperture [41], Using the widest angle lens available at UCCS for the AGA 780 camera, one with a 20° field of view, and positioning the camera at about 3 meters from the therm al paper, the image Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 area was a little larger th an twice the array area (the array area is 38 cm by 38 cm whereas the IR image area was about 94 cm by 115 cm). Given the dynamic range lim itations of the AGA 780 camera (about 20 dB), this field-ofview was quite sufficient; however a larger field-of-view (about 180 cm 180 cm) would be more desirable for this array antenna, if a camera with a greater dynamic range were used. 3.2 M ea su rem en t P rocedure The following m easurem ent procedure was used for all of the IR thermograms collected for this thesis research. The IU therm al range dial was set to 10. This was selected as a balance between achievable tem perature rise in the therm al paper at acceptable RF power levels for the array (less than about 50 watts) and minimization of the risk of introducing data errors from therm al drift in the equipment or the ambient environment. The IU therm al level vernier dial was then set such th a t the ambient background tem perature registered ju st above zero on the 8-bit digitizer output. These settings were then locked in and no further camera adjustm ents were made for the entire m easurem ent set. RF power was then applied with the amplitude adjusted such th a t the greatest tem perature rise for the entire m easurem ent set did not exceed the maximum m easurable tem perature rise (10 IUs above ambient). For the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 data processed by tbe Plane-to-Plane technique, a m easurem ent set was the amplitude m easurem ents of the array fields at the two chosen plane distances. For the data processed holographically, a m easurem ent set consisted of six amplitude measurements; the array alone, the reference horn alone, and the two antennas radiating simultaneously with relative phase shifts between them of 0, 90, 180, and 270 degrees. The selection of RF power level was, therefore, an iterative process, since it was also desirable from a dynamic range stand-point to ensure th a t the greatest tem perature rise of the measurement set was very nearly full scale, and for the holographic measurements th a t the peak amplitudes from the two antennas separately were approximately equal. Once the RF power level was selected and applied, the therm al paper was illum inated for approximately 10 m inutes to ensure th a t therm al stability had been reached in the paper. This was further confirmed by m arking the peak therm al amplitude (using one of the cameras two isotherm al m arker controls) and verifying th a t the peak therm al amplitude rem ained unchanged after an additional 1 m inute of RF illumination. Once the image was considered therm ally stable, 15 frames of the image (the maximum allowable by the GETDAT.EXE program) were captured and stored in a file. This therm al data was then converted to E-field m agnitude data as discussed in the next section. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 3.3 C onversion o f A G A 780 O u tp u t to E -F ield D a ta The raw IU therm al data captured and saved by the GETDAT.EXE program was then processed into E-field levels by three MATLAB programs listed in Appendix A; IR_AV_C.M, TQTEMP.M, and TEMP2E3.M. The first program, IR_AV_C.M, reads in a raw IU data file and displays the stored header information about the file. The header information includes date and time, therm al level and therm al range settings, am bient tem perature, RF power level, IR lens used, num ber of data fields per frame, total num ber of fields in the file, and 4 comment lines. The program then asks for the fram es th at should be averaged together. For this work, all 15 frames (the maximum) were averaged together for each file. The program then reads the appropriate fields and assembles them into frames and averages the frames together, storing the data in the 116x64 element m atrix variable 'frame'. A contour plot of the final averaged frame data is then displayed. The MATLAB program TOTEMP.M was then used to convert the averaged frame data, which h as levels from 0 to 255 digitizer units, to tem perature in degrees C. This code uses the IU to blackbody conversion equation (equation 15) modified to include emissivity of the therm al paper and atmospheric attenuation as described in the AGA m anual [40]. The code stores the data converted to tem perature in the m atrix 'tframe' and then Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 displays the maximum and minimum tem perature of the image and a contour plot of the entire image. This tem perature was then converted to E-field levels by the MATLAB function TEMP2E3.M, which finds the positive root of equation 13. This equation relates the E-field to a rise in paper tem perature above the ambient tem perature. Since it is quite difficult to determine the exact setting of the therm al level of the UCCS AGA 780 therm al camera, the baseline or ambient tem perature was determined from the minimum tem perature value of each image, rath er th an from an independent ambient tem perature measurement. In practice, it was determined th a t a choice of ambient tem perature about 0.3°C above the minimum tem perature of the image was best. An example of the comparison between the E-field determined from an IR thermogram m easurem ent and the expected result based on NIST near-field measurements of the array is shown in Figure 8. As shown in this figure, agreement between the curves is quite good down to about 18 dB to 20 dB below the peak, as expected from the particulars of the AGA 780 camera discussed in Chapter 2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 Comparison of Expected (*) to Measured (+) E-Field at 45.1 cm i f -15 -20 -25 100 -100 x-position (cm) Figure 8 - Comparison of IR M easured E-Field to Expected Levels 3.4 O ff-Axis Illu m in a tio n A current literature search of previous work on thermographic mapping of EM fields shows only parallel and normal incidence of the field on the therm al paper. The holographic techniques used in this thesis research required th at at least one of the antennas produce a field of illumination at an oblique angle to the therm al paper. The effect of this angular illumination on the power absorbed by the therm al paper was discussed by Metzger [34]. This effect in a thin therm al screen, such as the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Teledeltos paper used in this thesis research, for tangetial E-Fields, however, is negligable. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 CHAPTER 4: PLANE-TO-PLANE (PTP) PHASE RETRIEVAL 4.1 In tro d u c tio n o f P T P T ech n iq u e The setup used for the plane-to-plane (PTP) phase retrieval technique is shown in Figure 9 and the phase retrieval process is illustrated in Figure 10. First, various variables and constants are defined and an estim ate of the magnitude and phase of the aperture field is made. This estim ate is then "propagated" to m easurem ent plane 1 by Fourier transform ation techniques, the details of which are described in the next section (section 4.2). The convergence error is then calculated, defined as: <16) where M is the m easured m agnitude data and IAI is the calculated magnitude data a t each pixel location in the plane of interest. The calculated magnitude is then replaced with the m easured m agnitude with the calculated phase retained. This complex data is then propagated by Fourier techniques back to the original aperture plane. All data outside of the antenna aperture is then truncated and the truncated data propagated to the second m easurem ent plane. Again, the convergence error is calculated and the calculated m agnitude data replaced with the m easured m agnitude at plane 2 with the calculated phase retained, and th is data is then propagated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 back to the aperture plane. At this point in the process, the change in the convergence error from the previous iteration is checked, and if the change in convergence error is less th an a set tolerance, the iterations are halted. If, however, the change in convergence error is still sufficiently large, the above iteration is repeated, starting with a truncation of data outside the antenna aperture. The MATLAB code PTPLOOP.M th a t implements this algorithm is also listed in Appendix A. T h erm a Paper Source AUT Camera Plane 2 Plane 1 Ap e r t u re Plane Figure 9 - Schem atic of PTP M easurem ent Setup Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 Initialize Variables including Complex Aperture Estimate Truncate Data outside Aperture Plane Propagate to Plane 1 Plane 1 Measured Magnitude Calculate Convergence Error i j Impose Measurer-’ Magnitude Back-Propagate to Aperture Okay Truncate Data outside Aperture Plane Check# of Iterations Exceeded Propagate to Plane 2 END Plane 2 Measured Magnitude Calculate Convergence Error Impose Measured Magnitude No Check Convergence Yes Back-Propagate to Aperture Figure 10 - Plane-to-Plane (PTP) Phase R etrieval Process Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 Junkin has recently suggested [27] th a t a "phase change acceleration procedure" be imposed between iterations. This procedure reduces the possibility of PTP algorithm stagnation due to a local minimum, which is an increasing problem with decreasing scan plane separation. In this research, the scan plane separation used was over 1.5 wavelengths, or about 0.066 D2/a (the scan plane separation used by Junkin was 0.0033 D2/X); thus the utility of incorporating the phase change acceleration procedure may be minimal. In addition, Junkin and Trueba [28] have also suggested a center-of-gravity type algorithm to help in the alignment of the two planes of measurements, which becomes more critical with increasing antenna operating frequency. Both of these algorithm modifications should be looked a t in future research as improvements to the PTP algorithm developed for this research. 4.2 P la n a r N ear-F ield to F ar-F ield T ra n sfo rm a tio n s The PTP algorithm discussed above is based on planar near-field to far-field transform ations which are the result of the pioneering work of Kerns and his development of the plane-wave scattering m atrix theory [42, 43, 44, 45, 46]. The planar near-field m easurem ent was the first of the near field techniques to be developed, verified, and implemented as an operational Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 method of obtaining antenna param eters. An excellent review of the history of near-field antenna m easurements is given by Yaghjian in [47]. The fields exterior to a radiating antenna are typically divided into three regions, as illustrated in Figure 11. The specific transitions from one region to the next are not sharply defined, and vary based on the antenna type and the acceptable uncertainty in the use of the data. Very dose to the antenna, i.e., within about one wavelength, is the region called the reactive near-field or sometimes the evanescent region. In this region, the imaginary portion of the complex Poynting vector, which is typically proportional to the inverse of the radial distance to the power of 3 or greater, is not negligible. It is this region th a t contributes to the reactive p a rt of the antenna input impedance, and is, therefore, why this region is called the reactive near-field. Beyond about one wavelength and out to, typically, a radial distance of about 2 D2/X is a region called the radiating near-field, or sometimes the Fresnel region. In this region, the electric and magnetic fields are propagating, but do not yet exhibit the hWr dependence characteristic of the far-field. This region is where the near-field measurements in this thesis research were made. Finally, the far-field region, sometimes called the Fraunhofer region is th a t volume th a t extends from a radial distance of about 2 D2/X from the antenna out to in fin ity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 Reactive Near-Fieli Radiating Near-Field or Fresnel Region Far-Field or Fraunhofer Region - I 'D I X F igure 11 - E xterior Field Regions o f a R adiating A ntenna The basic idea of near-field to far-field transform ations is that: 1) the far-field region is th at region where the radiating field phase front is locally very nearly planar, 2) energy leaving an antenna always propagates in a straight line in a uniform medium, 3) near-field m easurem ents of the m agnitude and phase determine the phase front of the radiating energy and this can he transform ed into an angular spectrum of plane waves, 4) this angular spectrum of plane waves is equivalent to the antenna far-field p attern [48]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 Using the concept of superposition, the field at a distance, z = di, in front of a radiating antenna is a combination of a series of plane waves (analogous to the idea th a t a time domain waveform is the superposition of a combination of frequency spectral signals). Mathematically, this can be w ritten as [49]: co BXx,y,z = dt) = \ \ n k , , k y)-S(kx,k>) e ^ e ‘u-" t>»dkxdkr (17) -c o where Bo is the output of a probe at position (x,y,z), T(k) is the plane-wave spectrum (which is equivalent to the far-field pattern of the AUT), S(k) is the vector receive p attern of the probe antenna (set to unity for the therm al paper), and y = [(2:t/?i)2-(kx2 + ky2)]°'° is the wavenumber in the z direction (kz is often used in the literature instead of y). A slight re-arrangem ent of equation 17 with a replacement of D(kx, ky) = T(kx, ky) • S(kx, ky) gives: Be(x,y,z = d1)= ] \ e ^ D ( k x,ky) e ^ y)dkxdky (18) -c o This integral equation is the same as an Inverse Fourier Transform with the added multiplication of an ei7d term. The Fourier Transform pair to equation 19 is: D(kx, k ) = ~ 47C ~ A—coi/ 1 \B 0(x,y,z = dx)e'KkxX+k’y)dxcfy (19) where A is a m easurem ent insertion loss correction constant used to determine the absolute gain of the AUT. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 Equations 18 and 19 provide the m eans for transform ing from phase front (near-field) measurements to th e angular spectrum (which is an equivalent representation of the AUT far-field) and back. Since these equations are integral equations, they imply th a t m easurem ents m ust be made over a continuous (non-discrete) surface. It turns out, however, th at since the angular spectrum is band-limited, near-field d ata sampling can be performed at intervals of 7J2 in x and y and the Discrete Fourier Transform (DFT) used with no loss of generality [41, 50]. Since a discrete Fourier Transform can be used, standard Fast Fourier Transform (FFT) routines can be used to transform complex near-field data to the far field, or an inverse FFT (IFFT) used to transform from the far field in to the near field. In the MATLAB code PTPLOOP.M listed in Appendix A, the transform ations involve only a single line of code, such as for the aperture field (distance = 0) to the far-field and back to the m easurem ent plane 1: El = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(1)) .* evan)); In this code line, the complex aperture field matrix, Eap is first propagated to the far field by a two-dimensional FFT. The FFTSHIFT function is then imposed to re-arrange the FFT output into the correct quadrants (FFT algorithms result in an output in which quadrants 1 and 3 are swapped and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 2 and 4 are swapped). Since the input data to the Fourier Transform (Eap) is complex., the opposing quadrant data are not necessarily identical and the entire output m atrix is valid. This data then represents the far field of the antenna. To back-transform to m easurement plane i, the complex far-field data is m ultiplied by ei’/d, where d is the distance from the antenna aperture to m easurem ent plane 1, an FFTUNSFT function performed to swap the data quadrants in preparation for the inverse FFT, and then the inverse FFT performed. In addition, the data m atrix is m ultiplied by the m atrix EVAN ju st prior to the FFTUNSFT operation. The elements in the m atrix EVAN are one everywhere y is pure real, and are 0 otherwise. This multiplication, therefore, performs a band-limiting operation th a t perm its a discrete Fourier Transform operation with near-field data collected a t spacings of up to [41, 47]. a /2 Planar near-field, far-field transform ations using a modem complex, m atrix-oriented language such as MATLAB are, therefore, quite simple to implement and reasonably efficient (a complete loop of the code PTPLOOP.M, which includes 4 FFT-IFFT operations as well as convergence error calculations and m agnitude replacements for a non-power-of-2 57x57 element data m atrix on a 486DX2-100 is performed in about 4 seconds). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 4.3 P lane-to-P lane (PTP) P h a se R e trie v a l R e su lts This section discusses the results of the PTP algorithm performed on both sim ulated and actual IR m easured magnitude data. The two m easurem ent planes selected for the 36 element patch array antenna were at a distance of 32.4 cm and 45.0 cm. Since the array operates at a frequency of 4 GHz, these distances were approximately 4.3 X and 6 X. The exact distances were arbitrary, with the goal of being well outside the reactive near-field and of having a plane separation of greater than one wavelength, b ut not so far apart as to result in a large difference in peak therm al paper tem peratures. 4.3.1 Simulations Before processing the therm al m easured data, a set of simulations were performed. First, the array antenna was m easured by the National Institute of Standards and Technology (NIST) in their standard near-field antenna test range. The data provided by NIST on the array consisted of a 57x57 element m atrix of field m agnitude and phase data spaced 3.175 cm apart (about 0.4 A.) in a plane 38.1 cm in front of the array. The near-field to far-field FFT processing methods discussed above were then used to compute the m agnitude and phase of the array fields a t the two m easurem ent planes selected for the IR therm al m easurem ents (32.4 cm and 45.0 cm). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The 42 m agnitudes of these data were then used as an initial simulation of the capabilities of the PTP algorithm. Figure 12 is an overlay of the far-field pattern of the array as determined by the PTP algorithm (dashed *) and from the original NIST complex data (solid +). As the figure illustrates, the agreement between the PTP determined far-field pattern and the array's "real" far-field pattern is excellent. Comparison of Nist Far-Field (+) to Iterative from Nist M agnitudes (’) E-Plane -10 dB -15 -20 -25 -30 -35 <- -100 -50 50 100 Degrees Figure 12 - PTP G enerated Far-Field from NIST M agnitude D ata Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 The PTP algorithm was then re-run with the NIST magnitude data truncated at amplitudes 20 dB below the peak as an estimate of the dynamic range of the UCCS AGA 780 therm al camera. The result of this simulation is shown in Figure 13. As illustrated in this figure, the PTP algorithm was only able to reconstruct the antenna main-lobe and provide an indication of the location of the first two side-lobes (but not the correct amplitudes for the sidelobes). Comparison of Nist rar-Field (+) to Iterative from Nisi Mag Reduced to 20 dB Range (*) E-Plane -10 dB -15 -20 -25 -30 -35 -100 -50 50 100 D egrees Figure 13 - PTP Results Using NIST M agnitude Data T runcated to 20 dB Dynamic Range Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 Obviously, the results above from the simulations of AGA 780 type dynamic range are only m arginally useful; however, modem 1 2 -bit digitizing therm al cameras such as Rome Laboratories AGEMA 900 should have at least a 30 dB RF dynamic range [51]. The results of th e PTP algorithm applied to data with a 30 dB dynamic range are substantially better than for data with only a 20 dB dynamic range, as shown in the sim ulation results of Figure 14. As shown in these sim ulation results, data from thermograms collected with a camera such as the AGEMA 900 should be adequate for the PTP algorithm to faithfully reproduce the far-field pattern of antennas such as the array tested in this research. Future work will show the validity of this simulation and additional work will focus on investigating the utility of the algorithm for other antenna styles, particularly those with lower sidelobes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 Comparison of Nist Far-Fieid (+) to Iterative from Nist Mag Reduced to 3 0 dB Range (*) E-Plane -10 - dB -15 -20 -25 -30 >- -100 -50 50 100 D egrees Figure 14 - PTP Results from Sim ulated 30 dB Dynamic Range D ata 4.3.2 IR Thermogram Results Actual thermograms were then taken at these m easurement planes. Direct comparison of the field m agnitudes from the thermograms to the expected values based on the NIST m easured data confirmed that the therm al m easurem ents from the AGA 780 camera resulted in about 18 db 20 dB of usable dynamic range. The MATLAB code PTPLOOP.M was then slightly modified to account for the pixel spacing in the thermograms (this version, PTPLPTHM.M is also included in Appendix A). The result of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 PTP algorithm on this data is shown in Figure 15. As can be seen, the result of processing th e AGA 780 thermograms is very encouraging as it is approximately the same as the 2 0 dB dynamic range simulation. Com parison of Nist Far-Field (+) to Iterative Plane-to-Plane (*) E-Plane -10 -15 dB -20 -25 -30 -35 -40 •-100 -50 50 100 Degrees F igure 15 - PTP Results for AGA 780 Therm ogram s Another useful measure of the success of the PTP algorithm is a plot of the convergence error metric. Figure 16 shows an overlay of the convergence error metric of the PTP algorithm for the four cases discussed above (full range simulation, 30dB dynamic range simulation, 20dB dynamic range simulation, and AGA 780 thermogram data). Several observations can be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 made from this figure. First, th e convergence metric settles to a stable value for each case in less than 40 iterations, which represents only 2-3 minutes of processing time on a 486DX2-100 processor for these m atrix sizes. Secondly, the convergence metric stays stable for m any iterations (all runs were taken out for 200 iterations and all rem ained stable). Thirdly, it appears th a t the value of the convergence metric is a usable m easure of how well the algorithm was able to re-construct the AUT far-field pattern. Since in actual practice, the AUT p attern will be unknown to the user (or the user would not be trying to m easure it), the convergence metric may be very useful in determining the reliability of the PTP algorithm results. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 Comparison of Plane-to-Plane Iteration Convergence IR Thermal Data 2 0 dB Range Simulation 30 dB Range Simulation "Full11Range Simulation 100 150 200 Number of Iterations Figure 16 - Overlay of Convergence E rro r M etrics for Various PTP Runs 4.4 F u tu re W ork In summary, the PTP algorithm appears very well suited to the reconstruction of the far-field pattern from thermographic measurements on 2 near-field planes. pursued. Additional research in the PTP technique should be First, a camera with greater dynamic range, such as Rome Laboratories AGEMA 900 should be used to verify the results of the 30 dB dynamic range simulation shown in this work (an improved tem perature rise to E-Field conversion algorithm may be necessary for processing data from a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 higher dynamic range camera). In addition, the phase change acceleration and center-of-gravity concepts proposed by Junkin should be investigated for incorporation into the PTP algorithm developed here [27, 28]. Furtherm ore, several antenna styles with different side-lobe amplitudes should be m easured in order to build confidence in this technique. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 CHAPTER 5: HOLOGRAPHY 5.1 In tro d u c tio n to H o lo g ra p h ic T ech n iq u e Microwave holography techniques appear well suited to the determination of the complete (complex) field data from thermographic measurements. In general, a review of the literature shows th a t the term microwave holography is often used to m ean data containing phase information. The classical (optical) hologram, however, is a magnitude pattern created by th e constructive and destructive interference of two signals. Upon re-illum ination of this hologram interference pattern with one of the signals used to create it, the complete 3-dimensional, or complex, second signal is retrieved. Holography, in this thesis research, refers to this classical description of holography, which has not previously been applied to IR images of EM fields. A typical setup for creating a classical optical hologram is shown in Figure 17. A beam of coherent light (typically from a laser) is split into two beam paths. One beam directly illum inates a photographic plate, while the other illum inates the photographic plate after reflecting off of the object for which the holographic image is desired. Since the original beam was a coherent light source, the amplitude of the light a t the photographic plate is modulated by constructive or destructive interference between the two light Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 beams due to the difference in their p ath lengths. It is im portant to note th at the hologram is not like a standard photograph; when the hologram is reillum inated by the reference wave, the reference wave signal is modulated by the interference pattern of the hologram, and the result is a reconstruction in 3 dimensions of an image of the original object (discribed in the next section). Object t0 b e ( ^ Imaged Object Beam LASER Reference Beam Beam Splitter Photographic Plate Figure 17 - Typical Setup to Produce a Classical O ptical Hologram The setup for producing the microwave holograms in this thesis research, as shown in Figure 18, is very sim ilar to the classical hologram setup discussed above. Two antennas are set up to irradiate a sheet of therm al paper from which the therm al image is to be recorded. One antenna is the antenna under test (AUT) and the second antenna is a well known Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 reference (REF) antenna. The two antennas radiate a signal split from the same source, so th a t a static interference pattern is generated on the therm al paper. The relative phase difference of the fields from the two antennas at each location over the therm al paper produces an interference pattern. AUT Source IR Camera Thermal Paper Ref P hase - 1 Figure 18 - Setup to Produce a M icrowave Hologram For this thesis research, the AUT was a 36 element patch array antenna designed for operation at 4 GHz (previously described), and the reference antenna was a WR-187 waveguide standard gain horn (SGH) designed for operation over 3.95 GHz to 5.85 GHz. A schematic showing the layout of this setup is given in Figure 19. As shown in this figure, the AUT was centered over the therm al paper with the direction of propagation from the AUT normal to the surface of the therm al paper. The reference antenna was angled so th at the direction of propagation was at a 60 degree angle to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 the normal of the therm al paper. The E-Fields from both antennas were in the same direction and tangential to the therm al paper surface. 38 cm PATCH ANTENNA (AUT) 24.2 cm 45.1 cm E-FIELD DIRECTION POSTER BOARD 23.5 cm THERMAL PAPER Figure 19 - Schem atic of th e Setup for th e H olographic M easurem ents Examples of therm al images collected with this setup are shown in Figure 20. The four images in this figure are false color images of the tem perature distribution in the therm al paper (which can be related to the m agnitude of the electric field as previously discussed). In all four of these images, the top of the image is the edge closest to the reference antenna. The top left image is of the AUT antenna radiating alone (no radiation from the reference antenna). The top right image is of the reference antenna Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 radiating alone (the effect of tilting the reference antenna is clearly seen in the oblong shaped pattern of the field m agnitude in this image). The bottom two images are the interference p attern holograms (both antennas radiating). The difference between the two holograms is th a t an additional 180 degree phase shift was inserted into the reference antenna feed line for the image on the right. Notice th a t the peak tem perature on the left hand hologram occurs around pixel 32 on the vertical axis, whereas this same location in the right h an d hologram is a local minima; thus, it can be seen th a t a 180 degree phase shift of the reference signal converts constructive interference points to destructive interference points and vice-versa, as expected. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Figure 20 - Example of the Construction of a Microwave Hologram 5.2 D e term in in g the R eference A n te n n a F ield Processing these microwave holograms requires knowledge of the m agnitude and phase of the fields of the reference antenna at the locations of th e thermogram pixels. There are, at least, two methods for obta in in g this data; hard-wired vector m easurem ents of the fields at the locations of interest, or computation from a standard near-field scan. This section discusses one method of computing the desired reference field data from standard planar near-field scan data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 Consider the configuration illustrated in Figure 21. Using the Fourier transform ation techniques discussed in section 3.2, the complex planar n ear field data of an antenna can be readily calculated on any other near-field plane parallel to the aperture of the antenna (the region of accurate calculation was shown by Lewis and Newell [52] to typically extend from about r = X to r = 2D2IX). Calculation of the complex planar near-field data on a plane tilted with respect to the antenna aperture plane can be accomplished by picking off the appropriate rows (or columns) from a series of aperture parallel planes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 Planes Calculation Plane Interest 0-1) AY = Figure 21 - Setup for D eterm ining T ilted Plane Configuration This is illustrated in Figure 21. The height of the lower edge of the aperture from the plane of interest, hi, the length of the aperture, l x, and the angle between the aperture plane and the plane of interest, 0 , are specified. The distance di, which is the distance from the plane of interest to the center of the aperture along the plane parallel to the aperature is then determined from: h smd? / 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (20) 58 The distance from the aperture to the aperture parallel plane (plane of calculation) th a t intersects with the plane of interest for the row th a t coincides with di is then found from: RfA) = dx tan(0) (21) Since the location of di is at the center of the aperture, the original p lan ar near-field scan extends d(rovs = \) = dx- Ay((«+ 1)/ 2 ) from d{row = ri) = dx + Ay((« +1)/2), where n is the num ber of near-field to scan rows and Ay is the spacing between rows (typically slightly less th an 7J2). Thus, for each row in the original near-field data, the row distance, d(row), as defined above, is determined and the complete near-field at this row distance is computed. From this data, only the row in the plane of interest is saved. This is repeated for all rows in the original data until a complete m atrix of data of the same size as the original near-field data m atrix is obtained for the plane of interest. Since the plane of interest is tilted from the original aperture-parallel data, the distance between rows of data in the computed plane of interest has also been changed. The row spacing in this tilted plane of interest data is then found from: AY = cos# (22) The final step in determining the reference field data is an interpolation of the tilted plane of interest data to the specific pixel locations Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 of the hologram. Two separate two-dimensional interpolations are required; one for the field magnitude, the other for the field phase. The MATLAB program TILT.M, listed in the Appendix, is an implementation of the algorithm described above. This code determines, from a NIST supplied near-field scan, the complex near-fields of the SGH reference antenna in the configuration used in this thesis research (60 degree H-Field tilt). A contour plot of the computed m agnitudes of the fields of the reference antenna is shown in Figure 22a. Figure 22b is a contour plot of the fields of the reference antenna as determined from a m easured IR thermogram. Comparison of these plots shows good agreement, although in the thermogram m easurements, the reference antenna also had a slight EField tilt which is clearly seen in the contour plot. Com putaa Magntuda of TXad SGH IRTharmogram Ma*surad Magntuda ofTdtad SGH -20 •20 -50 •40 •20 0 20 -50 60 -60 ■20 0 20 40 60 Figure 22 - C ontour Plots of th e M agnitude of th e Field of the Reference A ntenna, (a) Computed from NIST Near-Field Data, (b) From IR Therm ogram M easurements. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 5.3 C lassical H olo g ra p h ic Im a g e R ec o n stru c tio n 5.3.1 Theory o f Classical Holosravhic Im ase Reconstruction Consider the two waves incident on the conductive sheet of therm al paper from which the therm al cam era obtains its image. One wave, Sa, is from the Antenna Under Test (AUT) for which the antenna p attern data is desired. The other wave, Sr, is from a second, reference, antenna. The conductive sheet was shown above to h eat in proportion to the square of the m agnitude of the electric field incident on the sheet. Therefore, IE t 12, where Et = E a + E r is the sum of the complex electric field from the AUT and the complex electric field from the reference antenna, is of interest in this holographic work. Thus: (23) then: |£,|2 = (£ . + £,X £ . + e J = f a + E, t E- * E ') (24) thus: (25) where the * indicates the complex conjugate. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 In classical (optical) holography, after producing the hologram, it is illum inated by a read-out wave, E 0, in order to see the stored complex image. M athematically, the reconstructed data (image), I, is: I = \Ea\2Ea +\Er\2E Q+EaE'rE0 +E'aErE0 (26) Normally (in optical holography) the read-out wave is identical to the reference wave used to generate the holographic interference pattern; however, since the therm al image hologram can be "read" by computer, the readout wave can be chosen to be: thus: != m . + E r+ ^ N ' N +E E . N (28) this can be further reduced to: f\F 1= I2 Er +Ea + E ’ae12* (29) where <j>is phase of the reference field relative to the AUT wave. The three terms of equation 29 above represent three optical images. The first term is an amplitude scaled version of the reference field, the second term is the desired complex field of the AUT, and the third term is a phase shifted complex conjugate of the AUT field. With appropriate positioning of the AUT and reference antennas, these three "images" from the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 hologram reconstruction are spatially separated. To obtain the desired image, E a, the “viewing" of the reconstructed hologram is restricted to the area of the desired image, ju st as is done in optical holography. 5.3.2 Sim ulation o f Classical Holographic Image Reconstruction A series of computer simulations of th is classical holographic reconstruction technique for various antennas and set-ups (relative positions of the AUT, REF and therm al screen) were performed [53, 54]. Figure 23 shows an example of one these simulations displayed next to the true farfield plot for a 36 by 36 element array antenna. In this simulation, the reference antenna is located a t the upper left com er of the plot. Comparing the two plots, shows th a t the center of the holographic reconstruction image (the antenna far-field m ain lobe and first side lobe) is a good representation of the true far field data for this antenna. Also clearly seen in the upper left and lower right portions of the hologram are the corruption due to the other image term s of equation 29. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Tn>* Fw*R*W of 32x32 0 *m «nt Array S«nul**d Hologram Far-FtoW of 32x32 Bamont Array 04 m 02 3* 0 £ 0 •02 -02 ■04 -0 4 -0.5 • 0.6 •0.8 •0.8 Figure 23- Sim ulated Classical H ologram R econstruction Com parison w ith True F ar Field for 36 by 36 Elem ent A rray Another simulation is shown in Figure 24. This simulation is for a by 6 6 element array antenna such as the one used for the AUT during this thesis research. This antenna has a much broader far-field m ain beam than the 36 by 36 element antenna discussed above. As a result, very little of the classical hologram contains un-corrupted data (only the first contour line of the far-field pattern appears sim ilar to the true far-field contour plot). Thus, these simulations show that, although in some cases this technique may be useful, classical holographic viewing will not be practical for all antenna types. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 Tnw Far-Ficld o f 6x6 Efenwtf A m y Sim ultftd Hotegr*n FwFwW o f 6x6 0*m w « Array 0.6 Q.6 04 02 2 0 -02 •0 4 •0.6 -0.8 F ig u re 24 - S im u la te d C lassical H o lo g ram R e c o n s tru c tio n C o m p ariso n w ith T ru e F a r F ie ld fo r 6 by 6 E le m e n t A rra y 5.4 Im p ro ved H o lo g ra p h ic Im a g e R eco n stru ctio n 5.4.1 Theory oflm vroved Holosravhic Imase Reconstruction With computerized data collection and processing, however, the holographic technique is not limited to a single m easurem ent of IEt 12. Given the hologram equation derived above: |Et\z = |Ea\2 +\Er\z +EaE m r +ElEr (30) This equation can be re-arranged and written as: !-£/! ~1^1 E,\\E. ~ l^ rl _ = e**'-*') + _ = 2 cos(4>a - <j>r) (31) Thus, the difference in phase between the AUT and reference antenna is: cos"1 hEX-- \ E\ z - \ E ^ 2\E1E„ = <f>a -<f,r =A0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (32) 65 Unfortunately, because of the inverse cosine function, this equation will produce answers only in the region of 0 to tc for the phase difference, rather th an the desired range of -it to it. This ambiguity, however, can be elim inated by processing a second hologram where a phase shift has been inserted into the reference antenna feed line. One method for elim inating this phase ambiguity is discussed below [55]. Re-arranging the terms in the hologram equation (equation 30), and defining an interm ediate term, H, gives: H = |£ ,f - |£„|! - | £ ,|2 = £„£,' + E:E, (33) writing E a and E r in term s of th eir real and imaginary components, this becomes: h =( e : + j e ' x e : - j e :)+( e :- je% e : +j e d m carrying out the multiplication and combining term s results in: H = 2(.E;Era + E irE'a) (35) Two holograms, differing only by the phase of the reference antenna field, result in: H(X)=2{E'rmE : +E ‘rmE'a) H(2)=2(Err(2)E :+ E !ri2)E ‘) (36) Re-arranging these two equations and solving for the unknown AUT field components results in: Er = * ~ 2{ E ^ E ^ - E ^ E ^ ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3 7 ) 66 and Ei=- (38) The procedure for determining the AUT phase is then as follows. Step 1, collect a thermogram with the AUT radiating alone (this gives the m agnitude of the AUT, Ea). Step 2 , collect a therm ogram with the reference antenna radiating alone (this gives the magnitude of the reference antenna, Er). Step 3, collect a holographic thermogram by radiating from both antennas. Step 4, collect a second holographic therm ogram by inserting a phase shift in the reference antena feed line. Step 5, compute the phase of the reference antenna at the pixel locations of the thermograms using standard m agnitude and phase near-field scan data as discussed in section 5.2 above. Step 6 , compute H(p and H® by subtracting the squared magnitudes of the reference and AUT fields from each of the holograms. Step 7, compute the complex components of the AUT field from equations 37 and 38 above. 5.4.2 Sim ulation of Improved Holosravhic Imase Reconstruction Four m agnitude input data sets (AUT alone, reference antenna alone, and the 2 holograms) were computed from the NIST calibration data for these antennas. The m agnitude data was then truncated at amplitudes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 below 20 dB down from the peak m agnitude of each data set to sim ulate the dynamic range of the UCCS AGA 780 therm al camera as discussed above. This sim ulated data was then processed as described above for the improved holographic image reconstruction technique. Figure 25 shows a comparison of the AUT far field pattern computed from this sim ulated holographic data to the pattern obtained from the NIST calibration data for the AUT. As can be seen in the figure, the reconstruction capability of the holographic technique is excellent; however, the logistics of determining the position and angle of the reference antenna, such th at the phase of the reference antenna field can be accurately computed, are non trivial. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Comparison of NIST Far-Field (*) with Holographic Far-Field (+), Simulated 20 dB Range H-Plane -10 dB -15 -20 -25 -30 -35 -100 -50 0 50 100 D egrees Figure 25 - AUT Far-Field Computed from Sim ulated Holograms 5.5 F u tu re H o lo g ra p h ic Work The results of the simulation of the improved holographic image reconstrction are very encouraging. Even with the "measurement" dynamic range limited to 20 dB in the simulations, this holographic technique appears able to accurately reconstruct the AUT far-field pattern. Thermographic m easurem ents are needed to confirm the results of the simulation. Extreme care m ust be taken, however, in the positioning of the reference antenna. Small positioning errors th a t are normally unim portant in m agnitude Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 m easurem ents can be very im portant to these holographic m easurem ents since significant phase errors are introduced with position errors of only a fraction of a wavelength. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 CHAPTER 6: SUMMARY Two basic techniques for extending m agnitude only IE, thermographic m easurements to the complex near-field m easurem ents of tr ansm itting antennas were investigated in this thesis research, a Fourier interative Plane-to-Plane (PTP) technique and a holographic technique. Simulations of the PTP technique were performed for various dynamic ranges of the m agnitude data. These simulations showed th at the technique produced a good representation of the the AUT far-field pattern for magnitude data with a 30 dB or greater dynamic range (a range th a t should be possible with modem therm al cameras). For m agnitude data with a 20 dB dynamic range, the PTP technique simulation produced a good representation of only the main lobe of the AUT. IR thermograms of the field magnitude were then made using the UCCS AGA 780 therm al camera. The PTP technique processed results from these thermograms, which had a dynamic range of approximately 20 dB, were in agreement with the simulation results. An error metric was also defined for the PTP technique th a t appears useful in determining the quality of the PTP processing results. Additional m easurements of other AUT types should be performed to confirm the utility of the error metric in determining the accuracy of the PTP results. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 Additionally, the phase change acceleraction and center-of-gravity data alignment concepts recently proposed by Junkin should be investigated for incorporation into the PTP algorithm. A second, independent, method of determining phase information of a field from IR therm al m easurem ents was also developed. This technique is based on an extension of classical holography. This holographic technique was shown by simulation to be less reliant on the dynamic range of the magnitude data from the thermograms than the PTP technique for an accurate reconstruction of an AUT far-field pattern. The trade-off is th at four therm al m easurem ents and a priori knowledge of the phase distribution of the reference antenna at the m easurem ent locations are necessary. Thermogram holographic measurements are needed to confirm the results of these simulations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 BIBLIOGRA PHY [1] G.E. Evans, "Antenna M easurem ent Techniques", Artech House, 1990. [2] Special Issue on Near-Field Scanning Techniques, IEEE Transactions on Antennas and Propagation, Vol 36, No 6, June 1988. [3] L.G. Gregoris and K. Iizuka, "Thermography in Microwave Holography", Applied Optics, Vol 14, No. 7, pp. 1487-1489, July 1975. [4] R.M. Sega and J.D. Norgard, "An Infrared M easurement Technique for the Assessment of Electromagnetic Coupling", IE EE Transactions on Nuclear Science, Vol. NS-32, No. 6, pp. 4330-4332, December 1985. [5] R.M. Sega and J.D. Norgard, "Infrared M easurements of Scattering and Electromagnetic Penetration Through Apertures", IEEE Transactions on Nuclear Science, Vol. NS-33, No. 6, pp. 1658-1663, Dec. 1986. [6] R.M. Sega and J.D. Norgard, "Expansion of an Infrared Detection Technique using Conductive Mesh in Microwave Shielding Applications", SPIE Vol. 819 Infrared Technology XII. pp. 213-219, 1987. [7] J.D. Norgard and R.M. Sega, "Microwave Fields Determined from Thermal Patterns", SPIE Vol. 780 Thermosense IX. pp. 156-163, 1987. [8] R.M. Sega, J.D. Norgard, and G.J. Genello, "Measured Internal Coupled Electromagnetic Fields Related to Cavity and Aperture Resonance", IEEE Transactions on Nuclear Science, Vol NS-34, No. 6, pp. 1502-1507, Dec. 1987. [9] J.D. Norgard, R.M. Sega, M. Harrison, A. Pesta, and M. Seifert, " Scattering Effects of Electric and Magnetic Field Probes", IEEE Transactions on Nuclear Science, Vol. 36, No. 6. pp. 2050-2057, Dec 1989. [10] J.D. Norgard, D.C. Fromme, and R.M. Sega, "Correlation of Infrared M easurem ent Results of Coupled Fields in Long Cylinders with a Dual Series Solution", IE E E Transactions on Nuclear Science, Vol. 37, No. 6, pp. 2138-2143, Dec. 1990. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 [11] R.M Sega, V.M. M artin, D.B. Warcnuth, and R.W. Burton, "Infrared Application to the Detection of Induced Surface Currents", SPIE, Vol. 304, Modern U tilization o f Tnfrared Technology VII. pp. 84-91, 1981. [12] J.P. Jackson and R.W. 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[19] D.L. Misell, "A Method for the Solution of the Phase Problem in Electron Microscopy", Journal o f Physics D, Applied Physics, Vol. 6, pp. L6-L9, 1973. [20] V.Yu.Ivanov, V.P.Sivokon, and M.A.Vorontsov, "Phase Retrieval from a Set of Intensity Measurements: Theory and Experiment", Journal of the Optical Society of America, Vol. 9, No. 9, pg. 1515-1524, Sept. 1992. [21] T. Isem ia, G. Leone, and R. Pierri, "New Approach to Antenna Testing from N ear Field Phaseless Data: The Cylindrical Scanning", IEE Proceedings, Vol. 139, Pt. H, pp. 363-368, August 1989. [22] O.M.Bucci, G.D’Elia, G.Leone, and R.Pierri, "Far-field Pattern Determination from the Near-field Amplitude on Two Surfaces", IEEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 Transactions on Antennas and Propagation, Vol 38, No. 11, pg 17721779, Nov. 1990. [23] A.P. Anderson and S. Sali, "Diagnostics, P art I: Error Reduction Techniques", IE E Proceedings, Vol. 132, Pt. H., pp. 291-298, August 1985. [24] R.G. Yaccarino and Y. Rahmat-Samii, "Phaseless Near-Field M easurements Using the UCLA Bi-Polar P lanar Near-Field M easurement System", 16th A nnual Antenna Measurement Techniques Association Symposium, pp. 255-260, October 1994. [25] R.G. Yaccarino and Y. Rahmat-Samii, "Phaseless Bi-polar Near-field Measurements: A Squared Amplitude Interpolation / Iterative Fourier Algorithm", 1995 Antenna Measurements Techniques Association 17th Meeting and Symposium, Williamsburg, pgs 195-200, Nov 13-17, 1995. [26] C.A.E. Rizzo, G. Junkin, and A.P. Anderson, "Near-field/Far-field Phase Retrieval M easurem ents of a Prototype of the AMSU-B SpaceBorne Radiometer Antenna a t 94 GHz", 1995 Antenna Measurements Techniques Association 17th Meeting and Symposium, Williamsburg, pgs 385-389, Nov 13-17, 1995. [27] G.Junkin, A.P.Anderson, C.A.E.Rizzo, W.J.Hall, C.J.Prior, and C.Parini, "Near-field/Far-field Phase Retrieval M easurement of a Prototype of the Microwave Sounding Unit Antenna AMSU-B at 94 GHz", ESTEC Conference on M illimeter Wave Technology and Applications, Noordwijk, N etherlands, 1995. [28] G.Trueba, G.Junkin, "A Numerical Beam Alignment Procedure for Planar Near-field Phase Retrieval", Electronics Letters, 1995. [29] T.Isemia, G.Leone, R.Pierri, "Phaseless Near-field Techniques: Uniqueness Conditions and A ttainm ent of the Solution", Journal of Electromagnetic Waves and Applications, Vol. 8, No. 7, pg. 889-908, 1994. [30] R.Barakat and G.Newsam, "Algorithms for Reconstruction of Partially Known, Band-limited Fourier-transform Pairs from Noisy Data", Journal of the Optical Society o f America, Vol. 2, No. 11, pg. 20272039, 1985. [31] Telephone conversations between J.D. Norgard and W. Kent of MRC, Dayton, Ohio. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 [32] D. Gabor, "A New Microscopic Principle", Nature, Vol 161, pp. 777-778, May 1948. [33] R.P. Dooley, "X-Band Holography", Proceedings o f the IEEE, Vol 53, p. 1733, Nov. 1965. [34] D.W. Metzger, "Quantification of the Thermographic Mapping of Microwave Fields", Ph.D. Thesis for the University of Colorado, Colorado Springs, 1991. [35] G.D. Wetlaufer, "Optimization of Thin-Screen M aterial Used in Infrared Detection of Microwave Induced Surface Currents a t 2-3 GHz", MSEE Thesis, University of Colorado, Colorado Springs, 1985. [36] W.C. Diss, "Techniques for M easuring Microwave Interference Using Infrared Detection and Computer Aided Analysis", MSEE Thesis, University of Colorado, Colorado Springs, 1984. [37] R. Segal and J. Howel, "Thermal Radiation H eat Transfer", McGrawHill, 1972. [38] M.D. Smith, "Infrared Detection of Electromagnetic Penetration Through Narrow Slots in a Ground Plane", MSEE Thesis, University of Colorado, Colorado Springs, 1990. [39] D. Fredal, R.M. Sega, J.D. Norgard, and P.E. Bussey, "Hardware and Software Advancement for Infrared (IR) Detection of Microwave Fields", SPIE Vol. 781, Infrared Image Processing and E n h ancem en t. pp. 160-167, 1987. [40] AGA Thermovsion® 780 Operation M anual, AGA Infrared Systems AB, 1979. [41] A.C. Newell, "Planar Near-field A ntenna Measurements", N ational Institute of Standards and Technology, Electromagnetic Fields Division N ear Field Course Notes, March 1994. [42] D.M. Kerns, "Analytical Techniques for the Correction of Near-field A ntenna M easurements Made with an Arbitrary but Known M easuring Antenna", Abstracts o f URSI-IRE Meeting, Washington, DC, pp. 6-7, April-May 1963. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 [43] D.M. Kerns, "Plane-wave Scattering-m atrix Theory of A ntennas and A ntenna-antenna Interactions", National Bureau of Standards, Monograph 162, Ju n e 1981. [44] D.M. Kerns, "Scattering M atrix Description and Near-field M easurements of Electroacoustic Transducers", Journal o f the Acoustic Society of America, Vol. 57, pp. 497-507, Feb. 1975. [45] D.M. Kerns, "Correction of Near-field Antenna M easurem ents Made with an Arbitrary but Known M easuring Antenna", Electronic Letters, Vol. 6, pp. 346-347, May 1970. [46] R.C. Baird, A.C. Newell, P.F. Wacker, and D.M. Kerns, "Recent Experimental Results in Near-field Antenna Measurements", Electronic Letters, Vol. 6, pp. 349-351, May 1970. [47] A.D. Yaghjian, "An Overview of Near-field Antenna Measurements", IE EE Transactions on Antennas and Propagation, Vol. AP-34, No. 1, pp. 30-45, Jan. 1986. [48] D. Slater, "Near-Field Antenna Measurements", Artech House, 1991. [49] J.J. Lee, E.M. Ferren, D.P. Woollen, and K.M. Lee, "Near-field Probe Used as a Diagnostic Tool to Locate Defective Elements in an Array Antenna", IE E E Transactions on Antennas and Propagation, Vol. 36, No. 6, pp. 884-889, June 1988. [50] A.D. Yaghjian, "Efficient Computation of Antenna Coupling and Fields Within the Near-field Region", IE E E Transactions on Antennas and Propagation, Vol. AP-30, No. 1, Ja n 1982. [51] Private conversations with Mike Siefert of Rome Laboratory RL/ERST about capabilities of th eir AGEMA 900 Thermal Camera. [52] R. Lewis and A. Newell, "An Efficient and Accurate Method for Calculating and Representing Power Density in the Near-Zone of Microwave Antennas", National B ureau of Standards, NBSIR 85-3036, December 1985. [53] C. Stubenrauch, "Holographic Antenna M easurements using Infrared Imaging", Presented a t the NIST Antenna and M aterials Metrology Group Seminar, May 18, 1995. [54] Private communications with C. Stubenrauch, NIST, Boulder, CO. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 [55] Derivation originally suggested by R. Cormack, NIST, Boulder, CO. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-l APPENDIX A: MATLAB CODES M E T 2.M ..................................................................................................................... 2 IR_AV_C.M................................................................................................................4 TO TEM P.M ............................................................................................................... 7 TEM P2E3.M ..............................................................................................................8 P T P L O O P.M .............................................................................................................9 PT PLPTH M .M ....................................................................................................... 11 TILT.M ..................................................................................................................... 13 FIL E R D .M ...............................................................................................................15 FFTU N SFT.M .........................................................................................................16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-2 MET2.M % Met2.m - Program to determine the temperature to E-field curve % using the equations derived in Metzger's PhD Thesis. % % John E. Will 1/29/9S % First initialize a bunch of stuff clear i; clear pi; % thermal conductivity h=0.93 ; % emissivity of paper epsilonir=0.96; % boltzmann constant boltzmann=5.7e-8; ambtemp=23+273; % ambient temo in oK eps0=8.854e-12; mu0=4e-7*pi; % freq in Hz freq = 4e9; epsrdiel=lO; % relative permitivity of paper sigma=8; % paper conductivity d=80e-6; % paper thickness % Now use the above values to generate some useful other stuff etaair= (muO/epsO) ~ .5 omega=2 *pi *freq; gammadiel=(i*omega*sqrt(muO*epsO*epsrdiel)*sqrt(1+sigma/(i*omega*epsO*epsrdiel)) ) ; alpha=real(gammadiel); beta=imag(gammadiel); etadiel=(sort(muO/(epsO*epsrdiel+sigma/(i*omega)) ) ) ; p=(exp(-gammadiel*d)); gamma=((etadiel-etaair)/ (etadiel+etaair)); % Now we find E+ and E- and power/sqm from the Einc lp=0 ; for it=10:10:900 lp=lp+l einca(Ip)=it; eir.c=it; e2plus=(einc*(gamma+1)/ (1-(gamma~2)* (p^2))); e2minus=(einc*(-gamma*pA2)* (gamma+1)/ (1-(gammaA2)* (p^2))); powerabspersqm=(sigma./(4.*alpha).*((abs(e2minus).~2).*(exp(2.*alpha.*d)-1)(abs(e2plus).~2 ) .*(exp(-2.*alpha.*d)1))+sigma./(2,*beta).*real(e2plus.*conj(e2minus).* i .*(exp(-2.* i .*beta.*d)-1))); powerincpersqm=einc.~2/3 77; % Now we find the surface temp eb=epsilonir*boltzmann; reman=powerabspersqm+h* amb temp+eb *ambtemp^ 4; x=solve('eb*TsA4+h*Ts=reman', 1T s '); (eval(x(l,:)}-273); (eval (x (2, :) )-273) ; surf temp (lp) = (eval (x (3 , :)) -273) (eval (x (4, :) )-273) ; % the third root above is the one we want to save end ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-3 % now 'surftemp' is an array of surface temperature inCfor % einc in V/m as saved in array ’e i n c a 1 an % so now try fiting a 2nd order polynomial to this data ambtemp=ambtemp-273; thermp=polyfit(einca,(surftemp-ambtemp),2) % thermp should now be a 3 element array with the coefficients for % thermp(1)*Einc~2 + thermp(2)*Einc + thermp(3) = Temp rise above ambient % with Temp rise in C and Einc in V/m % This can then be turned around using the MATLAB function ROOTS % (see TEMP2E3.M code) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-4 IR_AV_C.M % THIS CODE REQUIRES THE FULL VERSION OF MATLAB ################£####### % John E. Will June 1995 clear elf fid=-l; while fid==-l fnme=input('Filename for processing? ','s'),fid=fopen(fnme); if fid==-l di s p (['********** File not found, try again...']) end end % now read in the header field A=fread(fid,[116,64],'u i n t 8 '); (same total size as all fields) % print out the header info and decide what to do next % note current code doesn't give you many options, future % versions could include frame selection, averaging, etc. nmflds=A(2,1); % this location contains a code for fields/frame if nmflds==0 nmflds=4;end; % 0 implies 4 fields per frame if nmflds==255 nmflds=2;end; % 255 implies 2 fields per frame % I intend to also have a file type with only 1 field per frame %A(1,1) is the total number of fields stored in file, thus the %number of frames is fields/(num fields per frame) from above nmframes=A(1,1)/nmflds; dis p ( [' '] ) disp(['This file, ',fnme,', contains ',int2str(nmframes),' frames of data.']) %month is A(3,l); day is A(4,l); year is A(5,l) and A(6,l)-two byte val %hour is A (7,1); min is A(8,l); shot number is 2 bytes A(9,l) and A(10,l) d isp(['recorded on ',int2str(A(3,1)),'/', int2str(A(4,1)), '/',int2str((256*A(6,1))+A(5,1)) ,. . . ' at ',int2str(A(7,1)),':’,int2str(A(8,1)),' and is shot number ',int2str((256 *A (10,1))+A(9,l))]) %next is frequency of illumination saved as 2 byte base, 2 byte exponent %base is in (11,1) and (12,1); exponent in (13,1) and (14,1) freq=((256*A(12,1))+A (11,1)) * 10" ( (256*A (14,1) )+A (13 ,1) ) ; disp(['Frequency of illumation was ',num2str(freq),' Hz']) % Thermal range and level are in A(15,l) and A(16,l) thermlevl=A(16,1);thermrange=A(15,1); disp(['The Thermal Range Setting was ',int2str(thermrange),' Level of 1,... int2str(thermlevl)]) with Thermal % Ambient Temperature is next, again 2 byte base and exponent % base is (17,1) and (18,1); exponent is (19,1) and (20,1) ambtemp=((256*A(18,1))+A(17,l)) * 1 0 " ( (256*A(20,1))+ A (19,1)); disp(['The ambient temperature was ',num2str(ambtemp),' degrees C']) % Radiating power level is next 2 byte base and exponent % base is (21,1) and (22,1); exponent is (23,1) and (24,1) powerlev=((256* A (22,1))+ A (21,1)) * 1 0"((256*A(24,1))+ A (23,1)); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-5 disp(['The RF radiating power level was 1,num2str(powerlev),' dBm']) % Next is the IR Camera Lens (this will be needed to get correct cal curve) % Location is A(25,l) % 1 - is LW f/1.8 7deg % 2 - is LW f/1.8 20deg (wide angle) % 3 - is LW f/1.8 3.5deg (telephoto) % 4 - is SW f/1.8 7deg 1ensnum=A(25,1); if lensnum==l lenstype=(['LW f/1.8 7deg']); elseif lensnum==2 lenstype= ([1LW f/1.8 20 deg (wide angle)']),elseif lensnum==3 lenstype= ([' LW f/1.8 3.5deg (telephoto)']),elseif lensnum==4 lenstype=(['SW f/1.8 7deg']); end disp(['The lens used for this datafile was the ',lenstype]) %next is the number of lines per field in location A(26,l) %- I'm not sure what this means, but one note said %"Typically 64 lines/field, but others can be created" %so I'll not currently worry about displaying this % Now, all that's left is 5 lines of comments as follows: % Line 1 - A (1,9) through A (80,9) % Line 2- A(l,10) through A(80,10) % Line 3- A(l,ll) through A(80,ll) % Line 4- A(l,12) through A(80,12) % Line 5- A (1,13) through A(80,13) dis p (['File comments a r e : ']) for jj =9:13 ii=l; cmt = ’-'; while (A(ii,jj) < 128) & (ii < 80) cmt=[cmt A (i i,j j )]; ii=ii+l ,end disp(setstr(cmt)) end %********** a l l the rest of the first field of datafile is junk ( 2S2TOS) * * * * * * * * * * * % I would then follow this with a check of any possible changes %in case the file data is wrong (even allow a re-write of corrected info) framenum=input(['Range of frames to be averaged [start, stop]? ']); while ((max(framenum) > nmframes) | (min(framenum) < 1)) dis p (['********Invalid number. Input for this file must be between 1 and ',int2str(nmframes)]) framenum=input(['Range of frames to be averaged [start, stop]? ']) end fseek(fid,(29696*(framenum(1)-1))+7424,'bof'); Fl = zeros(116,64);F2=zeros (116,64); for ii=framenum(1):framenum(2) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-6 % now fieldl Al=fread(fid,[116,64],’uint8’); % now field2 Bl=fread(fid,[116,64],'uint8'); %now field3 Cl=fread(fid,[116,64],'uint8'); % now field4 Dl=fread(fid,[116,64],'uint81); % now we need to generate the real frame from the 4 fields % and adjust so that 0 is min temp, 255 is max temp % the first two fields are averaged together to get the odd scan lines % while the last two are averaged to get the even scan lines F1=F1+(255-((Al+Bl)/2)); F2=F2+(255-((Cl+Dl)/2)); end % now create the final full frame % BUT WE HAVE A LITTLE PROBLEM, seems as though the UCCS camera is % not giving us good even/odd scan lines, but are really the same set % so instead o f : % frame (1:116,1:2:127) =Fl/ (framenum(2) -framenum(l) +1) ,% frame(1:116,2:2:128)=F2/(framenum(2)-framenum(1)+1); % we will do the following: frame(1:116,1:64)=((F1+F2)/2)/ (framenum(2)-framenum(1)+1); % set up variables for plotting the full frame with the % full version of MATLAB (the Student edition % is limited in matrix and array size. X =1:64; % put this back in if camera is fixed ----> y = l :116; x=l:128; % now let's plot hold off contour(frame); %surfc(x,y,frame); title(fnme); %shading flat; %colormap hot,-colorbar; v i e w (90,90) % this sets the appropriate angle for viewing plot Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TO TEM P.M %code to convert a frame of raw or averaged IR data intorealtemperature % assumes the ir data is in an array called frame % first need to get some additional info ambtemp = input('Ambient temperature in degrees C(usually about 20) '); do = input('Distance from screen to camera in meters (use 1 if unknown) ') eps = input('Emissivity of thermal emitter (Teledeltos is .93) '); L0 = input('Thermal Level Setting '); Tr = input('Thermal Range Setting '); % the next constants assume we are using the AGA 780 LW sensor % at an aperature of f=l.8 A=552855; B=2994; C = .975 ; % now calculate the atmospheric attenuation effect coeff. tau = e x p (-0.008*(sqrt(do)-1)); % now we get the temperature in isothermal units IA = A/(C*exp(B/(ambtemp+273.15))-1) ; 10 = ((frame./256)-0.5).*Tr; 1 0 = ((L0+I0),/(tau*eps)) - (( (1/(eps*tau) )-1) *IA) % then convert to temperature degrees K tframe = B./log(((A./I0)+ 1)./C); % now to degrees C tframe = tframe-273.15; maxt=max(max(tframe)) mint=min(min(tframe)) %colormap(jet);surf(tframe);colorbar contour (tframe) ,-view (90, 90) ;text (140, 5, ['max temp = ' num2str (maxt) ' C •] ) t e x t (140,50,['min temp = ' num2str(mint) ' C']) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-8 TEM P2E3.M function [E]=temp2e3(tem,base) % TEMP2E - Function to convert to magnitude of E based on a polynomial fit % to the results of Metzger's equation. [E]=TEMP2E3(tem,base) where % E is the returned E field matrix, tem is the temperature matrix % from the thermal camera, and base is the base-line temperature % at which (and below) E is assumed zero, base, for this version % is typically min(min(tem)), since the typical 0.3degree offset % from the min temperature has been included in the roots below. % % John E. Will Jan 1996 for Ph.D. Research % now determine delta Temperature from temp and base deltaT=(tem>base). * (tem-base); %the first part assures deltaT only positive, and zero below base % now get Einc from polynomial minimization % For this version, the zeroth polynomial coefficient has been %set to zero, thus the 0.3 degree rise above min temp normally %used is not necessary. Use E=temp2e3(file,min(min(file))) for it=l:size(deltaT,l) for it2=l:size(deltaT,2) etmp=roots([3.le-5 .0035 (-deltaT(it,it2) )]) ; E(it,it2)=etmp(etmp>-le-17); %picks positive root only end; end; %Thaaat1s i t . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-9 P TP LO O P .M %PTPLOOP.M Program to iteratively find the phase from 2 planes of % magnitude only data using Fourier Transform Propagation. % Requires the function FFTUNSFT.M which reverses the effect % of the MATLAB provided FFTSHIFT.M function in order to properly % account for non-power-of-2 sized matrices. % % % % This particular version is hard-coded for the processing of magnitude only NIST near-field data on the 36 element array operated at 4 G H z . % % % Final output is complex matrix 'farap' which is the array far-field data. % % John E. Will - December 23, 1995 % first set up some constants that will be read in later versions ncol = 57; nrow = 57; delx = 3.175; dely = 3.175; AOB= 15.18; AOB = 10~(AOB/20); freq = 4; c = 29.979; % now calculate some other constants fk = 2*pi*freq/c; c3 = delx*dely/(4*pi*pi*A0B) cx = 2*pi/(delx*ncol) ,cy = 2*pi/(dely*nrow) ; % now generate the ksqr matrix and gama fk x = (1:ncol); fkx=fkx- ( (ncol+1) /2) fkx=fkx * cx; fky=(1:nrow); fky=fky-{(nrow+1)/2),fky=fky * cy; for Ll=l:ncol; for L2=l:nrow; fsqr(Ll,L2)=fkx(Llp2 + fky(L2)"2; end; end; gama = sqrt(fk^2 - fsqr); evan = imag(gama)==0; % evan will be 1 for gama real, 0 for gama imag % % NOW we can set up the data for looping load at3S_l % complex data at 3 8.1 cm load at72_0 % complex data at 72.0 cm Ml = abs(at38_l); %magnitude of measurement plane 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-10 dist (1)=38.1; M2 = abs(at72_0); dist (2)=72.0; %distance from antenna plane to meas %magnitude of measurement plane 2 %distance from antenna plane to meas plane 1 plane 2 kk=l; % now open a couple of files to store my measure of convergence plotting) fidl=fopen{'mdl','w'); fid2=fopen('md2','w'); (for later %first we need an estimate of the aperature plane Eap=zeros(nrow,ncol); la=round(((ncol+1)/2)-(38/(2*delx))),ra=round(((ncol+1)/2)+(38/(2*delx))); ua=round(((nrow+1)/2)+(38/(2*dely))),da=round(((nrow+1)/2)-(38/(2*dely))),Eap(la:ra,da:ua)=ones(size(Eap(la:ra,da:ua))); % left,right,up,and down aperature location - set all aperature to ones ap = Eap-=0; % ap should be 1 1s only inside aperature. Used to truncate data outside cnv=1000; perr=0; while ((kk < 201) & (cnv > 0.000001)) % truncate outside of aperature Eap = Eap .* a p ; % aperature to plane 1 El = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(1)) .* evan)); % calculate convergence error errl = sum(sum((abs(El)-Ml) .~2)) / (sum(sum(Ml.^2))) ; % now replace magnitude with measured El = (Ml .* cos(angle(El))) + (i*Ml .* sin(angle(El))); % now back to aperature Eap = ifft2(fftunsft(fftshift(fft2(El)) .* exp(-i*gama*dist(1)) .* evan)); % truncate outside of aperature Eap = Eap .* a p ; % aperature to plane 2 E2 = ifft2(fftunsft(fftshift(fft2(Eap)) .* e x p (i*gama*dist(2)) .* evan)); % calculate convergence error err2 = sum(sum( (abs(E2)-M2) .~2)) / (sum(sum(M2.~2))); % now replace magnitude with measured E2 = (M2 .* cos (angle (E2) ) ) + (i*M2 .* sin (angle (E2))) ,% now back to aperature Eap = ifft2(fftunsft(fftshift(fft2(E2)) .* exp(-i*gama*dist(2)) .* evan)); fprintf(1,'%s %g %s %g %s %g\n','loop number = ',kk,' ’,errl) ,fprintf(fidl,'%g\n',errl); fprintf(fid2,'%g\n',err2); err2 = 1,err2,1 cnv=abs (perr-err2) ,perr=err2 ; kk=kk+l; end; fclose(fidl);fclose(fid2); farap=(fftshift(fft2(Eap))) * c3 .* evan; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. errl = A -ll P TP LP TH M .M %PTPLPTHM.M Program to iteratively find the complex results % from 2 planes of Thermally measured data collected 12/19/95. % Adjust initialization parameters and file names for other data. % % % % Requires the function FFTUNSFT.M which reverses the effect of the MATLAB provided function FFTSHIFT.M in order to properly account for non=power-of-2 sized matrices. % % % Final output is complex matrix 1farap' complex far-field data. which is the AUT % % John E. Will - December 28, 1995 % first set up some constants that will be read in later ncol = 116; nrow = 64; delx = 1.0; dely = 1.49; AOB= 0; AOB = 10"(AOB/20); freq = 4; c = 29.979; % now calculate some other constants fk = 2*pi*freq/c; c3 = delx*dely/(4*pi*pi*AOB); cx = 2*pi/(delx*ncol); cy = 2*pi/(dely*nrow),% now generate the ksqr matrix and gama f kx=(1:ncol); fkx=fkx-((ncol+1)/2); fkx=fkx * cx; fky=(1:nrow); fky=fky-((nrow+1)/2); fky-fky * cy; for Ll=l:ncol; for L2=l:nrow; fsqr(Ll,L2)=fkx(Ll)"2 + fky(L2)~2; end; end; gama = sqrt(fkA2 - fsqr); evan = imag(gama)==0; % evan will be 1 for gama real, 0 for gama imag % NOW we can set up the data for looping load c:\ir\decl9\decl9_27.e % thermal magnitude data at 32.4 cm load c:\ir\decl9\decl9_29.e % thermal magnitude data at 45.0 cm Ml = decl9_27; %magnitude of measurement d ist(1)=32.4; %distance from antenna M2 = decl9_29; %magnitude of measurement d ist(2)=45.0; %distance from antenna plane plane plane plane 1 to meas plane 1 2 to meas olane 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-12 kk= 1 ; % now open a couple of files to store my measure of convergence plotting) fidl=fopen('mdl1, 'w') ; fid2 = fopen('md21, 'w') ; (for later %first we need an estimate of the aperature plane (38cm x 38cm) Eap=zeros(ncol,nrow); la=round(((ncol+1)/2)-(38/(2*delx))); ra=round(((ncol+1)/2)+(38/(2*delx))),ua=round(((nrow+1)/2)+(38/(2*dely))); da=round(((nrow+1)/2)-(38/(2*dely))); Eap(la:ra,da:ua)=ones(size(Eap(la:ra,da:ua))),% left,right,up,and down aperature location - set all aperature to zero ap = Eap-=0; % ap should be l's only inside aperature. Used to truncate data outside cnv=1000; perr=0; while ((kk < 201) & (cnv > 0.000001)) % truncate data outside of aperature Eap = Eap .* a p ; % aperature to plane 1 El = ifft2 (fftunsft (fftshift (fft2 (Eap) ) .* exp (i*gama*dist (1)) .* evan)) ,% calculate convergence error errl = sum(sum((abs(El)-Ml).^2)) / (sum(sum(Ml.A2 ) )); % now replace magnitude with measured El = (Ml .* cos (angle (El) ) ) + (i*Ml .* sin (angle (El) )) ; % now back to aperature Eap = ifft2(fftunsft(fftshift(fft2(El)) .* exp(-i*gama*dist(1)) .* evan)); % truncate outside of aperature Eap = Eap .* ap ; % aperature to plane 2 E2 = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(2)) .* evan)); % calculate convergence error err2 = sum(sum((abs(E2)-M2).A2)) / (sum(sum(M2.A2))); % now replace magnitude with measured E2 = (M2 .* cos(angle(E2))) + (i*M2 .* sin(angle(E2))); % now back to aperature Eap = ifft2(fftunsft(fftshift(fft2(E2)) .* exp(-i*gama*dist(2)) .* evan)); fprintf(1,'%s %g %s %g %s %g\n','loop number = ',kk,' ',errl); fprintf(fidl,1%g\n',errl); fprintf (fid2, '%g\n',err2); err2 = ',err2,' cnv=abs(perr-err2); perr=err2 ,kk=kk+l; end; fclose (fidl) ;fclose (fid2) ,farap=(fftshift(fft2(Eap))) * c3 .* evan; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. errl = A-13 TIL T.M % TILTH - Program to compute the complex fields of an Antenna on a tilted % near-field H-plane from the complex far-field data. This version % is currently hard-coded for the SGH used for thesis work. % % % % % Input file is farsgh.mat and Output is: result - matrix of complex tilted plane data at wantx,wanty - arrays of 'result' point spacings which should agree with Dec20_2x data files. % % -John E. Will Feb 1996 % first set up some constants that will be read in later ncol = 57; nrow = 57; delx = 3.175; dely = 3.175; AOB= 14.8 8; AOB = i(T(A03/20); freq = 4; C = 29.979; lambda=c/f req; % First, compute the original, measured data, spacings about zero center rowpos=((1:nrow)- ( (nrow+1)/2))*dely; colpos=((1:ncol)- ( (ncol+1)/2))*delx; % now calculate some other constants fk = 2*pi*freq/c; c3 = delx*dely/(4*pi*pi*A0B); cx = 2*pi/(delx*ncol); cy = 2*pi/(dely*nrow); % now generate the ksqr matrix and gama fkx = (1:ncol); fkx=fkx-((ncol+1)/2); fkx=fkx * cx; fky=(1:nrow); fky=fky-((nrow+1)/2) ; fky=fky * cy; % Pre-allocate for faster processing fsqr=zeros (ncol,nrow) ,for Ll=l:n c o l ; for L2=l:nrow; fsqr(L1,L2)=fkx(Ll)"2 + fky(L2)"2; end; end; gama = sart(fk^2 - fsqr) ,evan = imag (gama) ==0 ,% evan will be 1 for gama real, 0 for gama imag load farsgh % load the complex far-field data for the Standard Gain Horn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-14 % now for each row calcuate the distance and then the data % this is setup now for the Dec20_2X files hl=23.5; %height of lowest edge, cm ang=60; %antenna tilt angle in degrees ang=ang*2*pi/3 6 0 ; %convert to radians 11=22.75; %length of horn edge along the angle axis, cm (Wide side) d l = (11/2)+(hl/sin(ang)); %length of triangle side from horn center, cm % now pre-allocate the tilted plane matrix tiltplane=zeros(ncol,nrow); for row=1:nrow % compute the distance each row is from the aperture rowdist= (dl+rowpos (row) )*tan (ang) ,% compute the complex near-field matrix at this rowdist plane=ifft2(fftunsft((farsgh/c3) .* exp(i*gama*rowdist) .* evan)); % now pick off the row of interest and save for later tiltplane(row,:)=plane(row,:); end; % tiltplane now contains the tilted plane complex near-field data, % BUT, the point spacing has changed. So now we compute the new % point spacings. tilty=rowpos; tiltx=colpos/cos(ang); % Now we'll need to do some 2-D interpolation to get data at the points % of interest for the holographic processing. wantv=(-51:54)*.86; wantx=(-32:31)*1.72; % need to do the magnitude and phase seperately magresult=interp2(tilty,tiltx,abs(tiltplane),wanty,wantx,'cubic'); pharesult=ir.terp2 (tilty, tiltx, angle (tiltplane) ,wanty,wantx, 'cubic ') ,% now combine result=magresult.*exp (i*pharesult) ,V = 0 .001:.1:1.001; contour(wanty,-wantx,magresult/max(max(magresult)), V);axis('equal') title('Computed SGH Reference Magnitude for 60 degree Tilt') % this should overlay very well with %hold on; %load c:\ir\dec20\dec20_28.e2 % contour(wanty, -wantx,dec20_28'/max(max(dec20_28)) ,V , ':');axis('equal') %hold off; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-15 F ILE R D .M function [DATA] = filerd(filename) %File to read NIST fortran binary antenna data files % Written by John E. Will 7/27/95 (for use by inverse) % This is a code fragment, so I've hard set some stuff fid=fopen(filename) ,if fid == -1 disp(['Did not find file']) stop end % I've hard-coded the data array length to be 57 points here npoints=57; % now read header line A=fread(fid,112,'char'); % now the data for ii = l:npoints DATAmagtii, :) = fread (fid, npoints, 'float')' ,DATApha(ii,:) = fread (fid, npoints, 'float')',junk = freaa(fid,2,'float'); % takes care of extra bits at end of each chunk end fclose(fid); % Now, DATAmag is in like volts, DATApha is in degrees - so to convert: i = sqrt (-1) ; DATArad = DATApha .* pi / 18 0; DATA = (DATAmag .* cos(DATArad)) + (i*(DATAmag .* sin(DATArad))); % so now DATA is a (57x57) complex array of the file data Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A-16 F F T U N SF T.M function y = fftunsft(x) %FFTUNSHIFT Move zeroth lag to edge of spectrum. % Un-Shift F F T . For vectors FFTSHIFT(X) returns a vector with the % left and right halves swapped. For matrices, FFTSHIFT(X) swaps % the first and third quadrants and the second and fourth quadrants. % FFTSHIFT is useful for FFT processing, moving the zeroth lag to % the center of the spectrum. % % % % J.E. Will 9-19-95 Un-does the fftshift function originally written by: J.N. Little 6-23-86 Copyright (c) 1984-94 by The MathWorks, Inc. [m, n] = size (x) ; ml = l:floor(m/2); m2 = floor(m/2)+1 :m; nl = l:floor(n/2); n2 = floor(n/2+1):n; % Note: can remove the first two cases when null handling is fixed, if m == 1 y = [x(n2) x(nl)]; elseif n == 1 y = [x (m2) ; x (ml) ] ,else y = [x(m2,n2) x(m2,nl); x(ml,n2) x(ml,nl)],end Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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