A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

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Missile System Division under a Research Grant. This paper is based in part on a dissertation submit.ted by J. H. Bruning in part.ia1 fuliillment of t.he requirements for the Ph.D. degree.

Abstracf-In [SI, both low-and high-frequency solutions to the two-sphere problem were presented in a form suitable for efficient computer solution. Here, numerical results are presented using a method which has enabled the 6rst appearance of reliable results for the scattered field from two spheres of radii larger than one wavelength and as large as ten or more. Radar cross sections (RCS) are computed for numerous configurations of two spheres of various materials. Results for scattering by three collinear spheres are also given. An experimental program was undertaken and is briefly described. Whenever possible, these results are compared with the theory. In all cases the agreement is excellent. Depolarization due to multiple scattering is also investigated, revealing some interesting effects and practical applications to scattering range calibration.

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