Peter de Groot

High-speed noncontact profiler based on scanning white-light interferometry

We describe a system for fast three-dimensional profilometry, of both optically smooth and optically rough surfaces, based on scanning white-light techniques. The system utilizes an efficient algorithm to extract and save only the region of interference, substantially reducing both the acquisition and the analysis times. Rough and discontinuous surfaces can be profiled without the phase-ambiguity problems associated with conventional phase-shifting techniques. The system measures steps to 100 µm, scans a 10µLm range in 5 s, and has a smooth surface repeatability of 0.5 nm.

Surface Profiling by Analysis of White-light Interferograms in the Spatial Frequency Domain

Abstract We describe a scanning white-light interferometer for high-precision surface structure analysis. Interferograms for each of the image points in the field of view of the instrument are generated simultaneously by scanning the object in a direction perpendicular to the object surface, while recording detector data in digital memory. These interferograms are then transformed into the spatial frequency domain and the surface height for each point is obtained by examination of the complex phase as a function of frequency. The final step is the creation of a complete three-dimensional image constructed from the height data and corresponding image plane coordinates. The measurement repeatability is better than 0·5 nm r.m.s. for a surface height range of 100 μm.

Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window.

I propose a systematic way to derive efficient, error-compensating algorithms for phase-shifting interferometry by integer approximation of well-known data-sampling windows. The theoretical basi of the approach is the observation that many of the common sources of phase-estimation error can be related to the frequency-domain characteristics of the sampling window. Improving these characteristics can therefore improve the overall performance of the algorithm. Analysis of a seven-frame example algorithm demonstrates an exceptionally good resistance to first- and second-order distortions in the phase shift and a much reduced sensitivity to low-frequency mechanical vibration.

Determination of fringe order in white-light interference microscopy

Combining phase and coherence information for improved precision in white-light interference microscopy requires a robust strategy for dealing with the inconsistencies between these two types of information. We correct for these inconsistencies on every measurement by direct analysis of the difference map between the coherence and the phase profiles. The algorithm adapts to surface texture and noise level and dynamically compensates for optical aberrations, distortions, diffraction, and dispersion that would otherwise lead to incorrect fringe order. The same analysis also provides the absolute height data that are essential to relational measurements between disconnected surfaces.

Vibration in phase-shifting interferometry

Unexpected mechanical vibrations can significantly degrade the otherwise high accuracy of phase-shifting interferometry. Fourier analysis of phase-shift algorithms is shown to provide the analytical means of predicting measurement errors as a function of the frequency, the phase, and the amplitude of vibrations. The results of this analysis are concisely represented by a phase-error transfer function, which may be multiplied by the noise spectrum to predict the response of an interferometer to various forms of vibration. Analytical forms for the phase error are derived for several well-known algorithms, and the results are supported by numerical simulations and experiments with an interference microscope.

Measurement of transparent plates with wavelength-tuned phase-shifting interferometry

A wavelength-tuned Fizeau interferometer is applied to the problem of flatness testing of transparent plates. When the plate is positioned at a specific distance from the reference surface and an integer-math 13-frame phase-shifting algorithm is applied, the system directly filters out unwanted interference arising from backsurface reflections. The resulting front-surface profile exhibits less than 2 nm of residual error attributable to spurious reflections from within the plate.

Signal modeling for low-coherence height-scanning interference microscopy

We propose a computationally efficient theoretical model for low-coherence interferometric profilers that measure surface heights by scanning the optical path difference of the interferometer. The model incorporates both geometric and spectral effects by means of an incoherent superposition of ray bundles through the interferometer spanning a range of wavelengths, incident angles, and pupil plane coordinates. This superposition sum is efficiently performed in the frequency domain, followed by a Fourier transform to generate the desired simulated interference signal. Example applications include white-light interferometry, high-numerical-aperture microscopy with a near-monochromatic light source, and interference microscopy for thickness and topography analysis of thin-film structures and other complex surface features.

Extending the unambiguous range of two-color interferometers

The unambiguous distance measurement range in two-color interferometry is generally understood to be limited to the equivalent or synthetic wavelength, which is inversely proportional to the wavelength separation of the two colors. Here it is shown that one may extend the unambiguous range well beyond this limit by using optical phase information to determine the synthetic-wavelength fringe order.The unambiguous distance measurement range in two-color interferometry is generally understood to be limited to the equivalent or synthetic wavelength, which is inversely proportional to the wavelength separation of the two colors. Here it is shown that one may extend the unambiguous range well beyond this limit by using optical phase information to determine the synthetic-wavelength fringe order.

Principles of interference microscopy for the measurement of surface topography

Interference microscopy plays a central role in noncontact strategies for process development and quality control, providing full 3D measurement of surface characteristics that influence the functional behavior of manufactured parts. Here I briefly review the history and principles of this important technique, then concentrate on the details of hardware, software, and applications of interference microscopy using phase-shifting and coherence scanning measurement principles. Recent advances considered here include performance improvements, vibration robustness, full color imaging, accommodation of highly sloped surfaces, correlation to contact methods, transparent film analysis, and international standardization of calibration and specification.

Interferometric back focal plane microellipsometry

We present a technique for ellipsometric analysis of materials with high lateral resolution. A Michelson-type phase-shifting interferometer measures the phase distribution in the back focal plane of a high numerical aperture objective. Local measurements of the ellipsometric parameter delta are performed over the entire spectrum of angles of incidence. We show that delta is to leading order linearly proportional to the phase change on reflection of normally incident light. We furthermore invert the Fresnel reflection equations and derive expressions for the real and imaginary parts of the refractive index as functions of the phase change on reflection and the reflectivity at normal incidence, both of which are measurable with the same apparatus. Hence we accomplish local measurements of the refractive indices of our samples. Determination of the phase change on reflection permits correction of interferometric topography measurements of heterogeneous specimens.