Computer simulation of schlieren images of rotationally symmetric plasma systems: a simple method

Schlieren techniques are commonly used methods for quantitative analysis of cylindrical or spherical index of refraction profiles. Many schlieren objects, however, are characterized by more complex geometries, so we have investigated the more general case of noncylindrical, rotationally symmetric distributions of index of refraction n(r,z). Assuming straight ray paths in the schlieren object we have calculated 2-D beam deviation profiles. It is shown that experimental schlieren images of the noncylindrical plasma generated by a plasma focus device can be simulated with these deviation profiles. The computer simulation allows a quantitative analysis of these schlieren images, which yields, for example, the plasma parameters, electron density, and electron density gradients.     

Demonstration of a linear optical true-time delay device by use of a microelectromechanical mirror array

We present the design and proof-of-concept demonstration of an optical device capable of producing true-time delay(s) (TTD)(s) for phased array antennas. This TTD device uses a free-space approach consisting of a single microelectromechanical systems (MEMS) mirror array in a multiple reflection spherical mirror configuration based on the White cell. Divergence is avoided by periodic refocusing by the mirrors. By using the MEMS mirror to switch between paths of different lengths, time delays are generated. Six different delays in 1-ns increments were demonstrated by using the Texas Instruments Digital Micromirror Device as the switching element. Losses of 1.6 to 5.2 dB per bounce and crosstalk of -27 dB were also measured, both resulting primarily from diffraction from holes in each pixel and the inter-pixel gaps of the MEMS.     

Fourth-order optical aberrations and phase-space transformation for reflection and diffraction optics

One can derive fourth-order optical ray deviations for a mirror or grating from the optical path function by using the analytical code REDUCE. Some of the aberrations are discussed for normal-incidence and grazing-incidence monochromators. The nonlinear transformation of light from the source to the image plane of a mirror or grating is represented by a transformation matrix. The optical properties of a combination of several optical elements are given by the product of the matrices of the individual optical elements. The matrix elements can be interpreted as optical aberrations. A program has been written that optimizes a complete beam line with respect to various optical aberrations by minimizing an appropriate cost function that is built from a weighted sum of the matrix elements.     

Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field

We report on interferometric characterization of a deep parabolic mirror with a depth of more than five times its focal length. The interferometer is of Fizeau type; its core consists of the mirror itself, a spherical null element, and a reference flat. Because of the extreme solid angle produced by the paraboloid, the alignment of the setup appears to be very critical and needs auxiliary systems for control. Aberrations caused by misalignments are removed via fitting of suitable functionals provided by means of ray tracing simulations. It turns out that the usual misalignment approximations fail under these extreme conditions.     

Exact ray-trace beam for an off-axis paraboloid surface

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.     

High-aspect-ratio line focus for an x-ray laser by a deformable mirror

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 mum and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.     

Improved field scanner incorporating parabolic optics. Part 2: Experimental verification and potential for volume scanning

We investigated the experimental performance of an afocal scan engine employing two off-axis parabolic reflectors and it was found not to introduce astigmatism when compared to a freely propagated beam. The performance of the new afocal engine is very similar to an ideal single-mirror scan engine in terms of spot size and beam spot profile (or point spread function) and has an improved flatness of field over other two-dimensional laser scan engines. The parabolic scan engine is contrasted with a comparable spherical mirror arrangement and found to produce superior performance at the intermediate image plane when focused through a scan lens. Further modeling and experimentation point toward volume scanning applications. The significant performance improvement provided by this design, now verified experimentally, will result in superior image quality for fast scanning confocal and two-photon microscopy in particular.     

Automatic Design of a Czerny-Turner Spectrograph by a Nonlinear Optimization Method

Abstract

A generalized least-squares method not involving the calculation of derivatives has been adopted to the design of a Czerny-Turner spectrograph/monochromator system for use in coupling with a predisperser. A formula for the automatic orientation of an optical surface for ray tracing is applied to the system optimization during the computation. The designed spectrograph system satisfies design requirements, and the image performance of the system is shown by comparison with spot diagrams and geometrical line profiles of spectral images.     

Design of a high-throughput grazing-incidence flat-field spectrometer

The optical design of a high-throughput grazing-incidence flat-field spectrometer is presented. The spectral focal curve is almost a straight line because of the flat-field focusing properties of spherical variable-line-spaced gratings. The angular acceptance in the direction perpendicular to the plane of dispersion is maximized by means of a focusing spherical mirror mounted with its tangential plane coincident with the sagittal plane of the grating. Analytical calculations for the determination of the optimum mirror parameters are presented. A spectrometer for high-throughput experiments in the 800-60-eV region is designed with an extreme-ultraviolet-enhanced CCD detector: when the available flux is compared with that of a spectrometer with the same kinds of grating and detector but without a focusing mirror, the increase is as much as a factor 3.     

Off-axis mirror based optical system design for circularization, collimation, and expansion of elliptical laser beams

In this paper, we present two optical system design methods for beam circularization, collimation, and expansion of semiconductor laser output beam for possible application in LIDAR systems. Two different optical mirror systems are investigated: an off-axis hyperbolic/parabolic mirror system and an off-axis parabolic mirror system. Equations specific to these mirror systems are derived and computer package programs such as ZEMAX and MATLAB are used to simulate the optical designs. The beam reshaping results are presented.     

Surface gradient integrated profiler for X-ray and EUV optics

A new ultraprecise profiler has been developed to measure, for example, asymmetric and aspheric profiles. The principle of our measuring method is that the normal vector at each point on the surface is determined by making the incident light beam on the mirror surface and the reflected beam at that point of coincident. The gradient at each point is calculated from the normal vector, and the surface profile is then obtained by integrating the gradients. The measuring instrument was designed in accordance with the above principle. In the design, four ultraprecise goniometers were applied to adjust the light axis for normal vector measurement. The angle-positioning resolution and accuracy of each goniometer are, respectively, 0.018 and 0.2 μrad. Thus, in the measuring instrument, the most important factor is the accuracy of the normal vectors measured by the goniometers. Therefore, the rotating angle-positioning errors were measured and calibrated. An elliptical profile mirror for nanometer hard-X-ray focusing was measured, and compared with the measured profile using a stitching interferometer. The absolute measurement accuracy of approximately 5 nm (peak-to-valley) was achieved. Then the measurements of 1000-mm-long flat, spherical and parabolic mirrors were demonstrated. The surface profiles of the mirrors were obtained by integrating the interpolated gradient.     

Optical characterization of a reference instrument for gloss measurements in both a collimated and a converging beam geometry

A reference instrument has been developed at the National Research Council of Canada for rapid, reproducible specular gloss measurements. The design and validation of this instrument for specular gloss measurements in accordance with standard methods for paints and plastics at 20 degree, 60 degree, and 85 degree geometries [American Society for Testing and Materials (ASTM) D523 and the International Organization for Standards (ISO) 2813] have been recently reported. These standard methods require a collimated beam geometry. Here we present the optical design considerations and characterization of this instrument to extend its gloss measurement capabilities to specular gloss measurements of paper samples at 75 degree geometry in accordance with standard test methods requiring a converging beam geometry (ASTM D1223 and TAPPI T480). This is, to the best of our knowledge, the first reported reference instrument that provides direct traceability for both types of standard gloss method and applications. The design challenge was to convert from a collimated beam to converging beam geometry while meeting the rigorous requirements of beam uniformity at the sample and receptor apertures specified in the 75 degree geometry test methods. We describe the innovative design to achieve this degree of functionality and reference instrument performance. The instrument's optical performance has been characterized theoretically and by comparison with measurement results. The light collection and detection systems have been analyzed via Monte Carlo simulation and ray tracing. The instrument validation includes comparison of the measurement results with theoretical gloss values for quartz, black glass, Vitrolite, and mirror gloss working standards, giving agreement of better than 0.32%. Measurement validation also involved participation in the Collaborative Testing Services program interlaboratory comparison measurements of 75 degree gloss for white papers.     

High-resolution tunable spectrograph for x-ray laser linewidth measurements with a plane varied-line-spacing grating

We describe a spectrograph for x-ray laser linewidth measurements in the range 100-220 A. The design employs a plane varied-line-spacing grating operating in the convergent light produced by imaging of the entrance slit with a concave spherical mirror. By the appropriate choice of the linear term in the grating-spacing variation, two separate wavelengths can be focused at the same image distance. As a result all wavelengths within the range of interest are focused at or near the same distance. The spectrograph can be tuned by rotation of the grating to bring any wavelength within the range to the center of the focal plane, and the spectra are dispersed on a surface that is erect or practically flat and perpendicular to the principal ray. This allows the use of a planar detector. With a streak camera used as a detector, the instrument obtained time-resolved linewidth data on x-ray lasers with a resolving power of 1 x 10(4) to 2 x 10(4). This paper presents the design methods used to optimize the varied-line-spacing grating, the design of the tunable spectrograph, and the results from the instrument in operation.     

Optical design of freeform two-mirror beam-shaping systems

The problem of design of a two-mirror optical system for reshaping the irradiance distribution of a laser beam in a prescribed manner is considered in the geometrical optics approximation. The presented design equations are derived in a rigorous manner and are applicable to two-mirror optical systems not limited to radiance profiles and beam cross sections that are rotational or rectangular symmetric. The resulting mirrors are free-form surfaces not restricted by a priori constraints. Moreover, the presented approach shows also that even in the general case two different designs are available for the same data. In one of these designs the first mirror is always concave and the second is convex, while in the second design the resulting mirrors may be neither convex nor concave. Since, in general, the surface mirrors are aspherical, the availability of a design with convex and concave mirrors is particularly important for fabrication.     

Spherical-grating monochromator with a variable-line-spaced grating for synchrotron radiation

An optical design for spherical-grating monochromators for application to synchrotron radiation is presented. High spectral and spatial performance is obtained with a spherical variable-line-spaced grating coupled to a spherical mirror with its tangential plane coincident with the grating's equatorial plane. The monochromator works without an entrance slit in an off-Rowland configuration with a fixed entrance arm and demagnification on the exit slit. The law for groove-space variation of the grating compensates for the main spectral aberrations; spectral focusing in an extended energy range is ensured by a slight change in the exit arm with translations of the order of a few tens of millimeters. The inclusion of a spherical mirror ensures focusing on a plane perpendicular to the plane of spectral dispersion. The ultimate resolution is limited by the slope errors of a single spherical surface. The layout is applied to the design of a high-resolution monochromator for the 1000-250-eV region.     

Reshaping of a Divergent Elliptical Gaussian Laser Beam Into a Circular, Collimated, and Uniform Beam With Aspherical Lens Design

In this paper, we present a specific optical system of two aspherical lenses designed to circularize, collimate, and expand an edge-emitting semiconductor laser beam and transform its irradiance distribution from Gaussian to a uniform-square distribution for possible application in light detection and ranging sensors. It is verified that the diffraction effects are negligible so that geometrical ray optics is used to design this optical system. To accomplish the design, the source beam profile is decoupled into two independent beam profiles represented in two transverse directions. Analytical equations specific to this lens system are derived and MATLAB is used to solve these equations and simulate a design example. Results are presented for a specific example.      

Designing reflectors to generate a line-shaped directivity diagram

A novel method of designing a mirror surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the mirror surface for an arbitrary illuminating beam wavefront is derived as an envelope of a parametric family of surfaces. Each surface in the family transforms the input beam into a beam with plane wavefront of desired direction. For the spherical illuminating beam the mirror surface is given as the envelope of the family of rotational paraboloids. The envelope is represented as a family of curves given by the intersections of paraboloids with circular cones of rays from the point source.     

Development of a pumping laser system for x-ray laser research

A two-beam chirped-pulse-amplification Nd:glass laser system dedicated to x-ray laser research is described. Each beam provides an output energy of 20 J with a typical pulse duration of 1.3 ps. A prepulse of variable duration is generated by use of a novel, to our knowledge, optical system. A reflection optical system, comprised of an off-axis parabolic mirror and a spherical mirror, produces a line focus with 6-mm length and 165-microm width without chromatic aberration. By use of this pumping laser system, the nickel-like silver x-ray laser at a wavelength of 13.9 nm has been demonstrated.     

Generation of a flat-top laser beam for gravitational wave detectors by means of a nonspherical Fabry-Perot resonator

We have tested a new kind of Fabry-Perot long-baseline optical resonator proposed to reduce the thermal noise sensitivity of gravitational wave interferometric detectors--the "mesa beam" cavity--whose flat top beam shape is achieved by means of an aspherical end mirror. We present the fundamental mode intensity pattern for this cavity and its distortion due to surface imperfections and tilt misalignments, and contrast the higher order mode patterns to the Gauss-Laguerre modes of a spherical mirror cavity. We discuss the effects of mirror tilts on cavity alignment and locking and present measurements of the mesa beam tilt sensitivity.