Source reconstruction from the modulus of the correlation function: a practical approach to the phase problem of optical coherence theory*

Measurement of Wave Fields

“…Despite this, interferometric measurements have been sparingly applied to the measurement of fields with an arbitrary correlation function [29][30][31][32][33][34]. It is possible, however, to construct an interferometer capable of measuring the space-shift variant two-point correlation function for fields at a remote plane with arbitrary spatial coherence in a simple, accurate and effIcient manner [35].…”

Encoding of Information in Inverse Optical Problems

“…{(i<k>z)"F(z)}=d-(f(t)) . (21) Thus the derivatives of the object have the same zero distribution in z space as f(t), except for additional zeros at the origin . When the full complement of zeros is reached, f ~") (t) becomes discontinuous at the ends of the interval .…”

“…The idea of generating the function F off the real axis by means of exponential factors was suggested, in a related context, by Kohler and Mandel [21] . By sweeping the complex plane, complex zeros will successively pass through the x + iy axis, being seen as real zeros in the observed intensity .…”

On the inverse problem of source reconstruction from coherence measurements

“…In the Fresnel regime, some Fourier-based inversion methods use the van Cittert-Zernike theorem to recover the intensity distribution across incoherent sources [15], and the more complicated case of partially coherent quasihomogeneous sources [16][17][18]. Further algorithms use only the modulus of the Fourier transform [19,20], with various extensions (e.g., the use of apriori constraints [21] or coherent illumination [22]) which improve the recon-struction. However, the accuracy of these methods degrades with the increase in the coherence of the source.…”