Withington Stafford, Hobson Michael P, Berry Rachel H
Astrophysics Group, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, UK.
J Opt Soc Am A Opt Image Sci Vis. 2004 Feb;21(2):207-17. 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].
描述了一种通过使用超完备基集来表示部分相干光学系统行为的技术。该方案与伽柏函数理论密切相关。通过奇异值分解表明，如果E是一个包含采样基函数的矩阵，那么光学计算所需的所有信息都包含在S = EE† 和R = E†E中。对于超完备集，S可以求逆得到对偶基集E = S−1E，它可用于找到空间相干函数采样双峰展开的相关矩阵元素A。超完备相关矩阵在光学元件处很容易散射。它们可用于确定：(i) 场的本征模式；(ii) 场中的总功率，Pt = Tr[RA]；(iii) 处于不同相干态的两个场A和B之间耦合的功率，Pc = Tr[RARB]；以及(iv) 场的熵，Q = Tr[Zsigmar(I - Z)r/r]，其中Z = RA/Tr[RA]。
