Mixing inhomogeneous, partially coherent optical fields.
A phase-quadrature (p-q) description of a random optical field is suggested as an attractive alternative to the usual logamplitude-phase representation for the purpose of investigating the behavior of the optical heterodyne. Using the p-q representation, an expression is developed for the average signal-to-noise ratio at the heterodyne's output when both the signal and local oscillator (LO) fields are inhomogeneous and partially coherent. An examination of the expression for the signal-to-noise ratio indicates the general nature of the previously observed saturation effect. A coherence suppression phenomenon is also apparent. It is shown that the heterodyne's field of view may be drastically broadened (relative to that of a system which processes ideal plane waves) as a result of weak spatial coherence in either the signal or LO field. Recently published experimental data are examined in light of the results obtained i this paper, and good agreement between theory and experiment is observed.
Heterodyne detection of partially coherent optical signal
The SN ratio is studied for heterodyne detection of partially coherent plane wave optical signals when they are focused by a lens after passing through a circular aperture and are added to a coherent Gaussian beam local oscillator signal. We treat the case in which the intensity distribution of the signal over the aperture is uniform and the natural logarithm of its spatial coherence is expressed as the vth power of the distance between two arbitrary points on the aperture. Using a two-dimensional Fourier transform, we express the mutual coherence function of the signal on the detector surface in a series form. The results are used to present an expression for the SN ratio suitable for numerical calculations. The SN ratio is investigated numerically with the correlation length on the aperture and the detector radius as parameters. It is found that, regardless of the correlation length, the detector radius of the order of the Airy disk is sufficient for obtaining an SN ratio almost equal to the maximum value determined for each correlation length. We also find that the maximum SN ratio is approached in the case of partially coherent signals if we use the optimum beam parameter of local oscillator signals, which has already been determined.
A slowly rotating coil system for AC field measurements of Fermilab Booster correctors
A method for measurement of rapidly changing magnetic fields has been developed and applied to the testing of new room temperature corrector packages designed for the Fermilab Booster Synchrotron. The method is based on fast digitization of a slowly rotating tangential coil probe, with analysis combining the measured coil voltages across a set of successive magnet current cycles. This paper presents results on the field quality measured for the normal and skew dipole, quadrupole, and sextupole elements in several of these corrector packages.