Don M. Cottrell

Encoding amplitude information onto phase-only filters

We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.

Image processing with the radial Hilbert transform: theory and experiments.

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.

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator.

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.

Complete polarization control of light from a liquid crystal spatial light modulator.

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

Optical correlator performance of binary phase-only filters using Fourier and Hartley transforms

Theoretical studies of the performance capabilities of binary phase-only filters (BPOFs), constructed using both Fourier and Hartley transforms, are presented. A thorough analysis of the Fourier BPOF is given. We show that, although BPOFs constructed using Fourier transforms perform well in optical correlator systems, they are also subject to additional noise sources and have the possibility of generating large false correlation signals. We then present an analysis of BPOFs constructed using the Hartley transform. We show that BPOFs made using the Hartley transform provide superior false correlation rejection and more uniformly sized correlation signals for heavily multiplexed BPOFs, compared with those made using the Fourier transform. We also present a technique for constructing Hartley BPOFs. Therefore, although it is well known that the quality of the correlation signal depends on the object, this work demonstrates that the quality of the correlation signal can also depend on the technique used in the synthesis of the BPOF.

Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects

We report on the characteristics of a newly developed high- resolution (6403480 pixels) parallel-aligned liquid crystal spatial light modulator (LCSLM) as a function of wavelength. Phase-only operation over a range of 2p rad is easily achieved by operating at shorter wave- lengths. We also measure an unexpected effect—the transmitted light intensity changes with applied voltage. Our experiments show that thin- film interference and pixel diffraction effects are responsible for this ob- served behavior. The diffraction effect is caused by a nonuniform electric field across each pixel. This nonuniform electric field introduces a blazing effect that changes the intensity distribution in the various diffracted or- ders as a function of applied voltage. These same kinds of effects have been observed with several other twisted-nematic LCSLMs. Because of the complicated polarization effects caused by these twisted-nematic liq- uid crystal devices, however, the diffraction and interference effects are more easily studied using the parallel-aligned LCSLM.

Diffraction-free beams generated with programmable spatial light modulators

Diffraction-free beams are generated by the use of diffractive optical elements written on a spatial light modulator (SLM). By alteration of the pattern placed on the SLM, the axis of propagation can be both shifted laterally and rotated. We present experimental results obtained by use of a magneto-optic SLM.

Nondiffracting interference patterns generated with programmable spatial light modulators.

Nondiffracting beams are of interest for optical metrology applications because the size and shape of the beams do not change as the beams propagate. We have created a generating pattern consisting of a linear combination of two nondiffracting patterns. This pattern forms a nondiffracting interference pattern that appears as a circular array of nondiffracting spots. More complicated multiplexed arrays are also constructed that simultaneously yield two different nondiffracting patterns. We generate these Bessel function arrays with a programmable spatial light modulator. Such arrays would be useful for angular alignment and for optical interconnection applications.

Direct generation of accelerating Airy beams using a 3/2 phase-only pattern.

Accelerated Airy beams have previously been generated using a cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate the Airy beam using a 3/2 phase pattern encoded onto an LCD. Experimental results show a deflection that depends on the square of the distance from the LCD and match theoretical predictions. However the system length is much shorter.

Multiple imaging phase-encoded optical elements written as programmable spatial light modulators

We report a multiple imaging capability of replicated binary Fresnel phase-encoded lenses written on programmable spatial light modulators (SLMs). These lenses produce a large number (up to 9 x 9) of equally intense replica images from either an external object or from a pattern which is encoded onto the SLM along with the phase-encoded lens. Theoretical details and experimental results using the magnetooptic spatial light modulator are presented.