A cylindrical lens is a lens which focuses light which passes through onto a line instead of onto a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it onto a line parallel to the intersection of the surface of the lens and a plane tangent to it. The lens compresses the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to it (in the tangent plane). (From Wikipedia, the free encyclopedia)Reflection Tomography
The basic aim of reflection tomography is to construct a quantitative cross-sectional image from reflection data. One nice aspect of this form of imaging, especially in comparison with transmission tomography (i.e. Diffraction Tomography), is that it is not necessary to encircle the object with transmitters and receivers for gathering the “projection” data; transmission and reception are now done from the same side.Transmission tomography is sometimes not possible because of physical constraints. For example, when ultrasound is used for cardiovascular imaging, the transmitted signal is almost immeasurable because of large impedance discontinuities at tissue-bone and air-tissue interfaces and other attenuation losses. For this reason most medical ultrasonic imaging is done using reflected signals.
As for the mathematical model of reflection tomography, the measured time-domain reflected waveform
for viewing angle theta can be written as:
where pt is the incident pulse, c is the speed of light within the slice, 
is the projection of the object slice which are related to the object reflectivity edge map/function f. According to "Principles of Computerized Tombgraphic Imaging" by Avinash C. Kak and Malcolm Slaney, each measured waveform can be considered as a convolution of the parellel projection of the object's 2-D reflectivity function with the incident pulse, just as the first equation above. Thereby, the line projection can be recovered with a deconvolution method, e.g:
where 
represent the Fourier transform of the corresponding time or space domain signal. However, I actually have no idea about how can I get this equation. I tried to get it from the definition of the Fourier transform, but failed. Hornestly, I don't understand why this equation can be thought as a convolution. Just because of its format?In practice, of course, one may have to resort to techniques such as Wiener filtering for implementing the frequency domain inversion. In "Terahertz wide aperture reflection tomography", they usd a hybrid Fourier-wavelet regularized deconvolution algorithm to retrieve
from , "because it minimizes the artifacts that are associated with pure Fourier-basedapproaches".
