Showing papers on "Wavefront published in 1982"

Phase Retrieval And Diversity In Adaptive Optics

Abstract: Wavefront sensing by phase retrieval implies extraction of the Fourier transform of a complex signal based on observation of the modulus of the signal Only the image intensity from a system's focal plane array is required to estimate the phase aberrations These estimates are used to derive control signals to align (or to maintain alignment of) the optical system The concept can be used in both a predetection and postdetection mode In the former, the control system labors to keep the optics in a diffraction-limited mode all the time In the latter, the control system induces a phase or wavelength diversity that allows successive images to be restored to nearly diffraction-limited quality by postprocessing of the image This second mode is particularly interesting because it will reduce the design effort for both the optical system and the control system How the phase or wavelength diversity is achieved is not clear at this time If the method has utility, it provides an interesting challenge to designers of optical devices In this paper we describe the mathematics of the technique and show some computer simulations which involve both point sources and extended objects

Wavefront Array Processor: Language, Architecture, and Applications

Abstract: This paper describes the development of a wavefront-based language and architecture for a programmable special-purpose multiprocessor array. Based on the notion of computational wavefront, the hardware of the processor array is designed to provide a computing medium that preserves the key properties of the wavefront. In conjunction, a wavefront language (MDFL) is introduced that drastically reduces the complexity of the description of parallel algorithms and simulates the wavefront propagation across the computing network. Together, the hardware and the language lead to a programmable wavefront array processor (WAP). The WAP blends the advantages of the dedicated systolic array and the general-purpose data-flow machine, and provides a powerful tool for the high-speed execution of a large class of matrix operations and related algorithms which have widespread applications.

Computer-Originated Aspheric Holographic Optical Elements

Abstract: Holographic optical elements (HOEs) recorded with arbitrary aspheric wavefronts can now be analyzed with a holographic ray-tracing design program The recording wavefronts are defined by analytical phase functions, for example, a two-dimensional polynomial expansion The coefficients of the functional representations of the HOE recording wavefronts are used as parameters to optimize the performance of an optical system containing the HOE The optimum recording wavefronts are then produced with the help of computer-generated holograms Several useful arbitrary wavefront phase functions are discussed Design predictions and experimental results are presented for a holographic Fourier transform lens recorded with the aid of a computer-generated hologram

Polynomial fit of interferograms.

Abstract: Polynomial fit of interferograms is analyzed quantitatively. The errors from polynomial fit, such as fit error, digitization error, roundoff error, and finite sampling error, are explained. The advantage of using orthonormal polynomials are presented. The best reference wave front and the relative reference wave front are defined, and their characteristics are compared. The possibility of using nonorthonormal polynomials for analysis of noncircular aperture interferograms is discussed. A simulation using Zernike polynomials for an annular aperture interferogram is shown. Finally a method of obtaining the surface figure error information from several smaller subaperture interferograms is introduced, and a simulation of testing a large flat is shown.

Pencil Beam Interferometer For Aspherical Optical Surfaces

Abstract: An interferometer which provides for the precise figure measurement of optical surfaces through the interference of two pencil beams, reflected off the optical surface. Since reference surfaces are not required, the interferometer is also capable of analysing aspheric optical surfaces like axicons. The accuracy of the figure measurement is ± 2 nm.© (1982) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Combined shearing interferometer and Hartmann wavefront sensor

Abstract: A sensitive wavefront sensor combining attributes of both a Hartmann type of wavefront sensor and an AC shearing interferometer type of wavefront sensor. An incident wavefront, the slope of which is to be detected, is focussed to first and second focal points at which first and second diffraction gratings are positioned to shear and modulate the wavefront, which then diverges therefrom. The diffraction patterns of the first and second gratings are positioned substantially orthogonal to each other to shear the wavefront in two directions to produce two dimensional wavefront slope data for the AC shearing interferometer portion of the wavefront sensor. First and second dividing optical systems are positioned in the two diverging wavefronts to divide the sheared wavefront into an array of subapertures and also to focus the wavefront in each subaperture to a focal point. A quadrant detector is provided for each subaperture to detect the position of the focal point therein, which provides a first indication, in the manner of a Hartmann wavefront sensor, of the local wavefront slope in each subaperture. The total radiation in each subaperture, as modulated by the diffraction grating, is also detected by the quadrant detector which produces a modulated output signal representative thereof, the phase of which relative to modulation by the diffraction grating provides a second indication of the local wavefront slope in each subaperture, in the manner of an AC shearing interferometer wavefront sensor. The data from both types of sensors is then combined by long term averaging thereof to provide an extremely sensitive wavefront sensor.

Refraction at a Curved Dielectric Interface: Geometrical Optics Solution

Abstract: The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. We give explicit matrix formulas for calculating DF, illustrate its physical significance via examples.

Designing efficient aberration-free holographic lenses in the presence of a construction–reconstruction wavelength shift

Abstract: We have derived an analytic procedure for recording a flat, volume-phase-transmission holographic optical element at a wavelength different from that at which it is to be used. The procedure guarantees that the resulting element will have diffraction-limited aberration performance. Furthermore it guarantees, to a first order, that the Bragg condition for high diffraction efficiency will be satisfied. The technique gives simple analytic expressions for the required object and reference construction-beam phases at the element. In general, the object and reference construction beams must be realized by using computer-generated holograms in conjunction with conventional refractive or reflective optics.

Seismic parameters for media with elliptical velocity dependencies

Abstract: The concept of wavefront curvature has been discussed extensively in the literature to relate surface seismic reflection data to subsurface geologic parameters. Developed initially for the case of homogeneous, isotropic, but arbitrarily dipping layered media, this technique has been extended to the inhomogeneous case. Now with the advent of new seismic techniques, such as vertical seismic profiling, three‐dimensional seismic methods, and shear‐wave techniques, the problem of velocity anisotropy is of growing concern to exploration seismologists. The essence of this paper is to extend the method of wavefront curvature to the “elliptically anisotropic” case in which the ray velocity varies elliptically with the direction of propagation. A fundamental feature of wave propagation in the anisotropic medium is that the direction of propagation of the disturbance (or the ray velocity direction) generally differs from that of the wavefront (or the phase velocity direction). Based on the assumption of two‐dimensio...

Holography in Electron Microscopy

Abstract: Publisher Summary The chapter introduces a new method called holography, the actual purpose is to invent an electron optical device able to produce strongly magnlfied images, the aberrations of that can be eliminated afterward by light optical processing. The shadow electron microscope of Boersch can be used for the electron optical step. The optics of this system is identical with that of a modern scanning transmission electron microscope, using a fixed and slightly defocused electron probe. The chapter reveals that the electron holograms can be taken in a conventional electron microscope by applying large defocusings. The chapter presents the survey of the Fourier optical transfer theory. In the course of these considerations, it has become clear that the range of application of Gabor's method is restricted either to pure weak amplitude objects or to pure weak phase objects. The extension of this method to strong objects, however, is not possible and the problems are discussed in the chapter. The problems connected with off-axis holography are also discussed. The chapter explains that the object and reference waves in the electron microscope is created by splitting the illumination wave, using an electrostatic biprism. But in close analogy to the current light optical reconstruction methods, object and reference waves can also be generated by means of a scattering foil, and the interferometric method employing amplitude splitting by crystal diffraction instead of wave front splitting was recently brought to a successful conclusion by Matteucci. The chapter deals with recent investigations in this field.

Reciprocity principle and adaptive control of optical radiation parameters

Abstract: Several simplest variants of application of adaptive control of the parameters of a beam are suggested. They are based on the application of the principle of reciprocity of propagation of radiation in an inhomogeneous medium. Information on the necessary correction of a wavefront reaching an object is obtained from the intensity distribution in the image plane of the object. The problems of guiding the axis of a bounded beam and its focusing are considered.

Using the deformable mirror as a spatial filter: application to circular beams.

Abstract: Adaptive optics correction of a wave front by a deformable mirror that acts as a lossless spatial filter is studied. The decomposition of the wave front into Zernike polynomials provides a means for deriving the rms error of a corrected wave front in analytic form. The spatial filter is given in a functional form related to deformable mirror characteristics. A step filter approximation is derived and the conditions where the approximation holds are examined. An example is provided to demonstrate the utility of the spatial filtering concept for adaptive optics systems analysis.

The deconvolution of phase‐shifted wavelets

Abstract: The assumption that a seismogram can be represented as a convolution of a source wavelet with a set of real impulses breaks down when the wavelet is phase shifted upon reflection from a boundary. For plane waves and plane layers, this effect occurs only for wide‐angle supercritical reflections, but it may also occur in normal incidence seismograms when either the impinging wavefront or the reflective boundary is curved. We show that seismograms containing time‐displaced, phase‐shifted replications of the source wavelet can be deconvolved to recover both the amplitude and phase of the reflectivity coefficients. The method begins by writing the analytic seismogram as the convolution of a complex reflectivity function with an analytic source wavelet; linear inverse theory is then used to carry out the deconvolution.

Correlation properties of random phase diffusers for multiplex holography.

Abstract: Random phase diffusers used to individually code the reference beams employed in multiplexing a set of holograms are best characterized by their autocorrelation and cross-correlation properties. In this paper multilevel (n-level) phase diffusers and ground-glass diffuser models based on a spatial random telegraph wave are employed to investigate the performance of such diffusers for both plane wave and spherical wave illumination. The advantage of using balanced phase diffusers is indicated, and it is shown that a binary phase diffuser can, in principle, perform as well as a multilevel (n > 2) diffuser, and even as well as ground glass if the spatial fineness of the diffusers is comparable. Two signal-to-noise ratio measures of the performance of the various diffuser systems in a multiplex holography application are evaluated and discussed.

Applications of wavefront reversal by stimulated Brillouin scattering

Abstract: Wavefront reversal (WFR) via stimulated Brillouin scattering (SBS) is shown to possess the capability to compensate for phase aberrations in laser media and also to temporally compress long laser pulses. Such techniques, which involve passive and lightweight conjugator elements, are believed to be simple and practical.

Wavefront conjugation in nematic liquid crystal films

Abstract: We report the results of wavefront conjugation experiments in nematic liquid crystal films using low-power CW laser beams. The dependences of the efficiency on the film thickness and other parameters are discussed. The ability of the process to compensate for wave-front distortion is explicitly demonstrated.

Pressure actuated deformable mirror

Abstract: A deformable mirror system employs pressure-operated actuators that vary in extension in response to pressure changes within a cylindrical pressure vessel. Each pressure vessel has its pressure controlled in response to signals generated in a wavefront control system.

Wavefront sensor employing a modulation reticle

Abstract: An incremental slope wavefront sensor having an optical system which focuses an incident wavefront to a focal point. A novel modulation reticle is positioned at the focal point, and is driven in linear oscillation along a single axis. The modulation reticle has a modulation pattern formed thereon by alternating triangular light transmissive areas and inverted triangular light reflective areas. A first detector array detects the wavefront which has passed through the transmissive areas and diverged from the focal point in a two dimensional array of zones. A second detector array detects the wavefront which has been reflected by the reflective areas and diverged from the focal point in a two dimensional array of zones. The output signals from the first and second detector arrays for each corresponding zone are differentially combined to form a differential output signal for each zone. The y position of detected radiation in each zone of the wavefront is obtained by multiplying its differential output signal by a weighting function proportional to the instantaneous velocity of the reticle. The x position of detected radiation in each zone is obtained by multiplying its differential output signal by a weighting function proportional to the instantaneous velocity of the reticle and by a square wave function having respectively positive and negative values when the displacement of the reticle along the single axis is respectively positive and negative with respect to a coordinate system defined by the modulation pattern.

Wave-front aberration measurements on GRIN-rod lenses.

Abstract: A survey of the optical quality of commercial and experimental Selfoc GRIN-rod lenses was made using a digital Twyman-Green wave-front interferometer. The technique provides an accurate and reproducible method for predicting lens performance in microoptic devices. Wave-front aberrations are reported for ¼ pitch lenses measured in a double-pass configuration. It was found that spherical aberration is dominant in commercial lenses. SLW ¼ pitch lenses have lower aberrations than SLS lenses and are quite suitable for microoptic devices based on fiber-to-fiber coupling. Measured multimode coupling efficiency under steady-state modal propagation is compared to measured spherical aberration for a number of lenses. The slope of the coupling dependence on spherical aberration was found to be −0.1 dB/wave. Effects due to mechanical alignment and the modal distribution in the fibers had a greater influence on the measured coupling efficiency than the contribution due the intrinsic lens aberrations, especially for the SLW lenses. Comparison of this empirical dependence with theoretical predictions for a uniform distribution, which suggests a stronger dependence, is discussed. This work suggests that commercially available GRIN-rod lenses are suitable for use in microoptic components.

Active Optics - Don't Build A Telescope Without It!

Abstract: An analysis is made of the application of active optics of various degrees of complexity to large ground-based telescopes, using field stars as reference sources. The performance of active compensation systems is evaluated as a function of the number and size of the active zones, reference star magnitude, turbulence strength, and isoplanatic patch size. The results show that for nighttime observations, the average field star distribution allows real-time compensation not only for quasi-static wavefront errors due to optical misalignment and mirror figure, but also for image motion, dome seeing, and some atmospheric turbulence effects. Such compensation is especially valuable under good seeing conditions, when residual errors become a significant factor. It is suggested that all astronomical telescopes could benefit from the use of compensation systems with even a small number of active zones. In large segmented-mirror telescopes, the segments themselves can be used to compensate for random wavefront errors occurring in the entire optical path. In fixed-primary telescopes, the same function may be performed with an auxiliary deformable mirror.© (1982) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Time-shared aperture device

Abstract: A time-shared aperture device using the laser illuminated target to provide a return wavefront which passes through the optical train and beam expander. The distortions in this return wavefront are sampled by a rotating beam chopper which completely blocks the outgoing beam, thereby preventing scattered laser light in the optical train and beam expander from drowning out the fainter target return. Wavefront analyzers provide an indication of errors present in the optical system so that correction may be applied.

Nonlinear optical interferometer

Abstract: The interferometer described, based on the second harmonic generation of light, is useful in the contouring of refractive objects with large variations in optical depth. The device is a real-time common-path self-referencing interferometer that yields interferograms in the visible with an equivalent wavelength of the order of 50 microm. We describe experiments that show that it can serve as a useful device. The key to the device is the use of Y-cut LiNbO(3) configured for surface acoustooptic applications rather than for conventional second harmonic applications. The crystals are noncritically phase matched by temperature control and are used with a repetitively pulsed Nd:YAG laser operating at 1.06 microm.

Wavefront Compensation With Pseudoconjugation

Abstract: We discuss how novel arrangements of conventional (static /linear) optical elements can compensate for many classes of time -varying phase distortions in optical trains. Precision corner arrays, lens arrays, and K- mirror arrays are all applicable as pseudoconjugation elements in certain classes of problems. In some cases multipassing (four or more passes) of a distorting medium can offer improved performance. Although the compensation is more limited than that available from nonlinear optical phase conjugation (NOPC), problems associated with thresholds, pumps, and frequency translations are eliminated. Abstract. We discuss how novel arrangements of conventional (static/linear) optical elements can compensate for many classes of time-varying phase distortions in optical trains. Precision corner arrays, lens arrays, and K-mirror arrays are all applicable as pseudoconjugation elements in certain classes of problems. In some cases multipassing (four or more passes) of a distorting medium can offer improved performance. Although the compensation is more limited than that available from nonlinear optical phase conjugation (NOPC), problems associated with thresholds, pumps, and frequency translations are eliminated.

Effects of using different wavelengths in wave-front sensing and correction

Abstract: Adaptive-optics systems that use a return-wave concept for compensating for atmospheric turbulence distortions on a transmitted laser beam usually assume that the phase profile of the sensed radiation equals the appropriate phase profile for the laser wavelength. Certainly geometrical optics would predict this to within a scale factor directly related to the index of refraction of the air at the different wavelengths. Diffraction manifests itself in an interference phenomenon and amplitude modulation. Shorter wavelengths are more quickly affected than the longer wavelengths. When amplitude scintillation becomes important, the geometrical-optics-predicted wave-front distortions may differ from the real diffracted beam. The problem reduces to considering the phase difference measured at two different wavelengths after propagating through the same turbulence, and this paper describes these differences.

Measurement of ultrasonic velocity and absorption in liquids up 1.5 GHz by the high-resolution Bragg reflection technique

Abstract: A new UHF ultrasonic technique which is useful for simultaneous measurement of the velocity and absorption in liquids is introduced and described in detail. A ZnO film transducer excites a continuous ultrasonic wave in the test liquid which is illuminated by a highly collimated beam from a He-Ne laser. The light scattered by the sound is detected by an optical heterodyne technique and recorded as variations in the angle of optical incidence with respect to the sound wavefront. The recorded curve is associated with the k spectrum of the sound; the peak and the width give the ultrasonic velocity and absorption, respectively. The accuracy is better than 0.1% for nu and 5% for alpha . The experiment was performed in carbon disulphide and bromoform near room temperature, over a range from 50 MHz to 1.5 GHz. The results are combined with the data obtained by a pulse method and by spontaneous Brillouin scattering to present the ultrasonic spectra over the range from 3 MHz to 6 GHz.

Ring laser with wavefront conjugating beams

Abstract: An improvement for a ring laser gyro employs insertion of a wavefront conjugating coupling element inside a laser cavity to reduce the lock-in threshold and to reduce the imbalance between the amplitudes of the opposite direction traveling waves (ODTW) in homogeneously broadened rotating ring lasers.

Ion beam applications for precision infrared optics

Abstract: In applications involving steering optical beams, the wavefront rms distortion introduced by the optical train strongly influences the system deviation from diffraction‐limited, which in turn determines the system performance in focusing, imaging, etc. Substrate surface figures better than λ/10 (λ in the visible) are sometimes required; for optical coatings, uniformities of 2% or better can be essential. These can be severe requirements, particularly for large diameter optics. Ion beam techniques can be applied to improve the surface figure of metal and glass substrates as well as dielectric coating materials. This is done at the expense of increased surface roughness. Results are presented illustrating the increase of surface roughness with an amount of ion beam milling for a variety of materials. Other parameters are described which determine the effectiveness of the process. Ion beam milling techniques have been employed for adjusting the performance of an optical coating in situ without breaking vacuu...