By Leonid Yaroslavsky
Electronic holography and electronic snapshot processing are twins born through desktop period. They percentage foundation, theoretical base, tools and algorithms. the current booklet describes those universal basics ideas, equipment and algorithms together with picture and hologram digitization, information compression, electronic transforms and effective computational algorithms, statistical and Monte-Carlo equipment, picture recovery and enhancement, photograph reconstruction in tomography and electronic holography, discrete sign resampling and picture geometrical ameliorations, exact measurements and trustworthy objective localization in photos, recording and reconstruction of desktop generated holograms, adaptive and nonlinear filters for sensor sign perfecting and snapshot recovery and enhancement. The e-book combines idea, seriously illustrated useful equipment and effective computational algorithms and is written for senior-level undergraduate and graduate scholars, researchers and engineers in optics, photonics, opto-electronics and digital engineering.
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Additional info for Digital Holography and Digital Image Processing: Principles, Methods, Algorithms
2 SIGNAL TRANSFORMATIONS In optical systems, optical signals undergo various transformations. In general, one can mathematically treat signal transformations as a mapping in the signal space. For digital signals, this mapping, in principle, can be specified in a form of a look-up table. l). For discrete and continuous signals such a specification is all the more impossible. Therefore in practice, signal transformations are mathematically described as a combination of certain "elementary" transformations, each of which is specified with the help of a relatively small sub set of all feasible input-output pairs.
10) that describes the so called near zone diffraction. Eq. 10 can altemative1y be written as 2. Optical signals and trans/orms 35 + l) [ xl + yJ ]dxdy. 12) Eq. 12 describes also relationship between wave front complex amplitudes in front and rear focal planes of lenses. Consider l-D model of a lens (Fig. 2-12). Lens is fully defined by its property to convert light from a point source in the lens focal plane into a parallel beam tilted according to the position of the source with respect to lens optical axis.
57) When A = D =0 and B =1, ABCD-transform is reduced to Fourier transform, when A = B = D =1, ABCD-transform is reduced to Fresnel transform. 58) tancp tancp _oe> smcp Originally introduced in quantum physics (), it was later found to be convenient for describing optical phenomena such as wave propagation in graded index optical fibers ([24-27]). fx + Dfl ] d/. 60) 53 2. 4 Hilbert transform Hilbert transform represents yet another signal transform of the convolution type closely linked with Fourier transform.