The design, analysis, and performance of a small-angle scatterometer are presented. The effects of the diffraction background, geometrical aberrations and system scatter at the small-angles are separated. Graphs are provided that quantify their contribution. The far-field irradiance distributions of weakly truncated and untruncated Gaussian beams are compared. The envelope of diffraction ringing is shown to decrease proportionately with the level of truncation in the pupil. Spherical aberration and defocus are shown to have little effect on the higher-order diffraction rings of Gaussian apertures and as such will have a negligible effect on most scatter measurements. A method is presented for determining the scattered irradiance level for a given BRDF in relation to the peak irradiance of the point spread function. A method of Gaussian apodization is presented and tested that allows the level of diffraction ringing to become a design parameter. Upon sufficient reduction of the diffraction background, the scattered light from the scatterometers' primary mirror is seen to be the limiting component of the small-angle instrument profile. The scatterometer described was able to make a meaningful measurement close enough to the specular direction at 0.6328μm in order to observe the characteristic height and width of the scatter function. This allowed the rms roughness and autocorrelation length of the surface to be determined from the scatter data at this wavelength. The inferred rms roughness agreed well with an independent optical profilometer measurement of the surface. The BRDF of the samples were also measured at 10.6μm. The rms roughness inferred from this scatter data did not agree with the other measurements. The BRDF did not scale in accordance with the scaler diffraction theory of microrough surfaces. The scattering in the visible was dominated by the effects of surface roughness whereas the scattering in the far-infrared was apparently dominated by the effects of contaminants and surface defects. The model for the surface statistics is investigated. A K₀ (modified Bessel function) autocorrelation function is shown to predict the scattered light distribution of these samples much better than the conventional negative-exponential function. Additionally, a sampling theory is developed that addresses the negative-exponentially correlated output of lock-in amplifiers, detectors, and electronic circuits in general. It is shown that the optimum sampling rate is approximately one sample per time constant and at this rate the improvement in SNR is √(N/2) where N is the number of measurements.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/184794 |
| Date | January 1989 |
| Creators | Wein, Steven Jay. |
| Contributors | Wolfe, William L., Shack, Roland V., Palmer, James M. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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