Linear space-variant optical data processing

A short history of optical computing: rise, decline, and evolution

“…The setups of Figures 2 and 3 are coherent optical processors, however incoherent optical processors were also proposed with the advantage of the suppression of the coherent noise 13 . Linear optical processing can be decomposed into spaceinvariant operations such as correlation or convolution or space-variant operations such as coordinates transforms 14 . Non-linear processing can also be implemented optically 15 .…”

Simulation and correction of electron images of tilted planar weak-phase samples

“…For tilted samples, however, the point-spread function is not space invariant, hence the mathematical notion of a transfer function does not apply, and the classical CTF model is not accurate. The problem of image restoration of space variant blur is common and has been addressed long time ago (e.g., Robbins and Huang, 1972;Goodman, 1981), and one approach has been applied to restore tilt-series of thin sections (Winkler and Taylor, 2003). Another approach corrects the space variant psf by segmenting the images into stripes parallel to the tilt axis (Fernandez et al, 2006).…”

Incoherent spatial impulse response in variable-cross-section photoreceptors and frequency-domain analysis

“…This response represents the response of the system to a unit impulse. 9 As an immediate consequence (assuming spatial invariance), the Fourier-transform properties for the convolution operation between the input and the impulse response lead to a description of the phenomenon in the spatial-frequency domain by defining the transfer function as the Fourier transform of the impulse response. In this domain the behavior of the system can be interpreted as a spatial-frequency filtering process.…”