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ICNETS2.2017.8067928

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Space Bandwidth Product Analysis of Digital
Holography and Image Reconstruction Process
Lokesh Reddy B
School of Electronics Engineering
VIT University, Chennai Campus
Chennai, India
lokeshreddy.b2015@vit.ac.in
Praveen Phinehas M
Anith Nelleri
School of Electronics Engineering School of Electronics Engineering
VIT University, Chennai Campus VIT University, Chennai Campus
Chennai, India
Chennai, India
Abstract—Space Bandwidth Product (SBP) is a
process by which the imaging capacity of an optical is
measured. The space bandwidth product analysis for
inline and off-axis digital holography process is studied.
This paper deals the analysis of two essential
parameters i.e. image resolution and field of view of
both systems. By this demonstration the maximum
spatial frequency that captured by the CCD depends on
object size and pixel pitch of CCD camera when
distance between object plane to hologram plane is kept
constant.
Keywords—Digital Holography; Space bandwidth
product; Inline holography; Off-axis holography.
I. INTRODUCTION
The two important steps in digital holographic
processes are optical recording and numerical
reconstruction of digital holograms. This process can
be analyzed by means of Space Bandwidth Product
(SBP) of the imaging system. In 1996 Adolf W
Lohmann presented study of space bandwidth
product in digital holography. Lohmann investigated
three different holographic setups with respect to
Space Bandwidth Product (SBP) in recording
systems [1-2]. For an accurate retrieval of object
information from a digital hologram, the sampling
theorem needs to be addressed. A Signal must be
sampled at least twice the maximum spatial
frequency of the signals as defined by WhittakerShannon sampling theorem [3-4]. In other words two
pixels of the CCD must sample at one fringe period.
The Space bandwidth product addresses about
sampling criteria of optically recoding holograms
using CCD and reconstructed imaging performance
using numerical reconstruction So, The SBP of
digital holographic system must be larger than the
object. Let us consider object u(x, y) is a band
limited. This object has the lateral dimension Xx and
Xy, and the spatial frequency is limited in Ȗx and Ȗy.
The space bandwidth product is defined by
SBP=XxXyȖxȖy [5]. In this present paper, the
simulation of In-line Fresnel and off-axis Fresnel
holographic recording systems and its reconstruction
was carried out and analyzed with respect to SBP.
c
978-1-5090-5913-3/17/$31.00 2017
IEEE
II. METHODOLOGY
Consider the light propagation from object plane
to hologram plane or CCD Plane and it is given by
[6]
(1)
is the complex amplitude in the
Where
hologram-plane,
is the complex amplitude in
the object-plane, k=2ʌ/Ȝ is the wave number, Ȝ is the
wavelength and D is the distance between object and
hologram.
The CCD sensor at hologram plane
records
the interference pattern between object and reference
wave. The interference pattern obtained in inline
recording system can be described as [7]
(2)
Where
and
correspond to the amplitude of
reference wave and object wave and
is spatial
frequency of the object respectively. Therefore SBP
of an inline system in CCD plane [8] is given by
(3)
Where is lateral size of the object, ߣ is wavelength
and D is the distance between object to CCD camera.
The above equation shows the condition for
recording of an in-line digital holography system.
Now consider an off-axis hologram recording
system. The interference pattern occurs by incident
reference wave and object wave interfering at an
angle ș. The interference pattern obtained in off-axis
recording system can be described as.
(4)
The SBP of off-axis system can be described as [9]
(5)
The above equation shows that off-axis system
provides a SBP four times greater than the in-line
holographic system by using similar object.
Similarly to obtain the SBP of image plane in the
both system arrangements are given by [10-11]
194
(6)
(7)
Where N is the number of pixels, is lateral size of
is pixel pitch of the CCD camera.
the object and
TABLE I. SIMULATION PARAMETERS FOR DIGITAL INLINE SYSTEM
SIMULATION
OBJECT
NUMBER
PIXELS
DISTANCE
(D )
RECONSTRUCTED
PIXELS
1
196
25MM
196
2
576
25MM
536
3
1521
25MM
1489
4
1936
25MM
1931
5
2916
25MM
2912
6
4096
25MM
4092
Fig.1 Diffraction field of object beam
In Fresnel holography [12], the object wave
diffracts with an angle (Į) is defined as Ƚሺ ሻൌɉ Ǥ
Š‡”‡ ɉ ‹• ”‡…‘”†‹‰ ™ƒ˜‡Ž‡‰–Šǡ ‹• ‘„Œ‡…–
•’ƒ–‹ƒŽ ˆ”‡“—‡…›Ǥ Š‡ –‘–ƒŽ ‘’–‹…ƒŽ ˆ‹‡Ž† ƒ–
ሾͳ͵ǦͳͶሿǤ
Š‘Ž‘‰”ƒ’Žƒ‡‹•‰‹˜‡„›
The complete SBP simulation can be done in three
steps:
Step1:
Object function is generated in MATLAB. In each
simulation case, the object pixels are varied for the
both systems to analyze the SBP. We chose the
square object as sample for analysis.
Step2:
The hologram is produced by computing the
Fresnel propagation from the object plane to CCD
plane or hologram plane by interfering object wave
and reference wave. This field in the hologram plane
or CCD plane is called holographic recording. Find
the object pixels in the object plane.
Step3:
We want to retrieve the object field in the image
plane from the hologram plane. Thus we need to
perform back propagation from the hologram plane.
This step is called holographic reconstruction. Find
the total reconstructed pixels in the image plane or
reconstruction plane.
TABLE II. SIMULATION PARAMETERS FOR DIGITAL OFF-AXIS
SYSTEM
SIMULATION
OBJECT
NUMBER
PIXELS
DISTANCE
(D )
RECONSTRUCTED
PIXELS
1
196
240MM
192
2
576
240MM
510
3
1521
240MM
1434
4
1936
240MM
1849
5
2916
240MM
2812
6
4096
240MM
3970
The simulation parameters for inline recording
system are shown in Table I and similar range of
reconstructed pixels for digital off-axis recording
system as shown in Table II.
III. NUMERICAL SIMULATION AND RESULT
ANALYSIS
Numerical simulation was done to demonstrate
the space bandwidth product. The simulation
parameters are set as follows-CCD sensor size of
256X256 with of pixel pitch
, Ȝ=532nm,
the recording distance for DIn-line=25mm and Doffaxis=240mm.
2(a)
2017 International Conference on Nextgen Electronic Technologies
2(b)
195
2(c)
2(d)
Fig.2 Simulation results for digital inline system-2(a)
Reconstruction result for simulation No.1 2(b) Reconstruction
result for simulation No.2. 2(c) Reconstruction result for
simulation No.4. 2(d) Reconstruction result for simulation No.6.
3(c)
3(d)
Fig.3 Simulation results for digital off-axis system- 3(a)
Reconstruction result for simulation No.1 3(b) Reconstruction
result for simulation No.2. 3(c) Reconstruction result for
simulation No.4. 3(d) Reconstruction result for simulation No.6.
Fig. 2(a) shows the result for simulation No.1 for
inline system as shown in Table I and has a good
reconstruction result. The pixels of the object are
increased in each simulation case and consequently
the reconstructed pixels are reduced. The
reconstruction result for simulation No.2 looks same
as that of the original object. The reconstruction
results in simulation No.4&6 are not good agreement
with the original image and also there seems to be
some noise/unwanted pattern at the edges of the
background. Thus in comparison to the previous
reconstruction outputs the latter result has a low
resolution. This is due to the incorrect sampling.
In off-axis case, the reconstruction pixels
obtained are similar to object pixels at distance of
240mm. From Fig.3 (a) it is clear that the
reconstruction result for simulation No.1 of off-axis
system is similar to that of inline system and in all
other cases, off-axis has lower resolution
reconstructed image compared to inline system. The
above simulation results for both systems shows that
the reconstructed image in inline system gives good
resolution when compared with that of the off-axis
system. This is because the field of view in off-axis
hologram reconstructing scheme is one fourth of inline system.
Fig.4 Inline system - SBP vs Object size (mm)
Fig.5 Off-axis system - SBP vs Object size (mm)
3(a)
196
3(b)
Fig.4 and Fig.5 shows that comparison of inline
and off-axis system simulated using Eq. (6) and Eq.
(7). In inline system, limitations are not applied for
effective field of view when compared to that of offaxis system so more information can be detected with
higher resolution.
2017 International Conference on Nextgen Electronic Technologies
From the numerical experiment, we verified that
the maximum spatial frequency that captured by the
CCD depends on object size and pixel pitch of CCD
camera. In all simulated cases the off-axis system has
lower resolution image reconstruction than the inline
system.
ĐŬŶŽǁůĞĚŐŵĞŶƚ
The authors acknowledge the financial support
from the Defence Research and Development
Organization (DRDO), Govt. of India under the grant
No. ERIP/ER/1403162/M/01/1573.
ZĞĨĞƌĞŶĐĞƐ
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
U. Schnars and W. P. O. Juptner, "Digital recording and
numerical reconstruction of holograms," Measurement
Science and Technology 13, R85-R101 (2002).
D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J.
Naughton, “A practical guide to digital holography and
generalized sampling,” Proc. SPIE 7072, 707215 (2008).
L. Xu, J. Miao and A. Asundi, “Properties of digital
holography based on in-line configuration,” Opt. Eng. Vol.
39, no. 12, pp. 3214–3219, 2000.
R. Bracewell, The Fourier Transform and Its
Applications(McGraw-Hill, 1986), pp. 69–97.
A. W. Lohmann, “The space-bandwidth product, applied to
spatial filtering and to holography,” IBM Research Paper,
RJ-438 (1967).
Lei Xu, XiaoyuanPeng, ZhixiongGuo, Jianmin Miao and
AnandAsundi, “Imaging analysis of digital holography,” Opt
Express,13, 7 ( 2005).
Adolf W. Lohmann, Rainer G. Dorsch, David Mendlovic,
ZeevZalevsky and Carlos Ferreira, “Space–bandwidth
product of optical signals and systems,” J. Opt. Soc. Am.
A,13, 3 (1996).
Daniel Claus, Daciana Iliescu, and Peter Bryanston-Cross,
“Quantitative space-bandwidth product analysis in digital
holography” Appl Optics 50, 34 ( 2011).
Daniel Claus and John Marius Rodenburg, “Pixel size
adjustment in coherent diffractive imaging within the
Rayleigh–Sommerfeld regime,”Appl Optics 54, 8 ( 2015).
Anh-Hoang Phan, Mei-LanPiao, Jae-Hyeung Park, and Nam
Kim, “Analysis on the space-bandwidth product of digital
holography
for
video
hologram
recording
and
reconstruction,” Proceedings of SPIE 8384, 838416, (2012).
J. W. Goodman, Introduction to Fourier Optics (The
McGraw-Hill Companies, Inc. New York, 1996).
P.Hariharan,
Optical
Holography
(Cambridge
University,1984).
T. Kreis, Handbook of Holographic Interferometry: Optical
and Digital Methods (Wiley-VCH, 2005).
E. N. Leith and J. Upatnieks, “Wavefront reconstruction with
diffused illumination and three-dimensional object,” J. Opt.
Soc. Am., Vol. 54, pp. 1295-, 1964.
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