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.

Model-based phase shifting interferometry.

A general method of surface profiling with phase-shifting interferometry techniques uses iterative linear regression to fit the sequence of interferograms to a physical model of the cavity. The physical model incorporates all important cavity influences, including environmentally induced rigid-body motion, phase shifter miscalibrations, multiple interference, geometry-induced spatial phase-shift variations, and their cross-couplings. By incorporating an initial estimate of the surface profile and iteratively solving for space- and time-dependent variables separately, convergence is robust and rapid. The technique has no restriction on surface shape or departure.

Large-aperture, equal-path interferometer for precision measurements of flat transparent surfaces.

The measurement of flat optical components often presents difficulties because the presence of parallel surfaces generates multiple reflections that confuse conventional laser-based interferometers. These same parts have increasingly demanding surface finish tolerances as technologies improve over time, further complicating the metrology task. Here we describe an interferometric optical system for high-accuracy noncontact evaluation of the form and texture of precision flat surfaces based on an equal-optical-path geometry that uses extended, broadband illumination to reduce the influence of speckle noise, multiple reflections, and coherent artifacts by a factor of 10 when compared to laser-based systems. Combined with a low-distortion, fixed-focus imaging system and 4-Mpixel camera, the 100 mm aperture instrument offers surface height resolutions of 0.1 nm over lateral spatial frequencies extending from 0.01 to 10 cycles/mm. The instrument is vibration resistant for production-line testing of flat optics such as glass hard disks for the data-storage industry and flat-panel-display substrates.

Suppressing phase errors from vibration in phase-shifting interferometry.

A general method for reducing the influence of vibrations in phase-shifting interferometry corrects the surface phase map through a spectral analysis of a "phase-error pattern," a plot of the interference intensity versus the measured phase, for each phase-shifted image. The method is computationally fast, applicable to any phase-shifting algorithm and interferometer geometry, has few restrictions on surface shape, and unlike spatial Fourier methods, high density spatial carrier fringes are not required, although at least a fringe of phase departure is recommended. Over a 100x reduction in vibrationally induced surface distortion is achieved for small amplitude vibrations on real data.

Fourier-transform phase-shifting interferometry.

Phase-shifting interferometry is a preferred technique for high-precision surface form measurements, but the difficulty in handling the intensity distortions from multiple-surface interference has limited the general use of the technique to interferometer cavities producing strict two-beam interference. I show how the capabilities of phase-shifting interferometry can be extended to address this problem using wavelength tuning techniques. The basic theory behind the technique is reviewed and applied specifically to the measurement of parallel plates, where surfaces, optical and physical thickness, and homogeneity are simultaneously obtained. Basic system requirements are derived, common error sources are discussed, and the results of the measurements are compared with theory and alternative measurement methods.