Visible scattering is measured and compared with predictions based upon surface roughness measurements. The results indicate two scales of roughness, a short scale of the order of 1 μm and a long scale ranging from 30 to 150 μm. A study of the relative amount of scattering from the two scales shows that the short scale accounts for all the scattering for scattering angles larger than 3°. Furthermore, the analysis demonstrates the importance of spatial frequency bandwidth limits in optical scattering and finish measurements for a particular class of highly polished mirror surfaces.

Karl H. Guenther, Peter G. Wierer, and Jean M. Bennett Appl. Opt. 23(21) 3820-3836 (1984)

References

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Each TIS measurement on the 4-inch samples is an average of 15 points taken every 0.25 inch; each TIS measurement on the 6.5-inch samples is an average of 16 points taken every 0.40 inch. σ_{G}^{2} defined by Eq. (29) in text.

1/B and 1/D are correlation lengths in micrometers $\text{Fit error}\phantom{\rule{0.4em}{0ex}}=\phantom{\rule{0.4em}{0ex}}\frac{1}{\text{N}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\text{\u2211}_{i}\phantom{\rule{0.3em}{0ex}}{(\text{data}\phantom{\rule{0.2em}{0ex}}(i)\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\text{fit}\phantom{\rule{0.2em}{0ex}}(i)\phantom{\rule{0.2em}{0ex}})}^{2}$, where N is the number of fitting points

Table III

Long- and Short-Scale Contribution to Surface Roughness (Glass Samples)

Estimated ratio computed for the predicted versus measured scatter curves.
All TIS measurements made by P.C. Archibald at the Naval weapons Center.
TIS_{G} is calculated by integrating the predicted scattering curve over a hemisphere minus a 5° half-angle cone, as defined by Eq. (31) in text.
TIS_{scat} is obtained by extrapolating and integrating the measured scatter values.
Each TIS measurement is the average of 16 points taken every 0.4 inch.
Each TIS measurement is the average of 15 points taken every 0.25 inch.

Tables (7)

Table I

TIS and Talystep Profilometer Surface Roughness as Measured by the Naval Weapons Center on Some of our Samples

Each TIS measurement on the 4-inch samples is an average of 15 points taken every 0.25 inch; each TIS measurement on the 6.5-inch samples is an average of 16 points taken every 0.40 inch. σ_{G}^{2} defined by Eq. (29) in text.

1/B and 1/D are correlation lengths in micrometers $\text{Fit error}\phantom{\rule{0.4em}{0ex}}=\phantom{\rule{0.4em}{0ex}}\frac{1}{\text{N}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\text{\u2211}_{i}\phantom{\rule{0.3em}{0ex}}{(\text{data}\phantom{\rule{0.2em}{0ex}}(i)\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\text{fit}\phantom{\rule{0.2em}{0ex}}(i)\phantom{\rule{0.2em}{0ex}})}^{2}$, where N is the number of fitting points

Table III

Long- and Short-Scale Contribution to Surface Roughness (Glass Samples)

Estimated ratio computed for the predicted versus measured scatter curves.
All TIS measurements made by P.C. Archibald at the Naval weapons Center.
TIS_{G} is calculated by integrating the predicted scattering curve over a hemisphere minus a 5° half-angle cone, as defined by Eq. (31) in text.
TIS_{scat} is obtained by extrapolating and integrating the measured scatter values.
Each TIS measurement is the average of 16 points taken every 0.4 inch.
Each TIS measurement is the average of 15 points taken every 0.25 inch.