Jones matrix treatment for optical Fourier processors with structured polarization.

We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response.

Time-resolved Mueller matrix analysis of a liquid crystal on silicon display.

We present a full polarimetric characterization of a liquid crystal on silicon (LCoS) display, with time resolution measurements below the frame period of the device. This time-resolved analysis shows evidence of temporal fluctuations in the millisecond range in the state of polarization of the beam reflected by the display. We demonstrate that light reflected by the display is maintained fully polarized, but these temporal fluctuations result in an effective depolarization effect when detectors with long time integration intervals are used in the characterization of the display.

Tailoring the depth of focus for optical imaging systems using a Fourier transform approach.

We show how to tailor the depth of focus for an optical system using pupil functions obtained from a Fourier transform approach. These complex amplitude and phase pupil functions are encoded onto a single liquid-crystal spatial light modulator. Experimental results show excellent agreement with theory and indicate the power of this approach.

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display.

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display.

Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters.

To study the three-dimensional (3-D) behavior produced by complex filters, we have extended the expressions for the axial and the transverse gain to the case in which the best image plane is not near the paraxial focus. Super-Gaussian phase filters are proposed to control the 3-D image response of an optical system. Super-Gaussian phase filters depend on several parameters that modify the shape of the phase filter, producing tunable control of the 3-D response of the optical system.

Complex encoding of rotation-invariant filters onto a single phase-only spatial light modulator.

The accuracy and flexibility of the technique proposed by Davis et al. [Appl. Opt.

Rotation invariant color pattern recognition by use of a three-dimensional Fourier transform.

Recently, the use of three-dimensional correlation for multichannel pattern recognition has been introduced. In this work we propose the use of circular harmonic components with this new technique to obtain invariance under target rotations. The differences between this method and the previous use of circular harmonic filters for multichannel images are discussed.

Phase-only filtering on the three-dimensional Fourier spectrum of color images.

We propose what is to our knowledge a novel technique for filtering a two-dimensional multichannel color image based on its interpretation as a three-dimensional (3D) signal and the application of a 3D Fourier transform. The color image is considered to have the two usual spatial coordinates with the color distribution as the third dimension of the signal. This approach permits the 3D generalization of the usual phase-only filter and phase correlation, and color pattern recognition can be performed by means of a 3D correlation.

Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices.

We study the modulation of programmable birefringent devices when they are illuminated by elliptically polarized light. We apply the theory to liquid-crystal display panels (LCDs). We consider the setups at the input and the output sides of the LCD as polarization-state generators (PSGs) or detectors (PSDs).

Convergent optical correlator aligment based on frequency filtering.

The convergent correlator is widely used but it presents the drawback of the alignment requirements: fine focusing of the input scene Fourier transform on the filter plane, filter centering, scaling the scene Fourier transform to match the filter size, and azimuth matching of the filter with the input scene. We propose a set of tests to obtain a precise alignment of the convergent correlator. These methods are based on frequency filtering properties and they are applicable either for amplitude input or for phase-encoded input.