Abstract

Two dual-beam differential direct-phase-detecting optical interferometers for scanning moving surfaces are described. Two beams from these interferometers are focused ∼42 µm apart on moving surfaces, and the difference in their reflected path lengths is measured to provide the surface roughness measurement. These interferometers are exceptionally insensitive to environmental vibrations and to surface physical and chemical factors. Applications discussed include the measurement of the surface roughness of a rotating cylinder and a moving web.

© 1997 Optical Society of America

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References

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  1. J. H. Bruning, D. R. Herriott, J. E. Galagher, P. D. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  2. G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  3. J. C. Wyant, “Computerized interferometric measurement of surface microstructure,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 122–130 (1995).
    [CrossRef]
  4. R. W. Peterson, G. M. Robinson, R. A. Carlsen, C. D. Englund, P. J. Moran, W. M. Wirth, “Interferometric measurements of the surface profile of moving samples,” Appl. Opt. 23, 1464–1466 (1984).
    [CrossRef] [PubMed]
  5. G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
    [CrossRef]
  6. D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).
  7. G. M. Robinson, G. D. Hanson, E. E. Palmquist, “The analysis of interferometrically measured surface roughness data,” in Proceedings of the Sixth International Conference on Video, Audio, and Data Recording (University of Sussex, Brighton, England, 1986), pp. 1–8.
  8. G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).
  9. K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).
  10. A. Eiling, “Theoretical analysis of video recording,” IEEE Trans. Magn. 24, 3249–3258 (1988).
    [CrossRef]
  11. A. Eiling, “The importance of magnetostatics in video recording - a theoretical analysis,” IEEE Trans. Magn. 26, 3173–3179 (1990).
    [CrossRef]
  12. M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
    [CrossRef]
  13. M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
    [CrossRef]
  14. T. Wielinga, J. Melissant, “New optical devices for surface roughness measurements,” J. Magn. Magn. Mat. 120, 116–118 (1993).
    [CrossRef]
  15. C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
    [CrossRef]
  16. N. Bobroff, A. E. Rosenbluth, M. Hatzakis, “Scanning differential interferometer to measure index heterogenity,” Appl. Opt. 31, 6622–6631 (1992).
    [CrossRef] [PubMed]
  17. J. H. Stricker, W. W. Webb, “Signal measurements of multi-layer refractive write once data storage media,” in Optical Data Storage, D. B. Carlin, D. B. Kay, eds., Proc. SPIE1663, 104–111 (1992).
  18. E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
    [CrossRef]
  19. M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
    [CrossRef]

1996 (1)

K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).

1993 (3)

T. Wielinga, J. Melissant, “New optical devices for surface roughness measurements,” J. Magn. Magn. Mat. 120, 116–118 (1993).
[CrossRef]

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
[CrossRef]

1992 (3)

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

N. Bobroff, A. E. Rosenbluth, M. Hatzakis, “Scanning differential interferometer to measure index heterogenity,” Appl. Opt. 31, 6622–6631 (1992).
[CrossRef] [PubMed]

M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
[CrossRef]

1991 (2)

M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
[CrossRef]

G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).

1990 (1)

A. Eiling, “The importance of magnetostatics in video recording - a theoretical analysis,” IEEE Trans. Magn. 26, 3173–3179 (1990).
[CrossRef]

1988 (1)

A. Eiling, “Theoretical analysis of video recording,” IEEE Trans. Magn. 24, 3249–3258 (1988).
[CrossRef]

1985 (1)

D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).

1984 (2)

G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
[CrossRef]

R. W. Peterson, G. M. Robinson, R. A. Carlsen, C. D. Englund, P. J. Moran, W. M. Wirth, “Interferometric measurements of the surface profile of moving samples,” Appl. Opt. 23, 1464–1466 (1984).
[CrossRef] [PubMed]

1981 (1)

1974 (1)

Atkins, R. A.

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

Bobroff, N.

Brangaccio, D. J.

Bruning, J. H.

Carlsen, R. A.

Cuka, G. M.

M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
[CrossRef]

M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
[CrossRef]

Eiling, A.

A. Eiling, “The importance of magnetostatics in video recording - a theoretical analysis,” IEEE Trans. Magn. 26, 3173–3179 (1990).
[CrossRef]

A. Eiling, “Theoretical analysis of video recording,” IEEE Trans. Magn. 24, 3249–3258 (1988).
[CrossRef]

Englund, C. D.

Galagher, J. E.

Gibler, W. N.

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

Hanson, G. D.

G. M. Robinson, G. D. Hanson, E. E. Palmquist, “The analysis of interferometrically measured surface roughness data,” in Proceedings of the Sixth International Conference on Video, Audio, and Data Recording (University of Sussex, Brighton, England, 1986), pp. 1–8.

Hatzakis, M.

Herriott, D. R.

Karis, T. E.

M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
[CrossRef]

M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
[CrossRef]

Kassing, R.

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

Kobayashi, I.

K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).

Lee, C. E.

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

Liu, M.

M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
[CrossRef]

Masseli, K.

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

Melissant, J.

T. Wielinga, J. Melissant, “New optical devices for surface roughness measurements,” J. Magn. Magn. Mat. 120, 116–118 (1993).
[CrossRef]

Miyagi, K.

K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).

Moran, P. J.

D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).

G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
[CrossRef]

R. W. Peterson, G. M. Robinson, R. A. Carlsen, C. D. Englund, P. J. Moran, W. M. Wirth, “Interferometric measurements of the surface profile of moving samples,” Appl. Opt. 23, 1464–1466 (1984).
[CrossRef] [PubMed]

Nanami, M.

K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).

Oesterschulze, E.

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

Palmquist, E. E.

G. M. Robinson, G. D. Hanson, E. E. Palmquist, “The analysis of interferometrically measured surface roughness data,” in Proceedings of the Sixth International Conference on Video, Audio, and Data Recording (University of Sussex, Brighton, England, 1986), pp. 1–8.

Perry, D. M.

G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).

D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).

Peterson, R. W.

G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).

G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
[CrossRef]

R. W. Peterson, G. M. Robinson, R. A. Carlsen, C. D. Englund, P. J. Moran, W. M. Wirth, “Interferometric measurements of the surface profile of moving samples,” Appl. Opt. 23, 1464–1466 (1984).
[CrossRef] [PubMed]

Robinson, G. M.

G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).

D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).

G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
[CrossRef]

R. W. Peterson, G. M. Robinson, R. A. Carlsen, C. D. Englund, P. J. Moran, W. M. Wirth, “Interferometric measurements of the surface profile of moving samples,” Appl. Opt. 23, 1464–1466 (1984).
[CrossRef] [PubMed]

G. M. Robinson, G. D. Hanson, E. E. Palmquist, “The analysis of interferometrically measured surface roughness data,” in Proceedings of the Sixth International Conference on Video, Audio, and Data Recording (University of Sussex, Brighton, England, 1986), pp. 1–8.

Rosenbluth, A. E.

Rosenfeld, P. D.

Shah, M. J.

M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
[CrossRef]

M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
[CrossRef]

Somekh, M. G.

M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
[CrossRef]

Sommargren, G. E.

Stopka, M.

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

Stricker, J. H.

J. H. Stricker, W. W. Webb, “Signal measurements of multi-layer refractive write once data storage media,” in Optical Data Storage, D. B. Carlin, D. B. Kay, eds., Proc. SPIE1663, 104–111 (1992).

Suddendorf, M. B.

M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
[CrossRef]

Taylor, H. F.

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

Trochtrop-Mayr, M.

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

Webb, W. W.

J. H. Stricker, W. W. Webb, “Signal measurements of multi-layer refractive write once data storage media,” in Optical Data Storage, D. B. Carlin, D. B. Kay, eds., Proc. SPIE1663, 104–111 (1992).

White, A. D.

Wielinga, T.

T. Wielinga, J. Melissant, “New optical devices for surface roughness measurements,” J. Magn. Magn. Mat. 120, 116–118 (1993).
[CrossRef]

Wirth, W. M.

Wyant, J. C.

J. C. Wyant, “Computerized interferometric measurement of surface microstructure,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 122–130 (1995).
[CrossRef]

AIChE J. (1)

M. J. Shah, G. M. Cuka, T. E. Karis, “Effect of dispersion quality on particulate magnetic recording disk properties,” AIChE J. 37, 394–402 (1991).
[CrossRef]

Anritsu Tech. Bull. (Jpn) (1)

K. Miyagi, M. Nanami, I. Kobayashi, “Development of high resolution optical heterodyne interferometer,” Anritsu Tech. Bull. (Jpn) 71, 96–102 (March1996).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

M. B. Suddendorf, M. Liu, M. G. Somekh, “Noncontacting measurement of opaque thin films using a dual beam thermal-wave probe,” Appl. Phys. Lett. 62, 3256–3258 (1993).
[CrossRef]

Appl. Surf. Sci. (1)

E. Oesterschulze, M. Stopka, M. Trochtrop-Mayr, K. Masseli, R. Kassing, “Nondestructive evaluation of solids and deposited films by thermal-wave interferometry,” Appl. Surf. Sci. 69, 65–68 (1993).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. J. Shah, G. M. Cuka, T. E. Karis, “Dispersion quality measurement and particulate magnetic coating properties,” IEEE Trans. Instrum. Meas. 41, 3–9 (1992).
[CrossRef]

IEEE Trans. Magn. (3)

A. Eiling, “Theoretical analysis of video recording,” IEEE Trans. Magn. 24, 3249–3258 (1988).
[CrossRef]

A. Eiling, “The importance of magnetostatics in video recording - a theoretical analysis,” IEEE Trans. Magn. 26, 3173–3179 (1990).
[CrossRef]

G. M. Robinson, R. W. Peterson, P. J. Moran, “Applications of interferometric measurements of surface topography of moving magnetic recording materials,” IEEE Trans. Magn. 20, 915–917 (1984).
[CrossRef]

J. IERE (1)

D. M. Perry, P. J. Moran, G. M. Robinson, “Three-dimensional surface metrology of magnetic recording materials through direct-phase detecting microscopic interferometry,” J. IERE 55, 145–150 (1985).

J. Lightwave Technol. (1)

C. E. Lee, W. N. Gibler, R. A. Atkins, H. F. Taylor, “In-line Fabry–Perot interferometer with high-reflectance internal mirrors,” J. Lightwave Technol. 10, 1376–1379 (1992).
[CrossRef]

J. Magn. Magn. Mat. (1)

T. Wielinga, J. Melissant, “New optical devices for surface roughness measurements,” J. Magn. Magn. Mat. 120, 116–118 (1993).
[CrossRef]

Sci. Am. (1)

G. M. Robinson, D. M. Perry, R. W. Peterson, “Optical interferometry of surfaces,” Sci. Am. 265, 67–71 (July1991).

Other (3)

J. C. Wyant, “Computerized interferometric measurement of surface microstructure,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 122–130 (1995).
[CrossRef]

J. H. Stricker, W. W. Webb, “Signal measurements of multi-layer refractive write once data storage media,” in Optical Data Storage, D. B. Carlin, D. B. Kay, eds., Proc. SPIE1663, 104–111 (1992).

G. M. Robinson, G. D. Hanson, E. E. Palmquist, “The analysis of interferometrically measured surface roughness data,” in Proceedings of the Sixth International Conference on Video, Audio, and Data Recording (University of Sussex, Brighton, England, 1986), pp. 1–8.

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Figures (21)

Fig. 1
Fig. 1

Optical layout of the single-beam LSI.

Fig. 2
Fig. 2

Optical layout of the DLSI. This is a dual-beam interferometer with one frequency-shifted beam.

Fig. 3
Fig. 3

Optical layout of the TLSI. Both beams focused on the surface have been frequency shifted by the A/O cell.

Fig. 4
Fig. 4

Diagram showing how dual-beam interferometers can fail to detect periodic surface features whose distances apart are multiples of the separation of the two beams. The drawing shows a periodic wave on a surface whose wavelength is one-half the interbeam spacing of beams 1 and 2 of the interferometer. The two beams reflect with the same path length, resulting in no difference measurement. The difference, Δz, in the reflected path is zero at all other points, such as 1′ and 2′.

Fig. 5
Fig. 5

How dual-beam interferometers detect periodic and non-periodic surface features whose distances apart are not multiples of the separation of the two beams. The drawing shows a periodic wave on a surface whose wavelength is not equal to a multiple of the interbeam spacing of beams 1 and 2 of the interferometer. In this example, the dual beams reflect with different path lengths, resulting in difference measurements Δz.

Fig. 6
Fig. 6

Plot of the correlation coefficients for almost 50 web surfaces, obtained by simulation of a dual-beam interferometer from LSI data.

Fig. 7
Fig. 7

Relationship of the rms surface roughness for 23 web surfaces as measured with a dual-beam interferometer with simulated dual-beam data from measurements with the LSI.

Fig. 8
Fig. 8

Error in rms surface roughness measurements of dual-beam interferometers with a beam separation of 42 µm as a function of the correlation coefficient.

Fig. 9
Fig. 9

How a dual-beam interferometer was used to measure the surface roughness of a cylinder being turned on a lathe.

Fig. 10
Fig. 10

Two repeated difference surface profiles collected from a rotating cylinder on a lathe rotating at 30 m/min.

Fig. 11
Fig. 11

Two repeated difference surface profiles collected from a rotating cylinder on a lathe rotating at 214 m/min.

Fig. 12
Fig. 12

Surface roughness of the left, the center, and the right sides of the cylinder at the conclusion of grinding steps.

Fig. 13
Fig. 13

Three-dimensional interferometric map of the surface roughness of the surface of a replica of the cylinder at the conclusion of the third grinding step.

Fig. 14
Fig. 14

Three-dimensional interferometric map of the surface roughness of the surface of a replica of the cylinder at the conclusion of the final grinding step.

Fig. 15
Fig. 15

Correlation between a series of measurements of the surface roughness of the test cylinder collected with the DLSI and from the use of the microscope interferometer.

Fig. 16
Fig. 16

How a dual-beam interferometer is used to measure the surface roughness of a moving web exiting a manufacturing production line.

Fig. 17
Fig. 17

Effect of calendering on the surface roughness of a coated web. The middle portion of this graph is the roughness of the web when the calender is activated.

Fig. 18
Fig. 18

Ability of the on-line interferometer to detect process changes in the manufacture of a coated web. In this example, a process change occurred after 1400 m of web had been produced, and the process conditions were returned to the original conditions after 3400 m had been produced.

Fig. 19
Fig. 19

Detection of defects on a coated web by the on-line interferometer. The spikes and the high variability in the surface roughness data are caused by numerous defects in the web.

Fig. 20
Fig. 20

Chart of surface roughness for a defect-free web.

Fig. 21
Fig. 21

Correlation between surface roughness measurements of a series of coated webs by the on-line and the off-line Wyko Hi-Res interferometers. The correlation coefficient is 0.98.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

zt=λ/4πϕt,
z-μz=z-zR-μz-zR.
z1-z2-z1R-z2R=z1-z1R-z2-z2R.
z1-z1R-z2-z2R=μ1-z1R-μ2+z2R.
z1-z1R-z2-z2R-μ1+z1R+μ2-z2R=z1-μ1-z2-μ2.
σL=1nizi21/2.
2σΔ2=1niz1i-z2i2=1niz1i2+iz2i2-2 iz1iz2i.
2σL2-2 iz1iz2i=2σL21-iz1iz2iσL2=2σL21-iz1iz2iiz1i21/2iz2i21/2.
r=iz1iz2iiz1i21/2iz2i21/2.
2σΔ2=2σL21-r,
2σΔ=2σL1-r.
Error=1-1-r1/2.
σΔ=σL.

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