No such thing as σ: flowdown and measurement of surface roughness requirements

Dittman, Michael G.; Grochocki, Frank; Youngworth, Kathleen S.

doi:10.1117/12.678314

Cited by 7 publications

(7 citation statements)

References 3 publications

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“…(5) by Eq. (3)The excellent agreement between Elson's calculations and the predictions from Eq (19). renders Eqs.…”

mentioning

confidence: 57%

“…Both the numerator and the denominator thus become zero, and Eq. (19) (20) for all roughness values. Clearly, this asymptotic value of TIS/TIS ∞ will vary for different correlation widths.…”

Section: Parametric Total Integrated Scatter (Tis) Predictionsmentioning

confidence: 98%

“…(19) is valid for surfaces with arbitrary roughness, correlation widths and incident angles, a more thorough parametric analysis, providing even more insight of surface scatter phenomena can now be readily performed. Figure 4 illustrates a set of parametric curves of TIS/TIS∞ vs correlation width for different surface roughnesses (0.02 < / < 0.50) for a surface with a Gaussian ACV function.…”

Section: Parametric Total Integrated Scatter (Tis) Predictionsmentioning

confidence: 99%

“…After repeated discussions and admonitions by Church [6,14], Church and Takacs [15][16], Stover [17], Germer and Asmail [18], Dittman [19][20] and others; most of the optical surface metrology community is aware that when we associate surface roughness with scattered light, we must specify the spatial frequency band-limits of the effective roughness that is relevant to the particular scattering application. In other words, we must replace the total or intrinsic rms roughness, , with the relevant (or effective) bandlimited rms roughness, rel , in Eqs.…”

Section: Introduction and Overviewmentioning

confidence: 98%

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Domain of validity of the equation for total integrated scatter (TIS)

Harvey

Choi

2012

SPIE Proceedings

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The analytical expression for total integrated scatter (defined as diffuse reflectance divided by total reflectance) has been around for almost six decades 2 ) / cos 4 ( exp 1 i TIS .Most surface scatter analysts now realize that the expression is ambiguous unless spatial frequency band-limits are specified for the rms roughness, , in the expression. However, there still exists uncertainty about the domain of validity of the expression with regard to both surface characteristics and incident angle. In this paper we will quantitatively illustrate this domain of validity for both Gaussian and fractal one-dimensional surfaces as determined by the rigorous integral equation method (method of moments) of electromagnetic theory. Two dimensional error maps will be used to illustrate the domain of validity as a function of surface characteristics and incident angle. Graphical illustrations comparing the TIS predictions of several approximate surface scatter theories will also be presented.

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“…(5) by Eq. (3)The excellent agreement between Elson's calculations and the predictions from Eq (19). renders Eqs.…”

mentioning

confidence: 57%

Section: Parametric Total Integrated Scatter (Tis) Predictionsmentioning

confidence: 98%

Section: Parametric Total Integrated Scatter (Tis) Predictionsmentioning

confidence: 99%

Section: Introduction and Overviewmentioning

confidence: 98%

See 2 more Smart Citations

Domain of validity of the equation for total integrated scatter (TIS)

Harvey

Choi

2012

SPIE Proceedings

View full text Add to dashboard Cite

show abstract

“…After repeated discussions and admonitions by Church [6,16], Church and Takacs [17][18], Stover [19], Germer and Asmail [20], Dittman [21][22] and others; most of the optical surface metrology community is aware that when we associate surface roughness with scattered light, we must specify the spatial frequency band-limits of the effective roughness that is relevant to the particular scattering application. In other words, we must replace the total or intrinsic rms roughness, σ, with the relevant bandlimited rms roughness, rel σ , in Eqs.…”

Section: Introduction and Overviewmentioning

confidence: 98%

Determining parametric TIS behavior from optical fabrication metrology data

et al. 2011

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Optical manufacturers often have to deal with a specification on the total integrated scatter (TIS) or "Haze" from a given mirror surface. It is frequently thought that TIS or BRDF measurements are required to assure compliance with these specifications. TIS is determined by the spatial frequency banded-limited "relevant" rms surface roughness, the wavelength of light and the angle of incidence. For short-wavelength (EUV/X-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we show that the TIS can be accurately predicted, even for moderately rough surfaces, directly from the surface metrology data. We present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths and incident angles. Surfaces with both Gaussian and ABC or K-correlation power spectral density (PSD) functions have been modeled. These parametric TIS predictions provide insight and understanding regarding optical fabrication tolerances necessary to satisfy specific optical performance requirements

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Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles

Harvey

2012

Opt. Eng

173

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Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/13/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Abstract. Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited "relevant" root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we first discuss how to calculate the band-limited relevant roughness from surface metrology data, then present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths, and incident angles. Surfaces with both Gaussian and ABC or K -correlation power spectral density functions have been modeled. These parametric TIS predictions provide insight that is useful in determining realistic optical fabrication tolerances necessary to satisfy specific optical performance requirements.

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No such thing as σ: flowdown and measurement of surface roughness requirements

Cited by 7 publications

References 3 publications

Domain of validity of the equation for total integrated scatter (TIS)

Domain of validity of the equation for total integrated scatter (TIS)

Determining parametric TIS behavior from optical fabrication metrology data

Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles

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