Influence of the incident angle in the performance of liquid crystal on silicon displays.

In this paper we experimentally analyze the performance of a twisted nematic liquid crystal on silicon (LCoS) display as a function of the angle of incidence of the incoming beam. These are reflective displays that can be configured to produce amplitude or phase modulation by properly aligning external polarization elements. But we demonstrate that the incident angle plays an important role in the selection of the polarization configuration. We performed a Mueller matrix polarimetric analysis of the display that demonstrates that the recently reported depolarization effect observed in this type of displays is also dependant on the incident angle.

Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization.

In this paper we characterize the polarimetric properties of a liquid crystal on silicon display (LCoS), including depolarization and diattenuation which are usually not considered when applying the LCoS in diffractive or adaptive optics. On one hand, we have found that the LCoS generates a certain degree (that can be larger than a 10%) of depolarized light, which depends on the addressed gray level and on the incident state of polarization (SOP), and can not be ignored in the above mentioned applications. The main origin of the depolarized light is related with temporal fluctuations of the SOP of the light reflected by the LCoS. The Mueller matrix of the LCoS is measured as a function of the gray level, which enables for a numerical optimization of the intensity modulation configurations. In particular we look for maximum intensity contrast modulation or for constant intensity modulation. By means of a heuristic approach we show that, using elliptically polarized light, amplitude-mostly or phase-mostly modulation can be obtained at a wavelength of 633 nm.

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics.

In this paper we provide evidence of the temporal fluctuations of the phase modulation property of a liquid crystal on silicon (LCoS) display, and we analyze its effect when the device is used for displaying a diffractive optical element. We use a commercial twisted nematic LCoS display configured to produce a phase-only modulation, and we provide time resolved measurements of the diffraction efficiency that show rapid fluctuations of the phase modulation, in the millisecond order. We analyze how these fluctuations have to be considered in two typical methods for the characterization of the phase modulation: two beam interference and diffraction from a binary grating. We finally provide experimental results on the use of this device for displaying a computer generated hologram. A reduction of the modulation diffraction efficiency results from the phase modulation fluctuation.

Depth of focus increase by multiplexing programmable diffractive lenses.

A combination of several diffractive lenses written onto a single programmable liquid crystal display (LCD) is proposed for increasing the Depth of Focus (DOF) of the imaging system as a whole. The lenses are spatially multiplexed in a random scheme onto the LCD. The axial irradiance distribution produced by each lens overlaps with the next one producing an extended focal depth. To compare the image quality of the multiplexed lenses, the Modulation Transfer Function (MTF) is calculated. Finally we obtain the experimental Point Spread Functions (PSF) for these multiplexed lenses and experimental results in which an extended object is illuminated under spatially incoherent monochromatic light. We compare the images obtained in the focal plane and in some defocused planes with the single lens and with three multiplexed lenses. The experimental results confirm that the multiplexed lenses produce a high increase in the depth of focus.

A study of the point spread function in scintillation camera collimators based on Fourier analysis.

A new technique for evaluating the point spread function of parallel hole collimators in scintillation cameras is studied. The collimator function is developed into a Fourier series and the intensity distribution in the detector plane for a point source is given by a mathematical expression that depends on the object position and on the collimator parameters. The septal penetration effect is considered. The technique is applied to obtain the general formulae for collimators with hexagonal holes and the PSF is evaluated.

Using mathematical morphology to determine left ventricular contours.

The aim of this study is to investigate the use of mathematical morphology for the determination of left ventricular contours in scintigraphic images using multigated radionuclide angiography. We have developed a completely automatic method that first restores the image with a Wiener filter, then finds the region where the left ventricle is contained, and finally segments the left ventricle contour and a background zone. The contours depend on the values of the parameters that appear in the mathematical morphology method, which are related to the height and the slope of the count distribution. Results obtained with this method are compared with the contours and the background zones outlined by experts on the basis of the number of counts. We study the values of the parameters with which the optimum correlation is obtained.

Evaluation of the response of a round hole scintillation camera collimator by the Fourier analysis method.

The Fourier analysis method was used to investigate the response of scintillation camera collimators with parallel holes. This method which takes into account the septal penetration was applied to the case of round hole collimators having a hexagonal distribution. Modulation transfer functions, MTF have been determined to verify the accuracy of the computed Fourier coefficients of the collimator function. Comparisons between the geometric and the penetrating plus geometric transfer function are shown for round and hexagonal holes.

Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display.

We apply the polar decomposition of the Mueller matrix describing a liquid-crystal-on-silicon display to identify the diattenuator, depolarizer, and retarder contributions as a function of the gray level. The retarder contribution is expressed in terms of the equivalent Jones matrix to apply previous techniques to evaluate the phase modulation. This allows searching for optimized polarization configurations for phase- or amplitude-only modulation responses. We present results for lambda=633 nm showing a phase-only modulation up to 2 pi rad and flat intensity modulation.

Achromatic diffractive lens written onto a liquid crystal display.

We propose a programmable diffractive lens written onto a liquid crystal display (LCD) that is able to provide equal focal lengths for several wavelengths simultaneously. To achieve this goal it is necessary that the LCD operate in the phase-only regime simultaneously for the different wavelengths. We design the appropriate lens for each wavelength, and then the lenses are spatially multiplexed onto the LCD. Various multiplexing schemes have been analyzed, and the random scheme shows the best performance. We further show the possibility of finely tuning the chromaticity of the focal spot by changing the relative weights of the multiplexing among the various wavelengths.

Pattern recognition with quantized computer-generated filters.

The influence of the quantization levels used in the computer-generated filter on the correlation is studied. Two types of objects, binary characters and gray-tone objects, are used in the scene and in the test. The filters are codified by the method proposed by Burckhardt. Three different filters (a classical matched filter, a high-frequency-enhanced filter, and an amplitude-encoded phase-only filter) are generated, and the influence of the quantization levels in such cases is studied. Numerical and experimental results are obtained.

Polychromatic axial behavior of axial apodizing and hyperresolving filters.

The polychromatic behavior in defocused planes produced by different types of axial apodizing and hyperresolvingfilter is studied. The image quality is determined by comparing the illuminance and chromaticity distributions of the aberration free system with different filters and without a filter. The comparison is done in equivalent planes according to the normalized illuminance.

Phase-only filter with improved discrimination.

The optimization of a phase-only filter (POF) in terms of discrimination capability is presented. The notion of a phase-difference histogram and its modification are proposed for selecting the support function of the POF. Some numerical results obtained with the conventional POF and the optimized POF are given. The discrimination capability is increased significantly.

Real-time binary-amplitude phase-only filters.

A real-time binary-amplitude phase-only filter (BAPOF) implemented in available phase-only modulators is presented. The BAPOF has an amplitude transmission equal to one only in a region of support, while the transmission is equal to zero in the complementary region. To implement zero transmission in a phase-only modulator we propose to add a linear phase to the region of support. In this way the correlation desired is obtained off axis. Computer simulations and experimental results obtained with this technique are given.

Control of the polychromatic response of an optical system through the use of annular color filters.

The use of annular color filters as a tool to modify the polychromatic response of an optical system is investigated. The introduction of filters with transmission that depends on the wavelength produces a significant modification of the chromaticity response. In contrast, the position in the pupil of the annuli in which the color filters are placed modifies mainly the illuminance response. The influence of different types of annular color filter on the transverse and axial responses of the aberration-free system is studied.

Different strategies in optical recognition of polychromatic images.

We treat two different problems in the recognition of polychromatic images: (1) recognition of an object with a given shape and color combination; (2) recognition of an object regardless of its color combination. To solve each problem we propose different strategies. The number of filters and the objects to which the filters are matched vary with the strategy. Phase-only filters have been used to achieve recognition of both problems. Computer results are given for different targets and scenes to show the behavior of the proposed strategies.

Color pattern recognition with circular component whitening.

Polychromatic object recognition based on circular whitening preprocessing of red-green-blue components and multichannel matched filtering is described. Computer simulations and experimental results are provided to facilitate recognizing a color target among objects of similar shape but with different color contents. Experimental results are obtained with an optical correlator with two spatial light modulators, one to introduce the scene and the second one to introduce the filter.

Optimal filter approximation by means of a phase-only filter with quantization.

Approximate filters based on a phase-only filter for reliable recognition of objects are proposed. Good light efficiency and discrimination capability close to that of the optimal filter can be obtained. Computer simulation results are presented and discussed.

Nonlinearity effects in the pure phase correlation method in multiobject scenes.

The nonlinearity used in the pure phase correlation method can improve pattern recognition, but it causes high-order harmonics in the correlation plane in the case of multiobject scenes. High-order harmonics and the presence of aliasing may cause false alarms. We show that these effects are strongly diminished when the periodicity in the scene is broken (by different objects, random distribution, etc.).

Polychromatic axial behavior of aberrated optical systems: Wigner distribution function approach.

We propose a new method for the computation of the tristimuli values that correspond to the impulse response along the optical axis provided by an imaging optical system working under polychromatic illumination. We show that all the monochromatic irradiance distributions needed for this calculation can be obtained from the Wigner distribution function associated with a certain version of the pupil function of the system. The use of this single phase-space representation allows us to obtain the above merit function for aberrated systems with longitudinal chromatic aberration and primary spherical aberration. Some numerical examples are given to verify the accuracy of our proposal.