The Hankel transform may be defined as the two-dimensional Fourier transform of a circularly symmetric function. A new Hankel-transform algorithm based on this definition is described. The proposed algorithm efficient...
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The Hankel transform may be defined as the two-dimensional Fourier transform of a circularly symmetric function. A new Hankel-transform algorithm based on this definition is described. The proposed algorithm efficiently generates a rectangularly sampled two-dimensional output array by using the circular symmetry properties of the input array and two-dimensional vector radix fast-Fourier transform techniques. It accomplishes this by partitioning the input matrix into smaller and smaller processing blocks while removing redundant blocks from data manipulations. For applications that require the output data to be sampled on a two-dimensional rectangular raster, the convenience and the computational speed of the resulting algorithm offer advantages over the one-dimensional Hankel-transform algorithms currently available.
Diffused channel-waveguide couplers were fabricated on z -cut y -propagating LiNbO 3 crystals by the indiffusion of titanium. Both mode spot sizes and coupling lengths were measured. The fields and coupling lengths we...
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Diffused channel-waveguide couplers were fabricated on z -cut y -propagating LiNbO 3 crystals by the indiffusion of titanium. Both mode spot sizes and coupling lengths were measured. The fields and coupling lengths were computed for both TM and TE polarizations from fabrication conditions. Good agreement was obtained between the measured and computed mode spot sizes and coupling lengths. It is concluded that the calculation method could aid in the design of such couplers.
Analytical solutions to the refraction integrals appropriate for ray trajectories along slant paths through the atmosphere are derived in this paper. This type of geometry is commonly encountered in remote-sensing app...
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Analytical solutions to the refraction integrals appropriate for ray trajectories along slant paths through the atmosphere are derived in this paper. This type of geometry is commonly encountered in remote-sensing applications utilizing an occultation technique. The solutions are obtained by evaluating higher-order terms from expansion of the refraction integral and are dependent on the vertical temperature distributions. Refraction parameters such as total refraction angles, air masses, and path lengths can be accurately computed. It is also shown that the method can be used for computing refraction parameters in astronomical refraction geometry for large zenith angles.
The use of hole gratings in small-spot laser damage testing is discussed. If the intensity loss due to the transmission of the grating and due to the production of several spots can be tolerated, a hole grating is sho...
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The use of hole gratings in small-spot laser damage testing is discussed. If the intensity loss due to the transmission of the grating and due to the production of several spots can be tolerated, a hole grating is shown to increase the ease of establishing a damage threshold by the production of spots with a wide range of intensities whose ratios are well understood. It allows the investigation of defect-related damage since several regions are illuminated with equal intensities, and it permits the investigation of the effects of several closely spaced simultaneous illuminations. Several types of arrays of circles and ellipses are investigated, and the effects of hole size, hole spacing, hole shape, and elliptical hole orientation are discussed. The effects of apertures of the grating are also discussed. Two methods of suppression of diffraction spots lying outside the Airy disk are described and illustrated which utilize distributions of either circular hole sizes or of elliptical hole orientations. Two arrays are used in damage tests of metal surfaces to illustrate their use.
For general optical systems, the possibility of the existence of quasi-monochromatic planar sources with different states of coherence that generate identical intensity distributions at the output plane has been analy...
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For general optical systems, the possibility of the existence of quasi-monochromatic planar sources with different states of coherence that generate identical intensity distributions at the output plane has been analyzed. The common characteristics and the relationship that must be satisfied by the correlation functions of all these sources have been determined. As an illustrative example, the results have been applied to the particular case of free propagation and intensity data throughout the Fraunhofer zone, and agreement with a previously reported result by Wolf [ J. Opt. Soc. Am. 68, 1597 (1978)] has been obtained. Also it has been shown that all sources that generate identical intensity distributions at the output plane have identical total intensity at the input plane. Finally a procedure is stated for obtaining from intensity data a number of totally or partially coherent sources producing the same intensity at the output.
The existence of partially coherent planar sources with different states of coherence that generate identical radiant intensity distributions after light goes through a general optical system has been investigated. Th...
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The existence of partially coherent planar sources with different states of coherence that generate identical radiant intensity distributions after light goes through a general optical system has been investigated. The relationship that must be satisfied by the cross-spectral density functions of all such sources has been derived. A general procedure for obtaining the common part of these sources from measurable radiant intensity data is presented. Also, the possibility of the existence of planar sources producing both identical optical intensity distributions at the output plane of the system and the same radiant intensity in the far zone has been analyzed. The general functional relationship among the cross-spectral density functions of all these sources has been determined.
Parametric studies were done on the propagation characteristics of single-mode fiber using measured refractive-index profile data. Two types of profile were considered--a graded-index core with a depressed cladding (D...
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Parametric studies were done on the propagation characteristics of single-mode fiber using measured refractive-index profile data. Two types of profile were considered--a graded-index core with a depressed cladding (Delta' < 0), and a triangular index core with no depressed cladding. The computations employ accurate material dispersion data for the germania-doped silica core and the fluorine-doped silica cladding. The investigation also includes the use of an alpha-index profile as an idealized profile using the same computational method. We find that there is good agreement with the experiments.
Three methods of digital simulation of partially coherent imagery are presented and compared. The first method is a direct discretization of imaging equations. In the second, the computations are performed in the Four...
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Three methods of digital simulation of partially coherent imagery are presented and compared. The first method is a direct discretization of imaging equations. In the second, the computations are performed in the Fourier domain. The third method is based on a modal expansion of the imaging as an incoherent sum of a number of coherent modes; this allows full utilization of FFT algorithms. It is shown that when the imaging is of narrow point spread function, the modal expansion method is very efficient, especially for relatively high coherence. Examples of 1-D and 2-D images are shown.
The encircled energy is computed for large f/No. aberration-free annular aperture systems with linear obscuration ratios between 0.0 and 0.9. The computations are based on an algorithm due to Hopkins. The results are ...
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The encircled energy is computed for large f/No. aberration-free annular aperture systems with linear obscuration ratios between 0.0 and 0.9. The computations are based on an algorithm due to Hopkins. The results are displayed graphically as contour lines showing the fraction of the total energy which falls within small circles centered on the optical axis in selected receiving planes parallel to the geometric focal plane.
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