Estimator and signal-to-noise ratio for an integrative synthetic aperture imaging technique

An imaging system is described which uses the following concepts: laser illumination of objects, nonredundant apertures, and phase closure. A sparse transmitter array is envisioned, each aperture of which emits at a different laser frequency such that any pair of beams gives rise to a unique beat signal. The light reflected by an object thus irradiated is sensed by a spatially integrating detector array. An estimator is given for the Fourier components of the object at spatial frequencies corresponding to the unique temporal beats sensed by the receiver array. The standard deviation of the estimator is computed taking both shot noise and laser speckle into account. It is found that the signal-to-noise ratio for both kinds of noise increases with the square root of the area of the detector array. This allows the signal-to-noise ratio of the system to be increased independent of the resolution.