Jean M. Bennett, "Measurement of the rms roughness, autocovariance function and other
statistical properties of optical surfaces using a FECO scanning
interferometer," Appl. Opt. 15, 2705-2721 (1976)
A brief review of techniques for measuring surface roughness and optical figure
is given. One of the most promising of these techniques for measuring the
roughness of optical surfaces is interferometry employing fringes of equal
chromatic order (feco). A feco scanning interferometer is
described, which has been used to determine statistics of polished surfaces
having roughnesses under 100 Å rms. The scanning interferometer resolves
square surface elements 2 μm on a side and
statistically characterizes the surface in terms of these elements. Height- and
slope-distribution functions, rms roughness, rms slope, and modified
autocovariance length distributions have been measured for selected optical
surfaces. Nearly all surfaces had Gaussian distributions of heights and slopes,
but none had Gaussian distributions of autocovariance lengths. Surfaces such as
electropolished copper, electroless nickel, and single-point diamond-machined
copper were found to have smaller rms slopes than other surfaces of comparable
roughness and scattered less than predicted by simple scalar scattering
theory.1,2 On the other hand, heavily scratched surfaces such
as polished potassium chloride had larger slopes and produced more scattering
than expected from simple theory.
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J. B. Saunders, J. Res. Natl. Bur. Std. (U.S.) 47,
148 (1951).
D. R. Herriott, J. Opt. Soc. Am. 51, 1142
(1961).
T. Tsuruta and Y. Itoh, Appl. Opt. 8, 2033
(1969).
P. Langenbeck, “Advances of Multipass Interferometry” in
Optical Instruments and Techniques 1969, J. Home
Dickson, Ed. (Oriel Press, Newcastle Upon Tyne, England, 1970), pp.
276–285.
F. L. Roesler and W. Traub, Appl. Opt. 5, 463
(1966).
I. J. Hodgkinson, Appl. Opt. 8, 1373 (1969).
C. R. Munnerlyn, Opt. Eng. (U.S.) 11, 38
(1972).
M. P. Rimmer, C. M. King, and D. G. Fox, Appl. Opt.
11, 2790 (1972); R. Aspden, R. McDonough, and
F. R. Nitchie, Jr., Appl. Opt. 11, 2739
(1972).
R. M. Anderson and G. W. Neudeck, J. Vac. Sci. Technol.
8, 454 (1971).
W. T. Welford, Optica Acta 16, 371 (1969).
J. S. Zelenka and J. R. Varner, Appl. Opt. 8, 1431
(1969).
S. Yokozeki and T. Suzuki, Jap. J. Appl. Phys. 9,
585 (1970).
W. Jaerisch and G. Makosch, Appl. Opt. 12, 1552
(1973).
Table II
Techniques for Measuring Roughness of Optically Polished Surfaces; Roughness
Less Than 100 Å rms
Object illuminated in parallel light;
interference between sheared images in interferometer; rms roughness
and autocorrelation length obtained from fringe contrast ratio
50 Å rms
Multiple–beam Fizeau fringes in
interference microscopee
Microscope focusing on Fizeau
interferometer with silvered surfaces
~50 Å peak to valley
Multiple–beam fringes of equal
chromatic order (feco)f
Distributions of surface heights and
slopes obtained from interferograms of order of interference 1
Angular dependence of scattering of
machined metal mirrors yields Light scattering mirror rms roughness,
autoccrrelation function and surface density function; theory
assumes surface is composed of multiple sinusoidal gratings of
different amplitudes and spacings
Surface profiles of precision roughness
standards and ion bombarded sapphire; rms roughness and height
distribution function obtained from digitized data
Interference between polarized beams
reflected from surface; method very sensitive to scratches, digs,
sharp discontinuities, etc. but not to gradual undulations;
qualitative method only
~10 Å
S. Tolansky, Multiple-Beam Interferometry of Surfaces and
Films (Clarendon Press, Oxford, England, 1948);
Surface Microtopography (Interscience Publishers,
Inc., New York, 1960).
W. B. Ribbens, Appl. Opt. 8, 2173 (1969).
J. Motycka, Appl. Opt. 8, 1435 (1969).
C. H. F. Velzel, “Measurement of Surface Roughness by
Interferential Contrast--an Application of Shearing Interferometry to
the Study of Phase Objects” in Optical Instruments and
Techniques 1969, J. Home Dickson, Ed. (Oriel Press,
Newcastle Upon Tyne, England, 1970), pp. 238–248.
G. Trumpold, Meas. Tech. (U.S.) 14, 855
(1971).
I. J. Hodgkinson, J. Phys. E, Sci. Instr. 3, 300
(1970).
J. M. Eastman and P. W. Baumeister, J. Opt. Soc. Am.
64, 1369A (1974).
I. Ohlídal and F. Lukeš, Opt. Commun.
5, 323 (1972); I. Ohlídal and F.
Lukeš, Optica Acta 19, 817 (1972).
E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788
(1975).
J. F. Nankivell, Brit. J. Appl. Phys. 13, 126
(1962); J. F. Nankivell, Optik 20, 171
(1963).
D W. Butler, Micron 4, 410 (1973).
R. Young, J. Ward, and F. Scire, Rev. Sci. Instr.
43, 999 (1972).
I. J. Hodgkinson, J. Phys. E, Sci. Instr. 3, 341
(1970).
B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt.
13, 177 (1974).
H. E. Bennett, J. L. Stanford, and J. M. Bennett, “Scattering
from Mirror Surfaces Used in Space Applications” in
Space Optics, Proceedings of the Ninth International
Congress of the International Commission for Optics
(National Academy of Sciences, Washington, 1974), pp.
717–738.
J. B. Arnold, P. J. Steger, and T. T. Saito, Appl. Opt.
14, 1777 (1975).
J. C. Stover, Appl. Opt. 14, 1796 (1975).
J. C. Moody, I.S.A. Trans. 7, 67 (1968).
See ref. i, Table I.
C. J. Pellerin, J. Christensen, R. C. Jerner and J. H. Peavey, J. Vac.
Sci. Technol. 12, 496 (1975).
G. Nomarski and A. R. Weill, Bull. Soc. Franc. Miner. Crist.
77, 840 (1954); R. D. Allen, G. B. David, and
G. Nomarski, Z. Wiss. Mikrosk. 69, 193
(1969).
Table III
Techniques for Measuring the Roughness of Ground, Polished and Machined
Surfaces; Roughness Greater Than 100 Å rms
Optical focusing (depth of focus) for
heights >0.3 μ; optical stereomicroscopy with height
sensitivity ± 10 μ; interferometry for heights <
λ/2 with sensitivity 0.005 λ to 0.10 λ
depending on technique
Object illuminated in parallel light,
interference between sheared images in interferometer; rms roughness
and autocorrelation length obtained from fringe contrast ratio;
detects heights 50–750 Å for reflecting objects,
200–3000 Å for transparent objects; spatial
resolution ~5 μ, maximum correlation length ~500
μ
Extension of above method for measurement
of rougher surfaces using coherent light of two different
wavelengths; theory only
Two–beam and multiple–beam
Fizeau fringes in interference microscopeh
Interference microscopes of different
designs; general roughness range λ/20 to λ/2 but can
be rougher for surfaces with regular profiles or isolated scratches;
lateral resolution depends on magnification and numerical
aperture
Surface profiles of machined and spark cut
metals and ground glass; data digitized to yield roughness,
autocorrelation function and power spectrum; roughness range 0.9
– 44 μ
Moving rough surface; correlation between
speckle contrast in broadband illumination and roughness when
roughness is comparable to coherence length of light; ground,
polished, sanded, and machined metal surfaces in roughness range 0.1
– 6.4 μ
Moving rough surface illuminated with
diverging beam; roughness and correlation length determined from
degree of coherence of transmitted beam; roughness range 0.4
– 0.9 μ for ground glass surfaces; upper limit of
roughness related to magnitude of beam spread
Contrast in monochromatic speckle pattern
from ground glass determined by scanning detector; roughness range
0.2 – 0.5 μ; maximum roughness measurable ~0.5
μ
H. E. Keller, Microscope (G.B.) 21, 59 (1973).
P. F. Ostwald, Machine and Tool Bluebook 63, 112
(1968).
See ref. b, Table
II.
See ref. d, Table
II.
W. B. Ribbens and G. L. Lazik, Proc. IEEE 56, 1637
(1968); 57, 344 (1969); E. B. Felstead, Proc.
IEEE 57, 343 (1969).
W. B. Ribbens, Appl. Opt. 11, 807 (1972).
W. B. Ribbens, Appl. Opt. 13, 1085 (1974).
See ref. e, Table
II.
M. Fansa, Microsc. Acta (Germany) 74, 195
(1973).
J. P. M. Verbunt, Appl. Opt. 12, 1839 (1973).
P. Harihan and W. H. Steel, Appl. Opt. 13, 721
(1974).
J. Eastman and P. Baumeister, Opt. Commun. 12, 418
(1974).
M. Kubo, Acta Imeko 21, 115 (1964); M. Kubo, Rev.
Sci. Instr. 36, 236 (1965).
J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. (London)
A295, 300 (1966).
T. R. Thomas and S. D. Probert, J. Phys. D, Appl. Phys.
3, 277 (1970).
D. J. Whitehouse and J. F. Archard, Proc. Roy. Soc. (London)
A316, 97 (1970).
H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am.
51, 123 (1961); H. E. Bennett, J. Opt. Soc.
Am. 53, 1389 (1963).
S. Karp, R. B. Hankin, S. Spinak, E. J. Pisa and P. P. Barron, Proc. IEEE
54, 1484 (1966).
A. S. Toporets, Sov. J. Opt. Technol. 36, 439
(1969).
G. Häusler and G. Hohberg, Optik 30, 437
(1970).
D. P. Greenwood and E. J. Powers, J. Opt. Soc. Am.
61, 1589A (1971).
U. Köpf, Z. Angew. Phys. 31, 156
(1971).
C. A. Depew and R. D. Weir, Appl. Opt. 10, 969
(1971).
D. H. Hensler, Appl. Opt. 11, 2522 (1972).
T. Sawatari, Appl. Opt. 11, 1337 (1972); T.
Sawatari, P. N. Keating, and R. B. Zipin, Appl. Opt.
12 2598 (1973).
A. Abdulkadir and R. C. Birkebak, Rev. Sci. Instr.
45, 1356 (1974).
H. E. Bennett, M. J. Soileau, G. J. Hutcheson, “Testing the
Surface Quality of Optical Components,” Final Report, MIPR No.
3716–100–99–41–001, U. S. Army Missile
Command, Redstone Arsenal, Alabama, March 1974.
R. J. Whitefield, Appl. Opt. 14, 2480 (1975).
R. A. Sprague, Appl. Opt. 11, 2811 (1972).
K. Nagata, T. Umehara and J. Nishiwaki, Jap. J. Appl. Phys.
12, 1693 (1973).
G. Parry, Opt. Commun. 12, 75 (1974).
H. Fujii and T. Asakura, Opt. Commun. 11, 35
(1974).
Table IV
Comparison of rms Surface Roughness Determined from Visual Interferometric
Measurements and from Total Integrated Scattering Measurements
J. B. Saunders, J. Res. Natl. Bur. Std. (U.S.) 47,
148 (1951).
D. R. Herriott, J. Opt. Soc. Am. 51, 1142
(1961).
T. Tsuruta and Y. Itoh, Appl. Opt. 8, 2033
(1969).
P. Langenbeck, “Advances of Multipass Interferometry” in
Optical Instruments and Techniques 1969, J. Home
Dickson, Ed. (Oriel Press, Newcastle Upon Tyne, England, 1970), pp.
276–285.
F. L. Roesler and W. Traub, Appl. Opt. 5, 463
(1966).
I. J. Hodgkinson, Appl. Opt. 8, 1373 (1969).
C. R. Munnerlyn, Opt. Eng. (U.S.) 11, 38
(1972).
M. P. Rimmer, C. M. King, and D. G. Fox, Appl. Opt.
11, 2790 (1972); R. Aspden, R. McDonough, and
F. R. Nitchie, Jr., Appl. Opt. 11, 2739
(1972).
R. M. Anderson and G. W. Neudeck, J. Vac. Sci. Technol.
8, 454 (1971).
W. T. Welford, Optica Acta 16, 371 (1969).
J. S. Zelenka and J. R. Varner, Appl. Opt. 8, 1431
(1969).
S. Yokozeki and T. Suzuki, Jap. J. Appl. Phys. 9,
585 (1970).
W. Jaerisch and G. Makosch, Appl. Opt. 12, 1552
(1973).
Table II
Techniques for Measuring Roughness of Optically Polished Surfaces; Roughness
Less Than 100 Å rms
Object illuminated in parallel light;
interference between sheared images in interferometer; rms roughness
and autocorrelation length obtained from fringe contrast ratio
50 Å rms
Multiple–beam Fizeau fringes in
interference microscopee
Microscope focusing on Fizeau
interferometer with silvered surfaces
~50 Å peak to valley
Multiple–beam fringes of equal
chromatic order (feco)f
Distributions of surface heights and
slopes obtained from interferograms of order of interference 1
Angular dependence of scattering of
machined metal mirrors yields Light scattering mirror rms roughness,
autoccrrelation function and surface density function; theory
assumes surface is composed of multiple sinusoidal gratings of
different amplitudes and spacings
Surface profiles of precision roughness
standards and ion bombarded sapphire; rms roughness and height
distribution function obtained from digitized data
Interference between polarized beams
reflected from surface; method very sensitive to scratches, digs,
sharp discontinuities, etc. but not to gradual undulations;
qualitative method only
~10 Å
S. Tolansky, Multiple-Beam Interferometry of Surfaces and
Films (Clarendon Press, Oxford, England, 1948);
Surface Microtopography (Interscience Publishers,
Inc., New York, 1960).
W. B. Ribbens, Appl. Opt. 8, 2173 (1969).
J. Motycka, Appl. Opt. 8, 1435 (1969).
C. H. F. Velzel, “Measurement of Surface Roughness by
Interferential Contrast--an Application of Shearing Interferometry to
the Study of Phase Objects” in Optical Instruments and
Techniques 1969, J. Home Dickson, Ed. (Oriel Press,
Newcastle Upon Tyne, England, 1970), pp. 238–248.
G. Trumpold, Meas. Tech. (U.S.) 14, 855
(1971).
I. J. Hodgkinson, J. Phys. E, Sci. Instr. 3, 300
(1970).
J. M. Eastman and P. W. Baumeister, J. Opt. Soc. Am.
64, 1369A (1974).
I. Ohlídal and F. Lukeš, Opt. Commun.
5, 323 (1972); I. Ohlídal and F.
Lukeš, Optica Acta 19, 817 (1972).
E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788
(1975).
J. F. Nankivell, Brit. J. Appl. Phys. 13, 126
(1962); J. F. Nankivell, Optik 20, 171
(1963).
D W. Butler, Micron 4, 410 (1973).
R. Young, J. Ward, and F. Scire, Rev. Sci. Instr.
43, 999 (1972).
I. J. Hodgkinson, J. Phys. E, Sci. Instr. 3, 341
(1970).
B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt.
13, 177 (1974).
H. E. Bennett, J. L. Stanford, and J. M. Bennett, “Scattering
from Mirror Surfaces Used in Space Applications” in
Space Optics, Proceedings of the Ninth International
Congress of the International Commission for Optics
(National Academy of Sciences, Washington, 1974), pp.
717–738.
J. B. Arnold, P. J. Steger, and T. T. Saito, Appl. Opt.
14, 1777 (1975).
J. C. Stover, Appl. Opt. 14, 1796 (1975).
J. C. Moody, I.S.A. Trans. 7, 67 (1968).
See ref. i, Table I.
C. J. Pellerin, J. Christensen, R. C. Jerner and J. H. Peavey, J. Vac.
Sci. Technol. 12, 496 (1975).
G. Nomarski and A. R. Weill, Bull. Soc. Franc. Miner. Crist.
77, 840 (1954); R. D. Allen, G. B. David, and
G. Nomarski, Z. Wiss. Mikrosk. 69, 193
(1969).
Table III
Techniques for Measuring the Roughness of Ground, Polished and Machined
Surfaces; Roughness Greater Than 100 Å rms
Optical focusing (depth of focus) for
heights >0.3 μ; optical stereomicroscopy with height
sensitivity ± 10 μ; interferometry for heights <
λ/2 with sensitivity 0.005 λ to 0.10 λ
depending on technique
Object illuminated in parallel light,
interference between sheared images in interferometer; rms roughness
and autocorrelation length obtained from fringe contrast ratio;
detects heights 50–750 Å for reflecting objects,
200–3000 Å for transparent objects; spatial
resolution ~5 μ, maximum correlation length ~500
μ
Extension of above method for measurement
of rougher surfaces using coherent light of two different
wavelengths; theory only
Two–beam and multiple–beam
Fizeau fringes in interference microscopeh
Interference microscopes of different
designs; general roughness range λ/20 to λ/2 but can
be rougher for surfaces with regular profiles or isolated scratches;
lateral resolution depends on magnification and numerical
aperture
Surface profiles of machined and spark cut
metals and ground glass; data digitized to yield roughness,
autocorrelation function and power spectrum; roughness range 0.9
– 44 μ
Moving rough surface; correlation between
speckle contrast in broadband illumination and roughness when
roughness is comparable to coherence length of light; ground,
polished, sanded, and machined metal surfaces in roughness range 0.1
– 6.4 μ
Moving rough surface illuminated with
diverging beam; roughness and correlation length determined from
degree of coherence of transmitted beam; roughness range 0.4
– 0.9 μ for ground glass surfaces; upper limit of
roughness related to magnitude of beam spread
Contrast in monochromatic speckle pattern
from ground glass determined by scanning detector; roughness range
0.2 – 0.5 μ; maximum roughness measurable ~0.5
μ
H. E. Keller, Microscope (G.B.) 21, 59 (1973).
P. F. Ostwald, Machine and Tool Bluebook 63, 112
(1968).
See ref. b, Table
II.
See ref. d, Table
II.
W. B. Ribbens and G. L. Lazik, Proc. IEEE 56, 1637
(1968); 57, 344 (1969); E. B. Felstead, Proc.
IEEE 57, 343 (1969).
W. B. Ribbens, Appl. Opt. 11, 807 (1972).
W. B. Ribbens, Appl. Opt. 13, 1085 (1974).
See ref. e, Table
II.
M. Fansa, Microsc. Acta (Germany) 74, 195
(1973).
J. P. M. Verbunt, Appl. Opt. 12, 1839 (1973).
P. Harihan and W. H. Steel, Appl. Opt. 13, 721
(1974).
J. Eastman and P. Baumeister, Opt. Commun. 12, 418
(1974).
M. Kubo, Acta Imeko 21, 115 (1964); M. Kubo, Rev.
Sci. Instr. 36, 236 (1965).
J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. (London)
A295, 300 (1966).
T. R. Thomas and S. D. Probert, J. Phys. D, Appl. Phys.
3, 277 (1970).
D. J. Whitehouse and J. F. Archard, Proc. Roy. Soc. (London)
A316, 97 (1970).
H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am.
51, 123 (1961); H. E. Bennett, J. Opt. Soc.
Am. 53, 1389 (1963).
S. Karp, R. B. Hankin, S. Spinak, E. J. Pisa and P. P. Barron, Proc. IEEE
54, 1484 (1966).
A. S. Toporets, Sov. J. Opt. Technol. 36, 439
(1969).
G. Häusler and G. Hohberg, Optik 30, 437
(1970).
D. P. Greenwood and E. J. Powers, J. Opt. Soc. Am.
61, 1589A (1971).
U. Köpf, Z. Angew. Phys. 31, 156
(1971).
C. A. Depew and R. D. Weir, Appl. Opt. 10, 969
(1971).
D. H. Hensler, Appl. Opt. 11, 2522 (1972).
T. Sawatari, Appl. Opt. 11, 1337 (1972); T.
Sawatari, P. N. Keating, and R. B. Zipin, Appl. Opt.
12 2598 (1973).
A. Abdulkadir and R. C. Birkebak, Rev. Sci. Instr.
45, 1356 (1974).
H. E. Bennett, M. J. Soileau, G. J. Hutcheson, “Testing the
Surface Quality of Optical Components,” Final Report, MIPR No.
3716–100–99–41–001, U. S. Army Missile
Command, Redstone Arsenal, Alabama, March 1974.
R. J. Whitefield, Appl. Opt. 14, 2480 (1975).
R. A. Sprague, Appl. Opt. 11, 2811 (1972).
K. Nagata, T. Umehara and J. Nishiwaki, Jap. J. Appl. Phys.
12, 1693 (1973).
G. Parry, Opt. Commun. 12, 75 (1974).
H. Fujii and T. Asakura, Opt. Commun. 11, 35
(1974).
Table IV
Comparison of rms Surface Roughness Determined from Visual Interferometric
Measurements and from Total Integrated Scattering Measurements