We present a simple, yet accurate, method to obtain the intersection point of a ray in a gradient-index medium and the surface following the medium. The method does not involve additional ray tracing, unlike the commo...
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We present a simple, yet accurate, method to obtain the intersection point of a ray in a gradient-index medium and the surface following the medium. The method does not involve additional ray tracing, unlike the commonly used iterative technique, and the coordinates of the intersection point are obtained analytically.
The radii of the first three zeros and secondary maxima of the Airy disk diffraction pattern and the smallest radius for which the encircled energy is >90% are calculated for several values of f/No. and obscuration...
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The radii of the first three zeros and secondary maxima of the Airy disk diffraction pattern and the smallest radius for which the encircled energy is >90% are calculated for several values of f/No. and obscuration ratio. Formulas giving these radii as a function of the f/No. are also given.
The weighted-shift-and-add speckle imaging technique is analyzed using simple assumptions. The end product is shown to be a convolution of the object with a typical point-spread function (psf) that is similar in shape...
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The weighted-shift-and-add speckle imaging technique is analyzed using simple assumptions. The end product is shown to be a convolution of the object with a typical point-spread function (psf) that is similar in shape to the telescope psf and depends marginally on the speckle psf. A filter can be applied to each data frame before locating the maxima, either to identify the speckle locations (matched filter) or to estimate the instantaneous atmospheric psf (Wiener filter). Preliminary results show the power of the technique when applied to photon-limited data and to extended objects.
This paper describes the adaptation of Rouard’s method, a familiar computational technique used in thin-film coating design, to the analysis of waveguide diffraction gratings. The approach can be used to generate the...
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This paper describes the adaptation of Rouard’s method, a familiar computational technique used in thin-film coating design, to the analysis of waveguide diffraction gratings. The approach can be used to generate the spectral and the angular characteristics of arbitrary straight-line gratings (periodic or nonperiodic), is easy to implement on a computer, and provides an intuitively appealing picture of the operation of such gratings. The application of the thin-film method is extended to periodic gratings as well as to gratings having either a linear or a quadratic chirp in period. Specific examples are used to compare the results of the thin-film computational method with those predicted by previous authors.
The phase-perturbation method for the computation of fields scattered by rough surfaces is reviewed and then a method for calculating moments of the field scattered from randomly rough surfaces is investigated. In pre...
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The phase-perturbation method for the computation of fields scattered by rough surfaces is reviewed and then a method for calculating moments of the field scattered from randomly rough surfaces is investigated. In previous work, the authors have shown that the phase-perturbation method can provide an accurate approximation to the fields scattered from deterministic rough surfaces, even in cases when the rms surface-height variation is significant compared to the radiation wavelength. The present work employs cumulants to develop a systematic averaging procedure that retains this advantage, in the case of scalar-wave scattering from surfaces on which Dirichlet boundary conditions hold. The resulting expressions for the moments of the scattered field are shown to reduce to classical small roughness and physical-optics expressions in the appropriate limits. Numerical results for the magnitude of the coherent reflection coefficient in two test cases are also presented.
The Abel transform and its inverse appear in a wide variety of problems in which it is necessary to reconstruct axisymetric functions from line-integral projections. We present a new family of algorithms, principally ...
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The Abel transform and its inverse appear in a wide variety of problems in which it is necessary to reconstruct axisymetric functions from line-integral projections. We present a new family of algorithms, principally for Abel inversion, that are recursive and hence computationally efficient. The methods are based on a linear, space-variant, state-variable model of the Abel transform. The model is the basis for deterministic algorithms, applicable when data are noise free, and least-squares-estimation (Kalman filter) algorithms, which accommodate the noisy data case. Both one-pass (filtering) and two-pass (smoothing) estimators are considered. In computer simulations, the new algorithms compare favorably with previous methods for Abel inversion.
A powerful approach is presented for numerical solution of diffraction by a sinusoidal grating. Basically the method of solution is the mode-matching method with the smoothing procedure that we have already presented ...
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A powerful approach is presented for numerical solution of diffraction by a sinusoidal grating. Basically the method of solution is the mode-matching method with the smoothing procedure that we have already presented [J. Opt. Soc. Am. 72, 847 (1982); J. Opt. Soc. Am. 73, 1305 (1983)]. We invoke a mathematical technique that enables us to obtain rapidly an approximate solution in terms of a truncated plane-wave expansion. Numerical data for an E-polarized problem show the effectiveness of the present method: The computation time is reduced to one tenth compared with the numerical method in our previous work. The algorithm for an H-polarized problem is included.
A method for computing the optical path length in gradient-index media is presented. A comparison with other methods shows that this is more accurate and faster. This method is based on a series expansion of the refra...
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A method for computing the optical path length in gradient-index media is presented. A comparison with other methods shows that this is more accurate and faster. This method is based on a series expansion of the refractive index of the medium as a function of a suitable ray-trace parameter.
The extrapolated least-squares (ELS) optimization method is a new approach to improving the optimization efficiency of the least-squares techniques used in lens-design computer programs. The ELS method retains informa...
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The extrapolated least-squares (ELS) optimization method is a new approach to improving the optimization efficiency of the least-squares techniques used in lens-design computer programs. The ELS method retains information between iterative optimization cycles for the development of second-order extrapolation factors that include up to second-derivative terms. The extrapolation factors are used to update the first-derivative matrix of the residual vector to reflect optimization progress more accurately without requiring the recomputation of the residual vector’s first derivatives. For optical-design problems in which the first-derivative matrix is costly and time-consuming to compute, the ELS method may provide great benefit. The performance of the ELS optimization method and several conventional least-squares optimization methods are compared for a variety of test problems. Several problems include specific test functions that display a specific feature or limitation of the ELS method. Also, lens-design problems are used to provide a comparison of the ELS and conventional least-squares approaches to different types of optical-design optimization situations. The selected test problems demonstrate the predicted limitations of the ELS method as well as the expected improvement in efficiency of the ELS method when compared with conventional least-squares methods.
The formulas for a fast computation method are derived for the derivatives of transmittance and reflectance with respect to the thickness d, the refractive index n, and the extinction coefficient k of any layer in an ...
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The formulas for a fast computation method are derived for the derivatives of transmittance and reflectance with respect to the thickness d, the refractive index n, and the extinction coefficient k of any layer in an absorbing multilayer stack.
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