The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.
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The van Cittert-Zernike theorem states that the Fourier transform of the intensity distribution function of a distant, incoherent source is equal to the complex degree of coherence. In this Letter, we present a method for measuring the complex degree of coherence in one shot by recording the interference patterns produced by multiple aperture pairs. The intensity of the sample is obtained by Fourier transforming the complex degree of coherence.
View Article and Find Full Text PDFOptimal transmit apodization for the maximization of lag-one coherence with applications to aberration delay estimation.
Ultrasonics
July 2023
Department of Radiology, Stanford University School of Medicine, Palo Alto, CA, 94304 USA.
Phase aberration is one of the major sources of image degradation in medical ultrasound imaging. One of the earliest and simplest techniques to correct for phase aberration involves nearest-neighbor cross correlation to estimate delays between neighboring receive channels and the compensation of aberration delays in a delay-and-sum beamformer. The main challenge is that neighboring receive channels may not have sufficient signal correlation to accurately estimate the aberration delays.
View Article and Find Full Text PDFTo see through a random light field in real-time, single-shot generalized Hanbury Brown-Twiss experiments using a polarization camera are proposed. The target intensity distribution is obtained from a complex coherence function which is calculated from auto-correlation and cross correlation functions of phase-shifted speckle intensity distributions. The phase-shifted speckle intensity distributions are simultaneously obtained through a strategy of parallel phase-shifting digital holography.
View Article and Find Full Text PDFAutocorrelation functions and power spectral densities of the Stokes parameters in a polarization speckle pattern.
J Opt Soc Am A Opt Image Sci Vis
January 2023
The concept of ensemble-average polarization and coherence has been applied to studying fluctuating Stokes parameters in a polarization speckle observed when coherent light is passed through a birefringent polarization scrambler. With the aid of the ensemble-average van Cittert-Zernike theorem for the propagation of ensemble-average polar-coherence, we invesitgate the autocorrelation functions and power spectra of the Stokes parameters to expose the dependence of the polarization-related scale-size distributions on the optical geometries in which the polarization speckle arises. A generalized concept of the Stokes ensemble-average coherence areas is introduced to deal with the polarization-related average areas associated with polarization speckle.
View Article and Find Full Text PDFRonchi shearing interferometry is a promising technique for in situ wavefront aberration measurement of the projection lens in advanced photolithography systems. The Van Cittert-Zernike theorem has been used to analyze the interference signal of a Ronchi shearing interferometer in the effective interference area (overlapping area of the ±1st diffraction orders produced by the image grating). However, the applicability of this theorem has not been systematically studied.
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