Dual polarization Fourier transform processor using geometric-phase lenses.

This work presents a novel optical system for polarization image processing using geometric-phase (Pancharatnam-Berry) lenses. Such lenses are half-wave plates where the orientation of the fast (slow) axis follows a quadratic relation with the radial coordinate, and they present the same focal length but opposite sign for left and right circular polarizations. Therefore, they split an input collimated beam in a converging beam and a diverging beam with opposite circular polarizations. This coaxial polarization selectivity introduces a new degree of freedom in optical processing systems and makes it interesting for imaging and filtering applications that require polarization sensitivity. Here we profit from these properties to build an optical Fourier filter system with polarization sensitivity. A telescopic system is used to have access to two real Fourier transform planes, one for each circular polarization. A second symmetric optical system is used to recombine the two beams onto a single final image. As a result, polarization sensitive optical Fourier filtering can be applied, as demonstrated with simple bandpass filters.

Retrieving the phase of diffraction orders generated with tailored gratings.

A technique is performed to quantitatively evaluate the intensity and phase of the diffraction orders generated by tailored phase gratings displayed onto a liquid-crystal spatial light modulator (LC-SLM). The SLM displays the grating together with a lens to obtain the Fourier transform. The setup is converted into a polarization common-path interferometer by simply rotating a polarizer. This configuration allows a phase-shifting interferometry algorithm to be applied to retrieve the phase of the diffraction orders. The quadratic phase arising in the system, which must be subtracted, is calibrated using triplicator gratings of varying periods. Various tailored designs with controlled phase shift between diffraction orders are experimentally tested to prove the advantage and simplicity of the technique.

Achromatic linear retarder with tunable retardance.

We present a universal design and proof-of-concept of a tunable linear retarder of uniform wavelength response in a broad spectral range. It consists of two half-wave retarders (HWR) between two quarter-wave retarders (QWRs), where the uniform retardance can be tuned continuously by simply rotating one of the HWRs. A proof-of-concept of this design is built by using commercially available Fresnel rhomb retarders that provide retardation with almost wavelength uniformity in the visible and near infrared from 450 to 1550 nm. The design is universal, since other achromatic QWRs and HWRs could also be employed. The system is experimentally demonstrated to control the state of polarization of a supercontinuum laser.

Optical retarder system with programmable spectral retardance.

An optical system that works as a retarder waveplate with programmable spectral retardance is proposed. The system is based on a pixelated liquid crystal on silicon (LCoS) spatial light modulator (SLM). The input light beam is spectrally dispersed and different spectral components are projected onto different pixels of the LCoS-SLM. A different retardance is then addressed for each pixel, adapted to the incoming wavelength. Light reflected from the SLM is then recombined by the same setup. In this way a programmable polarization spectrum can be encoded. We illustrate the broadband characterization that is required for proper use of the system. Then several examples are shown, including spectral compensation to yield retarders with constant retardance, retarders with abrupt changes in the spectral retardance function, or bandpass variable retarder filters. The system is also demonstrated to provide programmable light spectrum generation.

Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM.

Multiple internal reflection effects on the optical modulation of a commercial reflective parallel-aligned liquid-crystal on silicon (PAL-LCoS) spatial light modulator (SLM) are analyzed. The display is illuminated with different wavelengths and different angles of incidence. Non-negligible Fabry-Perot (FP) effect is observed due to the sandwiched LC layer structure. A simplified physical model that quantitatively accounts for the observed phenomena is proposed. It is shown how the expected pure phase modulation response is substantially modified in the following aspects: 1) a coupled amplitude modulation, 2) a non-linear behavior of the phase modulation, 3) some amount of unmodulated light, and 4) a reduction of the effective phase modulation as the angle of incidence increases. Finally, it is shown that multiple reflections can be useful since the effect of a displayed diffraction grating is doubled on a beam that is reflected twice through the LC layer, thus rendering gratings with doubled phase modulation depth.

Liquid crystal spatial light modulator with very large phase modulation operating in high harmonic orders.

Unusually large phase modulation in a commercial liquid crystal spatial light modulator (LCSLM) is reported. Such a situation is obtained by illuminating with visible light a device designed to operate in the infrared range. The phase modulation range reaches 6π radians in the red region of the visible spectrum and 10π radians in the blue region. Excellent diffraction efficiency in high harmonic orders is demonstrated despite a concomitant and non-negligible Fabry-Perot interference effect. This type of SLM opens the possibility to implement diffractive elements with reduced chromatic dispersion or chromatic control.

Programmable color tuning of a multiline laser by means of a twisted nematic liquid crystal display.

An optical system useful to tune in a controlled way the color of a triline argon krypton (Ar-Kr) laser by means of a twisted nematic liquid crystal display (TNLCD) is presented. The optical setup employs a 4f system and two blazed gratings to first separate and then recombine the spectrum of the light beam. The TNLCD is included in the intermediate focal plane operating in the amplitude modulation mode to control the relative transmission of each spectral line. The resulting color is accurately predicted by using a previously developed physical model of the spectral and voltage dependence of the TNLCD birefringence. By simply changing the gray level image addressed to the display, the Ar-Kr laser is color modulated at a video rate, thus becoming an interesting, reconfigurable, coherent light source for applications such as multicolor holography or color inspection.

Generation of Bessel beam arrays through Dammann gratings.

In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.

Intensity invariant nonlinear correlation filtering in spatially disjoint noise.

We analyze the performance of a nonlinear correlation called the Locally Adaptive Contrast Invariant Filter in the presence of spatially disjoint noise under the peak-to-sidelobe ratio (PSR) metric. We show that the PSR using the nonlinear correlation improves as the disjoint noise intensity increases, whereas, for common linear filtering, it goes to zero. Experimental results as well as comparisons with a classical matched filter are given.

Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings.

We analyze the performance of a ferroelectric liquid crystal on silicon display (FLCoS) as a binary polarization diffraction grating. We analyze the correspondence between the two polarization states emerging from the displayed grating and the polarization and intensity of the diffracted orders generated at the Fourier diffraction plane. This polarization-diffraction analysis leads, in a simple manner, to configurations yielding binary amplitude or binary phase modulation by incorporating an analyzer on the reflected beam. Based on this analysis, we present two useful variations of the polarization configuration. The first is a simplification using a single polarizer, which provides equivalent results for amplitude or phase modulation as the more general operational mode involving two polarizers. The second variation is proposed to compensate the reduction of the diffraction efficiency when the operating wavelength differs from the design one (for which the FLCoS liquid-crystal layer acts as a half-wave plate). In this situation we show how the ideal grating performance can be recovered in spite of the phase-shift mismatch originated by chromatic dispersion. In all cases, we provide experimental results that verify the theoretical analyses.

Three-dimensional mapping and range measurement by means of projected speckle patterns.

We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.

Spherical nonlinear correlations for global invariant three-dimensional object recognition.

We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D filtering based on nonlinear operations between spherical correlations to achieve both scale- and rotation-invariant 3D object recognition.

Improved locally adaptive least-squares detection of differences in images.

We introduce a method for change detection under nonuniform changes of intensity using an improved least-squares method. A locally adaptive normalizing window is correlated with the two images, and a morphological postprocessing is then applied to isolate objects that have been added or removed from the scene. We use a modification of the least-squares solution to get rid of clutter caused by intensity changes that do not satisfy the model assumed for the least-squares solution.

Phase Fourier vector model for scale invariant three-dimensional image detection.

A scale invariant 3D object detection method based on phase Fourier transform (PhFT) is addressed. Three-dimensionality is expressed in terms of range images. The PhFT of a range image gives information about the orientations of the surfaces in the 3D object. When the object is scaled, the PhFT becomes a distribution multiplied by a constant factor which is related to the scale factor. Then 3D scale invariant detection can be solved as illumination invariant detection process. Several correlation operations based on vector space representation are applied. Results show the tolerance of detection method to scale besides discrimination against false objects.

Synthetic aperture superresolution with multiple off-axis holograms.

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.

Joint transform correlator with spatial code division multiplexing.

A joint transform correlator may suffer from overlapping of the zero diffraction order of the output, which does not contain relevant information, and the correlation peaks that appear in the first diffraction orders if objects are not sufficiently separated. Such overlapping significantly reduces the signal-to-noise ratio of the identification process. We propose a novel approach based on code division multiplexing technique in which the contrast of the identification peaks is significantly enhanced. The approach does not include placing the two objects side by side but rather includes code multiplexing them. Moreover, the code division multiplexing technique allows the space-bandwidth product to be improved. Optical implementation results are given.

Three-dimensional object detection under arbitrary lighting conditions.

A novel method of 3D object recognition independent of lighting conditions is presented. The recognition model is based on a vector space representation using an orthonormal basis generated by the Lambertian reflectance functions obtained with distant light sources. Changing the lighting conditions corresponds to multiplying the elementary images by a constant factor and because of that, all possible lighting views will be elements that belong to that vector space. The recognition method proposed is based on the calculation of the angle between the vector associated with a certain illuminated 3D object and that subspace. We define the angle in terms of linear correlations to get shift and illumination-invariant detection.

Superresolved imaging in digital holography by superposition of tilted wavefronts.

A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.

Superresolution using gray level coding.

In this paper we describe a super-resolving approach based upon gray level coding of the information. Thus, the imaged object should have limited number of gray levels. The proposed approach overcomes the resolution limitations caused either by the optics or by the finite size of the detector. In contrast to other existing super resolution techniques that use time or wavelength multiplexing, in this approach one does not need to pay neither in temporal nor in wavelength degrees of freedom, but in intensity dynamic range. After the gray coding and the imaging, the high frequency spatial resolution features are decoded using the decoding gray level lookup table.

Spatial information transmission using orthogonal mutual coherence coding.

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable cost.