Biomedical subjects
Publications and source records attributed to Emil Wolf.
We analyze the coherence properties of a partially coherent optical field emerging from two pinholes in a plane opaque screen. We show that at certain pairs of points in the region of superposition the light is fully coherent, regardless of the state of coherence of the light at the pinholes. In particular, this result also holds if each pinhole is illuminated by a different laser.
A method is described, based on a recently formulated unified theory of coherence and polarization, for determining the changes that the degree of polarization, the degree of coherence, and the spectrum of a random electromagnetic beam may undergo as the beam propagates. Propagation in free space as well as in linear media, both deterministic and random, is discussed.
We analyze the coherence properties of a partially coherent field emerging from two pinholes in an opaque screen and show that the spectral degree of coherence possesses phase singularities on certain surfaces in the region of superposition. To our knowledge, this is the first illustration of the singular behavior of the spectral degree of coherence, and the results extend the field of singular optics to the study of phase singularities of correlation functions.
We propose and experimentally implement a method for the generation of a wide class of partially spatially coherent vortex beams whose cross-spectral density has a separable functional form in polar coordinates. We study phase singularities of the spectral degree of coherence of the new beams.
It is known that some partially coherent Gaussian Shell-model beams may generate, in free space, the same angular distribution of radiant intensity as a fully coherent laser beam. We show that this result also holds even if the beams propagate in atmospheric turbulence, irrespective of the particular model of turbulence used. The result is illustrated by an example.
Expressions are derived for the spectrum of the field generated by a planar, homogeneous, secondary source of any spectral distribution and of any state of spatial coherence. It is shown that the state of coherence affects the contributions of the homogeneous as well as the evanescent waves of the emitted field. The near-field spectra are studied in detail. The analysis is illustrated by examples.
In usual measurements of the phase of an optical field it is generally assumed that the field is monochromatic. In reality this assumption is never justified. The distinction between monochromaticity and complete spatial coherence is first discussed, and it is then shown that with every spatially coherent field (e.g., a laser mode) one can associate a monochromatic wave that, in a well-defined sense, represents the average behavior of the field. Its phase can be measured by standard interferometric techniques and also by techniques developed in recent years for the measurement of the spectral degree of coherence of fields of arbitrary states of coherence.
The spreading of partially coherent beams propagating through atmospheric turbulence is studied by use of the coherent-mode representation of the beams. Specifically, we consider partially coherent Gaussian Schell-model beams entering the atmosphere, and we examine the spreading of each coherent mode, represented by a Hermite-Gaussian function, on propagation. We find that in atmospheric turbulence the relative spreading of higher-order modes is smaller than that of lower-order modes, whereas the relative spreading of all order modes is the same as in free space. This modal behavior successfully explains why under certain circumstances partially coherent beams are less affected by atmospheric turbulence than are fully spatially coherent laser beams.
Some published computational work has suggested that partially coherent beams may be less susceptible to distortions caused by propagation through random media than fully coherent beams. In this paper this suggestion is studied quantitatively by examining the mean squared width of partially coherent beams in such media as a function of the propagation distance. The analysis indicates under what conditions, and to what extent, partially coherent beams are less affected by the medium.
In a recent paper [Phys. Rev. Lett. 88, 013901 (2002)] it was shown that when a convergent spatially coherent polychromatic wave is diffracted at an aperture, remarkable spectral changes take place on axis in the neighborhood of certain points near the geometrical focus. In particular, it was shown that the spectrum is red-shifted at some points, blueshifted at others, and split into two lines elsewhere. In the present paper we extend the analysis and show that similar changes take place in the focal plane, in the neighborhood of the dark rings of the Airy pattern.
We introduce a hybrid tomographic method, based on recent investigations concerning the connection between computed tomography and diffraction tomography, that allows direct reconstruction of scattering objects from intensity measurements. This technique is noniterative and is intuitively easier to understand and easier to implement than some other methods described in the literature. The manner in which the new method reduces to computed tomography at short wavelengths is discussed. Numerical examples of reconstructions are presented.
It is shown that the recently discovered phenomenon of so-called spectral switches has a natural interpretation in the framework of singular optics with polychromatic light and that it should be regarded as being primarily a manifestation of diffraction-induced spectral changes rather than correlation-induced spectral changes as was suggested in the original papers [the first one appearing in Opt. Commun. 162, 57 (1999)] reporting this effect.
We study the structure of the second-order correlation function of scalar wave fields, which are generated by statistically stationary sources, fluctuating within a homogeneous dissipative medium. We derive a closed-form analytical expression for the spectral degree of coherence of the wave field. If the dissipation in the medium is sufficiently small, and the source fluctuations are statistically isotropic, the degree of spatial coherence of the field produced by any such source is shown to be proportional to the imaginary part of the Green's function of the system, with a proportionality factor depending on the dimensionality of the field. The result holds for wave fields in both three and two spatial dimensions, but not in one dimension. We discuss the physical nature of such universal forms of the spectral degree of coherence.