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In this work, we discuss the interest of using the indices of polarimetric purity (IPPs) as a criterion for the characterization and classification of depolarizing samples. We prove how differences in the depolarizing capability of samples, not seen by the commonly used depolarization index P_Δ, are identified by the IPPs. The above-stated result is analyzed from a theoretical point of view and experimentally verified through a set of polarimetric measurements. We show how the approach presented here can be useful in easily synthetizing depolarizing samples with controlled depolarizing features, just by properly combining low-cost fully polarizing elements (such as linear retarders or polarizers).

We propose a new complete snapshot Stokes polarimeter based on a single biaxial crystal. It presents different strengths (snapshot, complete polarimetric measurements, large data redundancy, and high sensitivity) in a simple and compact optical arrangement. The polarimeter is experimentally implemented and analyzed in terms of accuracy and repeatability.

This Letter proposes a new optical architecture based on a double-sideband filter, simultaneously applied at the Fourier plane, for inline digital holography. The proposed architecture not only allows removal of the conjugate images in the reconstruction process but also reduces the distortions that usually appear when using a single-sideband filter. We first introduce the mathematical model that explains the method and then describe the optical setup used for the implementation. The optical system includes a parallel aligned liquid crystal display placed at the Fourier plane that simultaneously filters positive and negative frequencies, when properly combined with linear polarizers. This feature makes the device useful to register dynamic processes. Finally, we tested the setup by registering a holographic movie of microscopic moving objects placed at different planes.

An optical setup able to generate arbitrary states of polarization (SOPs) with customized degree of polarization is presented in this Letter. Compared with the few alternatives existing in literature, it presents an easy-to-build optical setup and leads to a superior performance. In fact, experimental results are presented, providing an accurate control for the generation of SOPs (maximum error of 1.7% and 3.3% for ellipticity and azimuth, respectively) as well as for the associated degree of polarization (full experimental variation from 1 up to 0.003, with a 1.7% maximum error). The system proposed may be useful for different applications, for example, for polarimeters testing, speckle metrology, and biological applications.

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.

We propose a new technique that is able to generate a light beam with a controlled state of polarization (SoP) and a customized degree of polarization (DoP). The technique relies on the fact that effective depolarization can be achieved by temporally averaging a time-dependent SoP. Our proposed setup is based on a ferroelectric liquid crystal panel of retardance λ/2, with a fast polarization switching capability (33 Hz). A mathematical basis describing the experiment is given. In addition, simulation data is discussed, showing the possibility of generating any SoP with full control of the DoP. Finally, to prove the potential of the invention proposed, experimental results are provided as well, reaching an experimental minimum DoP of 0.14.

A method for polarization metrology based on the conical refraction (CR) phenomenon, occurring in biaxial crystals, is reported. CR transforms an input Gaussian beam into a light ring whose intensity distribution is linked to the incoming polarization. We present the design of a division-of-amplitude complete polarimeter composed of two biaxial crystals, whose measurement principle is based on the CR phenomenon. This design corresponds to a static polarimeter, that is, without mechanical movements or electrical signal addressing. Only one division-of-amplitude device is required, besides the two biaxial crystals, to completely characterize any state of polarization, including partially polarized and unpolarized states. In addition, a mathematical model describing the system is included. Experimental images of the intensity distribution related to different input polarization states are provided. These intensity patterns are compared with simulated values, proving the potential of polarimeters based on biaxial crystals.

We report a method to maximize the broadband modulation diffraction efficiency of liquid-crystal spatial light modulators for polychromatic applications requiring a wide range of wavelengths. An optimized encoding pattern based on the minimum Euclidean projection principle is applied in order to increase the diffraction efficiency at large wavelengths that exhibit phase modulation depth lower than 2π. We demonstrate modulation efficiencies over 80% on a wavelength range from 454 to 633 nm, which can reach up to 98% when the range is reduced to 60 nm. Experimental results are shown to confirm the calculations.

Improved expressions are given for the performance parameters for transverse and axial gains for complex pupil filters. These expressions can be used to predict the behavior of filters that give a small axial shift in the focal intensity maximum and also predict the changes in gain for different observation planes.

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.

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. The filters are capable of producing a wide range of optical effects: transverse superresolution with high depth of focus, 3-D superresolution, and transverse apodization with different axial responses.

We propose a new method for evaluating and correcting aberrations in a Vander Lugt correlator. The technique is achieved with liquid-crystal displays of the correlator and allows the task to be performed in situ. We present the theory on which the method is based and the experimental results that we obtained by applying it in a convergent correlator.

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.

Amplitude-transmitting filters for apodizing and hyperresolving applications can be easily implemented by use of a two-dimensional programmable liquid-crystal spatial light modulator operating in a transmission-only mode. Experimental results are in excellent agreement with theoretical predictions. This approach can permit the analysis of various filter designs and can allow the filters to be changed rapidly to modify the response of an optical system.

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.

We propose an input-image preprocessing method consisting of homogenization of the image to improve the discrimination capability of a correlation-based recognition process. This method is an approximation of the optimal filter. It offers the advantage that correlation with the preprocessed images can easily be implemented in an optical correlator working with phase-only spatial light modulators.