Signal modeling for low-coherence height-scanning interference microscopy

Abstract

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.

Spatial and temporal coherence effects in interference microscopy and full‐field optical coherence tomography

“…12). This undesirable effect is strongly evident when the illumination bandwidth is also wide as confirmed by DeGroot and Lega [77] using circular lenses. It becomes even worse when the space between the objective lens and the sample surface is not occupied with a suitable index-matching liquid, which in turn forces the application of a dynamic focusing compensation technique as it was shown by Dubois et al [78].…”

Infrared-light interferometry and a phase-stepping algorithm for measuring the three-dimensional topography of components covered with GaAs or Si

“…10) In this study, the variation error of the angle of incidence over the aperture of high-NA objectives and the dispersion of the wafers are neglected over the illumination bandwidth. 11,12) After 30 the repeated measurements of microstructures with the GaAs transmission method, the standard error of step A is 0.0203 m and that of step B is 0.0238 m. Similarly, with the Si transmission method, the standard error of step A is 0.0085 m and that of step B is 0.0137 m.…”

Applications of model-based transparent surface films analysis using coherence-scanning interferometry

“…It has been presented in various forms, [8][9][10][11][12] all using frequency-domain analysis to combine models for the system and of the part being measured. Thus a caveat with model-based CSI is that film properties must be at least partly known to bound the search space and avoid degenerate solutions.…”

“…2, where a ray bundle for a particular ðk; βÞ pair passes through a Mirau objective and reflects from the part. As previously presented in detail, 9 contributing ðk; βÞ pairs can be summed incoherently for each spatial frequency K, which is discretized using a conventional fast Fourier transform or equivalent.…”