Hadamard transform image coding.
Fourier transform algorithm introduction leading to image coding technique with image transformed by Hadamard matrix operator
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Fourier transform algorithm introduction leading to image coding technique with image transformed by Hadamard matrix operator
Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.
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By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.
Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers
Fourier telescopes permit observations over a very broad band of energy. They generally include synthetic spatial filtering structures, known as multilayer grids or grid pairs consisting of alternate layers of absorbing and transparent materials depending on whether neutrons or photons are being imaged. For hard x-rays and gamma rays high (absorbing) and low (transparent) atomic number elements, termed high-Z and low-Z materials may be used. Fabrication of these multilayer grid structures is not without its difficulties. Herein the alternate layers of the higher material and the lower material are inserted in a polyhedron, transparent to photons of interest, through an open face of the polyhedron. The inserted layers are then uniformly compressed to form a multilayer grid.
A technique for Fourier processing of images larger than the space-bandwidth products of conventional or smart spatial light modulators and two-dimensional detector arrays is described. The technique involves a spatial combination of subimages displayed on individual spatial light modulators to form a phase-coherent image, which is subsequently processed with Fourier optical techniques. Because of the technique's similarity with the mosaic technique used in art, the processor used is termed an optical MOSAIC processor. The phase accuracy requirements of this system were studied by computer simulation. It was found that phase errors of less than lambda/8 did not degrade the performance of the system and that the system was relatively insensitive to amplitude nonuniformities. Several schemes for implementing the subimage combination are described. Initial experimental results demonstrating the validity of the mosaic concept are also presented.
Image deblurring and aperture synthesis using a posteriori processing by Fourier transform holographic spatial filtering
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An onboard coherent optical data processing system was designed to handle large information content of imagery at high speeds, reduce redundancy in picture transmission, and detect specific image features. Theoretically derived Fourier transform characteristics for simple but representative two dimensional images served as a basis for predicting expected features of actual target images. Fourier transformation and spatial filtering of coherent optical images was accomplished theoretically and in the laboratory. The effect of various parameters such as optical aperature, incidence angles, the transparency assumption, the thin lens approximation on resolution, and performance of the system are predicted and tested.
An automatic Fourier transform diffraction pattern sampling system, used to investigate techniques for forestry classification of six band multispectral aerial photography is presented. Photographs and diagrams of the design, development and fabrication of a hybrid optical-digital Fourier transform detector are shown. The detector was designed around a concentric ring fiber optic array. This array was formed from many optical fibers which were sorted into concentric rings about a single fiber. All the fibers in each ring were collected into a bundle and terminated into a single photodetector. An optical/digital interface unit consisting of a high level multiplexer, and an analog-to-digital amplifier was also constructed and is described.
RHESSI X-ray imaging is possible with angular resolution as fine as 2 arcsec (FWHM) at energies from as low as 3 keV to >100 keV. However, taking full advantage of this capability has proven to be challenging given the Fourier-transform imaging technique that is used, specific instrumental considerations that must be taken into account, and the many different options of the available image reconstruction algorithms. Such considerations as the best reconstruction algorithm to use, the optimal weighting of the different Fourier components, deciding between short image integration times and rapid imaging cadence, the different energy ranges covered by the 9 detectors, the effect of pulse pile-up and albedo, etc. must all be taken into account in obtaining and interpreting RHESSI X-ray images. This poster describes different techniques for optimizing the image reconstruction depending on the science objectives - identifying compact or extended sources, searching for source motion, obtaining the best photometry, determining the believability of different features in an image, etc. The emphasis is on making full use of data from all the RHESSI detectors, including the ones behind the finest grids when warranted by the source structure. This is the case for the hard X-ray emission along the ribbons of the flare on 2005 May 13 reported by Liu et al. (2007) and this event will be used as an example.
The scientific and technical aspects of high-resolution gamma-ray and X-ray imaging of solar flares are discussed. The scientific necessity for imaging observations of solar flares and the implications of future observations for the study of solar flare electrons and ions are considered. Performance parameters for a future hard X-ray and gamma-ray imager are summarized. Techniques for high-energy photon imaging including direct collimation imaging, coded apertures, and modulation collimators are surveyed. The technique of Fourier-transform imaging is examined. The options for detectors and grid fabrication are reviewed. Several planned future high-energy imagers are described.
Optical imaging systems achieving aperture synthesis by lensless Fourier transform holography, noting X ray astronomy, ultrasonic and space applications
Extended source Fourier transform holography for single image synthesis of multiple identical images produced by multiple pinhole camera in X ray astronomy
A method of mitigating noise in source image data representing pixels of a 3-D image. The "3-D image" may be any type of 3-D image, regardless of whether the third dimension is spatial, temporal, or some other parameter. The 3-D image is divided into three-dimensional chunks of pixels. These chunks are apodized and a three-dimensional Fourier transform is performed on each chunk, thereby producing a three-dimensional spectrum of each chunk. The transformed chunks are processed to estimate a noise floor based on spectral values of the pixels within each chunk. A noise threshold is then determined, and the spectrum of each chunk is filtered with a denoising filter based on the noise threshold. The chunks are then inverse transformed, and recombined into a denoised 3-D image.
Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.