Logical Operations with Images in Accumulated Echo Holography
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Journal of Applied Spectroscopy, Vol. 87, No. 4, September, 2020 (Russian Original Vol. 87, No. 4, July–August, 2020)
LOGICAL OPERATIONS WITH IMAGES IN ACCUMULATED ECHO HOLOGRAPHY E. N. Ahmedshina,* A. R. Sakhbieva, and L. A. Nefediev
UDC 621.373.8
We consider the realization of logical operations for images using the accumulated long-lived echo hologram. It is shown that, depending on the phase difference between the exciting pairs of laser pulses, it is possible to carry out a number of logical operations, namely, combination and symmetric difference of sets as well as their superposition. Keywords: echo holography, wave front, logical operations with sets. Introduction. The term "echo-holography" means the recording and reconstruction of light wave fronts, at which the reference, object and reconstructed waves do not coincide in time [1–6]. The use of echo holograms allows you to record, reproduce and transform images. Since images are sets of points, logical operations with sets are suitable for transforming them. In [7], the implementation of logical operations on sets represented in the form of images using a stimulated echo hologram (SEH) is considered and it is shown that it can be used to implement the logical operation of intersection of sets. In [8], the implementation of the combining operation over sets represented in the form of images using the accumulated longlived echo-hologram (ALEH) mode is considered. To implement various logical operations, it is necessary to use a suitable recording mode for echo-holograms. The optimal options for filtering and transforming images are associated with multi-pulse excitation of the resonant medium. Recording information in the ALEH mode can also be effective. In this case, a sequence of pairs of laser pulses acts on the resonant medium. Each such pair, together with the readout pulse, causes the generation of a long-lived photon echo (LPE) response at the same time. Thus, the ALEH signal generated by the resonant medium after exposure to N pairs of excitation pulses and one readout pulse is a superposition of LPE signals. In this paper, we consider the implementation of the operations "symmetric difference and set merging for images using ALEH," and it is also shown that, depending on the phase difference for the exciting pairs of laser pulses, it is possible to perform logical operations that are their superposition. Operation "Symmetric Difference for Images in Optical Echo-Holography." Figure 1 shows a sequence of excitation pulses used in the implementation of logical operations "symmetric difference, union of sets and logical operations," which are their superposition. Such ALEH excitation can be carried out in a LaF3:Pr3+ crystal (3H4(0) –3P0 transition, λ = 477.7 nm), where τ is the time interval between pulses in pairs, can be tens of ns, τ′ is the time interval between pairs; τ″ is the time interval between the last recording pair and the reading pulse, can reach tens of minutes at helium temperatures of the crystal [9]. The union of sets A and B is
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