Abstract
The paper considers the general properties of various types of programmable acousto-optic filters under multifrequency control: dispersive delay lines, adaptive hyperspectral filters, and laser beam shapers. It is shown that the same mathematical apparatus based on the Fresnel transform is applicable for these types of devices for the synthesis of multifrequency control radio signals. Generation of arbitrary complex-valued filter transmission functions is enabled. For this purpose, we use a quadratic phase factor of the ultrasonic spectrum, which is proportional to the waveform duration and reciprocal to the instantaneous bandwidth. Arbitrary spectral transmission of tunable filters in spectral domain and laser beam shaping applications with circularly symmetric two-dimensional transfer functions are demonstrated.
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