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.

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.

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.

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.

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.

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...

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Abstract: This article summarizes the nonlinear optical methods allowing one to perform optical phase conjugation, i. e. spatial-phase reversal of an incoming electromagnetic wave. Special attention is given to the most powerful technique—to date—which is based on degenerate four-wave mixing (DFWM). One discusses the physical processes (one-photon and two-photon resonances) responsible for DFWM. The generation of light-induced Bragg gratings, and the analogy with real-time holography are emphasized, with a brief review of the applications in adaptive optics and imaging (wavefront rectification, etc.). Also described are the spectroscopic applications of DFWM (transient gratings, Doppler-free emission in gases, high-frequency heterodyne spectroscopy), the polarization properties of phase-conjugate mirrors, and the operation of phase-conjugate resonators.

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...

Abstract: A device is provided for recording and projecting holographic images. A laser illuminates a scene to be filmed and provides the spherical reference wave for recording the hologram on the film. The wave front diffused by the scene is amplified in an induced refraction index medium which receives a flat reference wave, also supplied by the laser. The amplified wave front falls on the high resolution film and the hologram is recorded.

Abstract: A system has been developed for the purpose of real-time rapid measurement of the optical path difference (OPD) between a reference wavefront and a measuring wavefront of an interferometer by measuring the phase difference between them. The system is capable of measuring accurately OPDs represented by interference patterns with any shape and degree of complexity within the spatial resolution limits of the detector. The interference pattern of the two wavefronts is modulated so that any given point in the interference plane has a sinusoidally varying light intensity with a phase that is proportional to the OPD between the two wavefronts. The individual diodes of an array camera detect the varying light intensity in the interference plane. The output voltage of each diode is digitized and stored. The phase is then computed from these data, and processed to obtain the OPD, peak-to-valley (P-V), and root-mean-square (rms) values of the measured wavefront.

Abstract: An experimental investigation was made of the wavefront reversal parameters and of the reflection coefficient of a stimulated Brillouin scattering mirror made of CCl4; the measurements were carried out in a wide range of pump energies using pulses of 0.5–10 nsec duration. A reduction in the pulse duration reduced the dynamic range (i.e., the range of the pump energies) in which wavefront reversal was observed. Specially shaped pulses with different values of the contrast were used for the reversal of radiation with a high peak power.