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. In this paper, we build on the ITF idea and introduce terms, mathematical definitions, and appropriate physical units for applying a linear systems model to surface topography measurement. These new terms include topographical equivalents of the point-, line-, and edge-spread functions, as well as a complex-valued transfer function that extends the ITF concept to systems with spatial-frequency-dependent topography distortions. As an example, we consider the experimental determination of lateral resolving power of a coherence scanning interference microscope using a step-height surface feature to measure the ITF directly. The experiment illustrates the proposed mathematical definitions and provides a direct comparison to theoretical calculations performed using a scalar diffraction model.

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 0.11nm. This same technique achieves a <1nm sensitivity to 80-nm lateral widths of 190-nm pitch gratings using a 570-nm mean wavelength.

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.