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.

When a spherical mirror interferometer is illuminated by an off-axis ray of light, the repeated reflections cause the ray to trace a path which lies on the surface of a hyperboloid, with the points of reflection on the mirrors on ellipses. Under special conditions, these ellipses may become circles, with the points of reflection displaced by an angle 20 after every round trip. When 2 vO = 24r, and g being integers, the rays retrace their paths. These ray paths give rise to additional resonances which were observed. Pictures of the points of reflection are reproduced. The theory is in good agreement with the experimental observations. In laser amplifiers these ray paths enable one to obtain long effective path lengths in the active medium which may be contained in a thin annular cylindrical or hyperboloidal shell.

A long optical path has been folded between two 7.5-cm diam spherical or aspherical mirrors to provide an output beam which can be well separated from previous reflections with 1000 or more passes between the mirrors. The 3000-m path provides 10 psec of delay. This system can be used as a dispersionless optical delay line for use in filtering or storage of information modulated onto the light beam. The pattern of beams between the two mirrors is obtained in one of two ways. A small perturbing mirror may be inserted to give a series of offset ellipses, or one or both of the mirrors can be made astigmatic to give a Lissajous pattern of spots on each mirror. The output beam can be separated from others by discriminating in both angle and position. The diffraction losses of the system are much lower than those for an open beam because of the periodic focusing of the spherical mirrors. The extreme dependence of the loss of the delay line upon the absorption and scattering loss of the mirrors makes the system dependent upon very low loss mirrors and also makes the system a suitable method for measuring mirror loss. Block diagrams are shown for some possible filtering and storage applications.

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