Fourier-transform Hologram Research Articles

Effect of reference and illuminating sources size in holography

The effects of a finite reference source size are described for the cases of Fourier-transform holograms and image-plane holograms. This paper derives expressions for the image distribution when the reference source and the source illuminating the recorded hologram both are extended sources at arbitrary positions. The particular hologram configurations considered are variations of the Fourier-transform holograms, the quasi-Fourier-transform hologram, and the general Fresnel hologram.

Alignment and Design Conditions for Optical Memory Systems Using Fourier Transform Holograms

In this paper we present the displacement tolerances of optical system elements for recording and reconstructing Fourier transform holograms. The position, modification and magnification of the image are given as functions of the displacements and the parameters of the reference and reconstructing beam. Calculations are carried out on the basis of the scalar wave theory using the paraxial approximation.

On a generalized view of holography in relation to the phase problem in electron microscopy

Let xO = ϕ (ζ1, ζ2) the object wave function describing a given wave function in a given plane, and let x be its "projection" in the complex Hilbert space E corresponding to the (sampled) domain under consideration. Let U1,…, Uj, …, Up be unitary operators in E, and let J be the "intensity mapping" :xk denotes the kth component of x (for simplicity, we assume that E is finite dimensional). The wave-retrieval (or wave-reconstruction) problem in holography is to solve simultaneous equations of the form :where some components xk are known a priori. JoUj denotes the mapping involved in the formation of the hologram yj. for example, when Uj the is the operator involved in Fresnel's diffraction, yj. is said to be a Fresnel hologram. Likewise, when Uj corresponds to the Fourier transform, yj is said to be a Fourier-transform hologram.

Generalization of Computer-Generated Fourier Transform Holograms

Generalization of Computer-Generated Fourier Transform Holograms

X-Ray Holographic Microscopy

Applications of the holography to the X-ray region are described. Two types of the image-reconstructing process are attempted. In-line holograms of line-like objects of chemical fibers and point-like objects of red blood cells are made by using Al Kα radiation (8.34A) from a two-stage fine focus X-ray generator. Magnified real images are reconstructed from the negative holograms using a He-Ne laser (6328A) . A resolution of about 4 μm is obtained in this imaging process. On the other hand, a lensless Fourier-transform hologram of a model object like a row of slits is made by using an electron synchrotron radiation (60A) . A magnified real image is reconstructed by a Fourier-transform method, where a magnification factor of 158 is obtained. Several factors limiting the image resolution are discussed.

Optoacoustic transducer for high-sensitivity orthographic imaging

A possible embodiment of a real-time, orthorgraphic, acoustic imaging system with piezoelectric detection which employs an electronically controlled, scanning, focused beam to probe the target has been described. {K. Wang and G. Wade, Proc. IEEE 62, (2), 650–651 (1974)]. The key element of this embodiment is an optoacoustic transducer (OAT) addressed by diffracted light emerging from a properly designed Fourier-transform hologram. The OAT under study is a sandwich structure containing a piezoelectric layer which is differentially activated from point to point across its surface via photoconductive switching. To be useful in the final system, the OAT has to be 20 cm × 20 cm in dimension and has to meet certain key requirements. For example, real-time capability requires that the photo-conductive relaxation time be no longer than 1 μsec. In addition it is essential that when a zone-plate pattern of light is incident on the OAT, the output acoustic amplitude distribution be such that the generated ultrasound converge to a good focus through propagation. Preliminary considerations and simulations on various OAT structures show that certain available materials may have the proper characteristics to produce good focusing. [Work supported by NSF ENG 74 22184.]

Solid-State Area Scanning Arrays as Interface Devices Between Optical and Digital Computing Systems–A Simulation Study

This paper describes how, in spite of occasional performance limitations generally due to process defects, large-area solid-state image sensors can be applied to scan pictorial data. First, it is estimated to what extent the direct imaging of pictorial matter onto a defective area-scanning device for acceptable scanning quality is possible. A novel concept is then proposed in which the optically generated Fourier-transform hologram of a picture rather than the picture itself is imaged onto a defective solid-state photosensitive array, scanned, digitized, filtered, and reconstructed by fast Fourier transform (FFT) techniques on a digital processor. The operating principle is discussed and the effects of scanner defects, digitization, and filtering on the scanning quality are investigated by computer simulation.

Image information by means of speckle-pattern processing*

When a laser beam is reflected from a diffuse surface, a granular scattering distribution is commonly observed, called a speckle pattern. We will discuss some of its ramifications: (1) this pattern is the time-independent analog of the signal used in the classic Hanbury Brown–Twiss stellar interferometer of the 1950’s; (2) this pattern can be processed by standard incoherent optical techniques to yield information pertaining to the object radiance distribution; (3) this same signal, when processed by coherent-optical techniques, is equivalent to the Gabor on-axis hologram or the Fourier-transform hologram, depending on the specific source configuration; and (4) signals processed by all of the above techniques are comparatively insensitive to atmospheric turbulence. An experiment is performed to illustrate the procedure of item (2) and then modified to show assertion (4).

Design Conditions of Optical Systems for Recording and Reconstructing Fourier Transform Holograms

Fourier transform holograms have a unique immobility characteristic. Immobility means that the images reconstructed from holograms do not move even if the holograms move. In this paper the fundamental requirements for recording lenses and reconstructing lenses for Fourier transform hologram are analyzed, F numbers and image angles for these lenses are discussed in relation to hologram conditions. Furthermore, the tolerance of the longitudinal displacement of the data to be recorded and the tolerance of the longitudinal displacement of the detector for the image are given.

Analysis of wave-front aberrations caused by deformation of hologram media

Analytical expressions for the wave-front aberration caused by deformation of the hologram medium have been derived. These expressions are used for the determination of allowable tolerance of deformation. In the case of nearly diffraction-limited imaging, the tolerance is determined by evaluating the wave-front aberration. For other cases, in which more aberration is allowed, the tolerance is determined by evaluating the geometrical aberration. The dependence of deformation tolerance upon the type of hologram, the size of hologram, and the recording arrangement, especially that of the object and the reference beam, is shown. For small-size holograms, which are attractive for high-density information storage, the tolerance depends mainly upon the recording arrangement, and not upon the type of hologram. For larger-sized holograms, Fourier-transform holograms with parallel reference beams are the best, with regard to deformation tolerance. Numerical examples of the tolerance are given for nearly diffraction-limited imaging, using the Rayleigh criterion.

Hologram conversion by computer

A technique of converting Fresnel-tranform holograms into Fourier-transform holograms by computer is discussed. A sound-wave hologram is processed with 64×64 sampling points and images are reconstructed optically from this processed binary hologram in the Fourier-transform plane, that is, a focal plane of a lens.

Fourier-transform hologram by zone plate

A simple technique is described and demonstrated as well that Fourier-transform holograms can be made with a zone plate.

Holography with Light Beams of Finite Spectral Width

The effects of spectral coherence on holographic images have been analysed in terms of the Fresnel-transform formulation of the process of holography. In this paper the case of very rough object or diffuse illumination has not been considered. The results have been obtained as contrast modulation in the image of a spatial frequency component in the object. The effect of polychromaticity in the recording beam is seen to be more severe than that due to the polychromaticity in the reconstruction beam. Fourier-transform holography seems to yield a better image. With the lensless Fourier-transform hologram recorded on monochromatic light, white light reconstruction seems to be possible if the illuminating beam is suitably dispersed before it falls on the hologram.

Magnification Aberrations in Fourier-Transform Optical Data Storage

Although holographic magnification may appear to increase greatly the versatility of holographic recording and retrieval systems, nevertheless, holographic lens aberrations often prevent the recording of Fourier-transform holograms directly from small transparencies and production of legible, page-size images by mere alteration of the convergence of the reference beam during reconstruction. The magnitudes of these aberrations are calculated for several different Fourier-transform-recording geometries; the optimum geometries are delineated. The most important aberrations that occur with the Fourier-transform method of holographic storage are astigmatism and curvature of field.

Spatial Noise in Optical Data-Storage Systems Using Amplitude Fourier-Transform Holograms

Calculations are performed to study the noise in the detector plane of an optical data-storage system with Fourier-transform holograms, caused by noise in the storage material. The signal-to-background ratio (SBR) and the signal-to-noise ratio (SNR) of the output signals in the detector plane are defined and calculated. Exact solutions are obtained by assuming gaussian-probability densities for amplitude and phase noise in the storage material.

Structural-information Storage in Holograms

The number of degrees of freedom, or structural-information content, of the object wave field recorded in a Leith-Upatnieks hologram is expressed in terms of the resolving power and dimensions of the recording medium, the coherence properties of the primary illumination and the position of the point reference source. In contrast with previous studies, the calculation does not involve the paraxial approximation. It is shown that of all holograms, the Fourier-transform hologram makes the most efficient use of available resolving power and coherence length.

Diffraction-Limited, Scalar Image Formation with Holograms of Arbitrary Shape*

A theory of image formation is presented for a large-angle, point reference hologram, whose recording arrangement consists of a surface of arbitrary shape, a point reference source, and the object. The hologram is illuminated by a spherical wave during reconstruction. The resulting image field is similar to that of a Fourier-transform hologram. An exact, integral formulation of monochromatic, scalar diffraction theory is used to find the image field. The hologram is modeled by surface sources determined from the irradiance of the recorded field. The image field produced by the holographic system approximates the field produced by the ideal system, which forms the image of a point object by launching a converging, spherical wave.

Use of a Random Phase Mask for the Recording of Fourier Transform Holograms of Data Masks

In a holographic page-oriented memory the information is stored in an array of holograms. It is advantageous to record the Fourier transform of the original data mask because the minimum space bandwidth is then required and the information about any one data bit is spread over the hologram plane. In the Fourier transform plane most of the light is concentrated in an array of bright "spikes" because the data mask consists of an array of equidistant data spots. Some means is needed to distribute the light more evenly. We report here on the use of a phase mask which imparts a phase shift of 180 degrees to half the data spots chosen at random. An analysis shows that the intensity in the Fourier transform plane is now proportional to the intensity of the Fourier transform of one single data spot.

Sampled Fourier Transform Hologram Generated by Computer

A technique to determine a real nonnegative function representing the transmittance of a synthesized hologram is described. The technique uses the positions of the samples in the synthesized hologram to record the phase information of a complex wavefront. Synthesized holograms are displayed on a flying spot scanner and recorded on film. The transmittance of the synthesized hologram is quantized into 256 levels because of a hardware limitation of the scanner.

Fourier-transform holography

The Fourier-transform relation between the spatial electric field-vector distribu-tion in a quasi-spherical unfocused wavefront, and the focused field near its center, was recognized at least as early as the begin-ning 1900's by A.A.Michelson (see e.g. refer-ences in G.W.Stroke,Diffraction Gratings pp. 426-754 in Vol. 29, Handbuch der Physik, Springer Verlag, Heidelberg 1967), and con-temporary operational image-formation rela-tions were used by him in his famous text Studies in Optics before 1927! Recently revived, thanks in particular to the work of Duffieux (1946), D.Gabor (1949), Peter Elias, D.Grey and D.Z.Robinson(1952),AiMarechal, E. L.O'Neill and others, Fourier-transform des-criptions of optical image formation and processing have become particularly powerful with their introduction into holography [Gabor(1949),Cutrona, Leith, Palermo and Porcello,(1960), B.J.Thompson and others(1964), etc.] especially since the introduction of the lensless Fourier-transform by Stroke(1964,1965), who showed that such a hologram, formed by interference of the field scattered by the and a reference field originating from a reference point situated near the object, had an intrinsic resolution gain which may exceed by more than three orders of magnitude the film-limited resolution capability of single-side band, off-axis Fresnel holograms. Among the several extensions and applications of the lensless Fourier-transform hologram arran-gement is that recently exploited by J.Goodman for remote object holography,where the traversal by the point-source reference beam of an air path similar to that of the object beam permits to surmount atmospheric turbulence and path-difference variation effects. In addition to these and other 3-D imaging applications, the author (in part with D. Gabor) has proposed and demonstrated several operational image-processing and computing applications, among which the multiply-expos-ed holograms used for image-synthesis. interferometry and computer-generated holograms, and, most recently, and new type of holographic Fourier-tranform division [Stroke and Zech, Physics Lett. 25A, 89(1967)] which has now permitted to restore into sharp focus images from ordinary blurred photographs of three-dimensional objects, photographed in ordinary white light [Stroke et. ali., Physics Lett. 25A, 443(25 March 1968).