Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor

A traditional Shack-Hartmann wavefront sensor (SHWS) uses a physical microlens array to sample the incoming wavefront into a number of segments and to measure the phase profile over the cross section of a given light beam. We customized a digital SHWS by encoding a spatial light modulator (SLM) with a diffractive optical lens (DOL) pattern to function as a diffractive optical microlens array. This SHWS can offer great flexibility for various applications. Through fast-Fourier-transform (FFT) analysis and experimental investigation, we studied three sampling methods to generate the digitized DOL pattern, and we compared the results. By analyzing the diffraction efficiency of the DOL and the microstructure of the SLM, we proposed three important strategies for the proper implementation of DOLs and DOL arrays with a SLM. Experiments demonstrated that these design rules were necessary and sufficient for generating an efficient DOL and DOL array with a SLM.     

Optical angular mapping for pattern recognition using self-pumped phase conjugation

An optical angular feature mapping of an object for pattern recognition is presented that uses self-pumped phase conjugation followed by a vertical projection. In this method the vertical contour features of an object are most enhanced and vertically projected at each angle as the object is rotated. The vertical enhancement of the contour and the projection are performed optically with self-pumped phase conjugation and a cylindrical lens, respectively. The peaks in the resulting projection at the angle are located and integrated to produce an angular signature function. The signature function is then energy normalized for scale invariance, and pattern recognition is performed by calculation of a cross correlation between two signature functions. The method exhibits invariance to shift, rotation, and variations in scale. Effects of a spatial filter and incident-beam conditions used for phase conjugation are also discussed along with experimental results.     

Probing the wave fronts based on autocorrelation

We proposed an easy method for probing the wave fronts via a typical Fourier transform system. An amplitude only spatial light modulator (SLM) was set on the front focal plane of a Fourier lens to control the wave front transmittance. A CCD was set on the back focal plane of the Fourier lens to record the intensity patterns. The Fourier transform of the intensity pattern is the autocorrelation of the wave front passing through the SLM. When we choose suitable pixels of the SLM to permit the wave front passing through, the information from the wave front illuminating the pixels can be directly extracted from the Fourier transform of the diffraction intensity pattern without complicated calculations. The complex amplitude of the wave front illuminated on the SLM can be probed using the above-mentioned method. The simulation results certifying our theory were also given.     

Radiometric theory of spatial coherence in free-space propagation

The radiometric theory of spatial coherence is presented with special attention to the validity of the approximations on which it is based. A new definition of the transverse coherence area is introduced and shown to be in general agreement with earlier definitions. In free-space propagation the product of the transverse coherence area and the intensity is shown to be constant along rectilinear rays, and, for radiation from uniform Lambert sources, a well-known paraxial formula for the transverse coherence area is extended to the extraparaxial domain. A decrease of the spatial coherence in free-space propagation takes place in regions with an increase of the intensity. For imaging systems this occurs in a finite part of image space whenever a real image of a diffusely radiating, extended object is formed at a finite distance.     

Holographic projection of arbitrary light patterns with a suppressed zero-order beam

We present what is to our knowledge a novel technique for efficient suppression of the zero-order beam inherent in light patterns projected via phase-only computer-generated holograms (CGHs). Encoding a CGH on a spatial light modulator (SLM) with a limited fill factor produces a disturbing zero-order beam at the optical axis. Here, we propose to derive a CGH, which includes holographic information to project a corrective beam that destructively interferes with the zero-order beam. The CGH for projecting arbitrary light patterns plus a corrective beam are derived using the Gerchberg-Saxton algorithm where the iterations impose both amplitude and phase constraints for the target field pattern at the Fourier plane. As proof of principle, we analyze the viability of the technique by simulating the performance when applied on a practical SLM with a limited fill factor, fixed number of phase-shifting pixels, and wavefront distortion associated with the surface roughness of the SLM.     

Spatial shift of spatially modulated light projected on turbid media

This work extends modulated imaging, a recently developed technique based on the projection of structured light on a turbid medium that is able to measure optical properties of the high-scattering medium and perform tomography. We observe that structured light obliquely projected on a turbid medium undergoes a spatial shift during propagation. We propose a method to measure the spatial phase shift of a sinusoidal fringe pattern projected in a turbid medium, and we present a model derived from the diffusion approximation to describe the light propagation. Experimental validation by measurements performed on liquid phantoms is presented.     

Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator

We present an analysis of the performance limit of an adaptive multichannel free-space optical interconnect based on a spatial light modulator (SLM). The SLM function is to provide an active alignment of the signal beam in the detector plane. A thorough cross-talk analysis based on the diffractive properties of an ideal SLM in an isoplanatic optical system is shown. We analyze the performance in terms of the bit-error rate (BER) due to cross talk between different channels in the optical interconnect for different alignment states and for different phase-modulation schemes.     

Laser with rapid tuning of the spectrum shape

We have studied a laser system with quick electronic tuning of the spectrum shape and continuous distribution. The proposed method is based on separate control of phase and amplitude spatial distributions of resonator transmittance. Evolution of the spectral function of the diffractively coupled dispersive resonators and the model for the formation of the resonator with the spectral function given by its moments are studied theoretically. The synthesis of continuous spectra is investigated experimentally in the laser with a novel control element including a spatial acousto-optic modulator and a tunable lens telescope.     

Optical synthetic aperture radar

A method is proposed for increasing the resolution of an object and overcoming the diffraction limit of an optical system installed on top of a moving imaging system, such as an airborne platform or satellite. The resolution improvement is obtained via a two-step process. First, three low resolution differently defocused images are captured and the optical phase is retrieved using an improved iterative Gershberg–Saxton based algorithm. The phase retrieval allows numerical back propagation of the field to the aperture plane. Second, the imaging system is shifted and the first step is repeated. The obtained optical fields at the aperture plane are combined and a synthetically increased lens aperture is generated along the direction of movement, yielding higher imaging resolution. The method resembles a well-known approach from the microwave regime called the synthetic aperture radar in which the antenna size is synthetically increased along the platform propagation direction. The proposed method is demonstrated via Matlab simulation as well as through laboratory experiment.     

Real-time speckle interferometry fringe formation with an adaptive phase mask

We describe what we believe is a novel speckle-pattern interferometry method of applying a spatial light modulator (SLM) as an adaptive phase mask to obtain real-time fringes of a deformed object without using conventional correlation methods of electronic subtraction or addition. The method is to use a SLM to cancel initial phase in the speckled image before the object is deformed. The fringes from the deformed object can be visualized directly after the initial phase has been canceled. A commercial liquid-crystal television is used as a SLM. The performance of using this SLM in an out-of-plane speckle interferometer is demonstrated.     

On a Bayesian approach to coherent radar imaging

In coherent imaging the object of interest is complex but only its amplitude is to be estimated. The object phase yields nuisance variables and in a proper Bayesian approach it is necessary to obtain a phaseless likelihood function. We investigate a two-dimensional case in which the target object is modelled as a collection of point scatterers having independent random phases. The phaseless likelihood function is determined exactly for a configuration of data samples in a uniformly spaced square array in spatial frequency when the target scatterers are confined to lattice positions of a “matched” spatial array. It is determined approximately when the target scatterers are arbitrarily positioned, at most one per conventional resolution cell. The relation between maximum likelihood and conventional Fourier transform imaging is explored and the feasibility of a CLEAN algorithmic technique in coherent imaging is considered.©1993 John Wiley & Sons Inc     

Modulation transfer function measurement method for electrically addressed spatial light modulators

The modulation transfer function (MTF), when used with amplitude modulation (m(A)) data, is a vital coherent optical performance measure for a spatial light modulator (SLM). A new image plane amplitude MTF (MTF(A)) measurement method is presented for electrically addressed SLMs. It involves digital analysis of the output image of a square-wave pattern written onto the SLM. Modulation-level effects are also addressed. Optical laboratory results are presented for two liquid-crystal SLMs. The need to consider amplitude rather than intensity modulation (when coherent optical processing applications are considered) is noted in terms of SLM biasing.     

Amplitude Apodizers Encoded onto Fresnel Lenses Implemented on a Phase-Only Spatial Light Modulator

We show that both a lens and a nonuniform amplitude transmission filter can be encoded simultaneously onto a twisted nematic liquid-crystal spatial light modulator (SLM) working in the phase-only mode. The inherent equivalent apodization that is due to the pixelated structure of the SLM is compensated for. In addition, different types of nonuniform transmission pupil such as transverse apodizing, transverse hyperresolving, and axial hyperresolving (multifocusing) filters are implemented. The excellent agreement between numerical and experimental results shows the capability of this method to encode amplitude apodizers on a phase-only SLM.     

Phase retrieval via spatial light modulator phase modulation in 4f optical setup: numerical inverse imaging with sparse regularization for phase and amplitude

The 4f optical setup is considered with a wave field modulation by a spatial light modulator located in the focal plane of the first lens. Phase as well as amplitude of the wave field are reconstructed from noisy multiple-intensity observations. The reconstruction is optimal due to a constrained maximum likelihood formulation of the problem. The proposed algorithm is iterative with decoupling of the inverse of the forward propagation of the wave field and the filtering of phase and amplitude. The sparse modeling of phase and amplitude enables the advanced high-accuracy filtering and sharp imaging of the complex-valued wave field. Artifacts typical for the conventional algorithms (wiggles, ringing, waves, etc.) and attributed to optical diffraction can be suppressed by the proposed algorithm.     

Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states

As a proof of concept, we experimentally demonstrate multiplexing of free-space optical signals in multiple channels labeled with different states of orbital angular momentum. The multiplexing process is carried out by a dynamic liquid-crystal spatial light modulator, while the phase function is calculated by an iterative algorithm. A binary amplitude computer-generated hologram serves as a demultiplexer.     

Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator

Parallel phase-shifting digital holography using a phase-mode spatial light modulator (SLM) is proposed. The phase-mode SLM implements spatial distribution of phase retardation required in the parallel phase-shifting digital holography. This SLM can also compensate dynamically the phase distortion caused by optical elements such as beam splitters, lenses, and air fluctuation. Experimental demonstration using a static object is presented.     

Three-dimensional phase step profilometry with a multicore optical fiber

This paper demonstrates the feasibility of using phase stepping and a multicore optical fiber to calculate an object's depth profile. An interference pattern is projected by an optical fiber onto the object. The distorted interference pattern containing the object information is captured by a CCD camera and processed using a phase step interferometry method. The phase step method is less computationally intensive compared to two-dimensional Fourier transform profilometry and provides more accuracy when measuring objects of high frequency spatial variations.     

Speckle dynamics for intensity-modulated illumination

We analyze the dynamics of laser speckle patterns, designed for sensing with a receiver, based on spatial filtering. The speckle translation arises after free-space propagation of light scattered from nonspecular surfaces of a solid object in motion. The speckle pattern is manipulated by modulating the intensity of the coherent light, illuminating the target. The space-time normalized cross covariance of speckle patterns incident on the spatial sensor is calculated for the field distribution of three Gaussian beams having arbitrary directions and separations when incident on the target. The modulation of the intensity distribution at the target introduce a higher spatial frequency component in the speckle pattern. The theoretical analysis provides the statistical parameters for both the speckles and the higher spatial frequency component. The analysis reveals that the speckles and the higher spatial frequency component do not necessarily translate as a rigid structure. The theoretical findings are supported by measurements.     

White-light-modified Talbot array illuminator with a variable density of light spots

A flexible array illuminator, comprising only two conventional optical elements, with a variable density of bright white-light spots is presented. The key to our method is to obtain with a single diffractive lens an achromatic version of different fractional Talbot images, produced by free-space propagation, of the amplitude distribution at the back focal plane of a periodic refractive microlens array under a broadband point-source illumination. Some experimental results of our optical procedure are also shown.     

Synthesis of three-dimensional light fields with binary spatial light modulators

Computation of a binary spatial light modulator (SLM) pattern that generates a desired light field is a challenging quantization problem for which several algorithms have been proposed, mainly for far-field or Fourier plane reconstructions. We study this problem assuming that the desired light field is synthesized within a volumetric region in the non-far-field range after free space propagation from the SLM plane. We use Fresnel and Rayleigh-Sommerfeld scalar diffraction theories for propagation of light. We show that, when the desired field is confined to a sufficiently narrow region of space, the ideal gray-level complex-valued SLM pattern generating it becomes sufficiently low pass (oversampled) so it can be successfully halftoned into a binary SLM pattern by solving two decoupled real-valued constrained halftoning problems. Our simulation results indicate that, when the synthesis region is considered, the binary SLM is indistinguishable from a lower resolution full complex gray-level SLM. In our approach, free space propagation related computations are done only once at the beginning, and the rest of the computation time is spent on carrying out standard image halftoning.