This PDF file contains the editorial “The Ark of Knowledge” for OE Vol. 42 Issue 11

We demonstrate an all-optical regenerative memory with full write/store capability of 40 Gb/s data packets. The memory uses an ultrafast nonlinear interferometer logic gate and does not perform data inverting in each pass. Regenerative storage of variable-length data packets with low switching energies and different storage times is verified.

We demonstrate a simple method for rate quadruplication of 10-GHz optical clock pulse trains by double pass filtering in a Fabry-Perot interferometer. The 40-GHz pulse train exhibits less than 0.12 dB amplitude modulation.

This PDF file contains the editorial “Laser Beam Shaping” for OE Vol. 42 Issue 11

We present a vector angular spectrum approach using self-iterative algorithms for beam shaping. This approach is rigorous and valid for subwavelength feature size. It is based on scalar angular spectrum theory and deals with beam polarization along three components of the wave vector in the spectral domain during the iteration. All self-iterative algorithms can be kept efficiently for any incident polarization. Algorithms such as Gerchberg–Saxton, input–output, and phase mixture algorithm are used to design the diffractive optical element for super-Gaussian beam shaping in uniform illumination with traditional scalar diffraction integrals and this new approach, respectively. The comparison of top profile error, mean square error, and diffraction efficiency of the simulated output beams shows that this new improved approach is more efficient at keeping the variation of the beam polarization.

We present a lossless method and apparatus to transform a collimated straight line beam into a collimated spherical arc beam. This apparatus consists of two coaxial axicons, and the propagation direction of the incoming beams is parallel to the optical axis of the two axicons. The same method can also be used to transform a collimated rectangular beam into a collimated meniscus shaped beam.

Structured microlens arrays are used for beam shaping, diffusion, and homogenization, providing the ability to perform complex beam shaping tasks, both intensity control and spatial energy distribution, with high efficiency (mostly limited by surface losses) and without the presence of artifacts such as zero order. Applications include excimer laser beam shaping, display screens, light-control films, and illumination.

An innovative method of optically combining the multiple emitters of high-power stripe laser diodes is presented. A multibeam integrator approach is used along with a means of optically rotating the emitters by 90 deg. The 90-deg rotation allows better balancing of the optical invariants in the slow and fast axis directions, making it easier to "circularize" the image for coupling into fibers or increasing the irradiance for laser machining applications.

The use of radially polarized light is known to produce, when focused by a high-numerical-aperture objective lens, a spot of light whose polarization is predominantly axial. We have generated accurately such radially polarized fields, which we have coupled into a high-numerical-aperture microscope objective so as to produce an axially polarized focal spot.

A pair of plano-aspheric lenses can be used to transform a collimated, radially symmetric, Gaussian beam to a radially symmetric flat-top beam. Diffraction of the output beam due to the choice of irradiance profile, as well as the finite aperture of the optics, must be considered if a propagating beam is required. Choosing both lenses to be positive, one can show that the aspheric surfaces are strictly convex, which facilitates fabrication by magnetorheological figuring. A fused silica lens pair is demonstrated, which can be used at any wavelength from 250 to 1550 nm to transform a Gaussian to a flat-top beam. Measurements of both the irradiance profile and phase of the output beam are presented and compared to the ideal design. These optics transform 78% of the total input beam power into the flat-top region of the output beam, which is uniform to better than 5% rms. For applications requiring uniform illumination, this represents a fourfold improvement in power utilization over the Gaussian input. The output wavefront is flat to a quarter wave at 514 nm, resulting in a beam that propagates approximately 0.5 m without significant change in profile.

A refractive-diffractive hybrid optical element for true beam smoothing is designed with the precise design method. The intensity of any point on the focal plane is fully filled with the required demand, besides the sampling points used in the optimization. An aspheric refractive surface gives a good initial intensity distribution on the focal plane and can decrease the phase depth of the diffractive surface. After the optimization, the phase depth of the diffractive surface is smaller than 1.1 π, which is correspondingly easy to fabricate.

We report on the analysis and optimization of a binary phase element for shaping a Gaussian laser beam to a flat-top beam. Simulation results indicate that a single-zone binary phase plate can achieve excellent flat-top beam shaping quality similar to that achieved by using multiple zones. The degradation of flat-top beam shaping quality due to etching depth errors, deviation of illuminating wavelength from design value, and variation of input beam size can be compensated to some extent through on-axis adjustment of the flat-top beam observation plane. Experiments verify these theoretical expectations. The increased beam shaper fabrication tolerance can be greatly beneficial for low-cost prototyping and production of flat-top beam shapers.

Recording and development of Gaussian gratings are analyzed, and utilizing these gratings for beam shaping is demonstrated. It is shown that by using only holographic recordings of gratings, diffractive shapers for transformation of Gaussian beams to super-Gaussian beams of the fourth degree, and more as well, can be obtained. Holographic shapers are fabricated by interference of natural-size laser beams as elements of a matrix, which can be used for flat-top beam shaping of laser beams of natural size. If appropriate shaping of a beam is demanded, the necessary shaper can be found among a number of realizations in the matrix, or in a set of such matrices, without any calculations or preliminary measurements.

When diffraction effects are not important, geometrical optics (ray tracing, conservation of energy within a bundle of rays, and the constant optical path length condition) can be used to design laser beam shapers by solving beam shaping equations or by optimizing a beam shaping merit function for the configurations, including aspheric elements or spherical-surface gradient-index lenses, which are required to change the input irradiance and phase profile into a more useful form. Geometrical optics-based methods are presented for shaping both rotationally and rectangular symmetric laser beam profiles. Solutions of the beam shaping equations are presented for a two-plano-aspheric lens system for shaping a circular symmetric Gaussian beam into a top-hat output beam profile and a two-mirror system with no central obscuration for shaping an elliptical Gaussian input beam into a Fermi-Dirac output beam profile.

The performance of a coherent telescope array (CTA) as an optical communications receiving system is analyzed with regards to the benefits and disadvantages in comparison to monolithic large-aperture single telescopes and conventional photon bucket systems, especially in terms of background photons. The bit error rates for differential phase-shift keying (DPSK) and binary pulse position modulation (BPPM) schemes are derived, the former using self-homodyne interferometry as a novel demodulation technique, in which the background photons interact incoherently. The possibility of further dividing the receiver's aperture into N>2 smaller subtelescopes is explored, and its adaptability for implementing the N binary phase-shift keying (N-BPSK) technique with optical code division multiplexing (OCDM) is discussed. An N-CTA receiver system with an N-BPSK/OCDM technique is envisioned not only to achieve multiterabit per second data transfer capability, but also to adapt a novel noise suppression technique based on photon correlations, which would render a need for expensive and complicated adaptive optics obsolete. Further combined with significant reduction in weight and overall costs, an N-CTA system with an N-BPSK/OCDM technique could serve in deep space communications as well as in defense to achieve information dominance in the battlefield.

A new effect during light propagation simulation in the Fresnel region is discovered. Image multiplying and high-frequency noise effects are caused by the sampling of the complex light field. Image multiplying is observed in the case of the standard integral calculation. High-frequency noise is observed in the convolution approach. These effects are observed in a computer simulation only and do not exist in nature. The analysis of these effects enable us to define the range of the numerical algorithms application.

White light interferometry has been used in the sensing area for many years. A novel data processing method for demodulating the information from the interference spectrum of a white light system is presented. Compared with traditional algorithms, both high-resolution and large dynamic range have been achieved with a relatively low-cost system. Details of this arithmetic are discussed. A compact white light interferometric system employing this algorithm has been developed, combined with fiber Fabry-Perot sensors. A ∓0.5-nm stability over 48 hours with a dynamic range on the order of tens of microns has been achieved with this system. The temperature dependence of this system has been analyzed, and a self-compensating data processing approach is adopted. Experimental results demonstrated a ∓1.5-nm shift in the temperature range of 10 to 45°C.

A minimax method for designing a Fourier filter flat-top (F³T) interleaver is proposed and demonstrated. Given a passband range, the proposed minimax method is able to produce an F³T interleaver with a specified bandwidth, minimal insertion loss, and higher isolation. In comparison with current interleaver design methods, the proposed approach has the advantage that the design parameters and the performance parameters of the interleaver can be obtained analytically.

A cantilever optical vibrometer using a fiber Bragg grating (FBG) is developed. The sensor head is made by attaching an FBG to a triangular beam to provide position-independent strain for the purpose of acceleration measurement. The vibrometer demonstrates a noise-limited acceleration resolution of 2.8×10^–4√Hz with repeatability error of less than 2.4%.

A new approach to the retrieval of fringe pattern frequency information is introduced. In this approach, strain information is extracted from fringe patterns by using either short-time Fourier transforms or wavelets. Space-frequency representation of the fringe signals is introduced as a tool to get the space localization of the strains. The idea of spectral energy density maxima to define the instantaneous frequency (ridge points) is presented. Examples of application are given. Results show that this approach provides an excellent tool for pattern analysis.

A diffractive-optical-element-based glossmeter (DOG) is used for optical inspection of local gloss variation of planar ABS-PC plastic samples possessing different surface roughness. The DOG was utilized to detect gloss differences, which were measured at successive microscopic areas by scanning a macroscopic surface area. The gloss variation is presented as a 2-D map of gloss measurements. It is suggested that DOG can provide a robust glossmeter for industrial use.

An experimental method is presented to measure microthermal deformation of an optical pick-up base by using holographic interferometry. Calibration tests are used to measure out-of-plane and in-plane deformations. A cantilever and a plate are deformed according to the prescribed motion, actuated by a piezoelectric transducer with 1-nm resolution, and the interferometric measurements are compared quantitatively with the analytic solution and measurements from finite element analysis (FEA). The thermal deformation of an aluminum pick-up base, manufactured from a die-casting process, are measured in actual thermal environments by using the present holographic interferometry. Finally, the experimental results obtained by using holographic interferometry are compared with those of the FEA with initial surface stress conditions obtained from x-ray diffraction measurements.

The ability to perform the same operations in the transform domain as in the spatial domain is important for efficient image transmission through a channel. We perform image resizing, which includes magnifying and reducing the size, in the discrete cosine transform (DCT) domain and the effects of the transform domain approach are analyzed in the corresponding spatial domain. Based on this analysis, the two resizing algorithms are proposed. The first one further compresses the images encoded by the compression standard by reducing the size before compression, and the other reduces the loss of information while maintaining the conventional compression rate. Because of its compatibility with standard codec, these algorithms can be easily embedded in JPEG and MPEG codecs, which are widely used for the purpose of image storage and transmission. Experimental results show a reduction of about half the bit size with similar image quality and about a 2- or 3-dB quality improvements in the similar compression rate.

In the absence of a priori knowledge about regions of interest, a rational system for progressive transmission chooses at any truncation time among alternative spatial orientation trees for further transmission, in such a way as to avoid certain forms of behavioral inconsistency. Some rational transmission systems might exhibit aversion to risk involving "gambles" on the tree-dependent quality of encoding, while others favor taking such risks, but risk-prone systems as well as those with strong risk aversion appear incapable of attaining the quality of reconstructions that can be achieved with moderately risk-averse behavior. Even though the problem of estimating the parameter that controls the risk attitude in a rational transmission system is a key issue, it is not clear how to pick the risk aversion parameter for different image content. We estimate the risk aversion parameter by integrating rationality and cooperative action with the aim of preventing disproportionately large benefit gains and strong oscillations in gain at very low bit rates. Experimental results show the comparative performance of the corresponding transmission system with both the state of the art in progressive transmission set partitioning in hierarchical trees (SPIHT) and the state of art coder JPEG2000.

A general technique for determination of residual wedge angles of high optical quality parallel plates using a Fizeau interferometer is discussed. In this technique the parallel plate to be tested for degrees of parallelism is used to introduce angular tilt in the Fizeau fringes of an air cavity of a known wedge angle. The parallelism is calculated from the angular tilt of the fringes. The technique is most suitable for highly parallel transparent plates with very low residual wedge angles.

Frequency shifting is a commonly used technique to determine the direction of motion and enable simpler processing of Doppler signals generated by laser Doppler velocimeter (LDV) and Doppler lidar systems. This shift is most commonly achieved by passing the reference, measurement, or injection-locking laser beam though an acousto-optic modulator (AOM). However, AOMs are expensive and require specialized drive electronics, hence methods of generating a frequency shift without the use of an AOM are desirable to reduce the overall cost and size of LDV systems. Various methods of frequency shifting without AOMs have been reported, along with direction discriminating processing systems that do not require a frequency shift. However, these systems are either not applicable to or are of limited use for pulsed Doppler lidar. We have developed a new frequency shifting technique that is applicable to pulsed Doppler lidar and does not require an AOM. The method is based on the principles of radio frequency single-sideband modulation. Two implementations are presented, along with the results from concept validation experiments that illustrate successful decoding, including direction discrimination, of Doppler signals. The first implementation is a fully electronic method that uses an electronic modulator fed with quadrature signals generated optically, and in the second, semioptical implementation the modulation function is performed optically.

The computational process of the sum of the absolute difference (SAD) and the multilevel successive elimination algorithm (MSEA) are theoretically analyzed, and a new improved MSEA is proposed. The proposed algorithm reduces the computations required for judging invalid candidate blocks. The simulation results show that the proposed algorithm achieves a computational time savings of about 30 to 40% without additional hardware, compared to the MSEA.

Time-delay and integration (TDI) arrays are of great interest, especially in connection with civilian applications such as document scanning and industrial product inspection. We consider here a staggered TDI system, in which the even field is delayed with respect to the odd field by 29 pixels. Because of cooling system vibrations and the field differences, pictures become distorted as a result of motion blur. The proposed algorithm improves image quality. We build an analytical model of this system to describe all motion in the picture, including object motion in addition to cooling system vibrations, or either type of motion. We present a number of approaches that can be useful to solve such problems. These solutions are based on different applications of a block-matching algorithm (BMA). Full-search BMA yields the lowest complexity but not necessarily the best image quality. Interpolation BMA yields the best image quality.

We describe an effective method for obtaining tunable pulse-duration parametric output with an optical parametric oscillator (OPO) pumped by a tunable pulse-duration laser. The influence of pump pulse duration on a parametric laser is also studied according to the coupled wave equations for three-wave mixing. In the experiments, a noncritical phase-matching KTP OPO, pumped by a dual-cell stimulated Brillouin scattering (SBS) wave with pulse duration ranging from 2 to 6 ns, has achieved tunable pulse duration from an OPO from 1.8 to 4.5 ns. The experimental results agreed quite well with theoretical calculations, and the method was feasible and efficient.

We grow and fabricate GaSe crystals for nonlinear optical applications. One possible application for this material is an optical parametric oscillator (OPO), which could be pumped with a Nd:YAG laser, but due to the large walk-off, is generally impractical. We present a noncollinear OPO design that significantly reduces the effect of walk-off, which could make an OPO possible with GaSe. The pump, signal, and idler propagation directions are arranged to form nearly collinear rays of power flow. The design minimizes the overlap angle between the rays, and as much as an order of magnitude improvement is obtained compared to the walk-off angle of a collinear OPO. With a 1.06-μm pump, an overlap angle as small as 0.35 deg can be achieved, which is half that of a conventional OPO using ZnGeP₂.

Optical constants of amorphous (AgSbTe)_x(In_1–ySb_y)_1–x films (AIST) for a typical composition (x = 0.4 and y = 0.7) deposited by the thermal evaporation technique, are calculated from transmittance spectra. They are also been calculated during the crystallization process induced by 1-h thermal annealing at different temperatures. The effect of heat treatment on the absorption coefficient, the extinction coefficient, and the refractive index of the films are studied. The optical gap for as deposited amorphous films is found to lie in near-IR region. The bandgap shifts resulting from annealing are also calculated for the crystalline films. Further, these results are used for a multilayer structure for AIST as the recording layer, illuminated by a laser beam. The flow of optical energy in the absorptive layers and hence the diffusion of the resultant heat throughout the structure are studied.

In an experimental investigation, photosensitivity was evaluated for continuous and pulsed illumination at a wavelength of 532 nm. Since exposure to light results in photoinduced structural changes that are associated with changes in the refractive index of the material, the recording characteristics can be optically traced without any additional treatment, such as etching or other chemical processes. Measurements performed by interferometric methods and diffraction effects indicate an increase in photosensitivity by a factor of about 70 for exposure with pulses of 10 ns, as compared to continuous wave recording.

The insertion loss of a fiber optical rotary joint depends on the mechanical misalignments of the collimating lenses. To achieve 3-dB or less insertion loss, the lateral misalignment of the graded-index (GRIN) lenses should be less than 100 μm, and the angular tilt of these lenses is limited to 0.1 deg. These requirements cause a high mechanical fabrication and assembly cost. To solve this problem, we design a single-channel optical rotary joint using a bulk optical detector. The requirement on lateral misalignment is relaxed to 500 μm, and the angular tilting is relaxed to 2 deg. Using this method, the cost of the optical rotary joint can be dramatically reduced.

In the detection and identification of a target, the position fusion of the measurements for sensors is necessary and the target's optimization trajectory is required for recognizing. A new position fusion algorithm is introduced. The measurements from multisensors (such as TV, IR, laser, radar, and so on) can be fused so as to achieve result of higher accuracy. The instantaneous weight values of the data are obtained utilizing the weight reciprocal propagation (WRP) to achieve a positional fusion to a single target. The simulations show that the method is an effective distributed fusion algorithm.

We propose and evaluate a novel configuration that employs a multibeam transmitter in an optical wireless system. Such a configuration borrows attractive features from diffuse and line-of-sight systems, resulting in great robustness and ease of use. A line strip multibeam transmitter placed on the communication floor is proposed to produce a line of diffusing spots on the middle of the ceiling. The results associated with the new structure show that a receiver SNR improvement of about 3.8 dB can be achieved compared to the conventional diffuse configuration. Other geometries including a diamond-shaped spot geometry and a uniform spot geometry are also considered. Power distribution, received pulse shapes, and a comparison with the conventional diffuse link are outlined. SNR results show that the proposed geometries are very attractive.

Human retinal blood vessel images possess certain characteristics that are suitable for personal identification and other advanced security applications. We propose an image processing algorithm for matching retinal blood vessel patterns based on the locations of intersections of blood vessels. The algorithm includes preprocessing, orientation registration, and similarity measurement. Preliminary experimental results show that our method achieves good discrimination among images from different subjects.

We present a method to obtain profilometry of a suitable object by fringe projection. The method is appropriate to the case of large objects as compared to the distance from the illuminating source, that is, a nonconstant equivalent wavelength. We develop an experiment to laterally displace a set of fringes on a sphere and obtain quantitative results. There are several orientation parameters involved in the method, and a minimization algorithm is developed to adjust the values of some of them. A series of numerical experiments are performed on this method to test its accuracy under various circumstances. We show that the method can currently attain precisions of ≈ λ_eq/80 (λ_eq stands for equivalent wavelength) and identify possible sources of error.

We describe some of the characteristics of intracavity CdTe Q-switch modulation in a CO₂ laser, which could be used in a pulsed heterodyne imaging lidar. We analyze the thermal influence of intracavity CdTe crystal on output power stabilization and frequency shift, and conclude that sufficient cooling and temperature control on CdTe modulation is the vital requirement for laser stabilization both in power and frequency. We also calculate the frequency chirps due to CdTe thermal index varieties during individual Q-switch pulse duration. The results show that the chirps may not obviously affect the passive frequency stabilization of the laser. For this laser, Q-switch pulses with peak power 360 W and full width at half maximum (FWHM) of 150 ns at 41.67 KHz are achieved. The experimental results also indicate that the passive frequency stabilization of the laser is better than 1.76×10^–8 and power stabilization in the EH₁₁ mode is better than 5% for more than 1 h of operation.

Any two-beam interferometer may be employed as a Fourier transform spectrometer. The two most commonly used for Fourier transform spectrometry are the Michelson interferometer and the Sagnac interferometer, the relative merits of which have been discussed in the literature. Typically, it is the interferometer that limits the acceptable range of angles for the input beam, and this maximum acceptance angle in turn limits the etendue, and hence limits the responsivity of the instrument when viewing an extended source. In designs where the interferometer is in a diverging or converging beam, the allowable range of input angles limits the focal ratio of the instrument, while in designs where the beam is collimated through the interferometer, this effect limits the field-of-view of the instrument. In a Michelson, it is a loss of fringe contrast that limits the range of acceptance angles; a limitation that is discussed in many general texts on optics. A Sagnac, however, suffers no such loss of contrast as the range of acceptance angles is increased. The maximum acceptance angle for a Sagnac is instead limited by vignetting, caused by the geometry of the interferometer. The limitation for a Sagnac has an origin and behavior entirely different from that found for a Michelson, and has not been previously discussed in the literature. It is therefore important to understand this limitation when designing a Sagnac interferometer for Fourier transform spectrometry. This vignetting limitation may be quantified by an aspect ratio, which we define as the ratio of the separation of the entrance and exit apertures to the width of these apertures in the plane of the interferometer. To facilitate the design of Sagnac interferometers for Fourier transform spectrometry, we discuss the limitations on the aspect ratio and derive equations for the limiting aspect ratios for nine variations of the Sagnac interferometer.

In designing an autostereoscopic imaging system based on either a lenticular, parallax barrier, or integral photography (IP) plate, geometrical parameters relating the viewing zone and image display panel combined with the plate are the first things to be determined for the system. To define parameters such as the size of the panel, multiview image arrangement, pitch and focal length of the plate, viewing zone distance from the panel, and others, an optical configuration composed of an image mask aligned in front of a point light source array is used. With this configuration, the geometrical parameters are calculated and their relationships are found. In addition, the concept of pixel cells is introduced to arrange multiview images in the display panel for full parallax image generation.

Disparity estimation plays a crucial role in many stereo image compression techniques. To reduce computational complexity most methods limit the estimation search area to a limited window. The performance of the disparity estimation depends on the choice of the limited search window. Most techniques use a predetermined value for the window size, which is not optimal over a wide range of images. We show how the choice of the window size affects the performance of the stereo image compression algorithm and propose a method to obtain a better search window size. Our simulation results indicate an improvement of up to 1.81 dB over rigid window size selection and with performance very close to the optimal selection.

We propose adaptive anomaly detectors that find materials whose spectral characteristics are substantially different from those of the neighboring materials. Target spectral vectors are assumed to have different statistical characteristics from the background vectors. We use a dual rectangular window that separates the local area into two regions—the inner window region (IWR) and outer window region (OWR). The statistical spectral differences between the IWR and OWR are exploited by generating subspace projection vectors onto which the IWR and OWR vectors are projected. Anomalies are detected if the projection separation between the IWR and OWR vectors is greater than a predefined threshold. Four different methods are used to produce the subspace projection vectors. The four proposed anomaly detectors are applied to Hyperspectral Digital Imagery Collection Experiment (HYDICE) images and the detection performance for each method is evaluated.

We present an unsupervised method for the fast detection of noisy objects of varying sizes and contrasts, which is implementable on an opto-electronic device. This method consists of first achieving multiresolution representation of the noisy data using successive Gaussian filterings. Then, the resulting set of Gaussian smoothings is compressed using principal component analysis (PCA). This compression is applied within regions of interest (ROI) that are previously detected using a fast technique adapted to the features of analyzed data. The different objects of interest are finally segmented using a standard valley thresholding technique, which is locally applied within each ROI. An experimental evaluation using synthetic images underlines the robustness of this method and its ability to achieve unsupervised detection of strongly noisy objects. Theoritical and experimental estimations of the computing power of a high-speed optical correlator and of a specialized digital processor have shown that it is faster to compute: optically global Gaussian filterings, the PCA-based compression being digitally performed. Experiments have also shown the potential of the proposed method for the fast detection of liver tumors from computer tomography (CT)-scan images. The feasibility of its hybrid opto-electronic implementation is demonstrated using an experimental optical correlator.

The low absorption presented by thermoplastic films to 10.6-μm CO₂ laser radiation makes the engineering use of welding parameters, predicted by models developed for thicker thermoplastics, very difficult. A new theoretical model is developed describing the temperature distribution in thin thermoplastic material during the laser welding process. The heat conduction equation is solved analytically by the Green function method and heating and cooling thermal stresses are taken into consideration. Engineering parameters predicted by the model are applied to lap welding of high- and low-density polyethylene and polypropylene samples, both transparent and white, with thicknesses between 10 and 100 μm, and experimentally validated. This validation is also accomplished by comparison with the measured temperature through the use of two diagnostic methods: schlieren interferometry and photothermal deflection spectroscopy. The first of these methods, combined with direct observation of Mie scattering, also puts in evidence the absorption of about 30% of the incident energy due to plasma formation in the air above the interaction interface. This plasma ignites after the initial release of chunks of material during the first moments of interaction. Proper modeling, and the introduction of a reflective substrate under the samples, allows an increase in process efficiency and the achievement of lap welding speeds up to 14 m s^–1 with this new transmission welding technique.

The diffraction characteristics of a broadband light source from a reflection grating in the far field are theoretically investigated with a prompt and precise mathematical derivation. We provide a rigorous treatment of a time-dependent Gaussian-shaped pulsed beam reflecting from a grating and give more accurate and concrete criteria judging the timing for the spectral red and blue shifts and the splitting of light distributions. In addition, the distortion of the space-time diffraction intensity distribution is also presented in detail.

Ultrashort pulsed laser irradiation is used to crystallize 100-nm amorphous-silicon (a-Si) films. The crystallization process is observed by time-resolved pump-and-probe reflection imaging in the range of 0.2 ps to 100 ns. The in-situ images, in conjunction with postprocessed scanning electron microscopy (SEM) and atomic force microscopy (AFM) mapping of the crystallized structure, provide evidence for nonthermal ultra-fast phase transition and subsequent surface-initiated crystallization.

A Shack-Hartmann wavefront sensor with a dual-focus holographic lenslet array and a known wavefront distortion is introduced. It enables measurement of a small phase distortion in optical waves under significant background wavefront aberrations and extending its angular dynamic range. The performance of the sensor is demonstrated using several phase objects of providing different wavefront shapes. The sensor performs as expected and the results are satisfactory.