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.
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.
We propose a practical theoretical model of an interference microscope that includes the imaging properties of optical systems with partially coherent illumination. We show that the effects on measured topography of a spatially extended, monochromatic light source at low numerical apertures can be approximated in a simplified model that assumes spatially coherent light and a linear, locally shift-invariant transfer function that accounts for optical aberrations and the attenuation of diffracted plane wave amplitudes with increasing spatial frequencies. Simulation of instrument response using this model agrees with methods using numerical pupil-plane integration and with an experimental measurement of surface topography.
The Fourier components of interference signals generated by scanning a high-numerical-aperture objective orthogonal to an object surface correspond to different angles of incidence on the surface. The phase and amplitude of these Fourier components relate to the structure of the object, including in particular the 3D topography and thickness profiles of thin-film layers.
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