We derive the graph-analytic representation of influence of the higher-order nonlinearities (including the third and fourth ones) of holographic recording on the associative properties of second-order holograms defined as ‘holograms between two holograms’. It is shown that the higher-order nonlinearities of the amplitude response of a hologram do not only cause the noise contribution into conjugate associative response, but in some scenarios of formation of the second-order hologram just predetermine reconstruction of this response. Using the proposed technique, we analyze various cases of imposed (sequential) record of partial signals within the framework of the model of multiple diffraction at hologram structure. We discuss the cases when reconstruction of the conjugate associative response is provided by the presence of the hierarchy of combination pseudogratings, rather than by the ‘direct’ interference mechanism that lies in the base of conventional holographic associative storage, using ghost-image holograms. The represented results expand considerably functional feasibilities of the phase-conjugation associative memories on the base of static holograms.
We represent the double phase conjugation technique for uncorrelated complex optical signals at arbitrarily different (incommensurable) wave lengths for implementation of long-term (archive) storage, i.e. coupling and mutual associative reconstruction of such signals. The essence of the proposed approach consists in exploiting natural recording nonlinearity of a static hologram that results in formation of the combined (summation) pseudogratings corresponding to the quadratic component of the amplitude response of a static nonlinearly recorded hologram. In contrast to earlier (real-time holography) version of the double phase conjugation using photorefractive crystals, we use for the each signal wave collimated (plane) reference wave, so that the wave vectors of two reference waves are strictly opposite to each other. It is shown that under these conditions nonlinear mixing of two sets of cross-gratings results in formation of the complete set of pseudogratings constituting a second-order hologram defined, following H.J. Caulfield, as ‘a hologram between two (linear) holograms’. Being read out by any of two stored signals or its incomplete/distorted version (in absence of the reference waves, just as in a photorefractive prototype), a hologram reconstructs the phase-conjugate replica of the second signal (heteroassociative response) at the wavelength of the readout beam, with predictable on the wavelength ratio scaling and angular shift from the nominal position. Especial attention is paid to determination of the experimental conditions for providing the combination pseudogratings to be thin (by applying the Klein’s parameter), if even the partial cross-gratings are thick (volume), by proper choice of the angular conditions of the experiment. If this condition is violated, the Bragg selectivity can hinder heteroassociative reconstruction.
We represent the straightforward techniques for differentiation of the phase structures of light beams of various origin but having similar intensity envelopes using doughnut-like beams as an example. Namely, we compare the phase structure of the set of beams: (i) a ring beam with smooth (vortexless) wavefront but with artificially introduced central amplitude zero, with Gaussian radial intensity distribution; (ii) Laguerre-Gaussian mode LG10+1 with the central vortex; (iii) combined beam assembled from uncorrelated weighed Laguerre-Gaussian modes LG10 and LG11 with the central screw dislocation and with the ring edge dislocation of the spatial coherence function; (iv) combined beam assembled from uncorrelated Hermite-Gaussian modes HG10 and HG10 ; (v) combined beam assembled from correlated but orthogonal in polarization Hermite-Gaussian modes HG10 and HG10 ; (vi) combined beam assembled from uncorrelated and orthogonal in polarization Hermite-Gaussian modes HG10 and HG10 . Experimental analysis and comparison of the phase structures (i) and (ii) can be performed using a common interference technique with off-axis reference wave. Other mentioned cases cannot be analyzed by applying this technique. To differentiate the corresponding phase structures and associated singularities, we attract the united technique based on edge diffraction and use of an opaque strip screen placed at the analyzed beam. In cases (v) and (vi), this technique is added by 2D Stokes polarimetry. The proposed techniques provide reliable diagnostics of common optical vortices, vortices of the spatial correlation functions, polarization singularities of completely (but inhomegeneously) polarized light beams, and the singularities of the complex degree of polarization from typical bending or a half-period shift of the Young’s interference fringes at the shadow of the strip screen.
The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].
In this paper we consider the application of recently suggested experimental techniques for diagnostics of phase singularities in scalar and vector combined optical fields, in part in the cases when conventional interferometric techniques are not applicable or possess restricted applicability. Such situation takes place, for example, in cases of partially coherent inhomogeneously polarized combined beams assembled from mutually incoherent Hermite-Gaussian modes. Meanwhile, not only new experimental techniques are introduced, but new singularities, missed in complete coherent fields, arise.
Recording nonlinearity is conventionally considered as the source of noise in holographic imaging. Important exclusion from this general statement is nonlinear holographic associative memory, where the quadratic recording nonlinearity causes true brightness rendering and the possibility for associative coupling and reconstructing optical signals of arbitrary complexity which are stored at the same carrier without interference. In this paper we discuss the role of nonlinearities of an amplitude response of a hologram of the orders higher than the quadratic one in implementing the second-ordered holographic associative memory. We show that higher-order nonlinearities are also involved in implementing this type of memory. This conclusion may be of importance for interpretation of biological/human memory also. The highlight of our study is the conclusion that reconstruction of the complex conjugate heteroassociative response is provided directly, viz. by the set of specified by us pseudogratings, rather than by the mechanism of sequential diffractions.
We highlight the milestones of fifty-year history of emerging holographic associative memory as the chronologically first proposed practical application of the laser holographic techniques (van Heerden, 1963). Holographic associative memories are considered here as an important aspect of correlation optics, and the forming associative response is interpreted with account of fine phase relations among numerous partial images involved into discrimination mechanism of reconstruction. Three main approaches proposed for implementation of holographic associative memories are discussed and compared, namely, classical ’linear’ ghost-image holography, the associateve memories based on resonator architectures using optical feedback and thresholding algorithms, and the quadric (second-order) hologrambased associative memories.
The problem of angular momentum of light beams associated with the state of polarization of them is considered within the framework of the light scattering concepts. By analogy with scattering, absorption and momentum cross-sections, usual in the theory of light scattering by small particles, the notion of angular momentum cross-section of light-scattering particle is introduced. On this base, the attempt is made to ground the statement that mechnical action of circularly polarized light wave is peculiar size (or edge) effect pronounsly manifesting itself when uncompensated (due to gradient of optical properties) torque moment at the particle edge becomes comparable with compensated part of the torque moment within the particle’s geometrical cross-section. This statement follows from that a particle disturbes homogeneity of priobing wave, for free propagation of which observing torque action of circularly polarized wave is impossible.
Experimental study of quasimonochromatic and polychromatic (“white-light”) radiation, that diffracts on very narrow (in order of several wavelength) slit in metallic screen is represented. It is shown that for monochromatic light slit acts similarly to linear analyzer. And for polychromatic light polarization action of a slit is accompanied with a spectral effect, viz. considerable predomination of blue component in total radiation. The chromascopic technique is applied for analyzing this spectral effect.
The autocorrelation technique applied to diagnostics of phase singularities arising in diffraction patterns is presented for the first time. The proposed technique is based on the Young-Rubinowicz model of diffraction phenomena (model of the edge diffraction wave) and consists in analysis of bending or shift of interference fringes, which are produced by the waves from two edges of narrow opaque strip placed in the beam. This original approach has been applied previously for detection and diagnostics of optical vortices in Laguerre-Gaussian beams, in combined partially coherent/ partially polarized beams as well as in speckle fields. Here we show applicability of the same experimental approach for detecting another type of optical singularities, viz. edge (rather than screw) dislocations of optical wave fronts. Such technique is of especial importance when the use of separate reference wave (cross-correlation approach) is hampered due to incomplete spatial coherence of the analyzed beam or its complex polarization structure. We demonstrate practicability of the proposed technique with instructive examples of typical diffraction patters both in Fraunhofer and Fresnel zones. Besides, our experiments show structural stability of edge dislocations in diffraction patterns. Namely, if even amplitude zeroes are ‘hidden’, then autocorrelation technique provides detecting at least component singularity.
Experimental study of diffraction of coherent (laser, completely polarized) and incoherent (temporal, polychromatic,
unpolarized) light radiation at slits whose width is restricted by a few wavelengths is made. It is shown that for diffraction
at the edge of metallic half-plane screen, the angular dependences of diffraction field intensity are considerably different
for orientation of the electric field vector parallel and perpendicular to the screen edge, so that metallic screen
causes polarization action on the probing beam. It is shown that as the width of a slit formed by two metallic half-planes
becomes less than ten wavelengths (being left larger than a wavelength), as the polarization effect is considerable even
for the forward direction, i.e. for the zero diffraction angle. It causes also spectral effect, if polychromatic radiation diffracts
at narrow slit at metallic screen. Namely, one observes pronounced blue shift of the maximum of the spectral distribution
of the forward diffracted polychromatic ('white-light') beam. We apply for the first time the Berry's chromascopic
technique for experimental data processing to elucidate such diffraction induced spectral changes.
It is shown that for an incoherent superposition of the orthogonally polarized laser beams the polarization singularities
of a new type arise at the transversal cross-section of a paraxial combined beam instead of common singularities,
such as amplitude zeroes (optical vortices) inherent in scalar fields, and polarization singularities such as C points
and L lines inherent in completely coherent vector fields. There are U contours along which the degree of polarization
equals zero and the state of polarization is undetermined (singular), and isolated P points where the degree of
polarization equals unity and the state of polarization is determined by the non-vanishing component of the combined
beam. Optical vortices of the orthogonally polarized component lie under P points. P points differ essentially
from C points of singular optics of coherent fields by the absence of topological charge and certain morphology of
heighborhood (S, M, L). Crossing U line is accompanied by step-like change of the state of polarization onto orthogonal
one (sign principle). U and P singularities are represented at a whole Stokes space, namely at and inside of the
Poincare sphere. Correlation among completely coherent and completely incoherent vector singularities is considered
for the first time. First experimental examples of reconstruction of the combined beam's vector skeleton
formed by U and P singularities as the extrema of the complex degree of polarization are given.
The model of intermediately rough surface as the specific anti-reflection layer is presented for explaining the coloring of
the regular component of a white-light beam forward scattered by a colorless glass with such surface. It is shown that
this model predicts the sequence of colors of the forward scattered component of a white-light beam that is observed in
practice. New experimental arguments supported this approach are provided.
The comparative analysis of several techniques for diagnostics of phase singularities in the optical vortex beams and fields
is performed. Both advantages and disadvantages in the implementation and applications of different techniques are discussed.
In this paper, the chain of mutual transformations of optical singularities is demonstrated, including coherence singularities,
polarization singularities of different kinds, and phase singularities. It is shown in what a way one can transform
some type of optical singularities into another by changing one of the experimental parameters. Convenient experimental
technique for diagnostics of such singularities is also described. It is shown that some of the considered singularities are
generic ones, while other are non-generic, implying specific experimental conditions.
Two original approaches for the diagnostics of phase singularities (such as optical vortices, screw dislocations of a wave
front) based on the Young-Rubinowicz mOdel of diffraction phenomena are represented. Both techniques are implemented
without using a separate reference wave, as in common interference techniques. That is why they are very convenient for
analysis of spatially coherent polychromatic fields. The first technique is based on the use of an opaque strip as the diffraction
device. Bending Young's interference fringes produced by the edge diffraction waves from two rims of the strip within
the geometrical shadow region reflect helicity of a wave front, so that the direction and magnitude of bending correspond
directly to the sign and the modulus of topological charge of the optical vortex, respectively. This technique is practicable
for diagnostics of isolated polychromatic vortices, such as "rainbow" Laguerre-Gaussian mode, where the condition of mutual
spectral purity is satisfied. Another technique is based on the use of knife-edge diffraction. The edge of an opaque
screen serves as the source of a reference wave, which interferes with the tested field within the directly illuminated region.
One observes typical interference forklets near the geometrical shadow boundary, which detect optical vortices. This technique
is more applicable to diagnostics of phase singularities in polychromatic speckle fields due to the condition of mutual spectral purity is satisfied automatically.
Coherent and completely polarized optical radiation, being stationary multiply scattered, becomes globally non-polarized.
Nevertheless, the degree of polarization equals unity at any point of the scattered field, which is characterized by nonuniform
spatial distribution of the polarization azimuth and ellipticity, so that the state of polarization changes from point to point. In
this paper we discuss some approaches to describe such "pseudodepolarized" optical fields and introduce convenient measures
of the distance between the states of polarization in two points of such fields connected with the observable quantities.
We report the feasibilities for revealing and diagnostics of unconventional phase singularities into optical fields, namely,
the singularities of spatial coherence functions into partially coherent vortex beams. It is shown that the vortices of the
spatial coherence function are comprehensively diagnosed through the strip version of the Thomas Young's interference
experiment. Namely, the magnitude of a topological charge and its sign are determined, respectively, by the magnitude
and the direction of bending of the Young's interference fringes, which are produced by the edge diffraction waves from
the rims of an opaque strip positioned in the vortex beam. Such experiment provides complete data on the azimuthal
behavior of a phase of the spatial coherence function. On the other hand, non-localized ring singularities of the spatial
coherence function and of the complex degree of coherence occurring in the radial distribution of a phase are detected
through conventional Young's interference experiment with two pinholes at an opaque screen. It is remarkable that the
last of the mentioned coherence phase singularities takes place, when amplitude zeroes of the field are absent. Instead of
this, the modulus of the complex degree of coherence vanishes alone.
Nongeneric polarization structures of the vortex beams resulting from coherent coaxial mixing of orthogonally polarized one-charged Laguerre-Gaussian modes with different mode numbers are analyzed. General solution is derived for a superposition of elliptically orthogonally polarized partial vortex beams, and the limiting partial cases when the mixed modes are polarized linearly or circularly are explored both theoretically and experimentally. It is established that in such combined beams unusual spatially stable polarization structures arise, such as closedC -- contours and L -- contours with a constant azimuth of linear polarization.
A simple method for creation of 'rainbow' polychromatic optical vortices using a point-like white-light source and the computer-generated hologram technique is reported. The conditions of spatial stability of long-distance propagating rainbow optical vortices are established, as well as the regularities governing the radial alternation of colors. The diffraction technique for revealing and diagnostics of vortices at partially coherent beam [Opt. Lett.28, 878, 2003] is for the first time applied to polychromatic beams supporting phase singularities.
Singular optics has been recognized as separate important branch of modern physics about 15 years ago. Actually, along this period it was developed as coherent singular optics. Fundamental properties of phase singularities and the most important regularities governing the formation of singular skeletons of the field (such as sign principles) have been established both for scalar (uniformly polarized) and for vector (spatially non-uniformly polarized) monochromatic optical fields. Development of coherent singular optics continues. The most interesting and promising event of the last years, especially since 2002, consists in the tendency to expand the singular optical principles on the field of partially coherent light fields. In this context, physically new singular optical concepts are derived, new experimental instrumentation is developed, and new promising applications of the singular optical approaches are elucidated. Analysis of last achievements in the field of singular optics leads to the conclusion on coming into being of new branch of this area of investigation, which can be referred to as the correlation singular optics. It is remarkable that fruitfulness of this new R&D direction is essentially determined by the concepts and results of classical wave optics, which were developed irrespective of the singular optical paradigm.
Original technique for a double phase conjugation using a static nonlinearly recorded hologram is introduced. Theoretical background is provided, as well as the experimental arrangement and demonstrations. On this base, heteroassociative reconstruction of mutually incoherent signals of arbitrary complexity with negligible level of cross-talks is implemented.
KEYWORDS: Diffraction, Holograms, Holography, 3D image reconstruction, Spatial frequencies, Near field optics, Near field, Wave propagation interference, Modulation, Geometrical optics
Slit diffraction of a light beam impinging at extremely large angles is elaborated within the framework of the Young-Rubinowicz model of diffraction phenomena, applying the concept of an edge diffraction wave. It is shown that diffraction pattern differs considerably both from a near-field pattern and a far-field one, which are formed with a normally incident probing beam. Imaging (holographic) properties of referenceless recording of such a pattern are revealed and demonstrated for the first time.
Negative imaging of an extended source of polychromatic radiation by an opaque screen is described within the framework of geometrical optics. Spatial domain behind the screen is determined where a negative image is observed, as well as the main optical characteristics of such image. Digital post-processing procedure for improving of an optically obtained negative image is introduced and implemented.
The problem of holographic associative memory and image processing is treated with account of the higher-order components of a thin hologram's amplitude transmittance and its higher diffraction orders. It is shown for the first time that a far-field nonlinear hologram of a diffraction aperture read out by the stored signal or its part provides full-image reconstructions (associative responses) in all observable diffraction orders. This result substantially develops so-called 'quadric holography approach' establishing that only error-corrected complex-conjugate associative response at the minus-second diffraction order of nonlinearly recorded thin hologram of a diffuse object can be reconstructed. Proceeding from the Young-Rubinowicz model of diffraction phenomena, it has been substantiated and proved experimentally that the higher-order associative responses turn out to be contoured being the higher-order reconstructions of the Young's edge diffraction wave. Besides, it is shown that a near-field nonlinear hologram from a half-tone input signal (without a diffuser) provides self-imaging of the stored memory in the form of its conjugate image with the inverted contrast.
A dramatic bicentenary history of the Thomas Young's wave interpretation of diffraction phenomena is briefly outlined. Both theoretical and experimental milestones substantiating the Young's diffraction paradigm are discussed. Vitality and topicality of the Young's views on the nature of diffraction are argued. Relation of the Young's concept of diffraction phenomena with the novel decomposition of the solution of the diffraction problem in the spirit of 'singular optics' is considered.
The effect of negative imaging of an extended source of polychromatic radiation by an opaque screen is elaborated. It is shown that such imaging is of geometrical optics (shadow) nature rather than of diffraction one, as it was assumed earlier. On the base of the geometrical optics model, we define spatial domain behind an opaque screen where the negative imaging is realized, and determine the dependencies of the image parameters on the experimental conditions. Negative images are demonstrated for the first time, and the qualitative confirmation of the geometrical optics model is given.
Experimental data on the angular dependence of the amplitude function of the edge diffraction wave originating behind a metallic knife edge that is illuminated nonenlarged laser beam are represented. It is shown that the scalar diffraction theory approximation (in particular, so-called `Rubinowicz's representation of the Kirhhoff's diffraction integral) is valid up to the diffraction angle approximately 206. Outside this angular region (especially at the diffraction angle from 60 degree(s) to 90 degree(s)), considerable polarization dependence of diffraction are observed. The obtained experimental data are discussed using various vector theories of diffraction. On the base of these results, some consequences of the scalar Young-Rubinowicz model of diffraction in holography are derived. In particular, the impulse response of a Young hologram is constructed following to Fourier optics approach, and the nature of the double contouring effect at the reconstruction of such a hologram is elucidated.
KEYWORDS: Fractal analysis, Holograms, Diagnostics, Correlation function, Diffraction, 3D image reconstruction, Chaos, Optical signal processing, Data processing, Analog electronics
The present-day state of fractalometry and fractalography is considered. Fractalographic techniques based on referenceless holograms and off-axis quadric holograms are introduced. The original technique for measurement of a chaos correlation dimension at the field is proposed as well as possibilities provided by implementation of this technique.
Implementation of an all-optical cryptograph with a double- random phase coding using nonlinearly recorded holograms is considered. This implementation is based on recently discovered ability of a nonlinearly recorded hologram with the standing reference wave to self-conjugate an object beam of arbitrary completeness. It is shown, that large apertures of a quibic hologram-based phase conjugate mirror permits to overcome the main practical difficulty hindering implementation of a double-random phase coding cryptography through diminishing the information losses due to spatial- frequency filtering of the time-inverted replica of the stored memory.
Several original versions of nonlinearly recorded hologram- based associative memories are summarized. All of them are realized using phase-conjugate properties of such holograms being associated just with nonlinear part of a holographic recoding. The photorefractive prototypes of some represented memories are pointed out. The introduced all-optical associative memories exhibit error-correcting properties, ability to edge enhancement into associative responses, and may be realized at arbitrary recording media (thin or volume, permanent or reversible).
Reproducible properties of referenceless fractalograms, including Fourier-transform and imaging ones, are studied for the first time for example of an aperture bounded with a Koch curve. Peculiarities of the images reconstructed from such fractalograms are explicated proceeding from the Young interpretation of diffraction phenomena. A registration zone of the comprehensive informativity of a referenceless fractalogram is determined, and multi-stage procedure for pre-processing of a fractal-containing optical signal is briefly outlined.
Performance of nonlinearly recorded reflection hologram read out in associative regime is studied. It is shown, that the combination gratings associated with the quadratic component of an amplitude response of such a hologram provide its unconventional imaging properties causing the conjugate imaging side by side with the primary image reconstruction or even instead of it. Static hologram-based double phase conjugation is reported for the first time.
Phase conjugating properties of a quadric hologram with a standing reference wave are grounded and demonstrated. It is shown that the quadratic component of an amplitude response of a nonlinearly recorded hologram provides auto- and heteroassociative image reconstruction in self-conjugation fashion. Error-correcting features of a quadric hologram- based associative reconstruction are discussed, and the possibilities for combining of optical phase conjugation with an image processing are explicated and demonstrated for the first time.
Special class of all-optical holographic associative memories with a nonlinearity in the filter domain is represented. Natural nonlinearity, just a nonlinear part of a holographic recording, lies in the basis of auto- and heteroassociative processes. It is shown, that the developed here class of quadric hologram-based associative memories is the widest generalization of a holographic matched filter technique including informative properties of ghost-image holography, Vander Lugt's correlator, so-called 'second-order holography' using photorefractive oscillators, and nonlinear holographic associative processor to archival data storage and implementation of optical interconnections are discussed.
New phase conjugator for pseudodepolarized laser beams resulting form multiple scattering is described. The phase conjugator is based on a so-called quadric hologram, i.e., a hologram whose amplitude response contains the terms of a power series expansion on exposure degrees up to the quadratic one, recorded with a standing reference wave. Phase conjugate mirror results from an interference among partial cross-gratings associated with two components of the standing reference wave. Being read out with pseudodepolarized signal beam only, a quadric hologram generates its time-inverted twin in self-conjugation fashion. Conditions for fine polarization structure of the signal beam to be reproduced in a phase-conjugated response are discussed.
The problem of an associative data reconstruction with a true brightness tone rendering for a general case of nonuniformly polarized stored signals is considered.It is shown that a quadric hologram technique with two cross- polarized reference waves gives a complete solution of the problem. Being addressed with an arbitrary partial version of the stored signal irrespective of its polarization, a quadric hologram reconstructs a complex-conjugated high- fidelity associative response.
Special class of all-optical holographic associative memories with a nonlinearity in the filter domain is represented. Natural nonlinearity, just a nonlinear part of a holographic recording, lies in the basis of auto- and heteroassociative processes. It is shown, that the here developed class of quadric hologram-based associative memories is the widest generalization of a holographic matched filter technique including informative properties of ghost-image holography, Vander Lug's correlator, so-called 'second-order holography' using photorefractive oscillators, and nonlinear holographic associative memories based on resonator-like architectures. Potentialities of a quadric hologram-based associative processor to archival data storage and implementation of optical interconnections are discussed.
Reduction of imaging (associative) properties of a reference- less hologram as the registration plane moves to far-field re- gion (i.e., as the wave parameter approaches unity) is •conside- red. It is shown, that anomal intensity decreasing at the ghost image in the nearest vicinity of the readout part of an object as well as reduction of signal-to-noise ratio at associative reconstructions are explaned with account of the filtering ac- tion of a free space and intrinsic scale of an object field, rather than from aperture limitation that is the main factor of image degradation figuring into conventional telescopic imaging or ofit-axis holography.
Imaging properties of a near-field pattern recorded without complementary reference wave is recognized proceeding from the Young-Rubinowicz concept of diffraction phenomena, and the spe- cial hologram type, the Young hologram, is introduced. Contour imaging by the Young holography technique is considered.
KEYWORDS: Diffraction, Holograms, Spiral phase plates, Near field optics, Holography, Opacity, Near field, 3D image reconstruction, Monochromatic aberrations, Image registration
Inequality of imaging by Young holograms from complementary diffraction devices are grounded using a stationary phase principle which causes a reduced recording distributivity. A holographic method for determination of an angular dependence of the secondary wave amplitude function associated with a diffraction screen edge is proposed, and the Rubinowicz representation for a diffraction integral at the primary illuminated are is verified on this basis.
KEYWORDS: Diffraction, Holograms, 3D image reconstruction, Holography, Microscopy, Near field, Image visualization, Microscopes, Opacity, Near field optics
A new version of a diffraction microscope developing the Young eriometer concept is presented. Recording of the near-field pattern is considered in the terms of the Young model of diffraction phenomena. According to the Young diffraction paradigm, a diffraction wave is divided in the direct (primary) wave and the secondary one retransmitted by the edge of a diffraction screen. Being readout with the primary wave, the recorded near-field pattern reconstitutes a contour image of the diffraction screen. A near-field concept is defined in the framework of the Young's approach. It is shown that the notion 'far field' is indefinable for an arbitrary convex opaque screen. That fact enables the construction of a microscope for a small particle contour imaging using a Young hologram as the diffraction objective. The Young holography method is compared with Michelson's experiment as well as B. Thompson's method of holographic microscopy using Fraunhofer holograms.
Results of an investigation of a referenceless hologram (RLH) associative response showing spatial variant brightness and signal-to-noise ratio (SNR) at the ghost image are presented. When an information page is one-side blocked, brightness and SNR are reaching their maximal magnitudes at the periphery of a ghost image, gradually decreasing as a running point approaches the readout fragment boundary. Spatial inhomogeneity of optical characteristics of the RLH's associative responses is explained with account of the singularity of an object field's power spectrum at the lowest spatial frequencies. Associative responses reconstructed by RLHs and some generalized holographic associative memories are compared.
We consider the problem of a holographic associative memory (HAM) which must reconstruct a 2-D optical signal with corrected amplitude errors. The experimental conditions for an associative reconstruction with true brightness tone rendering by a regular HAM based on the ghost-image hologram are determined. More universal all-optical error-correcting (EC) HAMs are also presented and demonstrated. These HAMs perform a reconstruction of the second image of a stored memory that is angularly separated from the readout beam of its partial version. We describe the scheme solution of an ECHAM problem using Denisyuk's hologram, which reconstructs an error-corrected associative response in reflection. Then the original all-optical ECHAM using the so-called quadric hologram (QH) is presented. This term here refers to a thin off-axis nonlinearly recorded hologram used as the matched filter of a regular coherent correlator. When a QH is read out by the partial or distorted version of the stored memory, the complex conjugated associative response is reconstructed at the output plane with an original brightness distribution. A QH-based ECHAM is equivalent in efficiency to nonlinear HAMs based on the resonator architectures using phase-conjugation techniques and external nonlinearities, but it differs from these in arrangement simplicity and implementation flexibility as an EC associative module of the more general neural network architectures.
We consider the problem of a holographic associative memory (HAM) which must reconstruct a 2-D optical signal with corrected amplitude errors. The experimental conditions for an associative reconstruction with true brightness tone rendering by a regular HAM based on the ghost-image hologram are determined. More universal all-optical error-correcting (EC) HAMs are also presented and demonstrated. These HAMs perform a reconstruction of the second image of a stored memory that is angularly separated from the readout beam of its partial version. We describe the scheme solution of an ECHAM problem using Denisyuk's hologram, which reconstructs an error-corrected associative response in reflection. Then the original all-optical ECHAM using the so-called quadric hologram (QH) is presented. This term here refers to a thin off-axis nonlinearly recorded hologram used as the matched filter of a regular coherent correlator. When a QH is read out by the partial or distorted version of the stored memory, the complex conjugated associative response is reconstructed at the output plane with an original brightness distribution. A QH-based ECHAM is equivalent in efficiency to nonlinear HAMs based on the resonator architectures using phase-conjugation techniques and external nonlinearities, but it differs from these in arrangement simplicity and implementation flexibility as an EC associative module of the more general neural network architectures.
Generalization of the linear matched filter concept to nonlinear matched filter is presented. It is shown that the nonlinearity introduced in the filter domain results in the component of the diffraction hologram structure which is associated with a whole set of a joint power spectrum for mutually incoherent (noninterfering) input signals. It is shown that a correlator with a holographic match filter whose amplitude transmittance expanded in powers of exposure contains up to and including second order terms (the so-called 'second order hologram') is a new class of 2D or 3D optical associative memories.
KEYWORDS: Holograms, 3D image reconstruction, Diffraction, Holography, Diffraction gratings, Heterodyning, Signal to noise ratio, Transmittance, Wavefronts, 3D image processing
Imaging properties of a second-order hologram (SOH), i.e., a thin off-axis hologram with the amplitude transmittance involving expansion terms up to quadratic in exposure, are investigated. It is shown that by reading such a hologram by a partial or distorted object image it is possible to obtain a complex conjugate associative response, i.e., reconstruct a conjugate object image. The advantages of a SOH over the linearly recorded 2-D and even 3-D ghost- image holograms are in that it is capable of reproducing the original intensity distribution in the conjugate image and permits a reciprocal associative reconstruction of noninterfering complicated wave fronts. Also discussed are the associative properties of volume SOH.
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