Three-dimensional displacement measurement for diffuse object using phase-shifting digital holography with polarization imaging camera

The amount of displacement of a diffused object can be measured using phase-shifting digital holography with a polarization imaging camera. Four digital holograms in quadrature are extracted from the polarization imaging camera and used to calculate the phase hologram. Two Fourier transforms of the phase holograms are calculated before and after the displacement of the object. A phase slope is subsequently obtained from the phase distribution of division between the two Fourier transforms. The slope of the phase distribution is proportional to the lateral displacement of the object. The sensitivity is less than one pixel size in the lateral direction of the movement. The longitudinal component of the displacement can be also measured separately from the intercept on the phase axis along the phase distribution of the division between two Fourier transforms of the phase holograms.     

Frequency and phase swept holograms in spectral hole-burning materials

A new hologram type in spectral hole-burning systems is presented. During exposure, the frequency of narrow-band laser light is swept over a spectral range that corresponds to a few homogeneous linewidths of the spectrally selective recording material. Simultaneously the phase of the hologram is adjusted as a function of frequency-the phase sweep function. Because of the phase-reconstructing properties of holography, this recording technique programs the sample as a spectral amplitude and phase filter. We call this hologram type frequency and phase swept (FPS) holograms. Their properties and applications are summarized, and a straightforward theory is presented that describes all the diffraction phenomena observed to date. Thin FPS holograms show strongly asymmetric diffraction into conjugated diffraction orders, which is an unusual behavior for thin transmission holograms. Investigations demonstrate the advantages of FPS holograms with respect to conventional cw recording techniques in freq ncymultiplexed data storage. By choosing appropriate phase sweep functions, various features of holographic data storage can be optimized. Examples for cross-talk reduction, highest diffraction efficiency, and maximal readout stability are demonstrated. The properties of these FPS hologram types are deduced from theoretical considerations and confirmed by experiments.     

Two methods of reducing the dynamic range of a holographic filter

Two methods of reducing the dynamic range of the transmittance of computer-generated interconnection holograms are presented and compared. The holograms are used in an optical implementation of an associative memory to connect the input and the output planes but are representative of more generalN(4) interconnection holograms. Because the holograms play a double correlation-reconstruction role, the standard spectrum-smoothing techniques (e.g., random phase) cannot be applied. We show, in computer simulations and optical experiments, that by using deterministic phase functions that can be realized in the optical system (defocusing the hologram or controlling the phases of the diffraction spots of a Dammann grating used in the system input) the hologram dynamic range can be lowered, reducing the errors during the hologram binarization and increasing the hologram's diffraction efficiency.     

Design and fabrication of computer-generated beam-shaping holograms

For the design of computer-generated holograms reconstructing certain intensity patterns with phase freedom, we use an object-oriented approach. The given intensity pattern is decomposed into elementary objects for which appropriate phase-only hologram functions can be constructed. The total hologram function is found by the subsequent superposition of its constituents, with a relative amplitude and phase weighting for each of them. Thus, the degrees of freedom are dramatically reduced compared with those of sampling approaches. The design algorithm allows us to compensate on the one hand for the intensity and phase distribution of the impinging laser beam and on the other hand for the shape of the hologram aperture. We report on the computer-aided design of such holograms, as well as their fabrication through the use of laser lithography and reactive ion etching. Optical reconstructions are shown.     

Substrate-mode holograms used in optical interconnects: design issues

We discuss a number of design issues that affect the performance tolerances of substrate-mode holograms used for optical interconnect systems. We examine the effects of emulsion uniformity, thickness variation, and index variation on the ability to determine the Bragg angle and the diffraction angle within the substrate accurately. The environmental stability with respect to temperature, laser irradiance, and humidity are considered. Experimental results are presented for substrate-mode holograms fabricated in spin-coated dichromated-gelatin emulsions. The coupling properties for a 1 × 2 multiplexed substrate-mode hologram with two superimposed gratings are also described.     

Experimental analysis in recording transmission and reflection holograms at the same time and location

Holographic recording media with a reflection layer are useful because they make it possible to maintain backward compatibility with CDs and DVDs, and a conventional servo system is easily attachable. The incident beam is fed back to the recording layer by the reflection layer, so there are four beam pairs to record the transmission and reflection holograms. We analyze the basic property of the transmission and reflection holograms and evaluate the problem when the transmission and reflection holograms are recorded at the same time. It is shown that the shrinkage in the photopolymer medium has a different effect on each hologram, so the readout image from the two holograms is misaligned. Those diffraction beams make the interference pattern, and the signal-to-noise ratio (SNR) of the output image decreased. Taking into account the difference in wavelength selectivity between the transmission and the reflection holograms, we propose a way to select one hologram to get the diffraction beam and eliminate the interference pattern using the tuning readout wavelength. By using this method, we can eliminate the diffraction beam from the reflection hologram and keep a high SNR.     

Hartley holograms

Binary holograms have become more interesting since spatial light modulators, capable of binary phase modulation, were developed. The primary restriction of these dynamic elements when used with the Fourier transform is the symmetry of the hologram reconstruction. I describe a new type of hologram that uses the Hartley transform instead of the Fourier transform. Despite their binary form, Hartley holograms offer maximal efficiency (theoretically 100%). Thus they can be presented as high diffraction-efficiency programmable elements. For practical reasons, I also propose a modified version for Hartley holograms that is easy to use. A theoretical analysis as well as experimental results are given.     

Suppression of undesired diffraction orders of binary phase holograms

A method to remove undesired diffraction orders of computer-generated binary phase holograms is demonstrated. Normally, the reconstruction of binary Fourier holograms, made from just two phase levels, results in an undesired inverted image from the minus first diffraction order, which is superposed with the desired one. This can be avoided by reconstructing the hologram with a diffuse light field with a pseudorandom, but known, phase distribution, which is taken into account for the hologram computation. As a consequence, only the desired image is reconstructed, whereas all residual light is dispersed, propagating as a diffuse background wave. The method may be advantageous to employ ferroelectric spatial light modulators as holographic display devices, which can display only binary phase holograms, but which have the advantage of fast switching rates.     

Optimally tuned spatial light modulators for digital holography

Digital holography and comparative digital holography are applications that require computer-addressable modulators for the optical reconstruction of digital holograms. The quality of the reconstructed holograms depends on the modulator's properties. Therefore a characterization of the modulators is required. We show the result of a modulator characterization and the modulator's influence on the quality of the reconstructed hologram. We then compare qualitatively and quantitatively the optical reconstruction of phase and amplitude holograms by considering their level of detail and their diffraction efficiency.     

Computer-generated microcooled reflection holograms in silicon for material processing with a CO(2) laser

We report on the design, fabrication, and testing of multilevel computer-generated reflection holograms in Si for CO(2) laser material processing for laser intensities of <2 kW/cm(2). The holograms are designed with an iterative method based on scalar diffraction theory. In this case the reconstructed intensity distribution is independent of the incident high-power laser mode. For achieving high diffraction efficiencies, multilevel staircase surface topologies are fabricated by multimask and reactive ion-etching technology on the front side of a polished Si wafer. For efficient hologram cooling, a gratinglike structure of microchannels is chemically etched on the back side of the Si wafer. Absorption and deformation measurements have been carried out on both a microcooled flat mirror and a reflection hologram. The maximum deformation amounts to 200 nm and is 10 times smaller than comparable conventional uncoated Cu mirrors. A diffraction efficiency of 88% is achieved with an eight-level reflection hologram and a 30-mm-diameter CO(2) laser beam with a power of 5 kW.     

Fast numerical generation and encryption of computer-generated Fresnel holograms

In the past two decades, generation and encryption of holographic images have been identified as two important areas of investigation in digital holography. The integration of these two technologies has enabled images to be encrypted with more dimensions of freedom on top of simply employing the encryption keys. Despite the moderate success attained to date, and the rapid advancement of computing technology in recent years, the heavy computation load involved in these two processes remains a major bottleneck in the evolution of the digital holography technology. To alleviate this problem, we have proposed a fast and economical solution which is capable of generating, and at the same time encrypting, holograms with numerical means. In our method, the hologram formation mechanism is decomposed into a pair of one-dimensional (1D) processes. In the first stage, a given three-dimensional (3D) scene is partitioned into a stack of uniformed spaced horizontal planes and converted into a set of hologram sublines. Next, the sublines are expanded to a hologram by convolving it with a 1D reference signal. To encrypt the hologram, the reference signal is first convolved with a key function in the form of a maximum length sequence (also known as MLS, or M-sequence). The use of a MLS has two advantages. First, an MLS is spectrally flat so that it will not jeopardize the frequency spectrum of the hologram. Second, the autocorrelation function of an MLS is close to a train of Kronecker delta function. As a result, the encrypted hologram can be decoded by correlating it with the same key that is adopted in the encoding process. Experimental results reveal that the proposed method can be applied to generate and encrypt holograms with a small number of computations. In addition, the encrypted hologram can be decoded and reconstructed to the original 3D scene with good fidelity.     

Concealed holographic coding for security applications by using a moiré technique

We present an optical coding technique that enhances the anticounterfeiting power of security holograms. The principle of the technique is based on the moiré phenomenon. The code in the hologram has a phase pattern that is invisible and cannot be detected by optical equipment, so that imitation is extremely difficult. Holographic, photographic, and embossing techniques are used in fabricating coded holograms and decoders.     

Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators

Dynamic interconnect holograms are designed by the use of a simulated annealing algorithm and written to a 128 × 128 pixel ferroelectric spatial light modulator that is used in a binary-phase mode. Dynamic holograms are used to implement a 2 × 2 crossbar with single-mode fiber inputs and outputs, which function with as high as 27 dB of isolation between output ports. The principle is extended to two-dimensional interconnection holograms, and arbitrary fan-out to as high as 64 points is demonstrated with good performance.

Images of interconnection holograms are transferred from the spatial light modulator to an optically addressed spatial light modulator that is used in a binary-phase mode. The addition of a fixed array generator computer-generated hologram permits replication of the hologram image, thus creating a larger hologram with a high space-bandwidth product on the optically addressed spatial light modulator.

Results of a preliminary experiment are presented.

     

In-line hologram reconstruction using Hartley transform

In reconstruction of in-line recorded holograms, zero-order and conjugate images appear on the same physical location as the object image. Here we propose a method, new to our knowledge, to separate the object image from the others by using two quadrature phase-shifted holograms. The method uses the Hartley transform and a phase retrieval type of algorithm on the difference hologram.     

Mirror hologram recording with a phase-change medium

We propose mirror hologram recording with a phase-change material, which has a large refractive-index difference between its amorphous and crystalline states. It offers excellent diffraction efficiency and is erasable and nonvolatile. We designed an optimum multilayer structure for high diffraction efficiency by simulating the effect of each film thickness on diffraction efficiency. Experiments with a germanium tellurium alloy as the phase-change material show a high diffraction efficiency close to the calculated value. This medium can also be used for directly drawing computer-generated holograms. Lee-type computer-generated holograms were drawn on this medium with optical-disk technology.     

Method for the characterization of hologram processing

Abstract

A novel method for the characterization of the processing of both absorption and phase holograms is proposed. Differently from the previous models, the square root of the diffraction efficiency of the processed hologram was directly related to the amplitude of the optical density modulation obtained at the developed step. This characteristic is a good indicator of the degree of nonlinearity of the hologram processing. While the Lin functions of phase holograms are similar to those of absorption holograms, the shape of the proposed function is completely different. The optical density and diffraction efficiency of holograms recorded using Agfa–Geveart 8E75HD plates and processed with AAC developer and a solvent bleach without a fixation step were measured and used to demonstrate the method.     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.     

Simultaneous two-dimensional endoscopic pulsed digital holography for evaluation of dynamic displacements

An endoscope is used in pulsed digital holography to simultaneously evaluate in-plane and out- of-plane transient and harmonic displacements on a flat metallic plate. The plate is illuminated from two different directions. The optical path for each illumination direction is matched to its corresponding reference beam, but also in such a way that each object-reference beam pair optical path is mismatched such that they are incoherent and can be stored in a single CCD frame. As is typical in these types of interferometric arrangement, two digital holograms are needed to compare two different states of the plate. Each hologram is Fourier transformed and due to the incoherence introduced, two separate spectra are readily identified, each belonging to an object-reference beam pair. On comparing by subtraction the phase obtained from the two pulsed digital holograms, it is possible to gather quantitative in-plane and out-of- plane results from transient and harmonic displacements.     

Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones

The single-sideband method of holography, as is well known, cuts off beams that come from conjugate images for holograms produced in the Fraunhofer region and from objects with no phase components. The single-sideband method with half-zone-plate processing is also effective in the Fresnel region for beams from an object that has phase components. However, this method restricts the viewing zone to a narrow range. We propose a method to improve this restriction by time-alternating switching of hologram patterns and a spatial filter set on the focal plane of a reconstruction lens.     

Redistribution of the zero order by the use of a phase checkerboard pattern in computer generated holograms

A checkerboard phase plate is proposed to be used together with computer generated holograms to eliminate the zero order by working as a convolution function that shifts the zero order away from the center of a reconstructed pattern. By performing a preshift in the desired hologram pattern, it is possible to obtain a reconstructed pattern that is free of zero order. Simulation results have shown that the technique is tolerant of fabrication errors in the hologram. The technique is also shown to effectively reduce the zero order intensity by two orders in the presence of phase depth errors in the checkerboard. Experimental results using a spatial light modulator support the results shown in the simulation.