Linear systems characterization of the topographical spatial resolution of optical instruments.

Lateral resolving power is a key performance attribute of Fizeau interferometers, confocal microscopes, interference microscopes, and other instruments measuring surface form and texture. Within a well-defined scope of applicability, limited by surface slope, texture, and continuity, a linear response model provides a starting point for characterizing spatial resolution under ideal conditions. Presently, the instrument transfer function (ITF) is a standardized way to quantify linear response to surface height variations as a function of spatial frequency.

Fourier optics modeling of interference microscopes.

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.

Metrology of optically-unresolved features using interferometric surface profiling and RCWA modeling.

Rigorous coupled wave analysis (RCWA) interprets 3D white-light interference microscopy profiles and reveals the dimensions of optically-unresolved surface features. Measurements of silicon etch depth of a 450-nm pitch grating structure correlate to atomic force microscopy with R(2)= 0.995 and a repeatability of 0.

Angle-resolved three-dimensional analysis of surface films by coherence scanning interferometry.

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.

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.

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.

Optical interferometry for measurement of the geometric dimensions of industrial parts.

We describe an instrument for the measurement of surface flatness, parallelism, and size (thickness) of plane-parallel parts in a single measurement to 1sigma gauge capability of 0.02, 0.03, and 0.