Johannes Schwider

Digital wave-front measuring interferometry: some systematic error sources.

Digital wave-front measuring interferometry is a well-established technique but only few investigations of systematic error sources have been carried out so far. In this work three especially serious error sources are discussed in some detail: inaccuracies of the reference phase values needed for this type of evaluation technique; disturbances due to extraneous fringes; and spatially high frequency noise on the wave fronts caused by dust particles, inhomogeneities, etc. For the first two error sources formulas of the resulting phase deviation are derived and compensation possibilities discussed and experimentally verified. To study the occurrence of wave-front irregularities caused by dust particles a model has been developed and countermeasures derived which assure sufficient regularity of contour line plots. The repeatability of the present experimental setup was better than λ/200 within the 3σ limits.

Accuracy of phase shifting interferometry

The accuracy of phase shifting interferometers is impaired by mechanical drifts and vibrations, intensity variations, nonlinearities of the photoelectric detection device, and, most seriously, by inaccuracies of the reference phase shifter. The phase shifting procedure enables the detection of most of the errors listed above by a special Lissajous display technique described here. Furthermore, it is possible to correct phase shifter inaccuracies by using an iterative process relying solely on the interference pattern itself and the Fourier sums used in phase shifting interferometry.

New compensating four-phase algorithm for phase-shift interferometry

Phase-shift interferometry suffers from periodic systematic errors caused by erroneous reference phase adjustments and instabilities of the interferometer. A new method is described that uses only four interferograms and eliminates the errors caused by linear adjustment deviations of the reference phase or the mean phase in the interferometer. Test results confirm the theoretical predictions.

Red-green-blue interferometer for the metrology of discontinuous structures

Discontinuous surface profiles, e.g., diffractive optical elements (DOEs), are commonly measured by white-light interferometry. White-light interferometry needs significantly more memory capacity and computer time than does phase-shifting interferometry; there are approximately ten times more frames to be taken to gather the required information about the object under test. But usually the grooves of the DOEs are too deep for single-wavelength phase-shifting interferometry. Here we show how phase-shifting techniques can be applied to DOEs. For this purpose three interference patterns are recorded simultaneously by a three-chip color CCD camera at three wavelengths (Red-green-blue). It is possible to calculate separately the optical path difference at each pixel from the three phase patterns modulo 2pi. The algorithms used and experimental results are presented.

Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures

White-light interferometry is a standard optical tool with which to measure profiles of discontinuous structures such as diffractive optical elements. But there is one outstanding technological problem: The interferometers have to be symmetric; i.e., the geometrical path lengths in glass have to be the same for both interferometer arms. If these paths in glass are not equal within the field of view, a dispersion error will occur that is rather complicated to compensate for. The error appears in the measured profile in the form of steps of lambda/2 in height. A simulation of interferograms disturbed by dispersion deviations is presented, and an algorithm is introduced that eliminates the steps without changing the actual phase information or averaging neighboring pixels. The results are shown with simulated and real data.

Dynamic range expansion of a Shack–Hartmann sensor by use of a modified unwrapping algorithm

An algorithm for expanding the dynamic range of Shack--Hartmann sensors is proposed. The distribution of the spot dislocations is treated with a modified unwrapping algorithm that is widely used in interferometry. The algorithm unwraps the spot dislocations and assigns the spots to their original subapertures, leading to a huge expansion of the dynamic range. For the proposed algorithm there remains a limitation on the maximum wave-front curvature instead of on the maximum wave-front slope. Examples are given that show spot fields that were wrapped four times; the measured wave front had a peak-to-valley value of 116 lambda .

ABSOLUTE SPHERICITY MEASUREMENT : A COMPARATIVE STUDY OF THE USE OF INTERFEROMETRY AND A SHACK-HARTMANN SENSOR

A comparison of absolute sphericity measurements with a ShackHartmann sensor and a TwymanGreen interferometer is presented. The absolute deviations of a test sphere from its ideal shape were calculated in both cases from the measured wave aberrations of three different positions. Very good qualitative and quantitative agreement of the results was achieved. The difference of the root-mean-square values of the two methods was 1/1000 of a wavelength.

Twyman-Green interferometer for testing microspheres

Testing of spherical surfaces using the Twyman-Green interferometer with a laser source suffers from the presence of spurious interference fringes and dust diffraction. By reducing the spatial coherence while maintaining the temporal coherence a tremendous improvement of the fringe quality can be obtained. To conserve sufficient contrast, the reference mirror must be positioned to suitable locations relative to the test arm of the interferometer. These conditions are described and examples are presented.

Array illuminator based on phase contrast

An array illuminator converts a uniformly wide beam losslessly into an array of bright spots. These spots provide the necessary illumination for microcomponents such as optical logic gates or bistable elements. Such elements may serve as devices in a 2-D discrete parallel processor. We propose an array illuminator with a phase grating on its front end. The phase grating is illuminated uniformly and then converted into an amplitude image by means of a phase contrast setup. The bright spots of the amplitude image are to be used for illuminating the array of microdevices of a digital optical computer.

Transferring resist microlenses into silicon by reactive ion etching

Reactive ion etching (RIE) is known as an effective technique for high precision anisotropic etching with a minimum loss of the critical dimensions provided by the photoresist or other masking materials. RIE can also be used to transfer continuous forms such as spherical resist microlenses into substrate materials (e.g., quartz glass or silicon). The form of the lenses can be considerably controlled by changing the etch rate ratio between resist and the substrate. This was achieved by varying the etch gas compound, especially the amount of oxygen, during the etching or by changing the applied power. Measured etch rates for silicon are given to demonstrate the possibilities of lens shaping. The surface roughness of the etched lenses was one of the main problems. The roughness could be minimized by adding helium to the etch gases for heat removal and by increasing the resist rinse time after the wet chemical development.