Showing papers in "Applied Optics in 1992"

One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods.

Abstract: It is shown that the Abel inversion, onion-peeling, and filtered backprojection methods can be intercompared without assumptions about the object being deconvolved. If the projection data are taken at equally spaced radial positions, the deconvolved field is given by weighted sums of the projections divided by the data spacing. The weighting factors are independent of the data spacing. All the methods are remarkably similar and have Abelian behavior: the field at a radial location is primarily determined by the weighted differences of a few projections around the radial position. Onion-peeling and an Abel inversion using two-point interpolation are similar. When the Shepp-Logan filtered backprojection method is reduced to one dimension, it is essentially identical to an Abel inversion using three-point interpolation. The weighting factors directly determine the relative noise performance: the three-point Abel inversion is the best, while onion peeling is the worst with approximately twice the noise. Based on ease of calculation, robustness, and noise, the three-point Abel inversion is recommended.

Three-dimensional sensing of rough surfaces by coherence radar

Abstract: We introduce a three-dimensional sensor designed primarily for rough objects that supplies an accuracy that is limited only by the roughness of the object surface. This differs from conventional optical systems in which the depth accuracy is limited by the aperture. Consequently, our sensor supplies high accuracy with a small aperture, i.e., we can probe narrow crevices and holes. The sensor is based on a Michelson interferometer, with the rough object surface serving as one mirror. The small coherence length of the light source is used. While scanning the object in depth, one can detect the local occurrence of interference within the speckles emerging from the object. We call this method coherence radar.

Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar

Abstract: Height profiles of the extinction and the backscatter coefficients in cirrus clouds are determined independently from elastic- and inelastic- (Raman) backscatter signals. An extended error analysis is given. Examples covering the measured range of extinction-to-backscatter ratios (lidar ratios) in ice clouds are presented. Lidar ratios between 5 and 15 sr are usually found. A strong variation between 2 and 20 sr can be observed within one cloud profile. Particle extinction coefficients determined from inelastic-backscatter signals and from elastic-backscatter signals by using the Klett method are compared. The Klett solution of the extinction profile can be highly erroneous if the lidar ratio varies along the measuring range. On the other hand, simple backscatter lidars can provide reliable information about the cloud optical depth and the mean cloud lidar ratio.

Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods

Abstract: A variety of frequency-modulation methods for high-sensitivity absorption detection of gas-phase species has evolved in recent years. The distinctions among these methods are mostly semantic. The mathematical derivations for wavelength-modulation spectroscopy and one- and two-tone frequency-modulation spectroscopies are presented; a common terminology is used to permit a comprehensive comparison of predicted detection sensitivities. Applying this formalism, I compare the optimum detection sensitivities of these different methods for a typical laser system, using the same parameters. As long as residual amplitude modulation is minimized by proper adjustment of the detection phase angle, high-frequency wavelength modulation and one- and two-tone frequency-modulation methods all achieve approximately the same sensitivities. The choice among techniques is most strongly driven by the individual laser tuning characteristics, the absorption linewidth, and the detection bandwidth. It is shown that excess laser noise cannot always be excluded from consideration, even at megahertz detection frequencies. Also, detection at harmonics of the modulation or beat frequency may present certain advantages in minimizing residual amplitude-modulation noise.

Light scattering by particles: Computational methods

Abstract: This book presents the separation-of-variables and T-matrix methods of calculating the scattering of electromagnetic waves by particles. Analytical details and computer programs are provided for determining the scattering and absorption characteristics of the finite-thickness slab, infinite circular cylinder (normal incidence), general axisymmetric particle, and sphere.The computer programs are designed to generate data that is easy to graph and visualize, and test cases in the book illustrate the capabilities of the programs. The connection between the theory and the computer programs is reinforced by references in the computer programs to equations in the text. This cross-referencing will help the reader understand the computer programs, and, if necessary, modify them for other purposes.

Tutorial survey of composite filter designs for optical correlators.

Abstract: A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.

Raman lidar system for the measurement of water vapor and aerosols in the Earth’s atmosphere

Abstract: A nighttime operating Raman lidar system that is designed for the measurement of high vertical and temporal resolution profiles of the water vapor mixing ratio and the aerosol backscattering ratio is described. The theory of the measurements is presented. Particular attention is given to operational problems that have been solved during the development of the system. Data are presented from Sept. 1987 and described in their meteorological context.

Frequency modulation and wavelength modulation spectroscopies:comparison of experimental methods using a lead-salt diode laser

Abstract: Wavelength modulation spectroscopy (WMS) and one-tone and two-tone frequency modulation spectroscopy (FMS) are compared by measuring the minimum detectable absorbances achieved using a mid-IR lead-salt diode laser. The range of modulation and detection frequencies spans over 5 orders of magnitude. The best results, absorbances in the low-to-mid 10−7 range in a 1-Hz bandwidth, are obtained by using high-frequency WMS (10-MHz detection frequency) and are limited by detector thermal noise. This sensitivity can provide species detection limits well below 1 part per billion for molecules with moderate line strengths if multiple-pass cells are used. High-frequency WMS is also tested by measuring the absorbance due to tropospheric N2O at 1243.795 cm−1. WMS at frequencies <100 kHz is limited by laser excess (1/f) noise. Both of the FMS methods, which require modulating the laser at frequencies ≥150 MHz, give relatively poor results due to inefficient coupling of the modulation waveform to the laser current. The results obtained agree well with theory. We also discuss the sensitivity limitations due to interference fringes from unintentional etalons and the effectiveness of etalon reduction schemes.

Mueller matrix dual-rotating retarder polarimeter

Abstract: A computer-controlled Mueller matrix polarimeter with dual rotating retarders is described. Bulk properties of optical materials are determined by controlling the input-polarization state and measuring the output-polarization state. The Mueller matrix of a sample is obtained from polarimetric measurements, and polarization properties, i.e., diattenuation and retardance as well as depolarization, are extracted from the Mueller matrix. Further, fundamental electro- and magneto-optical material properties such as the electro-optical tensor coefficients may be obtained from Mueller matrices measured with applied fields. The polarimeter is currently configured to operate over the 3- to 12-microm spectral region.

Use of polarized light to discriminate short-path photons in a multiply scattering medium

Abstract: We describe a method for discriminating short- and long-path photons transmitted through a multiply scattering medium that is based on the relationship between the polarization states of the incident and forward-scattered light. Results of Monte Carlo simulations and experiments show that if the scattering anisotropy of the scatterers is sufficiently small, absorbing barriers embedded in optically dense suspensions of polystyrene spheres can be resolved with good contrast by selectively detecting a component of the scattered-light intensity that has preserved its incident circular polarization state.The principles of operation of a polarization-modulation system capable of measuring small polarization fractions are explained. Using this system we were able to measure polarized light in a depolarized background over 1000 times as large.

The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans

Abstract: New measurements of the chromatic difference of focus of the human eye were obtained with a two-color, vernier-alignment technique. The results were used to redefine the variation of refractive index of the reduced eye over the visible spectrum. The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration. The resulting chromatic-eye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.

Second-harmonic generation in zinc tris(thiourea) sulfate

Abstract: The linear and second-order nonlinear optical properties of single-crystal zinc tris(thiourea) sulfate, or ZTS, are determined. The deduced nonlinear coefficients are |d31| = 0.31, |d32| = 0.35, and |d33| = 0.23 pm/V compared with a |d14| value of 0.39 pm/V for potassium dihydrogen phosphate. Because it exhibits a low angular sensitivity (δΔk/δθ), ZTS may prove useful for type-II second-harmonic generation from 1.06 to 1.027 μm. We present the phase-matching measurement data for ZTS and compare the calculated frequency conversion efficiency for ZTS with that of several other well-characterized materials.

Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations

Abstract: The reduced scattering cross section per unit of volume Σs′ ≡ Σs(1 − g) is an important parameter to describe light propagation in media with scattering and absorption. Mie calculations of the asymmetry factory g for nonabsorbing spheres and Qsca, the ratio of the scattering cross section Σs and the particle cross section, show that Qsca(1 − g) = 3.28x0.37(m − 1)2.09 is true to within a few percent, when the Mie parameters for relative refractive index m and size x are in the ranges of 1 < m ≤ 1.1 and 5 < x < 50, respectively. A ratio of reduced scattering cross sections for radiation at two wavelengths is also independent of the size within the range mentioned, even for mixtures of different size spheres. The results seem promising for biomedical applications.

Spatially resolved birefringence of the retinal nerve fiber layer assessed with a retinal laser ellipsometer.

Abstract: A retinal laser ellipsometer has been developed by coupling a Fourier ellipsometer to a laser scanning system. The instrument has been used to assess the origin and the amount of change in the state of polarization of a laser beam that has double passed the retina around the optic nerve head of postmortemhuman eyes. Eight eyes with no history of glaucoma were studied. At 200 points around the optic nerve head of each eye the Mueller matrices of the retina were examined for the amount of retardation, the orientation of the optic axis, and the amount of dichroism. The degree of polarization preservation of the detected light varied between 50% and 87%. Little dichroism was found, and there was no obvious correlation to the physical arrangement of any retinal structure. However, there was a substantial amount of linear uniaxial birefringence with the optic axis perpendicular to the incident laser beam. Furthermore the calculated optic axis direction showed a strong correlation with the physical orientation of the radial symmetrically arranged retinal nerve fiber axons around the optic nerve head. The local distribution of the corresponding retardation values showed two maxima that coincided with the areas of the thickest retinal nerve fiber layer. These results support the hypothesis that the thickness of the form birefringent retinal nerve fiber layer can be assessed by ellipsometric methods.

Imaging properties of axicon in a scanning optical system

Abstract: The imaging properties of a scanning optical system that incorporates an axicon are presented. Beam-shape characteristics including the axial distribution of the J0 beam and its control and aberration effects arising from off-axis illumination are experimentally studied. These parameters are relevant when the axiconis used in an imaging system operating in the beam-scanning mode. The J0 pattern produced by a blazed axicon transmittance grating is also presented.

Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames.

Abstract: A new method for the in situ optical determination of the soot-cluster monomer particle radius a, the number of monomers per cluster N, and the fractal dimension D is presented. The method makes use of a comparison of the volume-equivalent sphere radius determined from scattering-extinction measurements RSe and the radius of gyration Rg, which is determined from the optical structure factor. The combination of these data with the measured turbidity permits for a novel measurement of D. The parameters a and N are obtained from a graphical network-analysis scheme that compares R(se) and Rg. Corrections for cluster polydispersity are presented. The effects of uncertainty in various input parameters and assumptions are discussed. The method is illustrated by an application to data obtained from a premixed methane-oxygen flame, and reasonable values of a, N, andD are obtained.

Wave-front reconstruction using a Shack-Hartmann sensor

Abstract: An analysis of the problem of wave-front reconstruction from Shack–Hartmann measurements is presented. The wave-front aberration is assumed to result from passage of the wave front through Kolmogorov turbulence. Limitations of using Zernike polynomials as an orthogonal basis for wave-front reconstruction are highlighted, and the advantage of using the Karhunen–Loeve functions for computing the higher-order modes of the wave front is shown.

Branch cuts in the phase function

Abstract: It is shown that, when the scalar field associated with the propagation of a distorted wave function has nulls in its intensity pattern, the phase function that goes with that scalar field has branch points at the location of these nulls and that there are unavoidable 2π discontinuities across the associated branch cuts in the phase function. An analytic proof of this supposition is provided. Sample computer-wave optics propagation results are presented that manifest such unavoidable discontinuities. Among other things, the numerical results are organized in a way that demonstrates that for those cases the branch points are unavoidable. It is found in the sample numerical results that the branch cuts can be positioned so that the 2π discontinuities are located along lines of minimum intensity. This location tends to minimize the physical significance or importance of the discontinuities, a significant consideration for deformable-mirror adaptive optics, for which there is an unavoidable correction error in the vicinity of the branch cut. An algorithm is briefly described that allows the branch cuts to be located automatically and a phase function to be calculated that has discontinuities equal only to 2π discontinuities that are located at the branch cuts.

Antireflection surfaces in silicon using binary optics technology

Abstract: Binary optics processing methods were applied to a silicon substrate to generate an array of small pillars in order to enhance transmission. The volume fraction of the silicon in the pillars was chosen to simulate a single homogeneous antireflection layer, and the pillar height was targeted to be a quarter-wave thickness. A mask was generated, using a graphics computer-aided design system; reactive-ion etching was used to generate the pillars. An improvement in long-wavelength infrared transmission is observed, with diffraction and scattering dominating at shorter wavelengths.

Side-polished fibers.

Abstract: We report a reproducible technique of making side-polished fibers by embedding fibers in silicon V grooves and by polishing them mechanically. Details of V grooves and polishing techniques are described. The attenuation characteristics of polished fibers were measured by a liquid-drop method; the results are in excellent agreement with existing theoretical predictions. To facilitate comparisons, we cast expressions for the attenuation constant in terms of three generalized parameters: the V and b parameters for the fiber and a new generalized parameter V(ex) for the external medium. By using these generalized parameters, we can study the effects of the external medium on the attenuation constant of side-polished fibers in great detail, including in particular the region where the attenuation changes precipitously.

Fourier-transform holographic microscope

Abstract: We describe a holographic microscope with a spatial resolution approaching the diffraction limit. The instrument uses a tiny drop of glycerol as a lens to create the spherically diverging reference illumination necessary for Fourier-transform holography. Measurement of the point-spread function, which is obtained by imaging a knife edge in dark-field illumination, indicates a transverse resolution of 1.4 μm with wavelength λ = 514.5 nm. Longitudinal resolution is obtained from the holograms by the numerical equivalent of optical sectioning. We describe the method of reconstruction and demonstrate the microscope’s capability with selected biological specimens. The instrument offers two unique capabilities: (1) it can collect three-dimensional information in a single pulse of light, avoiding specimen damage and bleaching; and (2) it can record three-dimensional motion pictures from a series of light pulses. The conceptual design is applicable to a broad range of wavelengths and we discuss extension to the x-ray regime.

Binary gratings with increased efficiency

Abstract: Coupled-wave analysis is used to design binary gratings with high efficiencies (70-80%). The binary designs have grating periods greater than one wavelength but use subwavelength structures within each period in order to achieve high efficiency.

Edge technique: theory and application to the lidar measurement of atmospheric wind.

Abstract: The edge technique is a new and powerful method for measuring small frequency shifts. With the edge technique a laser is located on the steep slope of a high-resolution spectral filter, which produces large changes in transmission for small frequency shifts. A differential technique renders the frequency shift measurement insensitive to both laser and filter frequency jitter and drift. The measurement is shown to be insensitive to the laser width and shape for widths that are less than the half-width of the edge filter. The theory of the measurement is given with application to the lidar measurement of wind. The edge technique can be used to measure wind with a lidar by using either the aerosol or molecular backscattered signal. Examples of both measurements are presented. Simulations for a ground-based lidar at 1.06 microm using reasonable instrumental parameters are used to show an accuracy for the vector components of the wind that is better than 0.5 m/s from the ground to an altitude of 20 km for a 100-m vertical resolution and a 100-shot average. For a 20-m vertical resolution and a 10-shot average, simulations show an accuracy of better than 0.2 m/s in the first 2 km and better than 0.5 m/s to 5 km.

Method for the preparation of porous silica antireflection coatings varying in refractive index from 1.22 to 1.44.

Abstract: Coatings of refractive index that vary between 1.22 and 1.44 were prepared from combinations of a colloidal silica suspension and a polysiloxane solution. The polysiloxane acted both as a binder and a filler for the colloidal silica particles. Increasing ratios gave coatings of lower porosity, hence higher refractive index, and better abrasion resistance. This variation in refractive index allowed highefficiency quarter-wave antireflection coatings to be prepared on substrates whose index varied from 1.45 to 2.1. The laser damage thresholds of all the coatings were >50 J/cm(2) at a wavelength of 1.06 microm with a 10-ns pulse length.

Metrics for assessing pattern-recognition performance.

Abstract: Various metrics used to measure correlation filter performance are discussed. Their similarities and deficiencies are noted, and modifications are suggested. A computer simulation is included to highlight these differences.

Surface-roughness considerations for atmospheric correction of ocean color sensors. I: The Rayleigh-scattering component

Abstract: The first step in the coastal zone color scanner (CZCS) atmospheric-correction algorithm is the computation of the Rayleigh-scattering contribution, Lr(r), to the radiance leaving the top of the atmosphere over the ocean. In the present algorithm Lr(r), is computed by assuming that the ocean surface is flat. Computations of the radiance leaving a Rayleigh-scattering atmosphere overlying a rough Fresnel-reflecting ocean are presented to assess the radiance error caused by the flat-ocean assumption. The surface-roughness model is described in detail for both scalar and vector (including polarization) radiative transfer theory. The computations utilizing the vector theory show that the magnitude of the error significantly depends on the assumptions made in regard to the shadowing of one wave by another. In the case of the coastal zone color scanner bands, we show that for moderate solar zenith angles the error is generally below the 1 digital count level, except near the edge of the scan for high wind speeds. For larger solar zenith angles, the error is generally larger and can exceed 1 digital count at some wavelengths over the entire scan, even for light winds. The error in Lr(r) caused by ignoring surface roughness is shown to be the same order of magnitude as that caused by uncertainties of +/- 15 mb in the surface atmospheric pressure or of +/- 50 Dobson units in the ozone concentration. For future sensors, which will have greater radiometric sensitivity, the error caused by the flat-ocean assumption in the computation of Lr(r) could be as much as an order of magnitude larger than the noise-equivalent spectral radiance in certain situations.

Nonparaxial design of generalized axicons

Abstract: The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

Minimum noise and correlation energy optical correlation filter.

Abstract: A new distortion-invariant optical correlation filter to produce easily detectable correlation peaks in the presence of noise and clutter and to provide better intraclass recognition is presented. The basic ideas of the minimum variance synthetic discriminant function correlation filter (which minimizes noise variance in the output correlation peak/plane) and the minimum average correlation energy filter (which minimizes the average correlation plane energy over all the training images) are unified in a new filter that produces sharp correlation peaks while maintaining an acceptable signal-to-noise ratio in the correlation plane output. This new minimum noise and correlation energy filter approach introduces the concept of using the spectral envelope of the training images and the noise power spectrum to obtain a tight bound to the energy minimization problem that is associated with distortion-invariant filters in noise while allowing the user a variable parameter to adjust depending on the noise or clutter that is expected. We present the mathematical basis for the minimum noise and correlation energy filter and the initial simulation results.

Binary surface-relief gratings for array illumination in digital optics.

Abstract: Separable binary-phase array illuminators for fan-out up to 1024 x 1024 and ~65% two-dimensional efficiency are designed by simulated annealing with constraints for maximizing the minimum feature size. A new nonseparable trapezoidal coding technique is introduced and applied to design high-efficiency (~75%-80%) array generators for fan-out up to 16 x 16. A rigorous electromagnetic diffraction theory is used to evaluate the range of validity of the scalar designs (both grating period and input angle are considered), to analyze fabrication errors (slanted groove walls and undercutting), and to design binary resonance-domain one-dimensional array generators with 90%-100% efficiency. Trapezoidal gratings for low fan-out (8 x 8), separable gratings for high fan-out (up to 128 x 128), and a 1 x 5 resonance domain (100% efficient) reflection grating are demonstrated experimentally.