An eigenvalue analysis of the noise-prone image leads to (a) an analysis of the eigenfunctions and eigenvalues of the sin2(x)/x2 kernel; and (b) an expression relating an effective number Neff of degrees of freedom directly to the signal-to-noise ratio σ0/σv. The latter are the variances of object and noise, respectively. For the particular case of incoherent, diffraction-limited imagery, Neff is found to be reduced from its noise-free value, the Shannon number, by the factor (1 − σv/σ0). A maximum number Nmax of degrees of freedom is also defined. Comparing one-dimensional objects illuminated alternatively by coherent and incoherent light, we find they have the same number Nmax of degrees of freedom. However, for the corresponding two-dimensional case, the incoherent value for Nmax is double that of the coherent value.
© 1974 Optical Society of AmericaFull Article | PDF Article
OSA Recommended Articles
F. Gori and G. Guattari
J. Opt. Soc. Am. 64(4) 453-458 (1974)
F. Gori, S. Paolucci, and Laura Ronchi
J. Opt. Soc. Am. 65(5) 495-501 (1975)
J. Opt. Soc. Am. 67(1) 71-76 (1977)