This PDF file contains the editorial “Down in the DOS, out in the OS X” for OE Vol. 41 Issue 08

We propose and demonstrate an externally modulated AM-vestigial sideband (VSB) CATV erbium- doped fiber amplifier-repeated system which uses an optical single sideband modulation technique to improve the composite second order (CSO) and composite triple beat (CTB) performances in systems. In comparison with conventional externally modulated fiber optical CATV systems, excellent performances of carrier-to-noise ratio >50 dB, CSO?72 dB, and CTB?69 dB were achieved for the full channel band over a 100-km single-mode fiber transport.

Nonmechanical beam steering technologies utilizing acoustooptics enable us to achieve the high-bandwidth laser beam positioning required for optical communications, laser scanners, ladars, etc. The properties of the Bragg cell, which are chiefly responsible for the efficiency and attainable characteristics of the entire positioning system, are ensured by the successful design of this optical component. However, the design of Bragg cells is dominated by the experience and intuition of the designers, and the potential of this technology is not fully utilized. An optimal Bragg cell design problem is formulated on the basis of known equations of the underlying physical phenomena, and a genetic optimization scheme is applied for the solution of the resulting formidable problem. The approach not only yields a design solution, but also enables one to vary the design criterion and emphasize particular properties of the resultant component. The prowess of the proposed approach is demonstrated by design optimization examples.

Digilens is developing a new class of optical components based on the combination of electrically switchable Bragg grating (ESBG) and optical waveguide technology. One or more optical waveguides are formed on a substrate, which is used as one wall of a cell filled with an ESBG. The ESBG layer forms part of the waveguide cladding, so that the grating can interact with the evanescent field of the light energy traveling in the waveguide. This device architecture has been used to make electrically variable optical attenuators with more than 50 dB of controllable range, flat attenuation over the optical communications C band, fast (~ 100 ?s) switching speed, and encouragingly low polarization-dependent loss. initial results on a variable wavelength-selective filter are also reported.

To achieve precise energy distribution among light beams diffracted by a rough surface-relief grating in optical pickup heads, we model the grating with a scalar theory. The grating is assumed to be a trapezoid shape with different roughnesses for the top and the bottom surfaces. The model includes rectangle, triangle, and sawtooth shapes as special cases. Using this model, we investigate the influence of grating parameters on diffraction efficiencies and deduce Strehl ratios for different surface roughness values.

We realize for the first time a forward-looking IR (FLIR) system using a diffractive optical element (DOE) in its optics made of germanium in the 8- to 10-?m IR wavelength. We describe the design and the performance of the DOE optics. The IR diffractive lens made of germanium is proposed to correct the axial chromatic aberration in optics of the FLIR system. Compared with conventional optics of an FLIR system the optics using a DOE singlet instead of ZnSe achromat, we have a DOE system modulation transfer function (MTF) that is almost equal to the conventional one. The DOE singlet instead of ZnSe achromat appears to be enough to compensate for the chromatic aberration of the optical system. Using the DOE system, the numbers of lens elements, the mass, and the cost are reduced.

We present an electromagnetic analysis of diffractive optical elements (DOEs) fabricated on finite-thickness substrates. To this end we use the finite-difference time-domain (FDTD) method to solve the electromagnetic boundary value problem in the vicinity of the DOE and a semi-infinite propagation algorithm to determine the diffracted fields on the output side of the substrate. The formulation of the method and its application to the analysis of several finite-thickness diffractive lenses is presented.

Commercial EUV lithographic systems require multilayers with higher reflectance and better stability than those published to date. This work represents our effort to meet these specifications. Interface- engineered Mo-Si multilayers with 70% reflectance and 0.545-nm bandwidth at 13.5-nm wavelength and 71% reflectance with 0.49-nm bandwidth at 12.7-nm wavelength were developed. These results were achieved with 50 bilayers. These new multilayers consist of alternating Mo and Si layers separated by thin boron carbide layers. Depositing boron carbide on the interfaces leads to reduction in molybdenum silicide formation of the Mo-on-si interfaces. Bilayer contraction is reduced by 30%, implying that there is less intermixing of Mo and si to form silicide. As a result, the Mo-on-si interfaces are sharper in interface-engineered multilayers than in standard Mo-Si multilayers. The optimum boron carbide thicknesses have been determined and appear to be different for the Mo-on-Si and Si-on-Mo interfaces. The best results were obtained with 0.4-nm-thick boron carbide layers for the Mo-on-Si interfaces and 0.25-nm-thick boron carbide layers for the Si-on-Mo interfaces. The increase in reflectance is consistent with multilayers having sharper and smoother interfaces. A significant improvement in oxidation resistance of EUV multilayers has been achieved with ruthenium-terminated Mo-Si multilayers. The best capping-layer design consists of a Ru layer separated from the top Si layer by a boron carbide diffusion barrier. This design achieves high reflectance and the best oxidation resistance during EUV exposure in a water-vapor (oxidizing) environment. Electron- beam exposures of 4.5 h (in an effort to simulate EUV exposure perturbation of the top layers) in the presence of 5x 10-7-Torr water-vapor partial pressure show no measurable reflectance loss and no increase in the oxide thickness of Ru-terminated multilayers.

We review recent numerical models for both an erbium-doped fiber amplifier (EDFA) and a fiber Raman amplifier (FRA) based on the average power analysis technique and other similar approaches. By applying the basic characteristics of the models, a general computer model is proposed for both EDFA and FRA. A numerical solution for this general computer model is also thoroughly discussed.

We present experimental results on testing a twin-grating fiber optic sensor for the measurement of static strain and temperature. The sensor is built with two identical Bragg gratings closely spaced in a single-mode fiber. It produces a reflection spectrum modulated by interference. As in traditional fiber Bragg grating sensors, strain of the fiber leads to the wavelength shift of the reflection spectrum. This shift can be determined precisely by measuring phase changes for corresponding components of Fourier transform of the reflection spectrum. Such an approach allows an absolute strain measurement with an interferometric sensitivity. Resolution of 0.2 ?m/m and range to resolution ~ 104: 1 were demonstrated experimentally for static strain measurements using a pair of 0.7-mm-long Bragg gratings with reflectivity of 1% each.

The characteristics of the use of a hollow-core splice scheme for macrobend measurements are discussed both theoretically and experimentally. A perturbation theory for the modes of a bent hollow-core fiber and its loss characterization are developed so as to better understand the characteristics of the scheme. The maximal detection range of fabricated sensors with the proposed scheme is experimentally determined to be as large as a few hundred millimeters relative to the radius of curvature. In addition, the numerical estimation of the loss characteristics using the scheme shows modal trends which are in good agreement with experimental data.

We present an analysis of conditioned launch in a gradient- index multimode fiber (MMF). Selective mode excitation is obtained by nonaxial evanescent coupling between two highly asymmetric side- polished fibers: a single-mode fiber and an MMF with an exposed core. An index-matching slab improves the coupling efficiency and selectivity. The simulation shows that about 40% of modes, only high-order modes, are excited in the MMF. When compared to an overfilled launch, the bandwidth of a perturbed index fiber is enhanced more than twofold for large parameter variations.

A coherent optical imaging system consisting of recording a digital hologram by a CCD array and numerical reconstruction of the complex wavefield by the convolution method is subjected to a frequency analysis. The point spread function of such a system is a sinc function whose width depends on the aperture defined by the CCD array and parameters of the transfer function used in the reconstruction. A narrow point spread function and thus a sharp reconstructed image can be obtained by the numerical concept of cascaded free-space propagation, which is introduced and demonstrated.

We propose a novel method of tracking the gaze direction of human eyes using a neural network (NN). First, ten primary parameters are extracted from the image of a human face by using the mountain algorithm and some other fast algorithms. With these primary parameters the feature parameters that are directly related to the gaze direction can be deduced. Then a NN is constructed to indicate the gaze direction after trained by the feature parameters. We have used this method to classify intentional hand gestures in a human-machine interaction system based on gesture recognition. The experimental results show that the proposed method is simple and convenient and can work effectively under changing light conditions.

This work is motivated by the observation that it is not possible to reliably estimate simultaneously all the necessary hyperparameters in an image restoration problem when the point-spread function is assumed to be the sum of a known deterministic and an unknown random component. To solve this problem we propose to use gamma hyperpriors for the unknown hyperparameters. Two iterative algorithms that simultaneously restore the image and estimate the hyperparameters are derived, based on the application of evidence analysis within the hierarchical Bayesian framework. Numerical experiments are presented that show the benefits of introducing hyperpriors for this problem.

We present a prediction-based multiple-window approach to image restoration based on new hypotheses. The filter is an order statistics filter that incorporates the new hypotheses via the generation of a reference image to predict the original uncorrupted image. In addition, adaptive parameter selection based on the local signal content is employed, as well as off-line parameter optimization and training using a maximum-likelihood estimation algorithm. The experimental results are all carried out using 24-bit RGB images with each channel being processed individually. The new technique demonstrates a marked performance gain over existing state-of-the-art methods.

we characterize phase and amplitude apodization induced when a converging beam passes through an evanescent gap. The apodization is caused by vector transmission and reflection properties. General characteristics are described for solid immersion lens indices from nSIL= 1.5 to 3.1, gap heights from h = 0 to 300 nm, and marginal ray angles ?m = 0.7 or 0.84, where ?m is the direction cosine of the marginal ray angle inside the solid immersion lens. A small amount of defocus is found to be a good compensator of the phase apodization for low nSiL and h. After proper defocus is applied, asymmetry of focus in the spot may remain, primarily due to the uncompensated amplitude apodization. Simplification of the phase and amplitude characteristics is accomplished by applying a Jones-matrix expansion to the transmission coefficient through the gap. Simulation and experiment quantify the effect with a simple solid immersion lens geometry.

We explain the technologies used for high-performance long linear arrays based on HgCdTe/CMOS hybrid multiplexers with bidirectional time delay and integration (TDI) functions and describe the development of the first high-resolution iR imaging system with a superextended graphics array (SXGA) format. Long-wavelength IR photodiode arrays are fabricated using liquid-phase epitaxially grown HgCdTe on a CdZnTe substrate. Each photodiode array consists of 480x8 element n + /n-on-p diodes formed by B+ implantation. Diodes with a 10.3-?m cutoff wavelength have a typical zero-bias resistance of 10 M? and a shunt resistance of 1 G?. Four CMOS readout integrated circuits (ROICs) are used for bidirectional TDI and multiplex operations, where each ROIC sums up and multiplexes eight signals from 120 channels. The ROIC also includes pixel deselection and gain control circuits along with the corresponding memory and writing means. The IR focal plane arrays (IRFPAs) have a typical noise equivalent temperature difference (NETD) of 18 mKafterTDI with F/1.55 optics and 10-?s integration. The IR imaging system adopts an interlace scan using the 480x8 element IRFPAto demonstrate a high spatial resolution of 1280 horizontal lines by 960 vertical lines (SXGA format) and an NETD of less than 30 mK. The unique algorithm for image enhancement is successfully confirmed to be efficient.

The signal-to-noise ratio required to obtain 10-nm accuracy in the measurement of lateral position is studied with an interference microscope. Evaluations are performed using the rigorous coupled-wave analysis (RCWA) modal approach and Hopkins image formation theory.

Two new iterative algorithms to be used to reconstruct a tested wavefront from its cyclic radial shearing (CRS) fringe pattern are proposed. First, the phase difference (PHD) in the common area of the contracted and expanded tested wavefront are determined directly from the CRS fringe pattern of the tested wavefront by the Fourier transform method. Then, according to the PHD, the tested wavefront is reconstructed precisely by the two iterative algorithms. The numerical simulation of the reconstruction of a tested wavefront with distortion is implemented, showing that the wavefront reconstruction can be performed precisely by these algorithms with root mean square (rms)??/20. A CRS interferometer is constructed with a radial shearing ratio of s51:1.4 and is used to test a distorted wavefront with a one-step phase jump successfully. The results of numerical simulation and optical testing show that with these algorithms, the CRS interferometric technique can be easily used to make the evaluation of the optical component quality as well as testing of the wavefront distortion of a high-power laser. Finally, the convergence of two algorithms is also analyzed.

Upconverted lasing pulses could be achieved when 0.01-mol/l trans-4-[p-(N-hydroxyethyl-N-methylamino)styryl]-N-methylpyridinium p-toluene sulfonate (HMASPS) solution in dimethyl formamide was pumped in a 5-mm-path glass cell by picosecond lasing pulses from a mode-locked Nd:YAG laser. The upconverted fluorescent time of the solution was measured to be 108 ps. Because of the reflections at the surfaces of the cell, pulse oscillation can be observed in the output lasing pulses. Both the spectral and the temporal behavior of the lasing pulse have been analyzed. As a comparison, the superradiance and lasing from the 5-mm uncoated glass cell are also given.

We present a characterization of the dot-mirror output coupler in the case of low losses. The numerical procedure computes the eigenvalue and field distribution through the Fox-Li method applied to a bare laser cavity. The field associated with the lowest-order mode closely follows the Airy pattern. This fact allows estimating the effective reflectivity and the beam diameter in a simple way. The computed values are compared with the experimental data obtained in a transversely-excited- atmosphere CO2 laser. The measured reflectivity approximates the expected figure for the lowest-order mode and thus suggests that this cavity discriminates against the higher-order modes.

Flatbed scanners are high-quality digital image recording devices that are cost-effective and widely available. In this work, we demonstrate their ability to register shadow moire fringes for topographic analysis. The fringe image obtained in color had bluish and greenish regions that correspond, respectively, to the bright and dark fringes associated with the technique. The diffraction characteristic of light passing through gratings provided a ready explanation of this behavior. The grayscale fringe image, obtained via direct conversion of the color pattern, had rather poor contrast. Processing this gray-scale image produced only marginal improvements in contrast. The approach of separating the color image into its blue and green components, followed by gray-scale conversion, subtraction, and other processing operations, generated images with significantly higher contrast.

We present a high-speed moiré method of color grating projection, which performs phase-shifting 3-D contouring with only a single operation of fringe capturing. Three red, green, and blue pairs of projection and viewing gratings are fabricated on a single glass plate with predetermined lateral offsets. The glass plate is translated along with the color gratings during measurement at a fast speed, so that a color CCD camera simultaneously monitors three separate patterns of moiré fringes with 2?/3 phase offset. This time-integral fringe capturing enables us to obtain high-quality moire fringes with the line images of the original viewing gratings inherently removed, which leads to better measurement accuracy with less computational burden of fringe processing.

The scattered electromagnetic near fields due to fluctuations in the surface height and/or lateral variations in the electromagnetic medium parameters are evaluated using a full-wave approach. Since the scales of the height and medium fluctuations considered could be significantly smaller or larger than the electromagnetic wavelengths, the familiar perturbation and physical/geometrical optics solutions cannot be used nor is it possible to investigate subwavelength features based on far-field measurements. The full-wave approach employs complete field expansion that includes propagating and evanescent waves as well as lateral waves and surface waves, which are not accounted for in the perturbation and physical optics solutions. Exact boundary conditions for the electric and magnetic fields are imposed at the rough interfaces. The complete modal expansions do not uniformly converge at the irregular boundaries, therefore the interchange of orders of differentiation and summation/integration of the field expansions is avoided. Large-scale and small-scale (relative to electromagnetic wavelength) approximations for the full-wave near-field solutions are expressed as integrals over the complete scattered wave number variables. Random rough surfaces as well as periodic and quasiperiodic structures are also considered.

We describe the theoretical dependence of various important parameters of the fluid jet polishing process on the material removal rate: the processing time, abrasive concentration, abrasive diameter, particle velocity, and the effect of scanning. Some recent experiments are described that prove that it is possible to remove very small amounts of material, less than 1 nm/min, using either short processing times or an appropriate slurry. The removal spot in the stationary case is compared to that in the translational case both theoretically and experimentally. From both a theoretical and an experimental point of view it is shown that the removal is in the ductile regime.

We report on an optical parametric oscillator (OPO) based on periodically poled lithium niobate (PPLN) pumped by a Nd:YAG laser, and on extending its tuning range by difference-frequency mixing of OPO output waves in GaSe crystal. Maximum combined signal and idler pulse energy of 2.7 mJ and slope efficiency of 25% have been achieved. The tuning range is 1.71 to 1.98 ?m for the signal wave and 2.81 to 2.30 ?m for the idler wave, using a single set of mirrors. As an application of this PPLN OPO, the signal and the idler waves are difference-frequency- mixed in a GaSe crystal to produce tunable mid-IR from 4.35 to 14.25 ?m. The efficiency of the mixing has been analyzed, considering the experimental results.

We propose a way of single-beam photorefractive recording of subwavelength-size binary optical data using near-field scanning optical microscopy (NSOM). Data are recorded in the form of pure (without any change in the topography of the surface) refractive index changes induced near the surface of photorefractive crystal by the light intensity distribution from the subwavelength-size fiber tip of the NSOM. This change in the refractive index can modify the transmission characteristics of the NSOM. Therefore, the characteristics of the reading beam depend on whether the light from the tapered fiber tip was previously exposed (recorded) or not, and thus can be regarded as on-off (binary) data.

We develop a novel processing technique to fabricate a 3-D photonic bandgap material by filling the voids between the microspheres of a polystyrene colloidal crystal with silver. The transmission and reflection spectra of the composite crystal show an enlargement of the band- gap situated at a/? = 0.63 and the apparition of a second one, not predicted by the plane waves method, at a/? = 1.20 due to the increase of the dielectric contrast in the novel crystal in comparison with the pure colloidal polystyrene crystal. We also observe a shift of the first peak to the higher frequencies because of the decrease of the average refractive index in the composite crystal.

A method to obtain the complete electromagnetic scattering properties of discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new generalized scattering matrix, together with the generalized telegraph equations formulism and the modal matching technique. The cross sections of the optical waveguides are simulated by means of a grid of rectangular pixels enclosed by perfectly conducting walls. Radiation losses as well as reflection and transmission coefficients between proper modes can be obtained for single and multiple abrupt discontinuities in monomode and multimode optical waveguides with arbitrary refractive index profile functions. Single and multiple discontinuities in planar and channel optical waveguides have been analyzed. Numerical results on complex scattering coefficients are given. The possibilities of the method for analyzing waveguide photonic crystals as well as optical devices in periodic waveguide structures are demonstrated.

Sparse-aperture telescopes can be designed to capture the same resolution as a filled aperture but with a significant reduction in size and weight. image-chain models have been generated for several sparse-aperture remote sensing system concepts. These models are used to generate image simulations, which are used to quantify the image quality as a function of design parameters associated with various sparse-aperture designs. This study generated image simulation models for the Annulus, Golay 6, and Tri-Arm sparse-aperture designs. A psychophysical evaluation was conducted to determine the integration time necessary to maintain the image quality as the fill factor is decreased for these designs. Image simulations were also generated to determine the accuracy of the generalized image quality equation to predict the image quality differences between the different designs.

Using a Cr4+YAG saturable absorber, we realize the running of a laser diode end-pumped passively Q-switched intracavity- frequency-doubling Nd:YVO4/KTP laser. Pulses with pulse widths ranging from 49 to 55 ns and a pulse repetition rate ranging from 35 to 60 kHz are generated. The dependences of pulsewidth and pulse repetition rate on pump power are measured. A rate equation model is introduced to theoretically analyze the results we obtain in an experiment, in which the harmonic conversion is considered as one nonlinear loss of the fundamental wave, the diffraction loss due to the thermal effect of gain media is also taken into account. The numerical calculations of the rate equations are consistent with the experimental results. A further discussion based on the theoretical analysis is presented.

A compact, passively Q-switched and mode-locked Nd:YAP laser in oscillator-amplifier configuration was designed and constructed. Operation wavelength switching (between 1.34 and 1.08 xm) was achieved with a three-mirror cavity and mechanical shutter. For Q switching and mode locking of the 1.34-?m Nd:YAP laser transition, a V3 + -doped yttrium aluminum garnet (YAG) saturable absorber was employed. The optimal performance was found after variation of the resonator length (40 to 100 cm) and of the absorber initial transmission (52% to 89%). The duration of a single pulse in a train was around 1 ns. The saturation intensity of the V3 + :YAG absorber was determined to be 10 MW/cm2. A BDN II polymer thin-film saturable absorber was used for Q switching the 1.08-?m laser transition. After amplification, the maximum output energy reached was 27 mJ (train of mode-locked pulses at 1.34 ?m) or 94 mJ (Q-switched pulse at 1.08 ?m). The output laser radiation was delivered by means of a hollow glass waveguide coated with cyclic olefin polymer and Ag, with 95% and 80% efficiencies for 1.34 and 1.08 xm, respectively.

The issue of how best to distribute a large optical collecting area is revisited, including the added integration time required for a scene imaged by sparse-aperture configurations to be processed to equal that of a filled aperture, and also its influence on system architecture. The optical performance of three sparse-aperture configurations arising from a 1998 study is presented as a function of field angle and optimization criteria. Optimization of these three specific configurations shows ray FWHM and residual rms values small enough to assure excellent diffraction-limited imagery. Practical issues concerning fabrication, assembly, testing, and on-orbit phasing are identified.

The imagery and aberrations of a large space telescope using a 100-m-diam f/100 diffractive objective are evaluated. Excellent imagery can be obtained with flat membrane optical surfaces. Interactive effects of the spectral fan of a diffractive optical element with the free- flying system architecture are considered. The parametric relationships of achromatized diffractive optical elements (DOEs) and holographic optical elements (HOEs) are explored as a function of diffraction order, focal ratio, and wavelength. Practical aspects of a pair of crossed linear DOEs are discussed. Procedures to design achromatic DOE systems are detailed and typical results presented. A number of practical issues associated with making and using high-order transmissive and reflective DOEs and HOEs are identified.

Disparity-compensated residual coding (DCRC) is the most popular approach to stereo image coding because of its simplicity and good performance. Researches on DCRC have investigated two main topics: quantization of discrete cosine transform (DCT) coefficients and disparity field estimation and compensation. It is shown that quantization problems can be optimized in a rate-distortion (RD) sense under the fixed-disparity constraint and that the RD-optimized disparity field can be obtained under the fixed-quantizer constraint. This paper proposes a technique that jointly optimizes DCT coefficient quantization and disparity field estimation using the three-dimensional Viterbi algorithm with respect to the RD theory under three constraints: epipolar constraint, interblock disparity constraint, and intrablock disparity constraint. The proposed algorithm reduces not only the bit rate of the disparity map but also that of DCT coefficients, leading to performance improvement. Also, it overcomes shortcomings of conventional methods and is well applied to the narrow-angle stereo camera systems. The effectiveness of the proposed algorithm is shown via computer simulations.

Microscale optical spectroscopic probe techniques, mainly micro-Raman scattering (m-RS) and microphotoluminescence (?-PL) spectroscopy, are employed to study a variety of GaN thin film materials, undoped and Si and Mg doped, grown on c-sapphire substrates by lowpressure metal-organic chemical vapor deposition. The optical properties and correlated structural features of these epitaxial materials grown under different conditions are studied. Visible micro-Raman measurements show different mode behaviors under different laser incidence configurations. Raman line shape analysis through two sets of equations leads to the monitoring of the sample quality and stress, and the optical determination of electrical properties of GaN films. An approximate 3 cm-1 shift in the E1 (LO) mode frequency is observed across the GaN film from the sapphire/GaN interface to the GaN surface, indicating the spatial variation of strains along the film growth direction within a few micrometers thickness range. Combined Raman and PL spectra are obtained under UV excitation, and interesting high-order resonance Raman features are observed using a sensitive UV-Raman-PL microscope. A new way to characterize the p-type GaN is introduced. These fruitful results demonstrate the capabilities of ?-RS-PL technology for the research and development of GaN and other materials.

The sensitivity and hysteresis effects of ion-sensitive field- effect transistor (ISFET) devices based on a-WO3, Ta2O5, and a-Si:H thin films have been investigated. The pH sensitivity is one of the important characteristic parameters of ISFET devices, and the response of an ISFET is mainly determined by the type of the sensing membrane; therefore the sensing material plays a significant role. Furthermore, hysteresis leads to inaccuracy and instability of ISFET measuring devices. In this investigation the pH sensitivities of different sensing-gate ISFET devices were measured in different buffer solutions by current-voltage (I-V) measurement, and the hysteresis curves were measured by exposing the device to several cycles of pH values over different loop times. According to the experimental results, a-WO3 and a-Si:H are useful in acidic buffer solutions (pH 1 to 7), and Ta2O5 at pH 1 to 12. The pH sensitivities are all larger than 50 mV/pH, and it was found that the key parameter in determining the hysteresis width is the loop time.

Natural and synthetic guide stars can serve as beacons for Shack-Hartmann wavefront sensors in space-based applications. In this paper, the authors determine the key equations that govern the optimization of the wavefront sensor employed on a space-based imaging system. There are two major products of this analysis. First, the number of subapertures can be optimized. Second, the number of modes used in the wavefront recovery can be optimized. Finally, the process for optimizing these values is explained. For the examples shown, the optimal number of retrieved modes and the optimal number of subapertures are determined.

Laser reflectivity from an interface can be used to characterize, among other things, interface roughness, multilayer structure, and optical constants. In many cases, the reflectivity has sharp features that may be more apparent in a measurement of the angle derivative of the reflectivity.

In the development of new-technology solar coronagraphs based on the use of superpolished primary objective mirrors,1 several optical design solutions have been investigated.