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

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].

[1]  Ghassan Yassin,et al.  Theoretical analysis of planar bolometric arrays for THz imaging systems , 2003, SPIE Astronomical Telescopes + Instrumentation.

[2]  R. Penrose.  A Generalized inverse for matrices , 1955 .

[3]  Analyzing the power coupled between partially coherent waveguide fields in different states of coherence. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  Rachael Padman,et al.  Radiation patterns of few-moded horns and condensing lightpipes , 1991 .

[5]  P. Richards.  Bolometers for infrared and millimeter waves , 1994 .

[6]  G. Yassin,et al.  Power coupled between partially coherent vector fields in different states of coherence. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Stafford Withington,et al.  Representation of mirros in beam waveguides as inclined phase-transforming surfaces , 1995 .

[8]  Girish S. Agarwal,et al.  Coherence theory of laser resonator modes , 1984 .

[9]  E. Wolf.  Coherent-mode propagation in spatially band-limited wave fields , 1986 .

[10]  E. Wolf.  New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources , 1982 .

[11]  Vincenzo Galdi,et al.  Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensional scattering by moderately rough interfaces , 2001 .

[12]  M. Griffin.  Bolometers for far-infrared and submillimetre astronomy , 2000 .

[13]  Quasi-optical beam waveguide analysis using frame based Gaussian beam expansion , 2002 .

[14]  Serdar Yüksel,et al.  Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence. , 2002 .

[15]  Franco Gori,et al.  Coherent-mode decomposition of partially polarized, partially coherent sources. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  D. Castañón,et al.  Narrow-waisted Gaussian beam discretization for short-pulse radiation from one-dimensional large apertures , 2001 .

[17]  J. Murphy,et al.  Dyadic analysis of partially coherent submillimeter-wave antenna systems , 2001 .

[18]  Hendrik Bosma,et al.  On the theory of linear noisy systems , 1967 .