Adam Kozma

Holographic data storage in three-dimensional media.

The holographic storage of diffraction patterns in a three-dimensional media is described from a vector viewpoint derived from the Kirchhoff diffraction integral. The sensitivity of the reconstruction to wavelength and to the orientation of the readout beam is calculated, and experimental results are given.

Photographic Recording of Spatially Modulated Coherent Light

Photographic recording of spatially modulated coherent light, such as is encountered in wavefront reconstruction or coherent optical data processing, is described in terms of the amplitude transmittance (Ta) vs exposure (E) curve of the film. It is proposed that the Ta−E curve is more appropriate for this application than the D−log E curve. The nonlinear effects of recording are analyzed in this context using a nonlinear “circuit” model. A general expression for the resulting amplitude transmittance is derived by use of a Fourier-transform technique. A specific nonlinearity, the error-function limiter, is analyzed in detail to illustrate the effects of the film nonlinearity.

Spatial Filtering for Detection of Signals Submerged in Noise

Matched filtering is described as a spatial filtering operation. A technique for producing a matched filter, wherein the filter transfer function is modulated onto a spatial carrier and the resulting function is hard-clipped allowing a filter construction of completely opaque and transparent lines, is given. The effect of this nonlinearity on the S/N is shown to be small. The effects of extraneous frequencies in the filter is shown to be negligible if the spatial carrier is sufficiently high. Experimental results are presented showing the detectability of the signal in the presence of various levels of additive noise.

Tilted-Plane Optical Processor

A new optical system concept for processing data from synthetic-aperture radars is described. The optical systems are multilens, anamorphic telescopes including spherical and cylindrical lenses. The new method has as its basis two well-known properties of lenses: (a) the longitudinal magnification of an imaging system is equal to the square of the lateral magnification; and (b) a telescope provides an image with magnification independent of the object position.

Effects of speckle on resolution

The effect of speckle in the imaging of diffusely illuminated gratings and continuous-tone objects was studied. It was found that when imaging diffuse gratings, the aperture of a coherently illuminated system must be 2.6 times as large as that of an incoherent system to obtain comparable resolution. This factor must be increased to five when imaging continuous-tone objects and to a factor of seven if the coherent image is subsequently low-pass filtered. A coherent system can achieve resolution which is comparable to an incoherent system of equal aperture if the coherent image is smoothed so that the mean to standard deviation ratio is ten or more.

Recording Parameters of Spatially Modulated Coherent Wavefronts

Various parameters of recording spatially modulated coherent light have been studied, with particular emphasis on the parameters related to constructing holograms. These include the ratio of the reference beams intensity to that of the signal beam, the offset angle, the films transfer characteristic, and the recording wavelength. Experimental results were obtained by recording interference patterns on highresolution film using the 6328-å line of the He-Ne laser. The bias level of the interference pattern was varied so as to vary the operating point on the curve representing the films amplitude transmittance vs exposure characteristics. The percent modulation and the spatial frequency were also varied at each of the operating points. Interference patterns were recorded, using the 4880-åand 5145-å lines from the argon laser. From these data, the optimum bias level and the ratio of the signal beam to the reference beam for recording interference patterns are determined. The modulation transfer function of the film can also be determined.

Bias Level Reduction of Incoherent Holograms

The known techniques for making incoherent holograms succeed for an object containing a small number of points; however, they fail in practice for an object with a great many discrete points or for an object with a continuous intensity distribution. This results because the intensity pattern generated in incoherent holography in a superposition of random intensity patterns generated by the individual object points. Thus, the intensity pattern contains a large bias level which masks the relatively small spatial variations of the pattern in the recording film grain noise. This paper describes a technique for eliminating the bias. By introducing a narrow band time modulation of the light in one path of an interferometer used to generate the hologram intensity pattern, the spatially varying part of the hologram intensity pattern is modulated at the time frequency, while the bias part is unmodulated. The bias part can then be eliminated by performing a point-by-point time correlation over the hologram plane. Experimental results are presented.

An Analytical and Experimental Study of Nonlinearities in Hologram Recording

A theoretical analysis of the effect of recording nonlinearities upon the image reconstructed from a hologram made of a diffuse object is presented. Extensive experimental evidence which supports this theory is also given. In particular, it is shown that the magnitude of the nonlinearity noise can be calculated knowing the shape of the amplitude transmittance-exposure (T(a) - E) curve, the bias transmittance (T(b)), and the ratio of the reference beam to the object beam intensity (K). It is further shown that for diffuse objects the shape of the nonlinearity noise distribution can be calculated from the shape of the object.

Effect of Film Resolution and Size in Holography

A useful expression for the complex amplitude of the reconstructed holographic image is derived. This expression shows how the reconstructed image is affected by the optical transfer function of the recording media and by the size and shape of the hologram. Special cases that are studied include perfect film, very good film, Fourier-transform holograms, and large holograms. Detailed solutions for the general case are obtained by assuming a gaussian optical transfer function and either a rectangular hologram aperture or one having gaussian weighting.

Requirements for hologram construction

Holography has in the last two years undergone a tremendous resurgence. The laser has contributed immeasurably to this, through the remarkable coherence of its light, which permits previously performed experiments to be carried out with relative ease, and in addition allows the performance of experiments which were hitherto hardly conceivable. Old experiments have been repeated with vastly improved results, and the new interest has given rise to new ideas with exciting promise.