Showing papers on "Wavefront published in 1977"

Wave-front reconstruction for compensated imaging

Abstract: A critical component in a compensated imaging (CI) system is the wave-front sensor which measures the residual distortion of the wave front after reflecting off the active mirror. The sensor produces estimates of wave-front slopes or phase difference across the aperture. For many applications, the phase differences or slopes are not the most convenient form of data for processing or control, and they must be converted to absolute wave-front phases. This paper analyzes the conversion from phase differences to phases and derives the optimal linear estimator in terms of least noise propagation. Some remarks concerning hardware implementation are also made.

Generation of time-reversed wave fronts by nonlinear refraction*

Abstract: We describe a nonlinear method for generating, nearly instantaneously, a time-reversed replica of any monochromatic-beam wave pattern The method employs the interaction of the incident beam, of arbitrary wave front, with counter-propagating plane “pump” waves in a homogeneous, transparent, nonlinear medium Media are shown to exist in which time-reversed waves can be generated with high efficiency using available laser pump sources

A subjective method for the measurement of monochromatic* aberrations of the eye

Abstract: We have designed an aberroscope that differs from Tscherning’s classical instrument in that it makes use of an artificial astigmatism rather than an artificial myopia to defocus the image of a point source of light. A subject views the source through a ±5 D crossed cylinder lens with axes at 45° to the principal axes of an intercalated grid and sees a shadow image of the grid. The distortions of this grid image are quantitatively related to the wave aberration of the eye. Using this device we have obtained drawings for more than 50 subjects. These drawings of the grid pattern have been analyzed by means of a two-dimensional polynomial curve Fitting technique that computes Taylor polynomial terms to the fourth order. From the Taylor coefficients it is possible to reconstruct the wave aberration surface. Examination of the Taylor terms so obtained shows that the monochromatic aberrations of the eye are dominated by third-order Taylor terms within the range of physiological pupil sizes, and that spherical aberration frequently appears predominantly about one axis only, a condition that we have termed “cylindrical” aberration. We have computed the optical MTF of our subjects’ eyes and find that the role of aberrations in degrading the MTF may be greater than generally believed.

Conjugate wave‐front generation and image reconstruction by four‐wave mixing

Abstract: Operation of a new nonlinear backward‐wave optical device which produces the conjugate of an arbitrary incident wave front is demonstrated. Good‐quality reconstructed images are obtained through a phase distorting media.

Sensor system for detecting wavefront distortion in a return beam of light

Abstract: An improved apparatus for sensing wavefront distortions in a return beam of light, such as a beam returned through a turbulent atmosphere or through an imperfect optical system from a radiating or illuminated object is disclosed. This apparatus includes the components typically present in a Hartmann-type wavefront sensor, and additionally includes means to provide a modulated reference beam of light which is combined with the return beam. The use of a modulated reference beam eliminates the necessity for precise optical alignment, which is difficult or impossible to maintain in most operating environments.

Wave-front analyzer using a maximum likelihood algorithm

Abstract: A technique is described wherein the pupil phase profile is obtained from the image irradiance or point spread function. Results of numerical examples are shown that illustrate the procedure on spread functions with large aberrations and on irradiance measurements containing noise.

Optical resolution through a turbulent medium with adaptive phase compensations

Abstract: The theory of short-term average modulation transfer function developed by Fried is extended by considering the correlation between the turbulence-induced phase distortion and the residual phase aberrations after adaptive phase compensations. Calculation of the optical resolution shows that the original approximation is valid for the normalized lens diameter D/r0 less than 4.0; conversely, for D/r0 greater than 4.0 the optical resolution becomes arbitrarily large because the MTF is unrealistically overcorrected at high spatial frequencies. The extended formulation is then applied to the cases with higher-order phase compensations such as focus and astigmatism. The peak optical resolution occurs at larger values of D/r0 when the higher-order corrections are included.

Systolic pressure determining apparatus and process using integration to determine pulse amplitude

Abstract: OF THE DISCLOSURE Improved method and means for identifying and quantizing an effectively periodic, steeply-rising wavefront of an input signal in the possible presence of low amplitude interference, as for example in systolic pressure determin-ing means utilizing a pressure cuff A representation of the time-derivative of the steeply-rising wavefront is obtained The time-integral of the time-derivative is obtained over a certain interval in each repetition of the steep wave-front, as determined by the derivative exceeding a reference value A threshold level is established which is repre-sentative of the magnitude of substantially only the time-derivative corresponding with the steeply rising wavefront The time-derivative of the input signal is compared with the threshold level while the former exceeds the reference value to provide a control signal indicative of whether or not the time-derivative is representative of a valid steeply rising wavefront (as opposed to noise) Finally, the integral of a particular time-derivative is recognized as the quantized value of the steeply-rising wavefront only if the control signal indicates validity

Passive error compensating device for optical alignment

Abstract: A passive compensating device which compensates for angular and translational misalignment errors in a polarized beam and assures the projected beam centroid remains at the same position. The device splits the incoming beam into two beams. Thereafter, optical orienting means disposed to intercept the two beams is operative to rotate the wavefront of both beams so that the composite beam exiting a combiner has two components wherein one component has its wavefront rotated 180° about two orthogonal axes with respect to the other beam. Accordingly, the composite beam centroid is maintained at one position regardless of jitter of the beam entering the compensator device.

Turbulence effects on target illumination by laser sources: phenomenological analysis and experimental results.

Abstract: A phenomenological and analytical description is given of atmospheric turbulence effects on laser beam waves, including the improved target irradiance characteristics resulting from cancellation of turbulence-induced beam wander through reciprocity tracking. The mechanisms related to the mean irradiance include diffraction, wander, and wavefront distortion (beamspread), while irradiance-fading is caused by wander, first-order scintillation, and coherent fading. The phenomenological description unifies the often fragmentary and inconsistent treatment of beam wave phenomena found in the literature and is sufficiently accurate for engineering purposes. It will be shown that wander-cancellation and control of the transmitter beam diameter can result in substantial improvements in target illumination. The analyses are compared with experimental data for the detailed statistical and spectral characteristics of on-axis target irradiance.

Evoked responses: Electrogenesis, models, methodology, and wavefront reconstruction and tracking analysis

Abstract: This paper has two objectives. First, to present an overview of the electrophysiologial origins of brain waves, i.e, the evoked response (ER) and the electroencephalogram (EEG); to discuss models that have been used to reconstruct the ER and the EEG at the scalp; to describe the methodology of ER data acquisition; and to provide a few ER applications. This first section presents material which is generally common to the other ER papers in this special issue. The second objective is to illustrate how the spatio-temporal ER monitored by a multielectrode scalp array can be analyzed by the frequency-wavenumber (f - k→) spectrum analysis procedure to determine estimates of the velocity (direction and speed) of ER or EEG wavefronts propagating across the array. The problem of estimating the trajectories of multiple planewaves in a noisy environment is analyzed. First, the scalp electrode array is considered planar, a simplifying assumption. Estimates of the number of planewaves and their respective vector velocities are obtained from the f - k→power spectral density. The tracking of specific wavefronts is performed by the application of f - k→digital filters. The three-dimensional fast Filtering transform (FFT) is used in both the spectral estimation and digital filtering procedures. The analysis techniques are evaluated on simulated data and then applied to actual ER data. Next the scalp electrode array is considered to be nonplanar, i.e., three-dimensional, a realistic description due to the curvature of the skull. ER wavefront velocity vectors are reconstructed from their projections onto the planes of the three-dimensional array. Among the unique specific results to be illustrated and discussed are the planar ER vector velocity trajectory patterns and the reconstruction of nonplanar (three-dimensional) ER velocity vectors for various situations, e.g, the presentation of visual stimuli to normal humans. Thus for the first time the vector velocity of the "traveling wave" across the array is estimated as well as the vector velocity component of the wave emanating from within the brain (or along the z-axis). Problems of spatial aliasing and data interpolation are discussed among others. The work is described within the context of the computational complexity required to obtain the results presented.

Straight-line optical scanner using rotating holograms

Abstract: A flat disk contains a number of holograms made from the interference of a plane wavefront with spherical wavefront modified by a first cylindrical lens. The disk is rotated so that a plane reconstruction wavefront sweeps across the holograms. The resulting reconstructed wavefront is passed through a second cylindrical lens, resulting in a focussed point sweeping across an object surface in one or more substantially straight lines.

Bulk wave bragg cell

Abstract: An acousto-optic bulk wave Bragg cell having a transparent piezoelectric body and a single-layer interdigital transducer (IDT) signal input array on one surface of the body is adapted to be connected to a microwave (> 1 GHZ) energizing source for launching primarily bulk shear acoustic waves in the body transversely of the plane of the input surface. This Bragg cell is a signal transducer which converts the microwave input signal into an optical wavefront having spatial modulation directly proportional to the input signal and is utilized to diffraction modulate a laser beam directed through the cell transversely of the direction of acoustic wave propagation.

Pattern transfer optical system

Abstract: The invention relates to optical systems intended for the transfer of patterns onto a photosensitive surface. The system according to the invention comprises a source of coherent radiation which is intended to illuminate the photosensitive surface for a predetermined duration and which is associated with transmission means introducing a wavefront modulation of the radiation intended to average during the exposure time, the interference fringes produced by the coherence of the radiation.

High data rate frequency scan slotted waveguide antenna

Abstract: A frequency scan antenna utilizing either parallel or series beam spoiling for increasing the radar beam width and increasing the data rate is disclosed. As a radar beam is scanned from the horizon to a maximum altitude or angle above the horizon, the beam width is broadened or spoiled, thereby allowing a higher data rate collection and storage. A first embodiment according to the present invention utilizes coaxial cables of incrementally varying lengths connecting the delay line with an array of parallel line source radiators. The cables having the minimum length are connected at the extreme radiators while the maximum length cables are connected at the center line source radiators. The wavefront is bowed and a greater sector in space may be scanned. A second embodiment of the present invention utilizes a delay line with unequal tap spacings which is series coupled to the array of line source radiators. The time and consequently the phase delay of the signal applied to the delay line increases toward the upper radiators by incrementally increasing the length of the delay line segments coupled to subsequent radiators.

Measurement of second-order coherence in a light beam using a microscope and a grating

Abstract: The measurement of the complex cross-spectral density function of a light beam is discussed using a new type of shearing interferometer. This interferometer is composed principally of only an imaging lens system such as a microscope and an ordinary transparent diffraction grating replica. This interferometer is self-aligning, inexpensive, and able to introduce precise wavefront shears of the order of a few light wavelengths. A theoretical analysis of the instrument is developed giving expressions for calculating the magnitude and phase of the cross-spectral density function using observable properties of the interference pattern formed by the instrument. A simple experiment is described which demonstrates the operation of the instrument.

Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. I. Description of method, first results

Abstract: A method for analysing random phase perturbations of the wave surface impinging on the entrance pupil of an astronomical observation instrument (reflector or refractor) is given. These perturbations are observed by a Foucault test looking at the pupil through a diaphragm, the diameter of which, Delta theta , is a few arc second; this diaphragm is put at the focus of the instrument pointed in the direction of the solar limb. Simultaneous photographs of the pupil through two diaphragms are necessary to measure the intercorrelation of the observed perturbations, leading to a turbulent energy profile (versus altitude) by a triangulation method. Two kinds of spatial frequency filtering are effected by the diaphragms: the formed is the diffraction one, the latter is a wavefront integration effect.

Diagnostics Of Turbulence By Holography

Abstract: Methods for applying holographic interferometry in the study of turbulence are described. Examples of the effect of various types of turbulent cells on an optical wavefront are presented. Finally, a relatively new technique in which phase control on the two mixed reconstructed waves is discussed. It is concluded that the technique can ultimately provide an extremely high sensitivity for the viewing of phase objects and can provide the basis of automated data reduction based on heterodyne interferometry.

The Shack Interferometer

Abstract: This paper describes an unequal-path interferometer that requires only one precision component and that can be constructed as a compact and inexpensive instrument. Principles of operation are outlined, and requirements for optical components and alignment are investigated. An actual instrument and considerations for its design are described.

Proposal for the determination of the complex degree of spatial coherence

Abstract: With the help of a folded-wavefront type of interferometer, a sinusoidally phase-modulated wavefront can be superposed in parallel on another nonmodulated inverse wavefront. Spatial coherence is related to the fundamental and second-harmonic components of the modulation frequency included in the resultant intensity.

Optical Figure Inspection of Diamond-Turned Metal Mirrors

Abstract: This paper demonstrates that the optical testing of diamond-turned surfaces is best accomplished by interferometry and not by tests which measure wavefront slope. Certain conditions regarding the interferometer configuration must be met in order to generate meaningful and accurate interferograms. A 40 cm diameter aperture modified Mach-Zehnder interferometer mounted directly on the diamond-turning lathe to facilitate rapid testing of figure between fabrication cuts is described. Results for a spherical surface tested in a Twyman-Green interferometer and an off-axis parabola tested in the Mach-Zehnder interferometer are illustrated.

Theoretical aspects of thermal blooming compensation

Abstract: In this paper we present the theoretical background required for evaluating phase compensation as a technique for reducing the effects of thermal blooming. By using a time-dependent approach for thermal blooming, we can define and evaluate the instantaneous Green’s function for the heated atmosphere. The phase at the mirror is determined by propagating a point source from the focal point to the laser. The effectiveness of this technique is determined by propagating point sources within a diffraction-limited spot to the laser and comparing the resulting phase to the phase of a point source at the focal point. The phase difference will be small and the increase in irradiance large if the heating occurs where geometric optics is valid. The phase difference is large and the increase in irradiance small if atmospheric heating occurs where significant diffractive spreading is also occurring. The resulting gradients lie in the geometric shadow of the aperture and are not accessible to correction by contouring the mirror. Numerical results illustrating the analysis are presented for both cw and pulsed lasers.

Phase deflection aerial array - adds wanted focussing phase from memory to computed direction phase to control phase shifters

Abstract: The phase deflected aerial array has adders (17) to control the phase shifters (10) associated with the aerial elements. Each adder adds the wanted focussing phase read from a memory (16) to the wanted deflection phase calculated by the wavefront directing computer (15). The sum is applied to the input of a shift register (18) whose stages are in series with the control inputs of the phase shifters. The advantage lies in the simple design and in providing a flexible control which is not bound by the limits to which similar controls are subject.

Holography with local reference beam obtained by spatial frequency separation

Abstract: The holographic method disclosed in this paper allows holographic recording with a very high reference-to-object wave energy ratio without attenuating the rays diffracted by the object. In those holographic methods permitting local generation of the reference beam, which have been proposed so far, the reference beams are obtained by either wavefront or amplitude division of the wave of coherent radiation impinging onto the optical apparatus. It is readily seen that most of the incident energy is used to process the reference beam reducing drastically the energy of the object bearing wave. In the novel method proposed here the reference wave is obtained by separation of the low spatial frequency components from the high-order spatial frequency components which bear the object information. As a result of the removal of the low frequency components, a dark-field image is recorded and later reconstructed by the holographic plate. Even though the configuration is of the off-axis type, proper design may reduce the coherence requirements of the source of radiation to those for in-line holography. The paper discusses the basic properties of the method and experimental results are presented.