Joanna Schmit

Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.

Improved vertical-scanning interferometry

We describe a method that combines phase-shifting and coherence-peak-sensing techniques to permit measurements with the height resolution of phase-shifting interferometry without the interval-slope limitation of lambda/4 per data sample of phase-shifting interferometry. A five-frame algorithm is used to determine both the best-focus frame position and the fractional phase from the best-focus frame of the correlogram acquired through vertical scanning. The two surface profiles retrieved from the phase and the modulation contrast of the correlograms are compared in the phase-unwrapping process to remove fringe-order ambiguity.

Window function influence on phase error in phase-shifting algorithms

We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

N-point spatial phase-measurement techniques for non-destructive testing

Abstract Spatial phase-measurement interferometry techniques commonly used in non-destructive testing are affected by a number of fundamental error sources. This paper focuses on the major limitations for phase calculations using standard N -point algorithms. These limitations include: the wrong carrier frequency, unequally spaced fringes, detector non-linearities and variations in the dc fringe intensity. The character and magnitude of these errors are quantified by using computer simulations. A displacement measurement of a bent plate using different algorithms on the same data shows that practical limitations are unequally-spaced fringes and variations in dc intensity and fringe visibility. These errors limit the resolution of this type of measurement to about a tenth of a wave r.m.s.

Offset of coherent envelope position due to phase change on reflection

Different materials with different phase changes on reflection affect the surface-height measurement when interferometric techniques are employed for testing objects constructed of different materials that are adjacent to one another. We test the influence of this phase change on reflection when vertical scanning interferometry with a broadband source is used. We show theoretically and experimentally that the strong linear dependence of the dispersion of the phase change on reflection preserves the shape of the coherence envelope of the fringes but shifts it along the optical axis by approximately 10-40 nm for metallic surfaces.

Large field of view, high spatial resolution, surface measurements

It is difficult in interferometric metrology to maintain high spatial resolution over a large field of view. Interferometric microscope measurements yield high resolution, but only over a small area. Other conventional interferometric systems can measure large areas, but they fail to provide the necessary spatial resolution. High spatial resolution over a large field-of-view (FOV) can be obtained by stitching together multiple high spatial resolution measurements of adjacent areas of a measured surface. The measurements can be fit together in a global sense, or by matching the piston and tilt over the overlap region. Care must be taken in the stitching process to make sure the measurements are precisely overlapped to minimize errors. The larger the overlap the easier it is to match data sets, but of course more data sets are required to get a given field of view. This paper shows that a 20 percent overlap gives a good trade off between having good repeatability and obtaining a large field of view with a minimum number of data sets. Typical measurement results are shown for stitching as many as 285 sub-regions.

Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension

Spatial and temporal phase-measurement interferometry techniques are affected by a number of sources of error. This paper focuses on the influence of major error sources on the results of phase calculations using the most popular algorithms. These error sources include phase-shifter miscalibration for N-frame temporal methods and its equivalent of the wrong carrier frequency in N-point spatial techniques and detector nonlinearities. Other errors considered are detector nonlinearities and leakage in the Fourier-transform method. Computer simulations in one dimension with straight, equally spaced fringes reveal the character and magnitude of these errors.

Computerized interferometric measurement of surface microstructure

The addition of modern electronics, computers, and software to an interference microscope greatly increases the surface height measurement capability of the interference microscope. The RMS repeatability of surface microstructure measured using a computerized phase-shifting interference microscope can be less than 0.1 nanometer. While phase- shifting interferometry having sub-nanometer height precision has limited dynamic range, the dynamic range of an interference microscope can be extended to hundreds, or even thousands, of microns by using vertical scanning coherence peak sensing techniques. This paper describes the measurement capabilities of an interference microscope employing both phase-shifting phase measurement capability and coherence peak sensing. Typical measurements obtained using phase-shifting and coherence peak sensing are illustrated. Techniques for extending the measurement capability of computerized interference microscopes are discussed.

Improved polarization Mirau interference microscope

The Mirau interference microscope features a very compact interferometer incorporated in a single microscope objective. We describe a simple modification that results in the exiting beams being orthogonally polarized. This modification makes it possible to introduce achromatic phase shifts in the two beams, facilitating the use of the Mirau interferometer for white-light phase-shifting interference microscopy.

Errors in spatial phase-stepping techniques

Spatial phase-measurement interferometry techniques are affected by a number of sources of error. This paper focuses on the major limitations for phase calculations using standard N- point algorithms. These limitations are having the wrong carrier frequency, unequally spaced fringes, detector nonlinearities, and variations in the dc fringe intensity. Computer simulations reveal the character and magnitude of these errors.