Representing the behavior of partially coherent optical systems by using overcomplete basis sets

• Published in: Journal of the Optical Society of America. A, Optics, image science, and vision Vol. 21; no. 2; p. 207
• Main Authors: Withington, Stafford, Hobson, Michael P, Berry, Rachel H
• Format: Journal Article
• Language: English
• Published: United States 01.02.2004
• ISSN: 1084-7529
• DOI: 10.1364/JOSAA.21.000207

A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S = EE(dagger) and R = E(dagger)E. For overcomplete sets, S can be inverted to give a dual basis set, E = S(-1)E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, Pt = Tr[RA]; (iii) the power coupled between two fields, A and B, that are in different states of coherence, Pc = Tr[RARB]; and (iv) the entropy of a field, Q = Tr[Zsigmar(I-Z)r/r], where Z = RA/Tr[RA].