Abstract
The quantum theory of the parametric amplification and up-conversion of an optical image occurring simultaneously in a single nonlinear crystal in the case of a closely located object is developed. The collinear interactions of the pumping wave with waves carrying the optical images are considered. Expressions for means and variances of the photon number are obtained. The behavior of the signal-to-noise ratio for amplified and up-converted images is analyzed when the main parameters are measured before the initial image enters the nonlinear crystal.
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