Showing papers in "Journal of the Optical Society of America in 1977"

Electromagnetic propagation in periodic stratified media. I. General theory

Abstract: The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and laser technology are presented.

Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements

Abstract: The problem of fitting a wave-front distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem. The least-square equations have been developed as a set of simultaneous equations for a square array of phase-difference sensors, with phase estimates at the corner of each measurement element. (This corresponds to the standard Hartmann configuration and to one version of a shearing interferometer of a predetection compensation wave-front sensor.) The noise dependence in the solution of the simultaneous equations is found to be expressible in terms of the solution to a particular version of the measurement inputs to the simultaneous equation, a sort of “Green’s-function” solution. The noise version of the simultaneous equations is solved using relaxation techniques for array sizes from 4 × 4 to 40 × 40 phase estimation points, and the mean-square wave-front error calculated as a function of the mean-square phase-difference measurement error. It is found that the results can be approximated within a fraction of a percent accuracy by 〈(δΦ)2〉=0.6558[1+0.2444 ln(N2)]σpd2, where 〈(δΦ)2〉 is the mean-square error (rad2) in the estimation of the wave-front distortion, for a square array consisting of N2 square subaperture elements over which two phase-difference measurements are made—one phase difference across the x dimension and the other difference across the y dimension. Here σpd2 is the mean-square error (rad2) in each phase-difference measurement.

Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power

Abstract: Expressions for the total power radiated by magnetic and electric dipoles of arbitrary orientation located in a medium 1 at distance z0 from the interface to a homogeneous or planar stratified medium 2 are derived. A relation between the normalized powers radiated by magnetic and electric dipoles is established. For a homogeneous loss-free medium 2, curves of the normalized powers L(z0)/L∞ radiated by magnetic and electric dipoles versus the normalized distance z0/λ1 are presented for different values of the relative refractive index n = n2/n1 as the only parameter. The computer calculations are compared with analytical expressions derived for small and large distances. For n > 1, the contribution of the evanescent waves to the radiated power is calculated separately. We show that the classical results for the normalized radiated power yield the correct normalized spontaneous emission rates from an excited atomic state for electric and magnetic dipole transitions, respectively. We point out that the results for the electric dipole also give the change of the total power scattered by a small dielectric scattering particle when it is placed close to an interface.

The time-dependent physical spectrum of light*

Abstract: We investigate the time-dependent spectrum of light from an observational point of view and define a time-dependent “physical spectrum” of light based on the counting rate of a photodetector. The tunable element, the filter, that allows observation of different spectral components of the light is shown to play an essential role in the time-dependent spectrum. Its bandwidth cannot be taken arbitrarily narrow. We establish the connection between our physical spectrum and other time-dependent spectra associated with Page, Lampard, Silverman, and Kolmogorov, as well as with the Wiener-Khintchine power spectrum. Also, we show the conditions under which these earlier definitions can be used as the first approximations to the complete physical spectrum, and give an expression for the correction terms.

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.

Light scattering by small particles in an absorbing medium.

Abstract: Extinction for the scattering by small particles embedded in an absorbing medium is defined and a generalized form of an optical theorem is derived. In general, the extinction is related to both the forward and the backward scattering amplitude.

Bandwidth specification for adaptive optics systems

Abstract: A simplified expression for the bandwidth of an adaptive optics system is found to depend on a weighted path integral of the turbulence strength, where the weighting is transverse wind velocity to the 5/3 power. The wave-front corrector is conservatively assumed to match the phase perfectly, at least spatially, if not temporally. For the case of astronomical imaging from a mountaintop observatory, the necessary bandwidth is found to be less than 200 Hz.

Coherence and radiometry with quasihomogeneous planar sources

Abstract: The concept of a quasihomogeneous source is introduced. Unlike a source that is strictly homogeneous in its statistical properties, a quasihomogeneous source may be finite. Many physical sources, both primary and secondary ones, are adequately approximated by this model. Coherence and radiometric properties of light generated by such sources (assumed, for simplicity, to be planar) are discussed and an important reciprocity relation is shown to exist between light in the far zone and in the source plane. This relation implies that the degree of coherence in the far zone is given by the classic form of the van Cittert-Zernike theorem, even though the source may have a high degree of spatial coherence over arbitrarily large areas. The reciprocity relation also provides a generalization of a recently derived result that expresses the angular dependence of the radiant intensity in terms of the degree of spatial coherence of light in the source plane. The dependence of all the basic radiometric quantities on the distribution of the optical intensity across the source and on the degree of spatial coherence of the light emerging from the source is discussed and is illustrated, for some typical sources, by computed curves.

The 1s-3p Kβ-like x-ray spectrum of highly ionized iron

Abstract: Measurements of the fine structure on the high-energy side of the Fe Kβ x-ray line, obtained from low-inductance high-current vacuum sparks, are reported. Fully relativistic central field calculations for atoms, including magnetic Breit interactions and estimates of the Lamb shifts, correlate the experimental features to the 1s-3p transition of the various Fe ions. The features are shown to be emitted by ions from Fe ix to Fe xviii, and Fe xxiv to Fe xxvi.

Steady-state evoked potentials.

Abstract: The advantages of steady-state EP recording include (1) speed in assessing sensory function in normal and sick infants (e.g., in amblyopia) and in sick adults (e.g., in multiple sclerosis); (2) monitoring certain activities of sensory pathways that do not intrude into conscious perception; (3) rapidly assessing sensory function when a large number of subjects must be tested (e.g., in refraction); (4) objective measurement at very high suprathreshold levels where psychophysical methods are difficult or ineffective; (5) rapidly assessing sensory function in normal subjects when EP variability and nonstationarity preculde lengthy experiments; and (6) providing a speedy objective equivalent to behavioral test in animals.

Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation patterns of perpendicular oriented dipoles

Abstract: We have derived analytical expressions for the angular distribution P(α) of the power radiated by magnetic or electric dipoles located at distance z0 from a dielectric interface and oriented perpendicular to it. For dipoles in the rarer medium very close to the interface, evanescent waves in the dipoles’ near field give rise to strong radiation into the denser medium. The resulting large maximum of P(α) shows characteristic differences for magnetic and electric dipoles when the relative refractive index of the two dielectrics is greater than √2. For dipoles lying on the interface a symmetry relation is established connecting the power distributions P(α) for the values n and 1/n of the relative refractive index.

Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray lasers *

Abstract: The theory of electromagnetic Bloch waves in periodic stratified media is applied to the problems of birefringence and group velocity in these media. The relevance of periodic media to phase matching in nonlinear mixing experiments and to laser action in the x-ray region is discussed.

Real-time atmospheric compensation

Abstract: We have developed an active optical imaging system capable of correcting optical wave-front errors in real time at frequencies in the kilohertz range. Wave-front errors due to atmospheric turbulence in the propagation path, as well as optical figure aberrations and wave-front errors due to mechanical and thermal changes may be compensated. The system used an ac shearing interferometer, a parallel analog data processor, and a monolithic piezoelectric active mirror arranged in a closed-loop configuration. This compensation system can be applied to apertures of any size; experimental results are shown for a system with 21 correction zones.

Photoreceptor diameter and spacing for highest resolving power

Abstract: The maximum center-to-center angular spacing Δϕ of photoreceptors tolerated for reconstructing the highest spatial frequency passed by a diffraction-limited pupil of diameter D is Δϕ = λ/D √3 when the photoreceptors are packed in a hexagonal array, where λ is the wavelength in vacuum. This spacing gives the maximum signal-to-photon noise ratio when the inner segments touch. The mean luminance required for an eye to achieve its highest resolving power is independent of eye size, provided the retina is designed to sample the highest spatial frequency passed by the diffraction-limited optics.

Two-band model of heterochromatic flicker

Abstract: We have attempted to reconcile the results of several recent chromatic flicker studies. By adjusting the relative amplitudes of red and green sine-wave stimuli that were flickering in opposite phase, we obtained conditions varying from purely chromatic (red–green) stimulation, through each “silent-cone” condition, to purely luminous (homochromatic) stimulation. We also tested the effects of adapting backgrounds in each condition. Our results can be explained in terms of a low-frequency band that represents the opponent-color response, and a high-frequency band that represents the achromatic response. These two bands respond in various proportions, depending on the red–green stimulus ratio. Chromatic adaptation generally affects the low- and high-frequency bands differently and hence changes the shape of the flicker sensitivity curve. However, if the temporally varying waveform and the adapting background are both chosen to stimulate the same cone type, then the opponent-color and achromatic bands are both attenuated by the same amount. In this case, the shapes of the silent-red and silent-green flicker curves are preserved under chromatic adaptation. We conclude that none of these flicker curves are controlled by the temporal characteristics of independent cone types.

Color vision in the peripheral retina. II. Hue and saturation

Abstract: Hue and saturation of spectral lights were measured (direct scaling) in the fovea and at 45° in the periphery; all lights were of equal photopic retinal illuminance (1200 trolands). At each retinal location both large and small targets were used. As shown by previous studies, small peripheral targets appear desaturated and of uncertain hue, except long wavelengths which appear red. However, if target size is increased, saturation increases and a full range of hues is seen; the hue functions for large peripheral targets are comparable to foveal ones for very small targets. From a modified form of color matching, it was concluded that the color deficiency in the periphery is more tritanlike than deutanlike; this is strengthened by the observation that, for small peripheral targets, hues are generally apportioned between two hue categories and the change from one to the other is at about 580 nm.

Large-field trichromacy in protanopes and deuteranopes

Abstract: Protanopes and deuteranopes do not accept the classical dichromatic matches when field size extends to 8° visual angle. Their unique matches of spectral yellow to a mixture of red and green are then mediated by the photoreceptors of small-field dichromacy interacting with a photoreceptor with the spectral sensitivity of rhodopsin. Our data suggest that large-field trichromacy is a general feature of protanopia and deuteranopia.

Measurements of the optical constants of liquid H 2 O and D 2 O between 6 and 450 cm −1

Abstract: Various advances in technique have enabled new measurements to be made over a greatly extended frequency range (6<ν∼<450cm−1) of the optical constants n(ν∼) and α(ν∼) of liquid water and liquid D2O at 19°C. The origin of the polarization in this region is discussed.

Analysis of multiwave diffraction of thick gratings

Abstract: A general coupled-wave formalism describing the multiwave diffraction properties of thick gratings is presented. The analysis is applicable to refractive-index-modulated and/or absorption-modulated gratings of any modulation strength. The gratings may be slanted, nonuniform with thickness, nonsinusoidal, and lossy. The incident wave (of arbitrary polarization) may be at any angle of incidence including all Bragg angles. Example multiwave diffraction efficiency characteristics are calculated for some representative grating thicknesses and refractive-index modulations for sinusoidal, square-wave, and sawtooth gratings.

Representing Visual Information

Abstract: : Vision is the construction of efficient symbolic descriptions from images of the world An important aspect of vision is the choice of representations for the different kinds of information in a visual scene In the early stages of the analysis of an image, the representations used depend more on what it is possible to compute from an image than on what is ultimately desirable, but later representations can be more sensitive to the specific needs of recognition This essay surveys recent work in vision at MIT from a perspective in which the representational problems assume a primary importance An overall framework is suggested for visual information processing, in which the analysis proceeds through three representations; (1) the primal sketch, which makes explicit the intensity changes and local two-dimensional geometry of an image, (2) the 2 1/2-D sketch, which is a viewer-centered representation of the depth, orientation and discontinuities of the visible surfaces, and (3) the 3-D model representation, which allows an object-centered description of the three-dimensional structure and organization of a viewed shape Recent results concerning processes for constructing and maintaining these representations are summarized and discussed (Author)

An angular spectrum representation approach to the Goos-Hänchen shift

Abstract: The reflection of a beam of light at a plane interface is treated using the angular spectrum representation. The Goos-Hanchen shift is found to be proportional to the first derivative of the phase of the reflectance. The second derivative of the phase gives rise to a shift of the reflected beam along its direction of propagation. This new shift, called a focal shift, is different from the extra propagation distance of the beam predicted on the basis of a ray model for total internal reflection. Expressions are presented for the Goos-Hanchen and focal shifts for both s and p polarization.

The membrane mirror as an adaptive optical element

Abstract: A membrane mirror assembly is described that has a membrane deflected by a region of electrostatic actuators, consisting of conducting pads. The procedure for fabrication of typical membranes is described and involves evaporation of the material onto a substrate in a vacuum chamber. Parametric equations, developed from basic vibration theory, are given for establishing transient and steady-state performance criteria. Experimental data, using both titanium and nickel test membranes, shows that the performance satisfies the predicted requirements.

Describing holographic optical elements as lenses

Abstract: Optical systems including holographic optical elements and Fresnel gratings can be designed with ordinary lens optimization computer codes. Holographic elements are represented as lenses with very large indices of refraction and very small curvatures. As the index approaches infinity, the model becomes exact. General design parameters and image quality of holograms on both planar and spherical surfaces are discussed.

The multidither principle in adaptive optics

Abstract: Coherent optical adaptive techniques (COAT) offer promise for overcoming the deleterious effects of phase distortions experienced by optical beams propagating through distorting optics or via a turbulent and absorbing atmosphere. The theory of four classes of such systems, which employ similar multidither principles, is explored. Many modes of operating these systems are briefly reviewed and a detailed analysis of the most widely employed—a glint referencing system with sinusoidal dithers—is developed. A servo signal-to-noise analysis indicates how the optimum choice of dither magnitude depends on the system noise.

Gaussian beam modes by multipoles with complex source points

Abstract: It is shown that the complex Hermite-Gaussian wave functions proposed by Siegman can be generated in a straightforward manner by assigning complex locations to the source points in a multipole expansion of an optical field.

Optical constants of water in the infrared: Influence of temperature*

Abstract: We have compared the near-normal-incidence spectral reflectance of water at 1, 16, 39, and 50 °C with the corresponding spectral reflectance of water at 27°C, at which temperature the optical constants n(ν) and k(ν) have been previously determined. By applying Kramers-Kronig analyses to the resulting values of spectral reflectance we have obtained the optical constants of water at each of the above temperatures. We present the results in graphical form for the spectral region 400–5000 cm−1 and in tabular form in the vicinity of major absorption and dispersion features. The bearing of our results on the intermolecular structure of water is discussed.