Applied Optics Letters to the Editor

Accuracy of Holographic Images

R. F. Majkowski and A. D. Gara Research Laboratories, General Motors Corporation, Warren, Michigan 48090. Received 24 January 1972.

The purpose of the research described in this Letter is to mea­sure the accuracy of the holographic image of a large object and determine some of the experimental factors that may cause a deterioration of this accuracy. The results apply to either the real or the virtual image, but, since the virtual image is not readily accessible for measurements, our tests were limited to the real image.

I t is known that a hologram (unlike a lens) is theoretically capable of producing an exact distortionless image of a three-dimensional object. In order to obtain this result, the real image must be produced by the conjugate of the original reference beam.1 This requirement can be most easily satisfied by using a plane wavefront reference beam.

In image formation, the hologram plate itself must be con­sidered as an optical element in the system. The hologram plate is ideally treated as a uniformly thick photographic emulsion placed on a flat plate of homogeneous glass of uniform thickness. For the plane wavefront reference and reconstruction beams the above ideal plate introduces no harmful effects on the image. However, the photographic plates-normally used for holography (649F and 10E70) are not ideal and, as a consequence, do con­tribute a distortion to the images.2,3 The thickness of the emul­sion was found to have an average variation of 20%. In addi­tion, the glass substrates were found to have a significant varia­tion in thickness.

The principal effect of thie thickness variations on the images can be visualized for the simple case where the emulsion thick­ness variation is quadratic. e.g., assume the emulsion surface has a convex spherical shape. The emulsion media then acts like a lens in the system that introduces an unwanted magni­fication into the image. This problem was eliminated by putting the photographic plate in a liquid gate,3 which closely matched its refractive index to a pair of flat glass windows (Fig. 1). These windows were 2.5 cm thick optical flats and introduced less than one wavelength distortion in a plane wavefront passing through the windows. The index matching liquid was o-xylene. The index match was not perfect (1.506 for the xylene compared to 1.532 for the emulsion) but close enough to reduce significantly the observable emulsion thickness effects on the image accuracy.

The hologram accuracy test was made with a linear standard bar as the object. The bar was 5 cm thick and 15 cm high with an over-all length of 1 m. The center of the bar was positioned opposite the center of the 13-cm × 18-cm hologram plate. The angle between the reference beam and the hologram normal was approximately 35°. Two glass reticles were set in ports, 75 cm apart at opposite ends of the bar. Each reticle had a hori­zontal and vertical cross pattern with 25-μ graduations set 125 μ apart. The ports were tapered front and back to give an un­obstructed line-of-sight through the reticle to the hologram plate.

The precision with which the construction and reconstruction beams can be collimated to give a plane wavefront has a large effect on the hologram accuracy. The plane wavefronts were

Letters to the Editor should be addressed to the Editor, APPLIED OPTICS, AFCRL, Bedford, Mass. 01730

Fig. 1. Photograph of liquid gate plate holder.

aligned with an auto collimator that is made, in situ, of the optical parts in the reference and reconstruction arms. For a ƒ/10, 25-cm aperture collimating lens in the reference beam, a misalignment of the lens of the order of 1 part in 105 from its proper point of focus could be observed. This implies that the wavefront de­viated from a plane by less than one optical wavelength.

The reconstruction geometry for the 75-cm bar is shown in Fig. 2. The proper hologram orientation for reconstruction was determined by observing the quality of the image of NBS bar charts placed in the scene. The pitch and rotation of the holo­gram were manipulated to obtain the highest image quality. In the initial tests made without the liquid gate, the final holo­gram position was a compromise between the position for opti­mum image quality at the two ends of the bar. In the later tests with the hologram plate in a liquid gate, optimum image quality for both ends of the bar was achieved simultaneously.

Once the hologram was properly aligned, the bar was placed in the space of its real image. Two microscopes were first focused on the hologram image of the reticles (viewing through the actual glass reticles in the bar). The bar was then positioned such that the plane of each glass reticle coincided with its image. The hologram (13-cm × 18-cm aperture) and the microscope had a depth resolution shallow enough to focus on a single 25-μ gradua­tion of the reticle.

Results of these coincidence tests are listed in Table I. A small but significant error was observed for the initial tests where the liquid gate was not used, holograms 1, 2, 3, and 4. An attempt was made to correlate the observed image error with a calculated image error based on the measured thickness varia­tions. Assuming that the hologram emulsion behaves like a simple lens, Gara and Yu give the lateral magnification in the holographic real image as2

August 1972 / Vol. 11, No. 8 / APPLIED OPTICS 1867

Fig. 2. Reconstruction arrange­ment for 75-cm linear standard

bar.

Table I. Accuracy Test Results: Coincidence of 75-cm Linear Standard to its Holographic Real Image

All above holograms exposed to optical density 1.0 to 1.4. a No pretreatment-density holograms. b Annealed at 100% relative humidity at 30°C for 8 hr. c Emulsion water marked during annealing.

Table II. Magnification Effect of Hologram Emulsion

a The numerical values, given for astigmatism, are the distances between two planes of focus and the circle of least confusion. The effective focal length for astigmatism was indexed to the circle of least confusion.

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The calculated image errors for these holograms compare quite favorably with the measured values given in Table I(A). When compared with other observed image errors these results showed that emulsion thickness variation was indeed the probable cause of this error. Since the thickness variations were actually com­plex (and varied from plate to plate) it would be difficult to cor­rect for the image errors by computations. The liquid gate was used for the last six holograms [5 through 10, Table I(B)]. While there is still a trace of systematic error, it was less than 25 μ for all but one hologram in the series, and the data for this holo­gram are questionable since this emulsion was damaged during the preprocessing annealing step.

The accuracy results were obtained for holograms processed both in the usual manner (density type) and for holograms that were bleached to provide higher diffraction efficiency. For completeness, accuracy tests were made with a depth extension arm added to this standard bar. A x, y, z, micropositioner on the depth extension holds a glass base standard Air Force resolution target. The center of the target was approximately 35 cm to the rear of and 20 cm above the end reticle on the linear standard bar. The results of these observations made on two different hologram plates are consistent with the. previous results showing a measurement accuracy of one part in 104.

Thesejesults were obtained using a continuous He-Ne laser at 6328 Å for both hologram formation and image reconstruction. Image accuracy tests using a Q-switched ruby laser for making the hologram and a continuous ruby laser for reconstruction are how in progress.

References 1. R. Mittra and P. L. Ransom, in Proceedings of the Symposium

on Modern Optics (Polytechnic Press, Brooklyn, 1967), p. 638. 2. A; D. Gara and F. T. S. Yu, Appl. Opt. 10, 1324 (1971). 3. R. F. Majkowski, A. D. Gara, and P. V. Mohan, J. Opt. Soc.

Am. 59, 1530 (1969).

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