Tomographic Image Reconstruction From Laser Radar Reflective Projections

Abstract

Image reconstruction from projections has been extensively developed in the medical field. For example, Computer Assisted Tomography (CAT) scanners measures the absorption of X -rays along ray -projections through a slice of a body. Applying reconstruction algorithms to these projection measurements leads to two or three -dimensional distribution of the mass density. We have applied similar methods which demonstrate image reconstruction from reflective projections obtained with laser radars. These baseband SAR techniques can be applied to any N-dimensional measurements resulting in reconstructions of N + 1-dimensional images. For example, two -dimensional range-Doppler or angle -angle images taken from several views can be reconstructed into three -dimensional images. Shown in this paper, two -dimensional images have been reconstructed from one -dimensional range-time -intensity (RTI) data, Doppler -timeintensity (DTI) data, or a combination of both types of laser radar measurements. Typical RTI measurements can be obtained with either coherent linear FM waveforms, or with incoherent short pulse waveforms. In the DTI case, a cw waveform is sufficient and leads to true narrow -band imaging. We have applied these methods to both computer simulated data and field measurements, at both 10.6 Am and 0.53 µm wavelenghts, using various test targets. ABSTRACT Image reconstruction from projections has been extensively developed in the medical field. For example, Computer Assisted Tomography (CAT) scanners measures the absorption of X-rays along ray-projections through a slice of a body. Applying reconstruction algorithms to these projection measurements leads to two or three-dimensional distribution of the mass density. We have applied similar methods which demonstrate image reconstruction from reflective projections obtained with laser radars. These baseband SAR techniques can be applied to any N-dimensional measurements resulting in reconstructions of N + 1-dimensional images. For example, two-dimensional range-Doppler or angle-angle images taken from several views can be reconstructed into three-dimensional images. Shown in this paper, two-dimensional images have been reconstructed from one-dimensional range-time-intensity (RTI) data, Doppler-timeintensity (DTI) data, or a combination of both types of laser radar measurements. Typical RTI measurements can be obtained with either coherent linear FM waveforms, or with incoherent short pulse waveforms. In the DTI case, a cw waveform is sufficient and leads to true narrow-band imaging. We have applied these methods to both computer simulated data and field measurements, at both 10.6 jitm and 0.53 fim wavelenghts, using various test targets. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/17/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE Vol 999 Laser Radar Ill (1988) / 249 SPIE Vol. 999 Laser Radar III (1988) / 249 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/17/2015 Terms of Use: http://spiedigitallibrary.org...

<title>Imaging with heterodyne laser radar and reflection tomography</title>

“…The relationship is called the projection-slice theorem and is given by j: (v1 ) = G(v1 cos 6, v1 sin 8). (2)(3) In words, the Fourier transform ofthe projection at angle 6 is equal to the Fourier transform ofg(xi, x2) evaluated along a line through the origin oriented in the same manner in the (u1, u2) plane as the projection is in the (x1, x2) plane. Thus, we can get samples of G(u1, u2) from a projection ofg(xi, x2).…”

Field demonstration and characterization of a 10.6-μm reflection tomography imaging system

“…The two dimensional absorption cross section g(x1, yi) is integrated down to a one dimensional distribution, called a projection, by the X-ray sensors. Mathematically a projection is represented by: p(x2) = Jg(x2 cos8-y2 sin8,x2 sin8+ y2 cos8)dy2 (1) Thus a projection converts a two-dimensional distribution down to a one-dimensional function via line integration. The usefulness of tomography comes from the relationship of the Fourier transform of p0(x2), P9(u2), and the Fourier transform of g(x1,y1), G(u1,v1).…”

Modified radon-Fourier transform for reflective tomography laser radar imaging

“…Since the signal returned is reflected off the illuminated outer surface of an opaque target, only information about the exterior of the target can be obtained, and the images reconstructed using reflective tomography techniques is an outline view of the target cross section. The range-resolved Laser radar reflective tomography imaging laser radar was firstly introduced by researchers Parker [1,2] , Knight [3,4] at the Massachusetts Institute of Technology. Several years later, Matson [5][6][7][8][9][10][11] in Air Force began exploring the technique of using the HI-CLASS coherent laser radar system to obtain reflective images by carrying out a heterodyne system analysis, deriving and validating imaging signal to noise ratio expressions and so on.…”