Approximating fully complex spatial modulation with pseudorandom phase-only modulation

Acousto-optic holography for pseudo-two-dimensional dynamic light patterning

Optical systems use acousto-optic deflectors (AODs) mostly for fast angular scanning and spectral filtering of laser beams. However, AODs may transform laser light in much broader ways. When time-locked to the pulsing of low repetition rate laser amplifiers, AODs permit the holographic reconstruction of 1D and pseudo-two-dimensional (ps2D) intensity objects of rectangular shape by controlling the amplitude and phase of the light field at high (20-200 kHz) rates for microscopic light patterning. Using iterative Fourier transformations (IFTs), we searched for AOD-compatible holograms to reconstruct the given ps2D target patterns through either phase-only or complex light field modulation. We previously showed that phase-only holograms can adequately render grid-like patterns of diffraction-limited points with non-overlapping diffraction orders, while side lobes to the target pattern can be cured with an apodization mask. Dense target patterns, in contrast, are typically encumbered by apodization-resistant speckle noise. Here, we show the denoised rendering of dense ps2D objects by complex acousto-optic holograms deriving from simultaneous optimization of the amplitude and phase of the light field. Target patterns lacking ps2D symmetry, although not translatable into single holograms, were accessed by serial holography based on a segregation into ps2D-compatible components. The holograms retrieved under different regularizations were experimentally validated in an AOD random-access microscope. IFT regularizations characterized in this work extend the versatility of acousto-optic holography for fast dynamic light patterning.

Generation of combined half-integer Bessel-like beams using synthetic phase holograms

We discuss the generation of combined half-integer Bessel-like (CHB) beams using synthetic phase holograms (SPHs). We assess the efficiency and accuracy of the SPHs, in the task of generating CHB beams. The proposal is illustrated by the implementation of CHB beams, which are experimentally generated in a setup based on a phase spatial light modulator. Also, we analyze, numerically and experimentally, the propagation of the generated CHB beams. As the main result, the SPHs are able to generate several CHB beams with relatively high accuracy. Additionally, it is obtained that the efficiency values of the SPHs are close to the theoretical predictions.

Generation of periodic and quasi-periodic two-dimensional non-diffractive beams with inhomogeneous polarization

In this work, two-dimensional periodic and quasi-periodic non-diffractive spatial inhomogeneous polarization optical fields are generated, numerically and experimentally, by the superposition of multiple plane waves with different polarizations. For the experimental implementation of the fields, synthetic phase holograms are employed in conjunction with half-wave and quarter-wave retarder films as polarization modulators. The obtained spatially inhomogeneous polarization optical fields show good quality and are in good agreement with numerical results. The proposed method is highly efficient for the generation of these types of optical fields.

Generation of vector beams using synthetic phase holograms

We discuss a class of synthetic phase holograms (SPHs) applied to the generation of vector fields. Each SPH encodes the transverse components of the vector field, modulated by different linear phase carriers. Such components, which are spatially separated by the carriers, are modulated by appropriate orthogonal polarizations. A final stage that makes the components collinear allows the generation of the vector field. We assess the efficiency and accuracy of the different SPHs, in the task of generating vector fields. The proposal is illustrated by the implementation of vector Bessel beams, which are experimentally generated in a setup based on a phase spatial light modulator.

Amplitude-phase optimized long depth of focus femtosecond axilens beam for single-exposure fabrication of high-aspect-ratio microstructures

Fabrication of high-aspect-ratio (HAR) micro/nanostructures by two-photon polymerization (TPP) has become a hot topic because of the advantages of ultra-high resolution and true 3D printing ability. However, the low efficiency caused by point-by-point scanning strategy limits its application. In this Letter, we propose a strategy for the rapid fabrication of HAR microstructures by combining TPP with an amplitude-phase optimized long depth of focus laser beam (LDFB). The optimization of the LDFB is implemented by modulating the amplitude and phase on a phase-only spatial light modulator, which can suppress the side lobe and smooth energy oscillations effectively. The LDFB is used for rapid fabrication of HAR micropillars and various microstructures, which greatly increases the fabrication efficiency. As a demonstration, several typical HAR microstructures such as assemblies, microchannels, microtubes, and cell scaffolds are prepared. Moreover, the microcapture arrays are rapidly fabricated for the capture of microspheres and the formation of microlens arrays, which show focusing and imaging ability.

Low-noise high-efficiency double-phase hologram by multiplying a weight factor

This Letter describes a method of generating a phase-only hologram, which improves the lack of diffraction efficiency and peripheral noise phenomenon, which is a problem of the existing double-phase hologram (DPH) method. The proposed weight factor DPH method can be obtained by a simple matrix operation, so there is no need for additional computing power. The optimal weight factor value depends on the image size, so we have found the optimal value for each image size. The numerical simulation and optical experiments were conducted to compare the images generated using the proposed weigh factor DPH method, the existing DPH method, and the random phase method. The peak signal-to-noise ratio of the images obtained through the proposed weight factor is improved by 14.6% compared to the existing DPH.

Generation of multifocal irradiance patterns by using complex Fresnel holograms

We experimentally demonstrate Fresnel holograms able to produce multifocal irradiance patterns with micrometric spatial resolution. These holograms are assessed from the coherent sum of multiple Fresnel lenses. The utilized encoded technique guarantees full control over the reconstructed irradiance patterns due to an optimal codification of the amplitude and phase information of the resulting complex field. From a practical point of view, a phase-only spatial light modulator is used in a couple of experiments addressed to obtain two- and three-dimensional distributions of focal points to excite both linear and non-linear optical phenomena.

Generation of vector Bessel beams with diffractive phase elements based on the Jacobi-Anger expansion

We report the design and optimization of a diffractive phase element whose phase modulation is derived from the Jacobi-Anger relation, which allows the simultaneous generation of multiple scalar Bessel beams of different integer orders. In addition, by the appropriate treatment of a couple of such Bessel beams, we generate a vector Bessel beam of arbitrary order m. This beam is constructed by the collinear superposition of the scalar Bessel beam modes of orders m-1 and m+1, with circular orthogonal polarizations. We demonstrate experimentally both the simultaneous generation of the multiple scalar Bessel beams and the generation of vector Bessel beams of orders m=0 and m=1. These tasks are performed in an optical setup based on a pixelated liquid-crystal spatial light modulator.

Comparison of beam generation techniques using a phase only spatial light modulator

Whether in art or for QR codes, images have proven to be both powerful and efficient carriers of information. Spatial light modulators allow an unprecedented level of control over the generation of optical fields by using digital holograms. There is no unique way of obtaining a desired light pattern however, leaving many competing methods for hologram generation. In this paper, we test six hologram generation techniques in the creation of a variety of modes as well as a photographic image: rating the methods according to obtained mode quality and power. All techniques compensate for a non-uniform mode profile of the input laser and incorporate amplitude scaling. We find that all methods perform well and stress the importance of appropriate spatial filtering. We expect these results to be of interest to those working in the contexts of microscopy, optical trapping or quantum image creation.

Encoding complex fields by using a phase-only optical element

We show that the amplitude and phase information from a two-dimensional complex field can be synthesized from a phase-only optical element with micrometric resolution. The principle of the method is based on the combination of two spatially sampled phase elements by using a low-pass filter at the Fourier plane of a 4-f optical system. The proposed encoding technique was theoretically demonstrated, as well as experimentally validated with the help of a phase-only spatial light modulator for phase encoding, a conventional CMOS camera to measure the amplitude of the complex field, and a Shack-Hartmann wavefront sensor to determine its phase.

Spatial filters for complex wavefront modulation

In this paper we propose a method to generate independent and simultaneous phase and amplitude modulation by a phase-only spatial light modulator and Fourier filtering. The incident light is modulated by a suitable phase pattern containing high spatial frequencies. The modulated light is transmitted through a 4f optical system having an appropriate spatial filter in the Fourier plane in order to synthesize the expected complex modulated wavefront on the output of the system. We propose a simple method to generate spatial filters applicable for the phase-only to complex modulated wavefront conversion. We analyze the quality of the output image related to the ideal wavefront using the proposed filters. We show that more efficient complex modulation can be realized by the proposed method than by the earlier solutions.

Holographic generation of a class of nondiffracting fields with optimum efficiency

We discuss the accurate generation of complex optical fields using phase holograms that provide the optimum diffraction efficiency. In each considered case, the phase modulation of the employed hologram is identical to the phase of the desired optical field. We show that periodic and quasiperiodic nondiffracting optical fields, mathematically obtained through the superposition of multiple plane waves, can be generated with high fidelity using this approach.

Efficient generation of periodic and quasi-periodic non-diffractive optical fields with phase holograms

The superposition of multiple plane waves with appropriate propagation vectors generates a periodic or quasi-periodic non-diffractive optical field. We show that the Fourier spectrum of the phase modulation of this field is formed by two disjoint parts, one of which is proportional to the Fourier spectrum of the field itself. Based on this result we prove that the non-diffractive field can be generated, with remarkable high accuracy and efficiency, in a Fourier domain spatial filtering setup, using a synthetic phase hologram whose transmittance is the phase modulation of the field. In a couple of cases this result is presented analytically, and in other cases the proof is computational and experimental.

A high-resolution, adaptive beam-shaping system for high-power lasers

A high-resolution, high-precision beam-shaping system for high-power-laser systems is demonstrated. A liquid-crystal-on-silicon spatial light modulator is run in closed-loop to shape laser-beam amplitude and wavefront. An unprecedented degree of convergence is demonstrated, and important practical issues are discussed. Wavefront shaping for the applications in OMEGA EP laser is demonstrated, and other interesting examples are presented.

Zero order synthetic hologram with a sinusoidal phase carrier for generation of multiple beams

We discuss a phase synthetic hologram, for encoding arbitrary complex fields, whose design is based on a sinusoidal phase grating with a spatially modulated phase depth. An important feature of the hologram is that it encodes the complex field at the zero diffraction order of the carrier grating. The smoothness of this sinusoidal carrier grating facilitates the implementation of the hologram with a pixelated spatial light modulator. We take advantage of the hologram reconstruction at the zero-diffraction order for the simultaneous generation of a collection of complex beams.

Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators

We show that computer generated holograms, implemented with amplitude-only liquid crystal spatial light modulators, allow the synthesis of fully complex fields with high accuracy. Our main discussion considers modified amplitude holograms whose transmittance is obtained by adding an appropriate bias function to the real cosine computer hologram of the encoded signal. We first propose a bias function, given by a soft envelope of the signal modulus, which is appropriate for perfect amplitude modulators. We also consider a second bias term, given by a constant function, which results appropriate for modulators whose amplitude transmittance is coupled with a linear phase modulation. The influence of the finite pixel size of the spatial light modulator is compensated by digital pre-filtering of the encoded complex signal. The performance of the discussed amplitude CGHs is illustrated by means of numerical simulations and the experimental synthesis of high order Bessel beams.

Computer-generated holograms with optimum bandwidths obtained with twisted-nematic liquid-crystal displays

We discuss a computer-generated hologram for encoding arbitrary complex modulation based on a commercial twisted-nematic liquid-crystal display. This hologram is implemented with the constrained complex modulation provided by the display in a phase-mostly configuration. The hologram structure and transmittance are determined to obtain on-axis signal reconstruction, maximum bandwidth, optimum efficiency, and high signal-to-noise ratio. We employed the proposed holographic code for the experimental synthesis of first-order Bessel beams.

System for demonstrating arbitrary multi-spot beam steering from spatial light modulators

A graphical user interface is used to program sequences of analog phase patterns onto a 512 x 512 pixel, electrically-addressed spatial light modulator (SLM). Hand sketches made with a digital pen are used to prescribe the footprints, velocities and trajectories of multiple, independently-controlled diffracted spots. The interface is intended to demonstrate to potential end-users, who are not knowledgeable about diffractive optical design, to what degree SLM's may be considered to produce arbitrary multi-spot beam steering. Using the interface, scanning sequences are created, programmed, run through, and diffracted from a SLM that simultaneously scans multiple patterns on distinct trajectories.

Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices

A computer-generated hologram with minimum spatial complexity is proposed for encoding arbitrary complex transmittance with low-resolution phase-modulation devices. The phase modulation of the proposed hologram is determined such that on-axis reconstruction with high signal-to-noise ratio, optimum reconstruction efficiency, and the largest possible signal bandwidth can be obtained.

Enumeration of illumination and scanning modes from real-time spatial light modulators

Using a phase-only spatial light modulator (SLM) in a Fourier transform setup together with fast diffractive optics design algorithms provides a way to automatically generate complex and rapidly changing laser illumination patterns in the far-field. We propose a hierarchical software structure for the adaptive, on-line design of far-field illumination patterns. Using the on-line design system together with camera feedback of the illuminated scene would make it possible to detect and actively laser designate multiple objects in parallel. Possibilities for multispot, arbitrary trajectory scanning and also broad-area speckle-reduced illumination are demonstrated with experimentally measured diffraction pattern sequences from a 120 x 128 pixel phase-only SLM.

Improved-fidelity error diffusion through blending with pseudorandom encoding

Error diffusion (ED) and pseudorandom encoding (PRE) methods of designing Fourier transform holograms are compared in terms of their properties and the optical performance of the resulting far-field diffraction patterns. Although both methods produce a diffuse noise pattern due to the error between the desired fully complex pattern and the encoded modulation, the PRE errors reconstruct uniformly over the nonredundant band-width of the discrete-pixel spatial light modulator, while the ED errors reconstruct outside the window of the designed diffraction pattern. Combining the two encoding methods produces higher-fidelity diffraction patterns than either method produces individually. For some designs the fidelity of the ED-PRE algorithm is even higher over the entire nonredundant bandwidth than for the previously reported [J. Opt. Soc. Am. A 16, 2425 (1999)] minimum-distance-PRE algorithm.

Nonlinear effects of phase blurring on Fourier transform holograms

Liquid-crystal light valves can have intensity-dependent resolution. We find for a nematic liquid-crystal light valve that this effect is well modeled as a phase that has been blurred by a linear space-invariant filter. The phase point-spread function is measured and is used in simulations to demonstrate that it introduces intermodulation products to the diffraction patterns of computer-generated Fourier transform holograms. Also, the influence of phase blurring on a pseudorandom-encoding algorithm is evaluated in closed form. This analysis applied to a spot array generator design indicates that nonlinear effects are negligible only if the diameter of the point-spread function is a small fraction of the pixel spacing.

High-diffraction-efficiency pseudorandom encoding

Pseudorandom encoding (PRE) is a statistics-based procedure in which a pure-phase spatial light modulator (SLM) can yield, on the average, the prescribed diffraction pattern specified by the user. We seek to combine PRE with the optimization of an aperture-based target function. The target function is a fully complex input transmittance, unrealizable by a phase-only SLM, that generates a prescribed light intensity. The optimization is done to increase the diffraction efficiency of the overall process. We compare three optimization methods-Monte Carlo simulation, a genetic algorithm, and a gradient search-for maximizing the diffraction efficiency of a spot-array generator. Calculated solutions are then encoded by PRE, and the resulting diffraction patterns are computer simulated. Details on the complexity of each procedure are furnished, as well as comparisons on the quality, such as uniformity of the output spot array.

Modified minimum-distance criterion for blended random and nonrandom encoding

Two pixel-oriented methods for designing Fourier transform holograms--pseudorandom encoding and minimum-distance encoding-usually produce higher-fidelity reconstructions when combined than those produced by each method individually. In previous studies minimum-distance encoding was defined as the mapping from the desired complex value to the closest value produced by the modulator. This method is compared with a new minimum-distance criterion in which the desired complex value is mapped to the closest value that can be realized by pseudorandom encoding. Simulations and experimental measurements using quantized phase and amplitude modulators show that the modified approach to blended encoding produces more faithful reconstructions than those of the previous method.

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.

Pseudorandom encoding for real-valued ternary spatial light modulators

Pseudorandom encoding with quantized real modulation values encodes only continuous real-valued functions. However, an arbitrary complex value can be represented if the desired value is first mapped to the closest real value realized by use of pseudorandom encoding. Examples of encoding real- and complex-valued functions illustrate performance improvements over conventional minimum distance mapping methods in reducing peak sidelobes and in improving the uniformity of spot arrays.

Ternary pseudorandom encoding of Fourier transform holograms

Pseudorandom encoding is a statistical method for designing Fourier transform holograms by mapping ideal complex-valued modulations onto spatial light modulators that are not fully complex. These algorithms are notable because their computational overhead is low and because the space-bandwidth product of the encoded signal is identical to the number of modulator pixels. All previous pseudorandom-encoding algorithms were developed for analog modulators. A less restrictive algorithm for quantized modulators is derived that permits fully complex ranges to be encoded with as few as three noncollinear modulation values that are separated by more than 180 degrees on the complex plane.

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.

Pseudorandom phase-only encoding of real-time spatial light modulators

We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326°modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.

Random phase encoding of composite fully complex filters

The mapping of complex-valued functions onto phase-only spatial light modulators is examined. Random phase encoding effectively adds amplitude control to the phase-only filter and can be used to trade off systematic errors of the phase-only filter for random errors. This is illustrated for the problem of recognizing a threedimensional object from arbitrary views. The complex-valued composite filters that constitute a filter bank design are encoded by phase-only and pseudorandom methods. The best recognition probabilities are achieved by blending the two methods so that only the smallest amplitudes are randomly encoded.