To reveal some new results of a study concerning phase-closure imaging, first we introduce three key operators: the cophasing operator A, the phase-aberration operator B, and the phase-closure operator C. We then show that the generalized inverses of these operators are equal to their (Hilbert space) adjoints divided by the number of pupil pinholes. This remarkable property, which can be stated in terms of backprojection, plays an essential part in the understanding and the treatment of the inverse problems of aperture synthesis. The notion of backprojection is illustrated in a geometrical manner. As an example of applications we present a new self-calibration algorithm for solving the phase-restoration problem in radio imaging. The solution of this deconvolution problem is obtained without phase unwrapping by means of backprojection mechanisms. The implications of these structures in speckle imaging are also examined. Whenever possible, nonredundant configurations should be preferred. The main developments of our approach concern, in particular, the very-long-baseline array and the interferometric mode of the very large telescope.
© 1990 Optical Society of America
Original Manuscript: July 10, 1989
Revised Manuscript: November 1, 1989
Published: March 1, 1990
A. Lannes, "Remarkable algebraic structures of phase-closure imaging and their algorithmic implications in aperture synthesis," J. Opt. Soc. Am. A 7, 500-512 (1990)