A comprehensive series of speckle experiments is described for opal glass diffusers ranging in th... more A comprehensive series of speckle experiments is described for opal glass diffusers ranging in thickness from 10 to 500 μm. Wavelength decorrelation measurements are made using a cw dye laser source; and accurate square-law detection is provided by the use of an optic-fiber, photomultiplier combination rather than film. For this diffuser set intensity distribution functions, polarized and unpolarized, are plotted. Second-order correlation functions are presented for different apertures, relating diffuser motion and probe motion. Remote texture determination using contrast ratio and frequency decorrelation is illustrated.
A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rap... more A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR u (Δx,η 1,η 2) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR u (Δx,η 1,η 2) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.
The occurrence and smoothing of speckle are studied as a function of the line width for a highly ... more The occurrence and smoothing of speckle are studied as a function of the line width for a highly collimated illuminating source. A general theory is presented for speckling in the image of a partially diffuse, phase type of object, which has a variable number of random scattering centers per resolution element. Then, an expression is derived for the wavelength spacing required to decouple the speckle patterns arising from two monochromatic tones in an imaging system, thereby establishing that it is feasible to smooth speckle using multicolor illumination. This theory is verified in a series of experiments using both laser illumination and band-limited light from a carbon arc. With highly collimated sources, we show that speckle appears laserlike for an imaged diffuser even up to line widths of 5 A. Then, smoothing of speckle is demonstrated in the imaging of a diffuser and for a section of an optic nerve when the illumination is provided by six narrow lines spread over 1500 A. Since with color-blind, panchromatic viewing the speckle smooths, a direct extension of this method to holographic microscopy, using a multitone laser, should permit one to record and reconstruct holograms of diffraction-limited resolution that are essentially speckle-free.
Abstract We present some theoretical and experimental results for the averaging of speckle as a f... more Abstract We present some theoretical and experimental results for the averaging of speckle as a function of bandlimited and multi-tone illumination. In imaging various microscope specimens, we find that photographs taken with either 6 narrow lines spread over 1500 Å ...
A calculation is presented for the cross-correlation of the radar images obtained by processing t... more A calculation is presented for the cross-correlation of the radar images obtained by processing the same signal data over different portions of the chirp spectrum bandwidth as a function of the center frequency spacings for these portions. This is shown to be proportional to the square of the product of the characteristic function for ocean wave heights and the pupil function describing the chirp spectrum bandwidth used in the processing. Measurements of this function for ocean wave imagery over the coast of Alaska, the North Atlantic, and Monterey Bay, California, and correlation with the significant wave heights reported from ground truth data indicate that the synthetic aperture radar instrument can be used for providing wave height information in addition to the ocean wave imagery.
We derive the properties of the image obtained for an ocean wave whose cross-section may be given... more We derive the properties of the image obtained for an ocean wave whose cross-section may be given byσ w(x,y,y) and surface profile byh(x,y,t).σ w andh are functions representing the wave phenomena, but whose exact properties are determined by the ocean wave surface properties, for an ocean wavelength ofλ w, heightH, and orbital frequency ω. We calculate the effect of defocusing of the wave image due to its temporal motion, and derive both the resolution of the radar system if no focus compensation is provided in the processor and the necessary distance the azimuth telescope has to be moved to provide diffraction-limited imaging. We illustrate these results for data taken by the JPL synthetic aperture radar over Hurricane Gloria on September 30, 1976, and the ERIM radar over Marineland, Florida, on December 15, 1975.
A comprehensive series of speckle experiments is described for opal glass diffusers ranging in th... more A comprehensive series of speckle experiments is described for opal glass diffusers ranging in thickness from 10 to 500 μm. Wavelength decorrelation measurements are made using a cw dye laser source; and accurate square-law detection is provided by the use of an optic-fiber, photomultiplier combination rather than film. For this diffuser set intensity distribution functions, polarized and unpolarized, are plotted. Second-order correlation functions are presented for different apertures, relating diffuser motion and probe motion. Remote texture determination using contrast ratio and frequency decorrelation is illustrated.
A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rap... more A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR u (Δx,η 1,η 2) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR u (Δx,η 1,η 2) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.
The occurrence and smoothing of speckle are studied as a function of the line width for a highly ... more The occurrence and smoothing of speckle are studied as a function of the line width for a highly collimated illuminating source. A general theory is presented for speckling in the image of a partially diffuse, phase type of object, which has a variable number of random scattering centers per resolution element. Then, an expression is derived for the wavelength spacing required to decouple the speckle patterns arising from two monochromatic tones in an imaging system, thereby establishing that it is feasible to smooth speckle using multicolor illumination. This theory is verified in a series of experiments using both laser illumination and band-limited light from a carbon arc. With highly collimated sources, we show that speckle appears laserlike for an imaged diffuser even up to line widths of 5 A. Then, smoothing of speckle is demonstrated in the imaging of a diffuser and for a section of an optic nerve when the illumination is provided by six narrow lines spread over 1500 A. Since with color-blind, panchromatic viewing the speckle smooths, a direct extension of this method to holographic microscopy, using a multitone laser, should permit one to record and reconstruct holograms of diffraction-limited resolution that are essentially speckle-free.
Abstract We present some theoretical and experimental results for the averaging of speckle as a f... more Abstract We present some theoretical and experimental results for the averaging of speckle as a function of bandlimited and multi-tone illumination. In imaging various microscope specimens, we find that photographs taken with either 6 narrow lines spread over 1500 Å ...
A calculation is presented for the cross-correlation of the radar images obtained by processing t... more A calculation is presented for the cross-correlation of the radar images obtained by processing the same signal data over different portions of the chirp spectrum bandwidth as a function of the center frequency spacings for these portions. This is shown to be proportional to the square of the product of the characteristic function for ocean wave heights and the pupil function describing the chirp spectrum bandwidth used in the processing. Measurements of this function for ocean wave imagery over the coast of Alaska, the North Atlantic, and Monterey Bay, California, and correlation with the significant wave heights reported from ground truth data indicate that the synthetic aperture radar instrument can be used for providing wave height information in addition to the ocean wave imagery.
We derive the properties of the image obtained for an ocean wave whose cross-section may be given... more We derive the properties of the image obtained for an ocean wave whose cross-section may be given byσ w(x,y,y) and surface profile byh(x,y,t).σ w andh are functions representing the wave phenomena, but whose exact properties are determined by the ocean wave surface properties, for an ocean wavelength ofλ w, heightH, and orbital frequency ω. We calculate the effect of defocusing of the wave image due to its temporal motion, and derive both the resolution of the radar system if no focus compensation is provided in the processor and the necessary distance the azimuth telescope has to be moved to provide diffraction-limited imaging. We illustrate these results for data taken by the JPL synthetic aperture radar over Hurricane Gloria on September 30, 1976, and the ERIM radar over Marineland, Florida, on December 15, 1975.
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Papers by Atul Jain