350-1395 7 SR 15, 1946. , W - . warun nuum 2,409,405 A. F. TUR‘NEZR RBFLBGTIIG m1 FOR POLARIZED LIGHT, W Filed Feb. 22‘, 1943 2 Shataéhut 1 1. I “ X2575 "<7 ARTHUR ‘F. TURNER _ #7?» ‘I ' > mmvrox BY ' ~ , ’ A'J/dv?f ATTORNEYS‘ aearcn HW od. 15, 1946' ' - A» F. TURNER - 2,409,401 ' W11” m1’ FOR POLARIZED LIGH! Fil'odj-‘ob. 22. 1943 I 2 Sheets-Shut z FIG.4 60 § 62 ‘- 67 I64 ' ' , 56 FIGJO _ as I ' ' THUR ETURNER AR. ( INVENTOR. FIG." BY %_M ~ ATTORNEYS I UUU-l \III 2,409,407 UNITED STATES PATENT OFFICE 2,409,407 REFLECTING ELEMENT FOR POLARIZED LIGHT Arthur F. Turner, Brighton, N. Y., asslgnor to Bausch & Lomb Optical Company, Rochester, N. Y., a corporation of New York Application February 212, 1943, Serial No. 476,675 4 Claims. (01. 88-65) 1 This invention relates to optical elements and more particularly to an element for re?ecting 2 and, as understood by the art when referring to polarized light. an interference ?lm; I mean a ?lm having a geo metrical thickness which is of the order of the _ The total internal re?ection of plane polarized light introduces a phase shift between the electric vector vibrations in the plane of incidence and those in the plane perpendicular thereto. Such magnitude of a wavelength of light. The phase shift is dependent upon forming the optical element and the ?lm from materials which have suitably different indices of refraction and a phase shift which so alters polarized light is for a given combination of materials is con frequently undesirable in many optical systems, trolled by the thickness of the ?lm as well as the particularly systems employing analyzing means. 10 wavelength of light and the angle of incidence Hence, only in special cases and with special pre caution can a total re?ecting surface be used in an optical system in which polarized light is of the same on the re?ecting surface. There is no accompanying change of intensity of the light as a result of the phase shift, that is, the light is used. _ completely re?ected. Incidentally, the presence In its broadest aspect, my invention compre 16 of the ?lm does not change the value of the hends the modi?cation and/or control of the critical angle as will be evidenced by the appli ordinary phase shift created when polarized light cation of Snell’s law. ' of any description is re?ected, and an important feature of the present invention is the ability The invention is particularly adapted for em ployment with prisms used in polarized light through the use of the invention to free re?ected 20 vertical illuminators as well as with prism tele polarized light from undesired defects which are scopes and other instruments wherein a roof present after re?ectance. prism or a Form system makes the ocular an A light ray passing from one transparent medi alyzer of the latter-named instruments partially um into a contacting medium of lower refractive inoperative for its intended purpose of reducing index at any angle other than the normal isbent 25 glare caused by atmospheric polarization or par away from the normal to the boundary between tial polarization created by external re?ection. the two media at its point of incidence with the It is well known that plane polarized light in boundary. In accordance with the phenomena cident on a total re?ecting surface is in general of total re?ection, if the angle between the in changed to elliptically polarized light when it is cident ray and the normal is greater'than the 30 re?ected. critical angle, the ray will not pass into the sec The ability of the re?ecting element of the ond medium but will be completely re?ected in present invention to alter or modify phase shifts ternally within the ?rst medium. This condition is therefore invaluable for varying the phase can be changed, however, if a third medium of shift introduced into plane polarized light when any refractive index is interposed in contact be 35 the same is totally re?ected in order to cause such tween the ?rst and second mentioned media. If light to become circularly polarized or to be made the refractive index of the third medium is great elliptically polarized to a desired degree. Con er than Ng sin m, where N; is the index of the versely, the re?ecting element of the present in- ' ?rst medium and a1 is the angle of incidence, the vention can operate upon elliptically or circularly e?ect of interposing the third medium between 40 polarized light so as to change the state of the the two ?rst mentioned media is to shift the polarization as desired upon its re?ection.‘ occurrence of the total re?ection from within the In a modi?ed embodiment of the element of ?rst mentioned medium to the boundary between the present invention, a variable phase shift can the third and second mentioned media. be created by forming the interference ?lm so I have discovered that the phase shift due to 45 that the thickness thereof will vary over the re re?ection can be selectively modi?ed or controlled to a marked degree by the presence of an inter ?ecting surface. _ ference ?lm on the totally re?ecting surface of Where the ?lm is deposited on only a portion of the total re?ecting surface, the element can an optical element which is formed of glass or be used as a Zernike phase plate for phase con- ' other suitable transparent material and which is 50 trast microscopy. The thickness of the ?lm in employed for re?ecting polarized light. The ?lm this application of the present invention is such forms the third medium just mentioned and is of as to provide a 90° retardation or acceleration to an isotropic, homogeneous, ‘transparent and non-' the zero order of the Abbe diffraction pattern as ' metallic substance. As is well known, ?lms which required in the theory of the phase contrast cause interference of light are extremely thin 55 method. I IUU , _ 2,409,407 3 4 Other objects and advantages of the present in vention will appear from the- following descrip tion taken‘ in connection with the accompanying drawings in which: Fig. 1 is a. schematic view of a right angle prism 5 in?nitum until substantially all of the light energy which embodies my invention and shows the path of a light ray traced through the prism. Fig. 2 illustrates graphically the effect on pc larized light of a thin ?lm placed on a totally ray components Re through Ra. While, as noted, the multiple re?ections proceed ad in?nitum and of the ray L is transmitted out of the prism. The series of multiple re?ections gives rise to a‘ series of components of the ray L, those occurring after the ray component R2 being indicated by hence result in an in?nite number of ray com ponents, it should be kept in mind that Fig. l re?ecting surface, this being shown by curves of 10 is for the purpose of diagrammatically illustrat-l absolute and relative phase displacement for a ing the general e?ect of the prism and the inter speci?c ?lm-glass combination. ference ?lm on light and that only by grossly‘ Fig. 3 is a view similar to Fig. 2 but graphically exaggerating the thickness of the ?lm 24 is it pos shows curves of relative phase displacement for sible to indicate even a few re?ections and result two different ?lm-glass combinations. 15 ing ray components. Fig. 4 is a phase shift vector diagram showing The prism 20 and its ?lm 24 will cause both the phase shift caused by a particular ?lm-glass unpolarized and polarized light to be redirected combination. in a manner like that just described. However, Fig. 5 is a schematic view of a vertical illumi as heretofore noted, a shift in the phase of polar nator system which employs a right angle prism 20 ized light accompanies its re?ection. In the pres like that of Fig. 1. ent invention, the resultant phase shift for a ray Fig. 6 is a schematic view which shows my in-, of polarized light will be the vector summation vention embodied in a special type of deviating of the phase shifts of its individual re?ected com prism. ' ponents which can be vectorially represented by Fig. 7 is a schematic view showing a modi?ca 25 the components in, m and so on. The total phase tion of the ‘form of the invention illustrated in ‘ shift for ray L depends on the re?ection of light Fig. 6. at the prism-?lm surface, as well as on the total Fig. 8 is a schematic view of an embodiment re?ection at the ?lm-air surface and the geo-' of the invention which employs a rhomb. metrical thickness of the ?lm. This makes it Fig. 9 is a schematic view showing a modi?ed 30 possible to selectively alter the phase shift which form of the element of the present invention. ordinarily occurs in re?ected polarized light by Fig. 10 is a schematic view of a microscope suitably controlling the thickness and index of in which a still further modi?ed form of the ele refraction of the interference ?lm which is formed ment is used. I Fig. 11 is a schematic view of an element which can be substituted for the element of Fig. 10. One now preferred embodiment of the element of the present invention is shown by Fig. 1 where on a totally re?ecting surface. . In explanation of the theory underlying the alteration of phase shift for total re?ection by means of a thin ?lm, it is to be noted that the amplitude re?ectance r of a thin ?lm may be in the reference character 20 represents a simple expressed in the imaginary form in the following right angle prism which is formed of glass or other 40 manner, as is customary when ordinary Fresnel transparent substance of index no. Prism 20, re?ection as distinguished from total re?ection as shown, has a hypotenuse surface 2| which makes an angle of 45° with the side faces 22 and 23. A thin interference ?lm 24 of any suit able transparent material of index 111' and sub stantially uniform geometrical thickness d, of the occurs at each face of the ?lm. where “W (1) order of a wavelength of light, is carried by the a is the Fresnel amplitude re?ectance of one hypotenuse 2|. The prism 20 with its ?lm are surface of the ?lm; ‘ assumed to be in air. Fig. 1 traces a ray of light b. is the Fresnel amplitude re?ectance of the L through the prism 20, the ray L being perpen 50 second surface of the ?lm; dicular to the face 22, shown as the entrance face, e is the base of the Naperian logarithms; and as having an angle of incidence with the I i is, as usual, the \/—1; and hypotenuse surface 2| of a1 and an angle of a, the relative phase displacement between any refraction in the ?lm 24 of az. two successive ray components, R1 and R2, R2 When ray L strikes the hypotenuse surface and Re, etc., which is introduced solely by the 2|, a portion of the ray is re?ected and another geometrical thickness of the ?lm, and which portion is transmitted through the prism-?lm may be given by the following equation: interface into the ?lm 24 since the total re?ect ing properties of the prism have been shifted (2) from the hypotenuse face to the ?lm-air surface. 60 The re?ected portion of the ray is emitted ' through the exit face 23 and is shown as ray com it is the geometrical thickness of the ?lm; a2 is the angle of refraction in the ?lm; portion of the ray L proceeds through the ?lm 24 to the ?lm-air surface where it is totally re?ected 65 A is the wavelength in vacuum; and nr is the refractive index of the ?lm. in a direction substantially parallel to the ray component R1. In connection with the sign of a in the fore At the prism-?lm surface this just-mentioned going, it is pointed out that a ?nite ?lm thickness totally re?ected portion of the ray L is partially introduces a retardation between successive re re?ected and partially transmitted. The trans 70 ?ected ray components and hence in Equation 1, mitted portion of the latter forms the ray com a appears, by convention, with a minus sign. ponent R: which is substantially parallel to R1. Contained in the expression for r in Equation 1 At the second re?ection at the prism-?lm surface, are both the resultant amplitude of re?ectance the part of the ray so re?ected is directed back and its resultant phase angle. The latter, herein into the ?lm 24. This process proceeds ad 75 called u, is the vector summation of the indi ponent R1. On the other hand, the transmitted v 2,409,407 6 vidual phase‘ displacements expressed in terms Where 111 and a: are, as previously noted, the of angular measure. It is necessary to obtain the tangent of u and this may be determined through angles of incidence and refraction, respecg tively. the use of a well understood mathematical process ‘ The algebraic signs of a. and 0p are important. For example, in re?ection at a denser medium which involves building the quotient of the imaginary part of Equation 1 with its real part. This procedures gives rise to the following equa tion: there is a phase displacement in the s compo nent of 180° for all angles of incidence and Equa tion 7 furnishes a minus sign to express this. ‘ imaginary= (l-a’) b sin (~11) (3) 10 For the p component, there is also a 180° phase tan u shift up to the Brewster angle. Under custom real , a(1+b’)+b(l+a") cos (-a) ary practice, however, the p component is given The above equations (1) and (3) are well a plus sign in this range because the coordinate known expressions of general character for a system is so chosen that a plus sign denotes a thin ?lm. In applying them to the case of an phase shift. This convention cannot be employed interference ?lm on a totally re?ecting surface, 15. in the foregoimg calculations and the minus sign it is necessary to develop these equations into must be explicit where a, phase shift of 180‘ is forms where the phase shift caused by total re involved. As it is written, Equation 8_ for the 1) ?ection at the ?lm-air surface is an explicit fac— component furnishes the correct sign automati tor in them. A ray incident on the hypotenuse cally on both sides of the Brewster angle. face 2| of prism 20, for example, ?rstsu?ers an 20 Equation 6 requires a valuation of p, the phase ordinary Fresnel re?ection at the prism-?lm shift resulting from total re?ection at the ?lm interface and therefore the symbol a in Equation air surface at an angle or. This valuation may 1 can be left unaltered. However, the portion of be acquired by a calculation of the phase shift this ray which reaches the second surface of the for the s and p components by the use of the ?lm is totally re?ected and the amplitude re 25 following equations which are based on those, ?ectance of this portion at the second surface for example, set forth by Lord Kelvin in his may be written as follows: Baltimore Lectures. be"’=e“ (4) Where b is the amplitude re?ectance at the ?lm air surface and will equal unity where the re ?ection is total; and s is the phase displacement introduced into each of the individual ray components R2, R: and. As indicated by the signs in Equations 9 and so on by total re?ection at the ?lm-air surface 35 10, the 8 component is advanced in phase while for light incident on that surface at an angle the 1) component is retarded, a fact in connection (12, it being observed that no phase shift due with polarized light which was ?rst pointed out ‘ by Kelvin. to total re?ection is added to the ray compo nent R1 which originates at the prism-?lm The phase shift occurring in polarized light, 40 when re?ected by an optical element having a surface. totally re?ecting surface on which there is an interference ?lm, may be calculated from Equa When Equation 4 is incorporated into Equa tion 1 so as to obtain the factor 5 in .the latter, it may be shown that the amplitude re?ectance for a ?lm on a totally re?ecting surface assumes the value noted below. tion 6 for given refractive index combinations of the optical element and the ?lm. In con 45 ducting these calculations, Equations ’7 and 8 are ?rst used to ?nd the Fresnel amplitude re ‘?ectances as and up for a desired angle of in cidence m. The phase angles 55 and 5;) are then , calculated from Equations 9 and 10. Similarly, where the factor B appearing in 50 In practice, Equation 6 is solved separately for Equation 4 is introduced into Equation 3, the lat the s and p components by keeping a and p of that ter takes on the following form: equation constant while varying a, the ?lm thick ness in terms of angular measure, to obtain tan ‘its tan u= and up, each as a function of the ?lm thickness. 55 Knowing tan us and up, the angles they represent The incident or re?ected polarized light may are readily determined and it is merely a question be resolved into a component which is vibrating of adding us to up to obtain the relative phase in a plane perpendicular to the plane of incidence, shift produced by the given combination. herein called the s component, and into a com Since the phase shifts u are obtained as tan ponent which is vibratingin a plane parallel to 60 gents, there is an ambiguity as to whether an the plane of incidence, herein called the p com ponent. The phase angle u will be different for the s and p components since both the prism ?lm amplitude reflectance a and the phase shift angle will fall in'the I or III quadrant if the . sign is positive or in the II or IV quadrant if the sign is negative. However, where u is computed for the complete range of a. from 0° through 360°, ,8, the latter being due to total re?ection, are 65 the correct quadrant will become apparent from different in the two preferred directions. Re the continuity of the curve. “?ectances a. and ap for the s and p components With the ?lm thickness equal to zero, 1. e. with I may be obtained from the following Fresnel for a=0,-Equation 6 should give a value for tan a mulae: identical with that obtained in Equations 9 and 70 10 for no ?lm. That such is the case will be ap _sin (or-a1) ‘ parent when nu instead of ns and (11 instead of a: are used in the latter equations. It is to be ob served that the phase shift goes through a com— =Itan (cg-a1) tan (ai+a1) (8) plete cycle in the thickness range given by ¢=0° 75 to a=360°. . : - ‘ 2,409,407 7 8 Fig. 2 graphically plots ?lm thickness 4 against phase angle 11. for the absolute phase displace ments uliand up and the relative phase displace diagrammatically to scale and the phase resultant given for a ?lm of index 1.72 which is formed on material of index 1.34 to a thickness or of 210", the ment A or u. minus up for a particular case in order to illustrate the phase changes which the s and p'components undergo. Curves 25 and 26 angle of incidence for the parent ray L being 45°, In Fig. 4, the s and p values for the total phase shift suffered by each of the ?rst few multi ple re?ected ray components are disclosed. For of Fig. 2 are respectively for the u; and up com ponents while curve 21 gives the values for A. ' example, s and p values for the ray component R1 are represented, respectively, by the vectors parent medium of index 1.52 on which there is 10 v1; and mp, for the ray component R2 by the vec a ?lm of index 1.34, the angle of incidence m be tors 112s and. ‘172p and so on for the remaining ray ing equal to 45°, The ?lm thickness parameter a. components which are disclosed. Lines 12. and 17p is shown as varying from zero to 360°. For the represent, respectively, the resultants of the s and conditions regarding index and angle of incidence p vectors and connect the point of origin of the just set forth, curves of the character shown in 15 vector diagram to the s and p vectors for the last Fig. 2 give phase shifts at each ?lmed totally re ray component to be re?ected. The curves are plotted for the case of a trans fleeting surface of any type of optical element in cluding of course the right angle prism 20 of Fig. It will be noted that the angle between the two strongest vectors, namely, 02. and 172p for the ray 1 as well as the other forms of optical elements hereinafter described. component R2 which is re?ected directly from the 20 totally re?ecting surface of the ?lm, is independ In general of more importance than the phase angles u. and up taken separately is their di?er ence A. It is this difference which determines ent of the thickness of the ?lm. As the ?lm thick ness varies, vectors v2; and 172p rotate in ?xed rela tion to each other. It is the addition to them‘ of the elliptic defect when a totally re?ecting sur the remaining vectors which alters the phase an face is used in a system with polarized light. As 25 gle. For this reason, vectors v2; and we are drawn shown by curve 21 in Fig. 2, A increases in the ?rst in the vector diagram, although so far as negative direction from a value of 140° at zero the values of the resultants are concerned, the ?lm thickness to a maximum value of 164°, de-‘ vectors could have been laid out in any desired creases to a minimum of 134° and rises again to sequence. reach the zero thickness value of 140° at the com 30 Moreover, each pair of s and p vectors which pletion of the cycle or at a value of :1. equal to 360°. succeed the vectors w; and U2]: will also rotate in Fig. 3 shows relative phase displacement or A curves for two other examples. These curves compare the difference in effect when employing a ?lm which has a lower refractive index and one 35 having a higher index than the index of the opti cal element on which each ?lm is deposited. ?xed relation to each other as the ?lm thickness - changes. However, the rate of rotation is differ ent for each of the succeeding pair of vectors; Consequently, there will be large variations in the phase displacements between the s and p re sultants as will be apparent from the positions Curve 28 gives the relative phase displacement A of the vector ‘Us and up. From three to six of the for an optical element of refractive index 1.72 ?rst succeeding ray components must usually be with a ?lm of index 1.34 while curve 29 is for an 40 taken into account to obtain an accurate answer optical element having a refractive index of 1.52 with ?lm index of 2.30. In both curves the angle of incidence a1 is equal to 45°. The curves 28 and 29 will indicate the e?ect on polarized light by these graphical methods. In the latter con nection, it may be necessary to plot more of the 8 values than the p values in preparing the vector diagram as the s values are more copiously re caused by right angle prisms which are similar 45 ?ected at the ?lm-prism surface than are the p in outline to that shown in Fig. 1. Of noteworthy values and by the same token us is more affected interest is the opposite trend of the curves 28 and by the ?lm than up. 29 for like ?lm thicknesses. To more fully illustrate one useful application The foregoing will indicate the possibilities of of the theory heretofore set forth, I have shown altering the phase shift so as to obtain desired 50 in Fig. 5 the ?lmed right angle prism 20 of Fig. polarization in re?ected light. With speci?c ref l embodied in a simple type of vertical illumlnator erence to the two extreme cases in the three ex system employed with a microscope. The system amples set forth in Figs. 2 and 3, it will be evident shown in Fig. 5 is particularly adaptable for the that by varying the ?lm thickness it is possible examination of opaque anisotropic specimens in to alter the value of the phase shift which occurs 55 polarized light and comprises condenser lenses at an angle of incidence of 45° between the limits 30 which direct light from a source 3| through a of 116° to 178° for the index combination which polarizer 32. Plane polarized light emerging from curve 28 represents and between the limits of polarizer 32 is directed by lens 33 into the prism ‘72° and 154° for the index combination of vcurve 20 which is shown with an interference ?lm 24 ’ . 29. Greater divergence of the indices of the ?lm 60 on its hypotenuse. Prism 20 totally re?ects the and of the substance on which the ?lm is provided light downwardly through one side of the objec will widen these limits. tive lenses 34 onto the specimen 35. Light re The alteration in phase shift originates in the ?ected from the specimen ascends through the interference of the ray components broken off other side of the objective lenses 34 to analyzer from the parent incident ray L by re?ection at 65 36, from which latter, analyzed light is passed the two surfaces of the ?lm, as best illustrated to the eyepiece of the microscope. in Fig. 1. Since the ray components R1, R2, etc., ' If a right angle prism without a re?ectance all arise from the parent incident ray L, they are ?lm on its hypotenuse is employed in a system coherent and their phase displacements will add like that of Fig. 5, it may be demonstrated that vectorially. The relative phases of the individual 70 the phase displacement A, between the s and p ray components, as heretofore mentioned, will be components of plane polarized light which is to altered both by re?ection at the ?lm surfaces and tally re?ected by the prism, will equal 139° 45’ also by the retardation due to the thickness of for a prism having an index of 1.52. When a the ?lm. right angle prism without an interference ?lm Fig. 4 shows this vector addition carried out 75 is used in the semi-aperture type of system of 2,409,407’ Fig. 5, it is necessary to orient the polarizer 32 with extreme precision with regard to the prism so that the vibration direction of the polarizer surface 40 at 45°. The end or entrance and exit surfaces 4| and 42, respectively, of prism 31 are inclined at 45° to the totally re?ecting surfaces-I is parallel or perpendicular to a principal section 40 and 39. of the prism. Otherwise, the ellipticity introduced by total re?ection would not allow the analyzer The‘ phase shift normally introduced into po larized light by material of index 1.52 when the light is incident to a totally re?ecting surface at . to give vextinction. Even if the polarizer be oriented in this way, oblique rays will become el 45° equals 139° 45' as already noted. Assuming liptically polarized and only the center of the prism 31 to have a refractive index of 1.52, the 10 two re?ections at the totally re?ecting and un ?eld can approach good extinction. If the phase shift A can be made 0° or 180° ?lmed surface 40 will cause phase shifts A1 and or 360° etc., the elliptic defect will be substan As, each equal to 139° 45', to be introduced into tially eliminated when plane polarized light is polarized light which is traversing the prism. re?ected. In the case of e?ecting a phase shift The full phase shift thus caused by re?ection at of 180° by the employment of a, re?ectance ?lm, 15 the surface 40 will thus equal the sum of A1 and the totally re?ecting surface acts as a half wave As or 279° 30'. - plate rotating the direction of polarization but not creating ellipticity. As the curves of Figs. 2 and 3 show, the phase shift A of a right angle A phase shift also takesv place at the totally re?ecting surface 39, its value also equaling 139° 45' when 39 is un?lmed. However, if the total prism of index 1.52 can be varied within the range 20 phase shift desired is 360°, it will be apparent of 70° to 155° with a ?lm of ‘index 2.3 and with that the totally re?ecting surface 39 should pro in a range of 130° to 165° with a ?lm of index 1.34. None of the usable values of A, namely 0°, 180° or 360°, fall within the just-noted ranges. vide a shift A2 of only 80° '30’ so that A1, A: and‘ As will add to the sum of 360°. Referring now to Fig. 3, it may be noted that the desired value of However, a desired value for A of 180° may be 25 80° 30' for A2 may be obtained by providing a, ?lm reached by changing the glass .or other material of the prism to that of a higher index. 38 of index 2.3 on the totally re?ecting surface 1.72. This indicates that a prism of still higher index is needed when using a ?lm of index 1.34 and suggests the use of a prism formed of extra dense ?int of index 1.75 to give the desired A of The form of the invention shown in Fig. 6 sug gests the possibility of ?lming both re?ecting sur faces of the prism. Such practice is carried out 39 to a thickness on of 75° or a of 160° when the For example, curve 28 of Fig. 3 shows that a A prism 31 has an index of 1.52. Obviously, other of nearly 178° may be obtained when using a ?lm index combinations for the ?lm 38 and prism of index 1.34 with a of 210° on a prism of index 30 31 fall within the scope of the invention. in Fig. 7 which shows a prism 43 of a construc 180°. The foregoing examples, illustrating the 35 tion and design which is substantially similar to prism 31. The totally re?ecting surfaces of the effect of ?lm thickness and index, bring out an prism 43 are denoted by 44 and 45 and its en important aspect of the invention. This resides in the ability of the practices herein described to trance and exit surfaces by 46 and 41. If a phase shift of 360° is to be obtained, it would be index combination by the suitable selection of 40 desirable to have a phase shift of 120° at each of ?lm thickness. the three total re?ections of a ray La shown at In a system employing a right angle prism, an angle of incidence of 45°. A1, A1 and A: may, in this instance, be each given a value of 120° by such as the prism 20, the use of a phase shift of placing a suitable ?lm 48 on each totally re?ect 180° as compared to 0° or 360° will reverse the di rectional sense of rotation given an analyzer, lo 45 ing surface 44 and 45. For a prism of index 1.52, a ?lm 48 having an index of 2.3 and a thick cated behind the right angle prism, in following a ness 0: of 20° or 240° will provide the desired given rotation of the polarizer. A clockwise ro shift of 120° ~at each re?ection, reference being tation of the polarizer, as seen by looking towards again had to the curve 29 of Fig. 3. The inven the light source, can be followed by rotation of the analyzer in the same directional sense. The 60 tion also comprehends the use of other index combinations for the ?lm 48 and the prism 43, azimuthal rotation sense of the vibration from the analyzer is reversed by the act of re?ection ’ the foregoing merely being set forth as one illus trative example to indicate the scope of the in and also by the half wave or 180° phase shift. In vention. the case of the vertical illuminator system shown in Fig. 5, the re?ection at the surface of the speci 55 In the forms of the invention shown in Figs. 6 and 7, the values of A which are used, occur at men 35 again reverses the azimuthal rotation values of a where the curve 29 of Fig. 3 is ascend sense so that the tube analyzer 36, or a cap ing or descending. Accordingdy, _a small change analyzer if used, would have to be rotated coun in a will change the individual A’s and will destroy terclockwise to follow a clockwise rotation of the polarizer 32. 80 the condition that the overall phase shift be ex actly 360°. It is to be noted that a varies for a . Use of my invention is not limited solely to a given geometrical ?lm thickness, not only with the right angle prism. For example, it may be ap angle of incidence on the ?lm but also with the plied to a 90° deviating prism formed of a right wavelength. Preferred practice hence selects a angle prism and a rhomb cut from the same piece of glass or other transparent material. A prism 65 prism-?lm combination having the value of the desired phase shift A as a maximum or minimum 31 of this character is shown in Fig. 6 and it may in the curve of A plotted against 0:. be formed of materials which vary widely in in Thus in the prism 43 of Fig. 7 it is preferable dex. The prism 31 of Fig. 6 is shown with a thin to employ a ?lm of an index such that, the high ?lm 38 on its re?ecting face 39. The other totally provide a predetermined phase shift in a given re?ecting face 40 is left un?lmed. or the low points of the A and 0: curve will fall at a thickness a corresponding to a A of 120°. Fig. 6 schematically traces a ray L1 through Where the curve of A plotted against a ful?lls the prism 31, the multiple re?ections at the ?lm this condition, that is to say, when 38 being omitted from the drawingsyfor the pur pose of clarity. Ray L1 is shown as travelling in 1A the direction of the arrows and as incident to 76 do: 2,409,407‘ , equals zero, there will be but slight variation of A with a. change of 1 caused by change in wave length or in angle of incidence. Film material the use of the ?lm 54 on the surfaces 50 and 5|. .1: In the case of overcoming the elliptic defect of index'2.0 instead of 2.3 is suggested for de pressing the A and d curve sufficiently to satisfy this condition for the 120° phase shift needed in in plane polarized light, the ?lms 54 should be of such character as to cause A1 and A: to be each the prism 43. When the ordinary right angle equal to 90° thus causing a total phase shift of 180°. A suitable combination for this purpose prism 20 of Figs. 1 and 5 has an index of about 1.75 and a ?lm of index 1.34 is used to obtain a phase shift of 180°, the condition that 12 the total re?ection at the two air-glass surfaces.‘ This phase shift will,' of course, be altered by; is provided by a ?lm of index 2.3 at a thickness 10 on of 60° as will be apparent from a study of the curve 29 of Fig. 3. However, the preferred con in dition that do: _ dA equal zero is perforce satis?ed since a phase It; shift of 180° will just barely be reached by this 15 equal zero would not be satis?ed with this ?lm combination. While the combination described provides a index and it would, in general, be advantageous phase shift of 120° at each totally re?ecting to select a ?lm material of lower index. surface of the prism of Fig. 7 so as to cause in As previously mentioned, my invention compre cident plane polarized light to be emitted as 20 hends alteration of the phase shift to produce plane polarized light from the prism, such prac circularly polarized light. This can be effected with plane polarized light by the use of the right tice need not necessarily be followed. The value angle prism ‘20 of Fig. 1 ?lmed on its hypotenuse of the phase shift at each total re?ection is im material so long as the sum of all of the phase 2| to give a value for A of 90°. shifts caused by the prism of Fig. 7 adds to 360° if plane polarized light is to emerge therefrom. bination like that described in connection with the rhomb of Fig. 8 could be employed for this ’ purpose, the same reservation as to the value of It will hence be realized that my invention com prehends the use, on different totally re?ecting surfaces, of ?lms of different indices and/or _ (101 thicknesses as well as ?lms of like index and of 30 not equaling zero for this combination being here noted. Useful applicationof a circularly polariz ing prism of this nature can be expected in con nection with a polariscope as well as in other in the same or different thickness in obtaining a phase shift of any desired value, including a phase shift of 360°. While I am aware that the art has employed a 90° deviating prism of a geometrical shape sub stantially similar to the prisms of Figs. 6 and '7 for the purpose of eliminating ellipticity, the prior art effort, as exempli?ed by U. S. Patent No. 2,128,394, has depended entirely on the A ?lm-glass com ‘ struments. - ' A variable phase shift can be introduced into a beam of polarized light, referring now to Fig. 9, ' by forming the interference ?lm 55 of variable thickness on the total re?ecting surface 55 of the formation of the prism of glass of special refrac 40 prism 51. For example, if a ray such as ray L4 tive index to obtain this effect, namely, an index be directed so as to be incident on the surface 56 in an in?nite number of cases as by moving equal to the V3. My invention is distinguish ‘the stop 58 from the position shown in full linesv able therefrom on the basis that I employ a prism to the position shown in broken lines, a con of substantially any index as well as in the use tinuously varying phase shift will be created in of an interference ?lm with such a prism. It -‘ the ray L4. should also be noted that alteration of phase shift An element such as illustrated in Fig. 9 can is not limited in my invention to a single value, at any totally re?ecting surface but that the be used to compensate and measure an unknown retardation in a sample introduced in the ray. alteration may be selected, whereas the phase shift at each totally re?ecting surface of the just 50 I have found that one embodiment of the ele ment of the present invention can be used as a mentioned prior art prism must always be lim Zerm‘ke phase plate for phase contrast micro ited to 120°. Furthermore, since one is not lim ited to a glass of de?nite index, a glass which is resistant to weathering or staining can be used, In this embodiment of the present invention, so that the phase shift produced is permanent referring now to Fig. 10, an interference ?lm 50 is and is not altered by the spontaneous formation deposited on the re?ecting face SI of the prism 62. The ?lm E0 is formed on but a portion of the of a stain ?lm over long periods of time. scopy. Fig. 8 illustrates the invention in use with ‘ , surface BI and the ?lm should be of such a size another type of 90° prism, namely, the rhomb and area as to cover in projection the zero order 49 having the parallel totally re?ecting surfaces Abbe diffraction pattern in the back focal plane 50 and 5| which are joined by the parallel end faces 52 and 53, the latter being at an angle of 45° to the two totally re?ecting surfaces. A re , of the objective of the microscope and should be of such a thickness as to provide a 90° retarda tion or acceleration to the zero order as required ?ectance?lm 54 is formed on both of the re ?ecting surfaces 50 and 5|. Passage of a'ray Le, incident on ?lm 54 at 45°, is traced through the prism 49. As heretofore pointed out, glass of index 1.52 will introduce a phase shift of 139° 45’ in polar ized light which is totally re?ected in such me-v dium and is at an angle of incidence of 45°. Thus, if the rhomb 49 were un?lmed and were con structed of glass of index 1.52, there would be a total phase shift of 2 X 139" 45' or 279° 30' in polarized light passing through the prism due to in the theory of the phase contrast method. Since the retardation of the ?lm with respect to the un?lmed remainder of the totally re?ecting surface 6| will be different for light vibrating in r the p and s directions, polarized light would prob ably be preferable for illumination. For a ?lm in dex of 1.34 on a right angle prism of index 1.52, Fig. 2 shows that the ?lm thickness should be that corresponding to a of 85° for the p direction and a of a value of 120° for the s direction. If the ?lm thickness is one or the other of these two values, a variation in retardation between these ' “Uni ‘II I I \UU 2,409,401” 13 14 limits would be obtained by rotating‘the polarizer glass, the re?ectance ?lm may be provided by , from one position to the other. leaching out‘ acid soluble glass forming oxides; The prism 62 would be inserted in the optical to leave a layer which is rich in silica on the to»; system of the microscope as schematically shown‘ tally re?ecting surface of the optical element. in Fig. 10,-ln which the ocular and objective sys Films may be formed in many other ways and tems are indicated at 63 and 64, respectively, and by the use of many other materials so long as the specimen at 65. In this use of the element of the ?lms ful?ll the requirements as to refractive the present invention, the prism 62 would replace index and thickness previously mentioned. For the conventional Zernike phase plate which is example, a ?lm in the form of a thin layer of positioned in the back focal plane of the micro 10 glass, which answers theserequisites, falls within scope objective. the scope of my invention. Also contemplated It will be» obvious that an element such as shown are ?lms formed by the well known process of in Fig.- 11 could be used in place of the element 62 spraying such substances as titanium tetrachlo shown in Fig. 10. This element of Fig. 11 com-_ ride, silicon tetrachloride and the like on glass or prises a prism =66, the re?ecting surface 61 of 15 other transparent material. which carries, except on a predetermined por Therefore, while certain preferred embodiments tion thereof, an interference ?lm 68. In the ele of the invention have been illustrated and de ment 68 the un?lmed portion of the re?ecting scribed herein, it is to be understood that the surface 61 for the correct indices of the prism invention is not limited thereby but is suscepti and ?lm give a variation in phase acceleration 20 ble of changes in form and detail within the between certain limits by rotating the polarizer spirit of the invention and the scope of the ap pended claims. from one position to the other as in the case of I claim: While the foregoing illustrations have ‘all em ‘1. A transparent body having a plurality of ployed an angle of incidence of 45°, my invention 25 totally re?ecting surfaces from which light en may be carried into practical effect at other angles tering the body is successively re?ected, each of of incidence. Total re?ection at angles other said surfaces being characterized by introducing than 45° is often met in practice, for example, in a shift in the phase of the components of po roof prisms, where, as in military and other ob lariz'ed light which is passing through the body‘ servation instruments, atmospheric polarization 30 and which is re?ected by said surfaces; and the element 62. _ . must be considered. The effect of phase shift , caused in a. roof prism or a Porro system is to means on one of said surfaces for selectively forms an important aspect of my invention. Besides the single ?lms illustrated in the draw ings, my invention comprehends the use of mul tiple ?lms, that is to say, superposed ?lms of dif metallic interference ?lm, said ?lm being trans modifying the phase shift between the compo prevent the full effective use of an ocular analyz nents normally introduced in polarized light by er associated with such instruments. Thus, the re?ection at that surface whereby to selectively use of ?lms for angles of incidence other than 45° 35 alter the sum of the phase shifts occurring at all ferent indices. of the surfaces, said means comprising a non parent and substantially isotropic and having an index of refraction different from that of said In . connection with multiple 40 body and a substantially uniform geometrical ?lms, it may be pointed out that large effects are to be expected from their use because of the large values of the vector components to which they give rise. As a special case, my invention includes within its scope the bene?cial effects on phase shift ‘ derived in instances where degenerate total re?ec tion takes place due to the use of a ?lm of an in a thickness which is of the order of magnitude of a wavelength of light, the refractive index and thickness of the ?lm being chosen to produce the selected phase displacement of the polarized light re?ected by said surfaces. _ 2. An optical element formed of transparent material and having a surface positioned in a path of polarized light rays for totally re?ecting dex which is lower than the index of the ‘optical the polarized light rays, means for selectively. element or prism upon which it is placed. 50 altering the phase displacement between the com Examples of the invention have been described ponents which polarized light normally under in regard to the re?ection of plane polarized light. goes when it is totally re?ected at said surface, Obviously, the phase of elliptically or circularly said means comprising a thin homogeneous, non polarized light may be altered by the use of a suitable index combination of the ?lm and the 55 metallic transparent ?lm on said surface, said ?lm having a refractive index which is different optical element used for total re?ection. Thus, under suitable conditions, it is possible to alter elliptically polarized light so that on re?ectionv it is rendered plane or circularly polarized or is from that of the element, said‘ ?lm being sub stantially isotropic and having a substantially uniform thickness, the refractive index and elliptically polarized to a desired degree. Sim 60 thickness of the ?lm being chosen so as to pro duce the selected phase alteration in the polar ilarly, circular polarized lightv may on re?ection ized light re?ected by said surface. _ a be rendered plane or elliptically polarized. 3. An optical element of transparent materi Re?ectance or interference ?lms employed having a surface at which total internal re?ec throughout my invention are of well known types and their formation is well understood by the art. 65 tion-takes place for use in an optical system em ploying polarized light of a known wave length Under one practice, a ?lm suitable for use on a and which is incident on said surface at a pre totally re?ecting surface may be formed by de positing a metallic salt or oxide on such surface by a high vacuum process. While any suitable determined angle; and means on said surface for sorbing as to light, tin oxide and zinc sulphide to tally re?ected by said surface, said means com prising a relatively thin non-metallic interfer selectively controlling the phase displacement be transparent substance may be used to form an 70 tween the components of polarized light which is normally introduced ‘when polarized light is to evaporated ?lm, substances which are non-ab name two examples, are preferable but notessen- ’ ence ?lm covering said surface, said ?lm being tial. Where the optical element to be ?lmed is of 75 substantially isotropic ‘and having an index of 15 2,409,407’ refraction less than that of said element, the effective optical thickness of said film being less 16 polarized light which normally occurs when pom ' larized light is totally re?ected, said means com?‘ than a wave length 01' said light and varying from’ prising a thin, homogeneous, non-metallic, trans: a maximum thickness at one side of said surface parent ?lm, which is substantially isotropic and to a minimum thickness at the opposite side of has a refractive index different from that of said said surface. body; said ?lm having a, geometrical thickness 4. An optical element for re?ecting polarized which is of the order of magnitude of a wave a light comprising a body of transparent material length of light, the refractive index and thickness having a surface positioned in a path of'polar of the ?lm being chosen to produce the selected ized light rays for totally re?ecting said rays, 10 phase displacement of the components of the means on the surface for selectively altering the polarized light re?ected by the surface. phase displacement between the components of ARTHUR F: TURNER.