An irreducible support is one that ensures a unique solution to the phase problem without requiring that it be explicitly imposed as a reconstruction constraint. However, the only nontrivial support that has been shown to be irreducible is Eisenstein’s support. Herein a general description of support irreducibility is developed for discrete functions, both over positive, real and over complex numbers. In addition, a method of testing an arbitrary support of finite extent for irreducibility is introduced, and a number of simple irreducible supports are presented that are not of the Eisenstein type.
© 1987 Optical Society of America
Original Manuscript: December 11, 1985
Manuscript Accepted: September 2, 1986
Published: January 1, 1987
B. J. Brames, "Testing for support irreducibility," J. Opt. Soc. Am. A 4, 135-147 (1987)