introduction to surface roughness and mid-spatial
TRANSCRIPT
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Introduction to surface roughness and mid-spatial frequency errors
Jessica DeGroote Nelson
Optimax Systems, Inc.
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Outline
• What is surface roughness?
• How do we see surface roughness?
• How do we measure surface roughness?
• How do we quantify surface roughness?
• What are mid-spatial frequency errors?
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What is surface roughness?
• Roughness is a measure of the topographic relief of a surface
• Examples of surface relief include
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Polishing marks on optical surfaces
Machining marks on machined surfaces
Grains of magnetic material on memory disks
Undulations on silicon wafers
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Schematic representation of a rough surface
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Bennet and Mattsson, “Introduction to Surface Roughness and Scattering” 1999
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How do we see roughness?
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How do we see roughness?
• Unaided eye
• Microscopy
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Observing light scattered by the surface
Bennet and Mattsson, “Introduction to Surface Roughness and Scattering” 1999
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How do we see roughness?
• Unaided eye
• Microscopy
– Differential Interference Contrast (Nomarski)
– Electron
– Scanning Probe
– Confocal
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Nomarski diagram accessed April 21, 2012: http://www.microscopyu.com/articles/dic/reflecteddic.html
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How do we measure roughness?
• Surface profile measurements
– Contact methods
– Non-contact methods
• Scattering measurements
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How do we measure roughness?
• Surface profile measurements
– Contact methods
• Stylus (probe) touches the surface
• Height variations measured as stylus or surface is moved
– Non-contact methods
• Scattering measurements
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Mechanical Probe Measurements • With care, the surface measurement accuracy can
approach 1 Angstrom (Å)
– Surface does not need to be reflective
• Problems with mechanical probe measurements:
– Measure the convolution of the surface with the stylus instead of the surface alone
– Surface may be scratched during the measurement
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Image from: Experimental Methods in Tribology By Gwidon W. Stachowiak, Andrew W. Batchelor, Grazyna Stachowiak
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Atomic Force Microscopy (AFM)
• Surface topography of any solid surface
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J. Wyant, “Measurement of Surface Quality” 1998
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How do we measure roughness?
• Surface profile measurements
– Contact methods
– Non-contact methods
• Optical methods used to examine the surface
• Scattering measurements
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White light interferometer
J. Wyant, “Modern Optical Testing Short Course” 2009
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White light interferometer
J. Wyant, “Modern Optical Testing Short Course” 2009
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White light interferometer
J. Wyant, “Modern Optical Testing Short Course” 2009
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White light interferometer
J. Wyant, “Modern Optical Testing Short Course” 2009
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Phase information converted to areal
height map indicating x, y and z
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How do we measure roughness?
• Surface profile measurements
– Contact methods
– Non-contact methods
• Scattering measurements
– Two common measurements
• Total Integrated Scatter (TIS)
• Angle-Resolved Scattering (ARS)
– Scattering caused by particulate contamination will not correlate to roughness
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Comparison of methods for determining roughness
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Bennet and Mattsson, “Introduction to Surface Roughness and Scattering” 1999
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How do we quantify surface roughness?
• ISO 10110-8:2010 lists five statistical methods for describing optically smooth surfaces
– rms roughness, Rq
– rms waviness, Wq
– Density of microdefects
– Power spectral density (PSD) function
– rms slope
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Root Mean Square (RMS or Rq)
Vorburger, “In the Rough”, 2002
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Quantification of microdefects
• Localized pits on an optically smooth surface
• N indicates the permissible number of “markedly” deep pits occur in either a 10mm profile or 300 x 300mm areal region
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Power Spectral Density (PSD)
• Squared magnitude of the Fourier transform of the residual surface height along one dimension of the surface profile
Vorburger, “In the Rough”, 2002
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Relationship between PSD and rms surface roughness
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Specifying rms roughness on an optical drawing
• ISO 10110-8:2010 default spatial bandwidth if not given on drawing: 2.5 – 80mm
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Spatial bandwidth 2mm – 1mm
Maximum rms surface roughness:
5nm
Polishing grade of <16 microdefects per 10mm scan
rms roughness specification given as a note on a drawing: Note: Rq = 5nm over a 2mm – 1mm spatial bandwidth region
ISO method Note method
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Guideline for surface roughness tolerance
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Commercial Quality: 5nm rms Precision Quality: 2nm rms
High Precision Quality: 1nm rms Default bandwidth 2.5 – 80mm
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What is “mid-spatial frequency”?
J.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors, Proc. SPIE 2576-25
MSF ? ?
D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," (Optical Society of America, 2008).
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Figure is the range of spatial frequencies addressable with a simple Zernike expansion
J.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors, Proc. SPIE 2576-25
5 to 10 cycles
per aperture
27 D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," (Optical Society of America, 2008).
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Finish (a.k.a “gloss” or “roughness”) is results in total transmission loss due to scatter
J.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors, Proc. SPIE 2576-25
5 to 10 cycles
per aperture
?
28 D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," (Optical Society of America, 2008).
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Mid-Spatial Frequency bandwith limits help to define the MSF itself
J.E. Harvey and A. Kotha, “Scattering effects from residual optical fabrication errors, Proc. SPIE 2576-25
5 to 10 cycles
per aperture a = (l*OPL/10)1/2
MSF
29 D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," (Optical Society of America, 2008).
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Example: Spoke and Spiral Errors
Unfiltered data
Low spatial
frequency
Mid-spatial
frequency
High spatial
frequency
PV: 179.9nm
RMS: 28.6nm
PV: 152.8nm
RMS: 26.3nm
PV: 41.9nm
RMS: 4.8nm
PV: 17.1nm
RMS: 0.6nm
30 D. Aikens, J. E. DeGroote, and R. N. Youngworth, "Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems," (Optical Society of America, 2008).
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Characterizing MSF Errors
– Band Limited RMS and Power Spectral Density
– Slope Error
– Zernike Residual RMS
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Power Spectral Density (PSD)
• Deviation from straight line
1
10
100
1000
10000
100000
1 10 100 1000 10000
Spatial Frequency (1/m)
Sub-aperture polished surface Power (Sub-aperture polished surface)
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Power Spectral Density (PSD)
• Deviation from straight line
1
10
100
1000
10000
100000
1 10 100 1000 10000
Spatial Frequency (1/m)
Sub-aperture polished surface Power (Sub-aperture polished surface)
MSF errors occurring
between 0.5 and 3mm
periodicity due to sub-
aperture polishing
method
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Band-limited RMS and PSD • RMS is proportional to square root of area of PSD
– RMS is a function of the spatial frequency limits
• An RMS roughness specification without a spatial frequency limit is MEANINGLESS!
• Also important to consider how the surface will be measured
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Spatial Frequency, log
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Slope Specification
• Slope is the difference between the heights at two points on the surface divided by the distance between the two points – Expressed in angular units
• Complete slope specification contains – Slope specification (angular units)
• Specify Peak or RMS – Default: RMS
– Integration length • Default: 4% CA
– Spatial bandwidth
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Integration length corresponds to the unwanted “feature size”
1 – 2mm integration lengths are recommended when trying to pinpoint
sub-aperture polishing tool marks
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Slope data Pitch Polished Sub-aperture Rotationally Polished
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Zernike Residual RMS (after 37 term Zernike removed)
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Pitch Polished Sub-aperture Rotationally Polished
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Zernike Residual RMS
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Pitch Polished Sub-aperture Rotationally Polished
3x higher Zernike
Residual RMS
2.5x lower RMS wavefront error
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Conclusion • What is surface roughness?
• How do we see surface roughness?
• How do we measure surface roughness?
• How do we quantify surface roughness?
• What are mid-spatial frequency errors?
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Conclusion • What is surface roughness?
– Roughness is a measure of the topographic relief of a surface
• How do we see surface roughness?
• How do we measure surface roughness?
• How do we quantify surface roughness?
• What are mid-spatial frequency errors?
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Conclusion • What is surface roughness?
• How do we see surface roughness?
– Unaided eye and microscopic techniques
• How do we measure surface roughness?
• How do we quantify surface roughness?
• What are mid-spatial frequency errors?
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Conclusion • What is surface roughness?
• How do we see surface roughness?
• How do we measure surface roughness?
– Contact and non-contact profilers and scattering techniques
• How do we quantify surface roughness?
• What are mid-spatial frequency errors?
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Conclusion • What is surface roughness?
• How do we see surface roughness?
• How do we measure surface roughness?
• How do we quantify surface roughness?
– Recommended: rms value with spatial bandwidth
• What are mid-spatial frequency errors?
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Conclusion • What is surface roughness?
• How do we see surface roughness?
• How do we measure surface roughness?
• How do we quantify surface roughness?
• What are mid-spatial frequency errors? – Region between figure and finish typically causing
small angle scatter in a system • Worst offender: small tool polishing
– Recommend quantifying with band-limited rms and slope
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References: [1] J.M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering, Optical Society of America, 1999. [2] D.M. Aikens, J.E. DeGroote, R.N. Youngworth, Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems, in: Optical Fabrication and Testing, OSA, Rochester, NY, 2008, pp. OTuA1. [3] R.N. Youngworth, B.D. Stone, Simple estimates for the effects of mid-spatial-frequency surface errors on image quality, Applied Optics, 39 (2000) 2198-2209. [4] J.E. Harvey, K.L. Lewotsky, A. Kotha, Effects of surface scatter on the optical performance of x-ray synchrotron beam-line mirrors, Applied Optics, 34 (1995) 3024-3032. [5] ISO, 10110 Part 8, in: Surface texture; roughness and waviness, 2010.
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