2900-88-R Memorandum of Project Michigan THE EFFECT OF FILM-THICKNESS VARIATIONS ON COHERENT LIGHT ARTHUR L.. INGALLS October 1959 RADAR LABORATORY T H E U N I V ER S I T Y OF M I C H I G A N Ann Arbor, Michigan

DISTRIBUTION OF REPORTS Distribution control of Project MICHIGAN Reports has been delegated by the U. S. Army Signal Corps to: Commanding Officer U. S. Army Liaison Group Project MICHIGAN Willow Run Laboratories Ypsilanti, Michigan It is requested that information or inquiry concerning distribution of reports be addressed accordingly. The work reported herein was carried on by the Willow Run Laboratories for the U. S. Army Signal Corps under Project MICHIGAN, Contract No. DA-36039 SC-78801, for the U. S. Air Force Air Materiel Command under Contract No. AF 33(600)-38019, and for the U. S. Air Force Rome Air Development Center under Contract No. AF 30(635)-2905. University contract administration is provided to the Willow Run Laboratories through The University of Michigan Research Institute.

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2900-88-R PREFACE Documents issued in this series of Technical Memorandums are published by Willow Run Laboratories in order to disseminate scientific and engineering information as speedily and as widely as possible. The work reported may be incomplete, but it is considered to be useful, interesting, or suggestive enough to warrant this early publication. Any conclusions are tentative, of course. Also included in this series will be reports of work in progress which will later be combined with other materials to form a more comprehensive contribution in the field. A primary reason for publishing any paper in this series is to invite technical and professional comments and suggestions. All correspondence should be addressed to the Technical Director of Project MICHIGAN. Project MICHIGAN, which engages in research and development for the U. S. Army Combat Surveillance Agency of the U. S. Army Signal Corps, is carried on by the Willow Run Laboratories as part of The University of Michigan' s service to various government agencies and to industrial organizations. The work reported herein was jointly sponsored by the U. S. Army Signal Corps, the U. S. Air Force Air Materiel Command, and the U. S. Air Force Rome Air Development Center. Robert L. Hess Technical Director Project MICHIGAN iii

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R ABSTRACT This report describes the experiments which measured perturbations in monochromatic coherent light caused by variations in film thickness, and discusses the results. The introduction of commercial photographic film into the aperture of an optical system disturbs the coherence of the transmitted light, because of the variations in thickness and refractive index present in the film. Such variations in film may be made visible, as contour lines, by light interference between the front and back film surfaces. Photographs of the interference pattern were measured, and calculations of light-path variations made. A qualitative analysis showed that film-base thickness-variation was primarily responsible for deterioration of coherence. Formulas are given which show the effect of film variations on coherent light for both use and measurements; and figures are included which show the distribution of film quality. Few of the commercial films tested were found acceptable by Rayleighlimit standards; more were satisfactory when immersed in a liquid whose index of refraction nearly equaled that of the film. Index-matching specifications are included which show how nearly the film and liquid indices must match for any particular film quality to affect coherence, due to thickness, by no more than one Rayleigh-limit. 1 INTRODUCTION Photographic film is being used in a relatively new way recently, placing additional demands on the perfection of film manufacture. The film is used in the aperture of an optical The material of this report will be presented at the 1959 National Conference of the Society of Photographic Scientists and Engineers, Chicago, Illinois, October 26-30, 1959. 1

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R system rather than, as is usual, in the image plane. Geometric patterns are photographed, and this record, called a hologram, is placed in the optical aperture to control the phase of the transmitted light, thereby producing a desired effect in the image plane (Ref. 1 and 2). Unfortunately, variations in film thickness and refractive index affect the phase in random fashion, thus preventing the desired result. Under these conditions of use, variations in thickness, refractive index, and surface quality are of prime importance. The effect of placing film with nonuniformities in an optical-system aperture is to disrupt orderly wavefronts, causing a diffusion of the light at the image points. This diffusion can take the form of a displacement due to an optical wedge in the film, a defocusing of the image due to the lens power of a spherical depression or projection on the film, or a combination of both. Higher-order effects due to saddle curves and inflection points are also present. 2 EXPERIMENTAL PROCEDURES A study of these variations in film was made possible by taking photographs of the pattern resulting from interference in monochromatic light occurring at normal incidence between light reflected from the front and back surfaces of the film. The apparatus (Fig. 1) consisted of a 100-watt mercury arc lamp, a piece of flashed opal glass, a curved-object film holder (2-ft cylindrical radius), a 5461 A interference filter and a 4 x 5 view camera. The light source and camera lens were placed close together and approximately at the center of curvature of the film holder. In this way the front and rear surfaces of the film formed a double cylindrical reflector which was tilted to focus the reflected light from the source into the photographic lens, thus filling the lens field with light. It was necessary to close the lens to approximately f/45 in order to get contrasty fringes, as wider openings allowed displacement of fringes with consequent smearing. As a first test, interference pictures were taken with the above apparatus and sorted into a distribution of visually discrete steps of average fringe concentration. From this distribution, a quality chart (Fig. 2) was constructed with quality ratings ranging from A through H. A chart was also made of the distribution of various different films from six different manufacturers, of which three were domestic and three were foreign (Table I). At this point two questions needed an answer. They were: (a) whether the base or the emulsion were responsible for the optical variation; and then (b) whether the surface or index were more responsible. To determine these answers, second and third tests were performed. 2

WI L L W R UN L A B R ATORIES T E CHNICAL M E M O R A N D U M 2831 l 13-R/2900-88-R pi: FIG, 1. EXPERIIMENTAL APPARATUS. Equipment for photographing interference fringes, The second test was made by photographing five different films, with and without emulsion, to show whether the film base or the emulsion played the more important part in producing high fringe concentrations. The test was begun by taking a 4-ft strip of film and developing it clear. The film vas then cut into two pieces each 2 ft long. The emulsion was then stripped from one piece, and both pieces were photographed, using the techniques and appa atus described above, It was evident that far more difference existed between films than between the same film with and without emulsion (Fig, 3). The third test was performed to ascertain whether change of thickness or change of refractivrre index is the more responsible for the variation in optical path length. The test consisted of obtaining light interference between the back and front plano-glass surfaces of a cell and then noting the change in the interference pattern wben fhn alone or film and a liquid; of matching

W l-l LO W RUN L A B OR A TO0 R I E S T E C H N I C AL M E MO0 R A N D U M 2831-13-R/2900 88-R A E!B~~~~~~~~~C F D o H FIG, 2. FILM OPTICAL PATH VARIATION, Interference wavelength = 5461 A TABLE I. DISTRIBUTION OF FILM SAMPLES Quality Mfr A B C D E F G H 1 x xx ax 2 xxxx x x x xx xx 3 XX XX XXXX 3 xx x xx xxxx 4 x xx 5 x x xx 6 xx 4

W LLOW RUN LABORATORIES TECH NICAL MEMORANDUM 2831-13-R/2900-88-R With Emulsion Without Emulsion. A C E FIG. 3. EFFECT OF EMULSION ON OPTICAL PATH VARIATION. Interference wavelength = 5461 A. index were introduced into the cell (Fig, 4). The cell plates were half aluminized and adjusted nearly parallel so that very few fringes were present. The introduction of film altered the fringe pattern, but the addition of an index-matched liquidbrought the fringes back nearly to the original pattern. The same apparatus described above was used to photograph these fringes, except that the curved film holder was replaced by the liquid cell just described, Figure 4 shows the interference fringes for the cell alone with no film and for five cases of film with and without liquid, The fact that the wet-film interference pictures look nearly like the picture of the cell with no film indicates that most of the optical path variation is due to the film surface variation and very little is due to variation of film refractive-index. Film xthickness thus appeared to be mainly responsible for the variation in optical path length. 5

W I L L O W R U N L A B O R A T O R I E S T E C H N C AL M E M O R A N D U M 283 113-R/2900-88-R No Film Dry Wet A CE F G FIG. 4. SURFACE VS. INDEX VARIATION, USING LIQUID GATE It is noted that more fringes appear in the wet film than in lthe "no-film photographs. This is due to the shorter effective wavelength in the liquid. Also the fringe count in the case of dry film is one-third of that which appears in interference between the front and back surfaces of the film of'the firs't test. 3 DISCUSSION OF RESULTS Quantitative measurements were obtained by counting fringes linearly over a:measured distance on the film-surface-interference photographs. This permitted quantitative representations of the light deviation due to wedge, for the various quality ratings. Two values were obtained, one for average deviation and one for nmaximum deviation The average deviation was obtained by counting fringes linearly over'the interference photograph and dividing the number of fringes by the distance covered in millimeters, A computation was then necessary to express this as average deviation, Maximu m deviation1 was obtained by obtaining the fringe count divided by distance for a small length at the position where -the fringe system was the finest. 6

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R The formulation used was: (/ - 1) n D = 2 2,u S where D = deviation angle, u = refractive index (1. 478), X = wavelength of light (0. 0005461 mm), n = fringe count, and S = distance over which fringes were counted. Figure 5 shows the average results obtained using eleven different photographs. 4.0 -70 60 3.0 O -50 0 0o HE~~~~~~ ~~ ~-40 A E -20 n 1.0 >10 A B C D E F G H FILM QUALITY FIG. 5. WEDGE EFFECT IN FILM. From left to right, film quality varies from good to poor. Since the optical path variation defect was found to be principally due to variation in base thickness, the pattern of fringes obtained in the photographs of Fig. 2 are essentially a 7

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R topographical map of the optical thickness variation in the film. The space from one dark line to another shows a thickness change represented by: At = X/2/s = 0. 0005461/2 x 1. 478 = 0. 00018 mm/fringe = 0. 0000073 in. /fringe where At = thickness change. Maximum thickness variations can be obtained by counting fringes and multiplying by the above given thickness change per fringe. On this topographical map: (1) Parallel lines indicate a slope forming an optical wedge. The finer the line structure, the steeper the slope. (2) Concentric circles indicate either hills or depressions. (3) Saddle points usually separate two hills in one direction and two depressions in the 900 direction. (4) A hill and a depression are separated by more or less parallel fringes, where the finest line structure occurs at the inflection point. In order to determine the effect of film-thickness variation during use and measurement, three separate situations must be considered: Case A: Transmission of light through film. Case B: Light reflected from both surfaces of film. Case C: Light reflected from two glass plates having film, film and liquid or no film between them. Since these three cases are slightly different mathematically, they are treated separately. Case A (Fig. 6) In this situation film is in use in a gate which may or may not contain a liquid. It is assumed that light passes through thicker and thinner portions of the film and the optical path difference (OPD) is given by the formula OPD = (2 - l)At. 2 1 Case B (Fig. 7) This is the case where interference takes place between light reflected normally from the front and back surfaces of a piece of film. In this case black lines appear where a path difference between the front and back reflections is a whole number of wavelengths. The formula for change of thickness is At = nX/2=, 8

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R where n is the number of black (or white) lines counted between points. This applies to the pictures in Fig. 2 and 3. #1 r2 Glass Plates Incident Light,...' Transmitted Light Photographic Film... OPD=(#I2- i)At FIG. 6. TRANSMISSION OPTICAL PATH DIFFERENCE. Case A, liquid gate. Case C (Fig. 8) In this case, interference occurs due to combining light reflected from the partial mirror surfaces of the two glass plates. One of the reflected rays will have traveled twice through the film and its immersion medium. The formula for optical path difference is: OPD = 2(.. -.)At; and for the number of fringes associated with a change of thickness: At=n nX/2(p -p1)' From these cases, certain deductions follow. First, upon comparing Case B with Case C (dry cell) it appears that the number of fringes will be different for the same change of film thickness. 9

WILLOW RUN LABORATORIES T E C H N I C A L MEMORANDUM 2831-13-R/2900-88-R Photographic Film Incident Light V. i/ Air Reflected Light I- At FIG. 7. INTERFERENCE IN PHOTOGRAPHIC FILM. Case B. Mi i'2 P2 j5 I 2.'I * **rPhotographic Film Incident Light R / ^ ^:i:g..' ^^^^-=:= Partially Aluminized Glass Plates Reflected Light l... G ass Plates FIG. 8. INTERFERENCE IN LIQUID CELL. Case C. 10

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R For Case B, nB = 2/At/X; for Case C, nC = 2(p - l)At/X; therefore, nB = nC//(a - 1). This shows that, for / = 1. 478, the number of fringes for Case B is approximately three times the number of fringes for Case C. For this reason there are fewer fringes apparent in the Fig. 4 "dry" cell than in Fig. 3, although the same films were used. Secondly, upon comparing the "wet" cell with the "no film" cell it is noted that more fringes are apparent in the wet-cell case. This is to be expected, since the effective wavelength in the cell is X//2 which is smaller than the wavelength X for the same cell in air. This means that we should find nearly 50% more fringes in the wet-cell case due to this effect. 4 PERMISSIBLE LIMITS In order to select a film having acceptable variations, the Rayleigh limit may be employed. This specifies that no more than one-quarter of a wavelength of light of optical path difference is permissible over the active aperture. OPD due to thickness variations (At) of a film (of index p2) immersed in a medium (or index t l) can be represented by the formula: OPD = (2 - l)At (Fig. 6). If the Rayleigh limit of a quarter of a wavelength (X/4) is used as the maximum allowable departure from coherence, the formula for the maximum allowable thickness variation of the film becomes At max= X/4(M2 - 1) max 2 17 For film immersed in air and using a green mercury lamp for monochromatic light, the permissible variation in film thickness is approximately 0. 0001 mm, a very small variation indeed. However, film may be immersed in a liquid whose index approximates that of the film (Ref. 3). A plot of the Rayleigh allowable film-thickness variation vs. immersion-liquid index for a film index of 1. 478 is given in Fig. 9. The ordinate is also given in terms of number of fringes as counted on an interference photograph of film-thickness variation. (Film thickness per fringe is t/n = X/2/u). 11

WI LLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R FILM INDEX 1.478 10 0 9 H B 6 - A Quality 8 7 7 5 U), / \ -~6 | 4 z 3 4 2 _ ^ \ C Quality 8- 3 2~ 2 0 0 1.3 1.4 1.5 1.6 1.7 LIQUID INDEX FIG. 9. INDEX-MATCHING DIAGRAM By counting fringes on the quality chart (Fig. 2) it will be seen that C quality has a maximum of about nine fringes from hill to depression allowing an immersion-liquid index variation from about 1. 46 to 1. 50. For film in air, a variation of only a half fringe can be tolerated. For film immersed in water (n = 1. 33), variation of less than one and a half fringes can be tolerated. An additional advantage is gained by the use of a liquid gate. Scratches and rough surface present on the film give rise to scattered light. The scattered light from films used in the optical aperture produce loss of contrast in the final image. The use of liquid in a liquid gate fills in the scratches and rough surface, thereby eliminating scratched light from this source. When an immersion liquid is used, change of phase due to a relief image is eliminated. This phasing under some conditions may be in such a direction as to increase the illumination 12

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2831-13-R/2900-88-R in the final image. If this happens, the liquid serves to reduce illumination and its use is then classed as a disadvantage. 5 CONCLUSIONS Through the use of light interference measurements, change in film-base thickness is found to be the principal cause of variations of optical path through film. Variations between films are distributed over considerable differences. A high degree of excellence in manufacture is necessary to use film in an air aperture and maintain coherence of light within the Rayleigh limit. The use of a liquid gate with film has both advantages and disadvantages. The advantages are: (a) Reduced light-phase variation due to thickness variation, (b) Film easily retained in a plane by a glass plate cell; and, (c) Reduction of noise due to scratches and rough surface. The disadvantages are: (a) Liquid-handling difficulties, and (b) Elimination of phasing due to relief images. Some lack of match between liquid and film may be allowed without exceeding the Rayleigh limit for a particular film. It is evident that the sampling is too small to prove any trend conclusively. Enough evidence is available, however, to indicate the advisability of pursuing this study further, and to reveal the advantages of expending efforts to achieve a substantial improvement in film quality. REFERENCES 1. Gabor, D., "Microscopy by Reconstructed Wavefronts, " London, Proc. Roy. Soc. (London) A, 1949, Vol. 197, pp. 454-487; Proc. Phys. Soc. (London) B 1951, Vol. 64, pp. 244-255; pp. 449-469. 2. Kirkpatrick, P., and El-Sum, H. M. A., "Image Formation by Reconstructed Wavefronts," J. Opt. Soc. Am., 1956, Vol. 46, pp. 825-831. 3. "Printing Motion-Picture Films Immersed in a Liquid, " Part I: "Contact Printing, " by Stott, J. G., Cummins, G. E., and Breton, H. E.; Part II: "Optical Printing, "'by Turner, J. R., Grant, D. E., and Breton, H. E., J. Soc. Motion Picture Television Engrs., October 1957, Vol. 66, pp. 607-615; Part III: "Evaluation of Liquids, " by Delwiche, D. A., Clifford, J. D., and Weller, W. R., J. Soc. Motion Picture Television Engrs., October 1958, Vol. 67, pp. 678-686. 13

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2900-88-R DISTRIBUTION LIST 3, PROJECT MICHIGAN REPORTS 1 October 1959 -Effective Date Copies Addressee Copies Addressee Copies - Addressee 1 Office, Chief of R&D, DA 2 Chief, U. S. Army Security Agency 4 Office of Naval Research (Code 463) Washington 25, D. C. Arlington Hall Station Dept. of the Navy ATTN: Chief, Communicatios Arlington 12, Virginia 17th and Constitution Avenue, N. W. ATTN: Chief, Communications Washington 25, D. C. 2 Cdr., Army Rocket & Guided Missile 1 Office, Chief of R&D, DA Agency 2 Dir., U. S. Naval Res. Lab. 1OWashington 25, D. C. Redstone Arsenal, Alabama Washington 25, D. C. Washington 25, D. C. ATTN: Army Research Office ATTN: Tech. Library, ORDXR-OTL ATTN: Code 2027 ATTN: Army Research Office / 5 Dir., U. S. Army Eng. R&D Lab. 1 Office, Asst. C of S for Intel., DA Fort Belvoir, VirgniaCorona, California Corona, California Washington 25, D. C. 1 ATTN: Chief, Topographic Eng. Dept. ATTN: Chief, Combat Dev. 1 ATTN: Chief, Electrical Engrg. Dept. A N i ry G-2 Air Branch 3 ATTN: Tech. Documents Center 1 CO &Dir. 1 Commanding General, USCONARC 1 Comdt., USACGSC U. S. Navy Electronics Lab. Fort Monroe, Virginia Fort Leavenworth, Kansasan 52 California ATTN: ATSWD-G ATTN: Archives ATTN: Library 2 Commanding General 1 Comdt., U. S. Army Armor School 3 Dept. of the Air Force, Hq., USAF U. S. Army Combat Surveillance Agency Fort Knox, Kentucky Washington 25, D. C. 1124 N. Highland Street ATTN: Combat Dev. Group 1 ATTN: AFOIN-lB1 Arlington 1, Virginia ATTN: AFOAC-E/A 2 Asst. Comdt., USAAMS 1 ATTN: AFDRD Office of C Sig R, DA Fort Sill, Oklahoma 1 ATTN: Directorate of Requirements Office of C Sig O, DA Washington 25, D. C. 3 Asst. Comdt., US ARADSCH 3 CinC, Hq., SAC 27 CO, U. S. Army Signal R&D Lab. Fort Bliss, Texas Offutt AFB, Nebraska Fort Monmouth, New Jersey 1 Comdt., USAES 1 ATTN: DINC ATTN: SIGFM/EL-DR Fort Belvoir, Virginia2 ATTN: DORQP ATTN: SIGFM/EL-DR ATTN: Combat Dev. Group 1 Commanding General, USAEPG 4 Hq., Tactical Air Comd. Fort Huachuca, Arizona 1 Comdt., USASCS Langley AFB, Virginia Fort Monmouth, New Jersey ATTN: Technical Library 1 ATTN: TOOA ATTN: SIGFM/SC-DO 3 ATTN: TORQ 1 Office of the Dir. 1 Office of the Dir. 1 Comdt., U. S. Army Avn. School Defense R&E Fort Rucker, Alabama 1 Cdr., Air Tech. Intel. Center Technical Library Wright-Patterson AFB, Ohio Dept. of Defense 2 President Washington 25, D. C. U. S. Army Artillery Board ATTN: AFCIN-4B/a Fort Sill, Oklahoma 10 ASTIA (TIPCR) 1 Dir., WSEG 1 President Arlingn Hl Room 1E880, The Pentagon U. S. Army Air Defense Board Arlington 12, Virginia Washington 25, D. C. Fort Bliss, Texas 1 President 9 Cdr., WADC 1 Chief of Engineers, DA 1 Chief of Engineers DU. S. Army Aviation Board Wright-Patterson AFB, Ohio Washington 25, D. C. Fort Rcker, Alabama Fort Rucker, Alabama ATTN: R&E Div. ATTN WCOL-9 1 ATTN: WCOL-9 1 President 1 Office, Chief of Ordnance U. S. Army Airborne and R&D Div., DA Electronics Board 2 Cdr., Rome Air Dev. Center Washington 25, D. C. Fort Bragg, North Carolina Griffiss AFB, New York ATTN: ORDTB 1 ATTN: RCVSL-1 Res. & Special Projects President 1 ATTN: RCWIR Army Intelligence Board, USAINTC 1 _~, ~,,ro Fort Holabird, Maryland 1 CO, AMS Fort Holabird, Maryland 3 Comdt. of the Marine Corps Corps of Engineers Of O s Hq., U. S. Marine Corps 1 Office, Chief of Naval Operations U. S. Army Op-07T Building T-3 Washington 25, D. C. Op-07T Building T-3 Washington 25, D. C. Dept. of the Navy 2 ATTN: Code A02 ATTN: Document Library Washington 25, D. C. 1 ATTN: Code A04E 14

WILLOW RUN LABORATORIES TECHNICAL MEMORANDUM 2900-88-R DISTRIBUTION LIST 3 1 October 1959 -Effective Date Copies Addressee Copies - Addressee Copies - Addressee 4 Central Intelligence Agency 1 Operations Research Office 1 Control Systems Lab. 2430 E. Street, N. W. The Johns Hopkins University University of Illinois Washington 25, D. C. 6935 Arlington Road Urbana, Illinois Bethesda, Maryland ATTN: OCR Mail Room W ashington 14, D. ATTN: Librarian Washington 14, D. C. THRU: ONR Resident Rep. 5 Natl. Aeronautics and Space Admin. ATTN: Chief Intel. Div. THRU: ONR Resident Rep. 1209 W. Illinois Street 1520 H. Street, N. W. Urbaa Illinois Washington 25, D. C. 2 Director, HUMRRO 2 Combat Surveillance Project The George Washington University 1 Columbia University P O. Box 3596 Cornell Aeronautical Lab., Inc. P. 0. Box 3596 Box 168 lectronics Res. Lab. Washington 7, D. C. Box.~~~ 168,.~~~~~,632 W. 125th Street Arlington 10, Virginiak27, New Yor ATTN: Library ATTN: Tech. Library ATTN: Tech. Library ATTN: Tech. Library 1 The U S. Army Aviation RU 1 The U. S. Army Aviation HRU THRU: Cdr., Rome Air Dev. Center P. 0. Box 428 1 The Rand Corporation Griffiss AFB, New York Fort Rucker, Alabama 1700 Main Street Santa Monica, California ATTN: RCSSTL-1 1 Visibility Laboratory ATTN: Library Scripps Inst. of Oceanography University of California San Diego 52, California 1 Chief Scientist, R&D Div. Office of C Sig 0, DA 2 Cornell Aeronautical Lab., Inc. 1 U. S. Continental Army Command Washington 25, D. C. 4455 Genesee Street Liaison Officer Buffalo 21, New York Project MICHIGAN, Willow Run Lab. Ypsilanti, Michigan 1 Stanford Research Institute ATTN: Librarian Document Center THRU: Bureau of Aeronautics Rep. 1 CO, U. S. Army Liaison Group Menlo Park, California 4455 Genesee Street Project MICHIGAN, Willow Run Lab. ATTN: Acquisitions Buffalo 21, New York Ypsilanti, Michigan 15

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