Frank Reil

Heterodyne measurement of Wigner distributions for classical optical fields

We demonstrate a two-window heterodyne method for measuring the x-p cross correlation, ??(*)(x)? (p)?, of an optical field ? for transverse position x and transverse momentum p. This scheme permits independent control of the x and p resolution. A simple linear transform of the x-p correlation function yields the Wigner phase-space distribution. This technique is useful for both coherent and low-coherence light sources and may permit new biological imaging techniques based on transverse coherence measurement with time gating. We point out an interesting analogy between x-p correlation measurements for classical-wave and quantum fields.

Time-resolved two-window measurement of Wigner functions for coherent backscatter from a turbid medium

For the first time we are able to observe the time-resolved Wigner function of enhanced backscatter from a random medium using a novel two-window technique. This technique enables us to directly verify the phase-conjugating properties of random media. An incident divergent beam displays a convergent enhanced backscatter cone. We measure the joint position and momentum (x, p) distributions of the light field as a function of propagation time in the medium. The two-window technique allows us to independently control the resolutions for position and momentum, thereby surpassing the uncertainty limit associated with Fourier transform pairs. By using a low-coherence light source in a heterodyne detection scheme, we observe enhanced backscattering resolved by path length in the random medium, providing information about the evolution of optical coherence as a function of penetration depth in the random medium.

Time-resolved optical phase space distributions for coherent backscatter

We explore enhanced backscatter from a random medium using time-resolved optical phase space measurement, i.e. measurement of joint position and momentum (x, p) distributions of the light field as a function of propagation time in the medium. Enhanced backscatter is a coherent effect and is not predicted by radiative transport theories. By using a low-coherence source in a heterodyne detection scheme, we observe enhanced backscattering resolved by path length in the random medium, effectively providing timing resolution. Such time-resolved studies are important for exploring the evolution of optical coherence as a function of penetration depth in the random medium. Optical phase space methods provide a visual as well as quantitative method of characterizing the spatial coherence properties and wavefront curvature of the input and scattered fields. These techniques may provide new venues for using optical coherence in medical imaging.

Wigner phase space distribution and coherence tomography

We demonstrate the measurement of path-length-resolved optical phase space distributions as a new framework for exploring the evolution of optical coherence in a turbid medium. This method measures joint transverse position and momentum (i.e., angle) distributions of the optical field, resolved by optical path length in the medium. The measured distributions are related to the Wigner phase space distribution function of the optical field, and can provide complete characterization of the optical coherence in multiple scattering media. Optical phase space distributions are obtained as contour plots which enable a visual as well as quantitative method of characterizing the spatial coherence properties and wavefront curvature of the input and scattered fields. By using a broad-band source in a heterodyne detection scheme, we observe transmission and backscatter resolved by path length in the random medium, effectively providing timing resolution. New two-window heterodyne detection methods permit independent control of position and momentum resolution with a variance product that surpasses the uncertainty limit associated with Fourier transform pairs. Hence, high position and angular resolution can be simultaneously achieved. These techniques may provide new venues for using optical coherence in medical imaging.

Classical-wave analogs of quantum state measurement

Summary form only given. It is well-known that in the paraxial approximation, the transverse mode of an optical field of frequency /spl omega/ obeys an equation which is formally identical in structure to the Schrodinger wave equation of quantum mechanics: i /spl part//spl epsiv/(x,y,z)//spl part/z = /spl nabla//sup 2//sub tr//spl epsiv/(x,y,z)/2k - 2/spl pi//spl kappa//spl Delta//spl chi/(x,y)/spl epsiv/(x,y,z). We employ a local oscillator (LO) comprising a phase-locked super-position of a large collimated Gaussian beam and a small focused Gaussian beam to directly measure the real and imaginary parts of the correlation function.