Fundamentals of wide-field sparse-aperture imaging

Wide-field sparse-aperture imaging systems are desirable for space-borne surveillance applications because they have the potential for improving resolution while minimizing the weight penalty implied by a bigger deployed aperture. Exploiting this potential requires image processing in Fourier space to correct the effects of the badly compromised point spread functions. Consideration of how the SNR in Fourier space depends on sparsity reveals an unexpected, fundamental, highly disadvantageous limit on exposure time, expressed by the Fienup theorem. The merits of different types of aperture configurations are discussed in terms of the resulting point spread and modulation transfer functions, and the effect of dividing a broad spectral range into sub-bands is introduced