Optical implementation of the hopfield neural network with matrix gratings

We propose a new method for the optical implementation of the Hopfield neural network with a universal tool. The tool is a matrix grating constituted with a group of element gratings. The algorithms for designing a matrix grating are proposed, and a matrix grating is created to execute recognition experiments by use of the Hopfield neural network. The experimental results demonstrate that the proposed method performs well. The stability of the light efficiencies of different optical components used in optical networks is also considered.     

Short-coherence digital microscopy by use of a lensless holographic imaging system

An optical system based on short-coherence digital holography suitable for three-dimensional (3D) microscopic investigations is described. The light source is a short-coherence laser, and the holograms are recorded on a CCD sensor. The interference (hologram) occurs only when the path lengths of the reference and the object beam are matched within the coherence length of the laser. The image of the part of the sample that matches the reference beam is reconstructed by numerical evaluation of the hologram. The advantages of the method are high numerical aperture (this means high spatial resolution), detection of the 3D shape, and a lensless imaging system. Experimental results are presented.     

Writing long holographic diffraction gratings by use of a novel scanning method

A novel method for writing holographic diffraction gratings is proposed in which the two interfering beams are moved together across the recording medium in such a way that the interference pattern at the medium is unchanged. The phase compensation is discussed both for an idealized setup and for a realistic experimental arrangement.     

Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material

An optical system that employs holographic recording in a photorefractive material is proposed and experimentally demonstrated for the implementation of a wavelet transform of two-dimensional mages. A scaling operation, to derive the family of wavelet filters from a mother wavelet filter, is performed by the use of an optical feedback loop. The selection of a desired wavelet filter from the family and the correlation for a wavelet transformation are made by the use of a holographic recording in a photorefractive material. The principle of operation of the system relies on the frequency detuning introduced inside the loop and the subsequent variation in the holographic grating diffraction. Experimental results on wavelet-filter selection and wavelet transformation are presented. This nonlinear optical wavelet-transform system is advantageous for pattern recognition applications.     

Theory of spherical holographic gratings recorded by use of a multimode deformable mirror

We present the theory of spherical holographic gratings recorded by use of a deformable plane mirror and consider its application to the optimized Rowland Mounting. We illustrate the efficiency of such a mounting by computing two high-resolution gratings (3800 grooves/mm) with f/24 and f/10 apertures.     

Optical sectioning by holographic coherence imaging: a generalized analysis

A theory of optical sectioning by image plane holography is developed, emphasizing the use of broad-spectrum holographic methods to enhance the process. It is shown that a broad-spectrum source in a grating interferometer imitates the behavior of a monochromatic broad source.     

Speckle-reduced three-dimensional volume holographic display by use of integral imaging

We propose a method to implement a speckle-reduced coherent three-dimensional (3D) display system by a combination of integral imaging and photorefractive volume holographic storage. The 3D real object is imaged through the microlens array and stored in the photorefractive crystal. During the reconstruction process a phase conjugate reading beam is used to minimize aberration, and a rotating diffuser located on the imaging plane of the lens array is employed to reduce the speckle noise. The speckle-reduced 3D image with a wide viewing angle can be reconstructed by use of the proposed system. Experimental results are presented and optical parameters of the proposed system are discussed in detail.     

Fractional fourier domain encrypted holographic memory by use of an anamorphic optical system

We propose and demonstrate a fractional Fourier domain encrypted holographic memory using an anamorphic optical system. The encryption is done by use of two statistically independent random-phase codes in the fractional Fourier domain. If the two random-phase codes are statistically independent white sequences, the encrypted data are stationary white noise. We exploit the capability of an optical system to process information in two dimensions by using two different sets of parameters along the two orthogonal axes to encode the data. The fractional Fourier transform parameters along with the random-phase codes constitute the key to the encrypted data. The knowledge of the key is essential to the successful decryption of data. The decoding of the encoded data is done by use of phase conjugation. We present a few experimental results.     

Technique for narrow-band imaging in the far ultraviolet based on aberration-corrected holographic gratings

We have developed a new family of imaging spectrometer designs that combine the imaging power of two-element telescopes with the aberration control of first-generation holographic gratings. The resulting optical designs provide high spatial resolution over modest fields of view at selectable wavelengths. These all-reflective designs are particularly suited for narrow-band imaging below 1050 A, the wavelength below which there are no transmitting materials in the UV. We have developed designs to efficiently map the spatial distribution of UV-emitting material. This mapping capability is absent in current and future astronomical instruments but is crucial to the understanding of the nature of a variety of astrophysical phenomena. Although our examples focus on UV wavelengths, the design concept is applicable to any wavelength.     

Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings

The total-field-scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite-difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings. Furthermore, the convergence of the FDTD results to the rigorous coupled-wave analysis results is investigated as the number of grating periods and the incident beam size increase.     

Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror

To reduce the uncorrected higher-order aberrations for holographic gratings requiring an extreme dispersion, we have modified the Rowland mounting by moving the recording laser sources away from the grating. Then, with a multimode deformable plane mirror to record the grating, the correction of all the aberrations up to the fourth order inclusive is found sufficient to obtain a high-quality image. Applied to the FUSE-LYMAN grating, with a groove density of as much as 5740 grooves/mm, for which a resolution of 30,000 was required, this new recording device produces a resolution from 139,000 to 222,000 over the spectral range.     

Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors

We propose a new way of recording in which a spherical blank and a deformable mirror are used to obtain high-resolution holographic gratings. The reflection of one of the two laser recording waves upon this mirror provides the deformations necessary to image correction to as much as seventh-order aberrations inclusively.     

Viewing-angle enhancement of speckle-reduced volume holographic three-dimensional display by use of integral imaging

In a conventional integral imaging system the viewing angle is limited by the f-number of the microlens. To overcome this limitation we employ a phase-conjugate beam to read out elemental images, which are stored in photorefractive volume holographic storage, while the rotating diffuser reduces the speckle noise. In the proposed system the viewing angle can be enhanced over the f-number limitation. Experimental results and discussions of viewing parameters are presented.     

Analysis of voltage effect on holographic gratings by modulation transfer function

The experimental data allow us to determine the imaging quality of holographic gratings with photosensitive film using organic material based on a polyvinyl alcohol matrix doped with potassium dichromate and nickel (II) chloride hexahydrate. The diffraction efficiency is estimated by different spatial frequencies, and the readout image quality is analyzed by the modulation transfer function. The experiment is carried out, with and without voltage application, at different spatial frequencies to obtain the image quality of photosensitive film.     

Hyperbolic holographic gratings: analysis and interferometric tests

The aberrations of hyperbolic diffraction gratings produced with two spherical waves are analyzed theoretically and experimentally. The behavior of these gratings in collimated illumination indicates that for a grating of a given size there is a critical spatial frequency above which the aberration remains constant for all spatial frequencies. Aberrations associated with geometrical errors in the recording geometry are derived. With simple interferometric tests, misalignments in the recording process can be identified easily.     

Design of an in-line, digital holographic imaging system for airborne measurement of clouds

We discuss the design and performance of an airborne (underwing) in-line digital holographic imaging system developed for characterizing atmospheric cloud water droplets and ice particles in situ. The airborne environment constrained the design space to the simple optical layout that in-line non-beam-splitting holography affords. The desired measurement required the largest possible sample volume in which the smallest desired particle size (～5 μm) could still be resolved, and consequently the magnification requirement was driven by the pixel size of the camera and this particle size. The resulting design was a seven-element, double-telecentric, high-precision optical imaging system used to relay and magnify a hologram onto a CCD surface. The system was designed to preserve performance and high resolution over a wide temperature range. Details of the optical design and construction are given. Experimental results demonstrate that the system is capable of recording holograms that can be reconstructed with resolution of better than 6.5 μm within a 15 cm(3) sample volume.     

Improving holographic data storage by use of an optimized phase mask.

A method for improving the spectral distribution and for reducing the reconstruction error in optical holographic data storage is proposed. By use of an optimized phase mask in the input plane, the uniformity of the spectral distribution is optimized and the reconstruction error minimized. The phase mask is designed by use of amplitude-phase retrieval algorithms. Simulation results show the merits of the proposed method.     

Spatial-frequency response of holographic gratings photodeposited from inorganic colloids

Surface photodeposition is a photon-assisted process by which thin films are formed on substrates immersed in colloid solutions. We experimentally evaluate the resolution capabilities of the photodeposition process with amorphous selenium colloids by recording holographic gratings at different spatial frequencies, up to 2200 lines/mm. The experimental diffraction efficiencies are analyzed in terms of a theoretical model, which relates the spatial-frequency response to optical recording parameters and colloid particle sizes. The maximal experimental diffraction efficiency reaches 13% with a spatial frequency of f = 1100 lines/mm. The diffraction efficiencies decrease monotonically with spatial frequency, and drop to half of the maximal diffraction efficiency at f ≈ 1500 lines/mm. These resolution capabilities are achieved with colloid particle sizes extending up to 80 nm. The theoretical derivation indicates that to obtain spatial frequencies above 3000 lines/mm, one should restrict the colloid particle size to a(max) ≤ 30 nm.