A simple phase-characterization method for spatial light modulators is proposed. The low-cost method permits high-precision measurement and provides data for the setting of the spatial-light-modulator operating point in the phase-modulation mode. The dynamic phase response is used to perform efficient kinoform recording. In order to record the kinoform, we modify the global iterative coding to compute phase holograms. Finally, modified phase–phase correlation is introduced. The phase–phase correlator permits sharper correlation peaks, better energy transmission, and higher discrimination than an amplitude–phase correlation. Optical experimental results are presented.

Phase calibration and applications of a liquid-crystal spatial light modulator

We present a unified treatment of the diffraction properties of stratified volume holographic optical elements (SVHOE’s). We show that the relative phasing of the diffraction orders as they propagate from layer to layer gives rise to a unique notched diffraction response of the +1 order (for the case of Bragg incidence) as a function of the normalized buffer-layer thickness, the grating spatial frequency, and the readout wavelength. For certain combinations of these parameters Bragg diffraction behavior characteristic of volume holographic optical elements (VHOE’s) is observed, whereas for other combinations pure Raman–Nath behavior periodically recurs. By using these same relative-phasing arguments, the principal features of the periodic angular sensitivity of the +1 and −1 orders can be predicted. In addition to examining the fundamental aspects of SVHOE diffraction behavior, we discuss several possible applications, including optical array generation, spatial frequency filtering, and wavelength notch filtering. With the use of the SVHOE concept, holographic materials with otherwise exemplary characteristics that are currently available only in thin-film form can be used in structures designed either to access unique SVHOE diffraction properties or to emulate conventional VHOE’s.

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Diffraction Properties of Stratified Volume Holographic Optical Elements

A model to determine the influence of the phase and amplitude mismatching on the diffraction orders is proposed. The coupling between amplitude and phase in liquid crystal televisions (LCTV) is also considered. The effect on the impulse response of the nonlinearities is studied from experimentally determined amplitude and phase modulations. It is shown that even with these nonlinearities one of the orders corresponds to the impulse response of the kinoform. The proper diffractional order may be separated by adding phase codes. Experimental results of impulse responses and correlations are given for different configurations of the spatial light modulator (SLM).

Effects of Amplitude and Phase Mismatching Errors in the Generation of a Kinoform for Pattern Recognition

The hybrid optoelectronic processor, presented in this paper, realizes the dual nonlinear correlation (DNC) in a set-up based on a two-step nonlinear joint transform correlator architecture. In the first step three power spectrum distributions (input scene power spectrum, reference target power spectrum, and the joint power spectrum) necessary for the nonlinear processing are captured with a CCD camera. Nonlinear modification of the joint power spectrum, which does not have to be symmetrical in the input and reference channels, is introduced digitally. In the second step, the modified joint power spectrum is Fourier transformed optically. Numerical analysis of this processor shows a crucial influence of the dynamic range and the limited number of grey levels of the CCD camera during image acquisition in the first step, on the output signal parameters and the discrimination capability of the set-up. Optical results of recognition obtained for noise-free segmented input scenes show that the set-up ...

Dual nonlinear correlator based on computer controlled joint transform processor: Digital analysis and optical results

Images taken in noncooperative environments do not always have targets under the same illumination conditions. There is a need for methods to detect targets independently of the illumination. We propose a technique that yields correlation peaks that are invariant under a linear intensity transformation of object intensity. The new locally adaptive contrast-invariant filter accomplishes this by combining three correlations in a nonlinear way. This method is not only intensity invariant but also has good discrimination and resistance to noise. We present simulation results for various intensity transformations with and without random and correlated noise. When the noise is high enough to threaten errors, the method trades off intensity invariance in order to achieve the optimum signal to noise ratio, and the peak to sidelobe ratio in the presence of clutter is always greater than one. In the presence of random disjoint noise, the signal to noise ratio is independent of the target contrast and of the level of the noise.

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Recognition of unsegmented targets invariant under transformations of intensity.

Optoelectronic implementation of the quasi-phase correlator

Recognition of partially occluded objects by correlation methods

Intensity invariant pattern recognition is achieved by a normalization of the correlation signal. Fourier for segmented and multiobject input are derived with the Holder's inequality.

Normalization of correlation filters based on the Hoelder's inequality

The implementation of nonlinear procedures in optical 
inforraation processing systems is the recently studied proruising step 
in the optical correlators development . Optical correlators with 
phase-only filters and binary phase-only filters belong to the class 
of such a nonlinear systems with the nonlinearity in the Fourier 
transfornt plane. 
The generalization of nonlinear matched filtering such that 
both the filter transfer function and the Fourier transform of the 
input objec are processed nonlinearly are recently under 
investigation. Pattern recognition by using phase nomation 
only is the particular case of nonlinear matched filtering. As a 
result of the nonlinear procedure one keeps only phase information 
about both the target and the input scene, and the pure phase-only 
correlation is realized. The discrimination capability of the 
phase-only correlation method is enhanced, even in comparison with the
results obtained in the case of the phase-only filtering, and the 
autocorrelation signal is the diffraction limited delta function.

Katarzyna Chalasinska-Macukow

Papers

Optoelectronic implementation of the quasi-phase correlator

Recognition of partially occluded objects by correlation methods

Normalization of correlation filters based on the Hoelder's inequality

Performance of the pure phase-only correlation method for pattern recognition

Comparison of nonlinear effects in amplitude and phase holograms recorded in photographic materials