Many techniques in the field of optical computing, that employ the high spatial-parallelism and large information-carrying capability of light have been studied. Many of these optical computing techniques are discussed in a spatial frequency domain, such as with a joint transform correlator or matched filtering; with the use of the spatial Fourier transform, a spatial image can be decomposed to its spatial spectral components, which are then spread spatially.
In the field of laser mode-locking techniques, on the other hand, many femtosecond pulse laser systems have been developed. Because some of them are inexpensive and easy to operate, these lasers have been widely applied in many physical and industrial fields such as optical communications, industrial and biomedical measurement, and the ultrafast control of physical and chemical properties of materials. To achieve such applications, we have to control such ultrafast light pulses with great temporal accuracy. In most cases, the high accuracy control is achieved by employing a spectral-modulating pulse shaper. The pulse shaper spatially decomposes the temporal spectrum components of an ultrafast light pulse by the use of a grating-lens pair, then modulates the spectrum and reconstructs a temporally modulated light pulse using another grating-lens pair.
These techniques, as used in both the optical computing and lasermode-locking fields, have theoretical relationships because the spatial and temporal behaviors of light are expressed by similar equations. Furthermore, both the techniques employ the spatial or temporal optical Fourier transform.
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