Showing papers on "Wavefront published in 1983"

Digital wave-front measuring interferometry: some systematic error sources.

Abstract: Digital wave-front measuring interferometry is a well-established technique but only few investigations of systematic error sources have been carried out so far. In this work three especially serious error sources are discussed in some detail: inaccuracies of the reference phase values needed for this type of evaluation technique; disturbances due to extraneous fringes; and spatially high frequency noise on the wave fronts caused by dust particles, inhomogeneities, etc. For the first two error sources formulas of the resulting phase deviation are derived and compensation possibilities discussed and experimentally verified. To study the occurrence of wave-front irregularities caused by dust particles a model has been developed and countermeasures derived which assure sufficient regularity of contour line plots. The repeatability of the present experimental setup was better than λ/200 within the 3σ limits.

Focusing of spherical Gaussian beams.

Abstract: Simple procedures and formulas for tracing the characteristics of a spherical Gaussian beam through a train of lenses or mirrors are described which are analogous to those used in geometrical optics to trace repeated images through an optical train.

Optimal wave-front correction using slope measurements

Abstract: In adaptive optical systems that compensate for random wave-front disturbances, a wave front is measured and corrections are made to bring it to the desired shape For most systems of this type, the local wave-front slope is first measured, the wave front is next reconstructed from the slope, and a correction is then fitted to the reconstructed wave front Here a more realistic model of the wave-front measurements is used than in the previous literature, and wave-front estimation and correction are analyzed as a unified process rather than being treated as separate and independent processes The optimum control law is derived for an arbitrary array of slope sensors and an arbitrary array of correctors Application of this law is shown to produce improved results with noisy measurements The residual error is shown to depend directly on the density of the slope measurements, but the sensitivity to the precise location of the measurements that was indicated in the earlier literature is not observed

Reshaping collimated laser beams with Gaussian profile to uniform profiles.

Abstract: A set of holographic filters was developed to convert the Gaussian intensity distribution of a collimated laser beam into a uniform one. The design and the fabricating method of the holographic filters are presented and experimental results are shown.

Measurement of electrical signals with picosecond resolution

Abstract: Electrical signals are measured (analyzed and displayed) with subpicosecond resolution by electro-optic sampling of the signal in an electro-optic crystal, the index of which changes in response to the electric field produced by the signal, in accordance with the Pockels effect. The crystal is disposed adjacent to a transmission line along which the signals propagate the line may be a coplanar wave guide having a plurality of parallel strips of conductive material on the surface of the crystal. The crystal may be disposed adjacent to and in the fringe field of a line on a substrate, which may be part of an integrated circuit, for measuring signals propagating along the line during the operation of the circuit. A beam of short optical (laser) sampling pulses in the picosecond range is focused so that the region where the beam is confocal is disposed where the field is parallel in the crystal. The confocal region (where the optical wavefront is planar is preferrably close to the surface of the crystal and perpendicular to the optical axis of the crystal. The optical pulses transmitted through the crystal are processed to provide a display affording a measurement of the electrical signal.

Elliptical anisotropy—Its significance and meaning

Abstract: Nonspherical wavefronts in anisotropic media are often assumed to be approximately elliptical. However, in transversely isotropic media only the wavefront of SH waves is always an oblate ellipsoid. The wavefront of SV waves is never an ellipsoid, and the wavefront of P waves is an oblate ellipsoid if and only if the expression (c11-c44)(c33-c44)-(c13+c44)2 vanishes. This cannot happen if the anisotropy is due to lamellation (periodic layering with a spatial period small in comparison to the wave length). The occurrence of elliptical wavefronts cannot be detected on the basis of surface observations of times alone, since the complete wave field can be transformed into one with spherical wavefronts everywhere by simple stretching of layers. Neither arrival times nor apparent slownesses (and thus Snell’s law) are affected by this transformation. All concepts and algorithms applicable to spherical wavefronts are applicable to elliptical wavefronts, in particular the determination of a velocity as the zero‐off...

Coherent scattering of a spherical wave from an irregular surface

Abstract: The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.

Interferometric wavefront measurement

Abstract: Apparatus is disclosed for the phase measurement of an interference pattern produced by an unequal path interferometer. The invention comprises in one embodiment the use of a diode laser light source whose wavelength is varied so that the phase difference between the two wavefronts producing the interference pattern is modulated by a known amount. The modulated interference pattern is photosensed with an imaging device, and the signals processed to provide a phase map representing the optical path difference between the reference and measurement wavefronts of the interferometer.

Creeping waves and resonances in transient scattering by smooth convex objects

Abstract: Scattering by smooth convex objects, excited by a transient field with broad spectral content, has been analyzed either by ray formulations, which are useful at observation times descriptive of the early arrivals, or by the complex resonances of the singularity expansion method (SEM), which are most appropriate at intermediate and late observation times. Within the framework of SEM, efforts have recently been made to show that in a grouping of the resonances along "layers," rather than along the conventional "arcs" based on an angular harmonic field representation, the higher order resonances behave collectively like a wave traveling circumferentially around the object. This observation has provided the stimulus for the present investigation in which the relation between the wavefront arrivals (creeping waves) and the SEM resonances is placed on a rigorous basis. Using a perfectly conducting circular cylinder as a canonical model, this is done by direct application of the theory of characteristic Green's functions to construct alternative field solutions, and by collective summation of groups of wavefront arrivals or groups of resonances. The connection between creeping waves and resonances thus having been established, hybrid formulations are developed which combine the creeping waves and the SEM resonances within a single rigorous framework so as to maximize the utility of each over the entire range of observation times. These results are then generalized to smooth cylindrical objects with noncircular convex shape.

Characteristic Initial Data and Wavefront Singularities in General Relativity

Abstract: The structure of singularities (caustics), self-intersections of wavefronts (null hypersurfaces) and wavefront families (null coordinates) in arbitrary space-times is discussed in detail and illustrated by explicit examples of stable wavefront singularities in Minkowski space. It is shown how characteristic initial data determine the caustics and the self-intersections of the characteristics of Einstein’s field equations.

Aberrations of holographic toroidal grating systems.

Abstract: Expressions are derived for the sixteen wave front aberration coefficients of a single grating. These give the wave aberrations to the fourth order for a plane symmetric grating system. The contributions from each mirror and grating can be added to give the aberrations in the final image. Problems encountered with intermediate astigmatic images are overcome by defining the wave front aberration with respect to an astigmatic reference surface. There is one field variable describing displacement of the object point from the symmetry plane. The aperture stop may be placed anywhere in the system, and equations are given for the aberration changes produced by sifting this position.

Optical performance of a diffraction-limited molded-glass biaspheric lens

Abstract: Optical performance results are reported for a molded-glass biaspheric lens. The 6-mm optical diam lens is intended for use in a laser-based optical disk application. The design with fabrication tolerances has an expected on-axis transmitted wave-front performance of 0.06-wave rms optical path difference (OPD) when tested at 0.6328 μm and a numerical aperture of 0.45. Transmitted wave-front aberrations were measured on actual molded lenses using a heterodyne interferometer. Typical performance was 0.05–0.08-wave rms-OPD. Experimental results involving mold rotation indicate that lens performance is primarily limited by a surface figure accuracy of one of the molds.

Optimum holographic elements recorded with nonspherical wave fronts

Abstract: The problem of designing a flat, aspheric, holographic optical element that images a finite set of input wave fronts into a finite set of output wave fronts is rigorously analyzed. The optimum phase transfer function of the holographic optical element is analytically determined. The optimum phase transfer function is defined as the one for which the element has minimum mean-squared wave-front error averaged over the set of input wave fronts. It is also shown that in general it may not be possible to obtain a low value for this average mean-squared wave-front error by using a single holographic element. Furthermore, the performance trade-off of spherical aberration, coma, and astigmatism versus geometric distortion is clearly indicated by example.

Scanning pulsed-polarization spectrometer applied to Na 2

Abstract: We report on a computer-controlled system for pulsed-polarization-labeling spectroscopy using a Fizeau-wedge wavemeter and a scanned narrow-band probe. Constants for n=3-7 Σ1g+ states in Na2 are presented.

Interferometry of wave fronts reflected off conical surfaces.

Abstract: Interferometry of wave fronts reflected off conical surfaces requires new interferometric schemes. The pencil beam interferometer is proposed as a metrology tool for conical as well as for spherical optical surfaces. The instrument employs two narrow pencil beams which scan the optical surface to be measured. An electronic fringe position readout system, which measures the location of the fringes that develop through interference of the pencil beams, provides high accuracy surface information. Metrology on a waxicon indicates a measurement precision of ±6 nm. Due to the differential nature of the instrument, alignment requirements are relatively modest.

Wave front sensor

Abstract: An improved wave front sensor for analyzing, measuring and controlling optical wave fronts incorporates detectors having a large number of photosensitive elements smaller than the beam spot size so that source and reference beam spot centers may be more accurately located and greater alignment errors may be tolerated. A reference beam may be switched on intermittently, thereby improving signal-to-noise ratio.

Technique for real-time high-resolution adaptive phase compensation

Abstract: An “all-optical” approach for the realization of adaptive optical systems potentially containing in excess of a million spatial-resolution elements is reported. A phase-measurement and -compensation technique called an interference phase loop is employed in conjunction with a monolithic optically addressed spatial light modulator (SLM). Wave-front phase compensation and shaping, and the ability to ignore amplitude fluctuations and compensate phase in real time over multiple π radians of dynamic range, were demonstrated in two discrete-channel laboratory test systems containing one and nineteen resolution elements. All-optical phase compensation with a monolithic SLM was also successfully demonstrated.

Aberration-free nonparaxial self-imaging

Abstract: The fields diffracted by planar one- or two-dimensional periodic objects, and in particular their Fourier and Fresnel self-images, can be computed with the aid of a ray-tracing technique based on the Fermat principle. This method (geometrical self-imaging) yields accurate results for any numerical aperture and image field. An analytical study of the image formation, carried out in the fourth-order approximation for the phase, leads to the definition of self-imaging aberrations. These aberrations are strongly dependent on spatial frequency and render the well-known relationships derived by Rayleigh for the location and magnification of self-images approximate at best. The aberrations can be described graphically by a phase diagram and a magnification diagram, which permit interpretation of the properties of high-aperture, large-field self-images and the prediction of optimal imaging conditions. In the case of large magnifications (100× and larger), we present a simple method to eliminate all fourth-order aberrations completely and even sixth-order ones partially. This method consists of introducing a compensating spherical aberration to the incident wave, e.g., by the insertion of a glass plate of appropriate index and thickness just before the object. Thus object spatial frequencies up to about 800 mm−1 can be imaged almost without aberration for several image periods.

Image transmission through a turbulent medium using a point reflector and four-wave mixing in BSO crystal.

Abstract: A method of one-way image transmission through a turbulent medium is presented using four-wave mixing in BSO crystal. In this method, a pointlike reflector is placed on the observation plane to return part of the incident wave, giving the instantaneous wave propagation function of the turbulent medium to the image transmission side. The returned wave together with the plane reference wave and the Fourier-transformed input image wave is impinged in BSO crystal to modulate the image wave by the phase-conjugate wave, so that transmission of the image with reduced turbulence effects is achieved. The principle and laboratory experimental results are given.

Instantaneous Phase Measuring Interferometry

Abstract: Conventional phase measuring interferometry normally requires one-half to sixty seconds acquisition time, limiting measurement to stationary phenomenon such as optical element wavefronts. We have developed an instantaneous PMI that measures displacements at one point to a resolution of 0.003 microns. We will describe this instrument and an interferometer measuring phase to lambda/2000 with a measurement aperture of less than one microsec. Also described is an attached system for analysing and displaying wavefronts at up to 10 Hz.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Real-time diffraction interferometer

Abstract: A real-time diffraction interferometer for analyzing an optical beam comprises converging means (13) for bringing the beam to a focus at focal point (14), and an apertured grating structure (20) positionable adjacent the focal point (14). The apertured grating structure (20) comprises a transparent substrate (10'), an obverse surface of which is coated with a translucent coating (11) except for a pinhole-sized spot (12) that is left uncoated so as to function as an aperture in the coating (11). A reverse surface of the substrate (10') has a lenticulate surface configuration, which functions as a diffraction grating. The beam incident upon the apertured grating structure (20) is separated into a major portion, which is transmitted with attenuated intensity through the translucent coating (11), and a minor portion, which is transmitted with undiminished intensity through the pinhole aperture (12). The major portion of the beam is diffracted into spatially separated diffraction components, and the minor portion of the beam is diffracted by the pinhole aperture (12) so as to acquire a spherical wavefront. Interference patterns produced by interference of the spherical wavefront with each of the wavefronts of the zeroth order and the positive and negative first-order diffraction components of the intensity-attenuated beam transmitted by the coating (11) are separately imaged on conventional solid-state photodetectors (21, 22 and 23).

Determination of the refractive index of a lens using the Murty shearing interferometer.

Abstract: An innovative nondestructive technique for mesuring the refractive index of a simple lens is described. The proposed method is superior to existing ones because the focusing error and the spherical aberrations are reduced. Apart from this, the strength parameters (i.e., r1 and r2) of a lens are not required at all since the derived lens-index formula is independent of the lens's physical parameters. The shearing interferometric technique is a sensitive aid for detecting the focal plane of the test lens. A modified criterion for determining the focal length has been used. In this case two miscible liquids or compounds are not necessary. The well-known liquid immersion method is the particular case of this technique. The Murty shearing interferometer has been used as an optical device to observe the defocusing defect in the form of fringes. The amount of defocusing is easily calculated. An equation for this error has been theoretically deduced and experimentally verified. The technique described is quick to perform and easy in handling. The various effects due to the lens's aperture and aberrations, thickness of the glass cell, liquid column, etc. are also discussed. For N liquids, there are N (N − 1)/2 ways of calculating the lens′s index. Owing to its nature this is termed the nondestructive nonmiscible-liquid immersion technique for index measurement of a lens.

Passive synthetic aperture system for imaging a source of electromagnetic radiation

Abstract: A vehicle-mounted passive synthetic aperture system for locating sources of electromagnetic radiation having a given wavelength λ. The system includes first and second receiving antennas, a phase sensitive receiver and a signal processor. The first and second antennas are mounted to a vehicle and spaced apart from each other in the principle direction of motion associated with the vehicle. The first and second antennas respectively provide first and second received signals in response to a wavefront of electromagnetic radiation having the given wavelength λ. The phase sensitive receiver is coupled to the first and second antennas and responds to the first and second received signals by providing a phase difference signal that indicates a phase difference φ between the wavefronts of the radiation of the given wavelength received by the respective first and second antennas when the received radiation is radiated spherically from its source. The speed of the vehicle also is measured. The signal processor processes the phase difference signal in combination with the measured vehicle speed to provide imaging signals for an object-space display of an image of the source of the electromagnetic radiation in relation to the location of the vehicle. The image is displayed. The system of the present invention effectively uses the motion of the vehicle to synthesize an aperture. The synthesized aperture is long relative to the spacing between the receiving antennas (which spacing is limited by vehicle size) so that angular resolution is greater than that of a fixed antenna system with a baseline length equal to the spacing between the receiving antennas of the present system.

Separating Misalignment From Misfigure In Interferograms On Off-Axis Aspheres

Abstract: Two procedures are presented that allow for unambiguous separation of misalignment from misfigure in off-axis asphere interferograms. In the first method the coma observed is used to locate the element, while in the second method the element is located by minimizing the observed mean-square wavefront error. With either procedure, the misalignment-induced aberrations can be calculated and subtracted from the interferogram so that only true misfigure remains.

Photolithography experiments using forced Rayleigh scattering

Abstract: Phase conjugate wavefront generation by degenerate four‐wave mixing has been used to project images with spatial resolution greater than 500 line pairs per millimeter. The nonlinear medium, a solution of rhodamine 6G in acetone, produced the images by forced Rayleigh scattering. These images were bright enough to expose photoresist in 30 sec and their quality was adequate for fine‐line lithography and consistent with theoretical expectations.

Comparison Of Wavefront Sensor Configurations Using Optimal Reconstruction And Correction

Abstract: Recent work on optimal reconstruction of wavefronts from slope measurements has developed methods based on more realistic models of sensor devices. These methods also resolve certain ambiguities present in earlier reconstruction methods. In the present paper, these methods are applied to sensor configurations which have been proposed in the literature and the errors in estimating and correcting wavefronts are compared.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Aberrations Of Optical Systems With Large Tilts And Decentrations

Abstract: A computer program has been developed to analytically describe the first and third order properties of systems with large tilts and decentrations. The program describes the imagery through analytic formulae, in both the pupil and field variables, rather than by interpretation of ray trace data at sample points in the field. The first order properties of both the image and the pupil are described in terms of tilt, decentration, magnification, keystone distortion, and anamorphic distortion parameters. In computing these parameters, it is important to take into account the transferred components of the parameters, which are due to the first-order properties of the previous surfaces. The third order properties are computed by representing the surface aberration contributions as vector fields and summing them vectorially. The third order properties are described in terms of a coma field with a node displaced from the center of the image, a binodal astigmatism field, a trinodal distortion field, and a focal surface that is curved and displaced from the Gaussian image in both the transverse and longitudinal directions. The program is applied to several systems, and the results are compared to ray trace data. The interaction between large first order aberrations of intermediate images and pupils, and the third order properties of the image is discussed. Applications of the vector aberration field technique toward an automated design procedure are considered.

Holographic local-oscillator beam multiplexing for array heterodyne detection

Abstract: Linear holographic gratings have been developed that can be used for amplitude and phase matching of local oscillator (LO) and signal wave fronts in heterodyne detection with infrared imaging arrays. With these holographic gratings the system’s signal-to-noise ratio and resolution can be maximized, and the LO power dissipation on the focal plane can be minimized. A holographic surface relief pattern multiplexes the LO beam when a single LO laser beam illuminates it. Each beam of this multiplexed set then has the same amplitude shape as and is collinear with each element of the signal wave front illuminating the array.

Linear Methods In Phase Retrieval

Abstract: On-orbit wavefront sensing and active alignment control are essential features of many spaceborne optical systems currently being developed. Phase retrieval is an especially appropriate wavefront sensing technique for this application, because it directly monitors system image quality and eliminates or reduces the need for auxiliary wavefront sensors. Although the general phase retrieval problem is highly complex and requires sophisticated nonlinear estimation techniques, properly selected linear methods provide satisfactory and efficient solutions to a number of important special cases. This paper discusses the per­ formance of several such linear phase retrieval algorithms. One method yields noise-optimal estimates of small wavefront errors, while a second approach can be used with arbitrarily large errors but is much more sensitive to noise. These two phase retrieval algorithms are actually special cases of a general linear algorithm that can be tuned as a function of wavefront error characteristics, measurement noise statistics, and focal plane detector geometry.Introduction the utility of linear phase retrievalOptical systems with large apertures and high resolution over a wide field of view will be required for a variety of future infrared- and visible-wavelength space sensors. The optical forms selected for these systems frequently consist of fast, off-axis mirrors that are highly sensitive to misalignments. Passive structural approaches to achieving the required opto-mechanical tolerances in such telescopes are often not feasible because sensor weight must be kept low; periodic or active on-orbit alignment sensing and control are then necessary when conventional passive approaches are inadequate. Phase retrieval from focal plane imagery is an attractive approach to alignment error sensing for this application, because it controls alignment directly on the basis of optical system performance and avoids the physical complexity of auxiliary alignment sensors, which are subject to drift or failure.Although the general phase retrieval problem is highly complex and requires sophisticated nonlinear estimation methods for its solution,1"5 three aspects of the phase retrieval application summarized above suggest that a simpler approach may prove satisfactory in this case. For near- to mid-term applications, the wavefront errors to be estimated will arise from rigid body mirror misalignments or from low-frequency mirror thermal deformations. The number of wavefront degrees freedom will therefore vary from three to approximately twenty.The phase retrieval algorithm need not obtain an exact value for wavefront error in a single application, but must instead produce satisfactory optical alignment after several cycles of alignment error estimation and correction. Point sources in the form of stars or beacons can be assumed for many potential systems. Granted these simplifying assumptions, it appears that properly devised linear phase retrieval algorithms possess sufficient accu­ racy and range to "fine tune" the alignment of optical systems with wavefront errors of up to 0.3 to 0.4 waves rms. These linear algorithms impose comparatively modest signal processing requirements, and therefore would be valuable when (as is usual) sensor signal processing requirements must be minimized.The remainder of this paper describes the theory and application of linear phase retrieval algorithms in greater detail. First, the advantages and limitations of two early attempts at linear phase retrieval are described, and then an optimal linear algorithm that a) is tunable as a function of operating conditions, b) permits performance analysis via closed-form equations of expected estimation accuracy, and c) can be specialized to the two previously described methods as limit cases, is presented. Then several additional applica­ tions of this linear phase retrieval algorithm are discussed.90