Abstract

A novel bidirectional thickness profilometer based on transmission densitometry was designed to measure the localized thickness of semitransparent films on a dynamic manufacturing line. The densitometer model shows that, for materials with extinction coefficients between 0.3 and 2.9D/mm, 100500μm measurements can be recorded with less than ±5% error at more than 10,000 locations in real time. As a demonstration application, the thickness profiles of 75mm×100mm regions of polymer electrolyte membrane (PEM) were determined by converting the optical density of the sample to thickness with the Beer–Lambert law. The PEM extinction coefficient was determined to be 1.4D/mm, with an average thickness error of 4.7%.

© 2010 Optical Society of America

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2008

S. Molloi, T. Xu, J. Ducote, and C. Iribarren, “Quantification of breast arterial calcification using full field digital mammography,” Med. Phys. 35, 1428–1439 (2008).
[CrossRef] [PubMed]

2006

N. Kotwaliwale, P. R. Weckler, and G. H. Brusewitz, “X-ray attenuation coefficients using polychromatic x-ray imaging of pecan components,” Biosyst. Eng. 94, 199–206 (2006).
[CrossRef]

A. Larena, F. Millán, and G. Pinto, “Iterative method for the optical characterization of biaxially oriented poly(ethyleneterephthalate) films,” Opt. Mater. 28, 1013–1019 (2006).
[CrossRef]

S. J. Doran and N. Krstajic, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45–57 (2006).
[CrossRef]

R. P. Shukla, D. V. Udupaa, N. C. Dasa, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38, 552–557 (2006).
[CrossRef]

2003

J. Jarrett, “High-temperature and engineering films in the marketplace,” IAPD Magazine , 40–41 (2003).

2002

J. F. Power, “Inverse problem theory in the optical depth profilometry of thin films,” Rev. Sci. Instrum. 73, 4057–4141(2002).
[CrossRef]

2001

G. Cox and C. J. R. Sheppard, “Measurement of thin coatings in the confocal microscope,” Micron 32, 701–705 (2001).
[CrossRef] [PubMed]

1999

Ö. Pekcan and F. Kemerolu, “Photon transmission method for studying void-closure kinetics during coalescence of hard latex particles,” J. Appl. Polym. Sci. 72, 981–988 (1999).
[CrossRef]

1998

Ö. Pekcan, F. Kemeroglu, and E. Arda, “Measuring backbone activation energy at polymer-polymer interfaces during latex film formation by using a photon transmission method,” Eur. Polym. J. 34, 1371–1378 (1998).
[CrossRef]

Ö. Pekcan, E. Arda, K. Kesenci, and E. Piskin, “Photon transmission technique for studying film formation from polystyrene latexes prepared by dispersion polymerization using various steric stabilizers,” J. Appl. Polym. Sci. 68, 1257–1267(1998).
[CrossRef]

Ö. Pekcan and E. Arda, “Effect of molecular weight on latex film formation: photon transmission study,” J. Appl. Polym. Sci. 70, 339–351 (1998).
[CrossRef]

1997

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
[CrossRef] [PubMed]

1995

A. Larena, G. Pinto, and F. Millán, “Using the Lambert-Beer law for thickness evaluation of photoconductor coatings for recording holograms,” Appl. Surf. Sci. 84, 407–411 (1995).
[CrossRef]

1994

J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

1990

H. Alius and R. Schmidt, “Interference method for monitoring the refractive index and the thickness of transparent films during deposition,” Rev. Sci. Instrum. 61, 1200–1203 (1990).
[CrossRef]

1986

B. T. Jones and J. D. Winefordner, “Molecular fluorescence in thin liquid films,” Anal. Chem. 58, 2870–2872 (1986).
[CrossRef] [PubMed]

1978

M. L. Parker, S. Chow, P. R. Steiner, and L. A. Jozsa, “Application of x-ray densitometry to determine density profile in waferboard: relationship of density to thickness expansion and internal bond strength under various cycles,” Wood Sci. 11, 48–55 (1978).

1972

1966

W. A. H. Rushton, “Densitometry of pigments in rods and cones of normal and color defective subjects,” Invest. Ophthalmol. Visual Sci. 5, 233–241 (1966).

1964

1960

O. S. Heavens, “Optical properties of thin films,” Rep. Prog. Phys. 23, 1–65 (1960).
[CrossRef]

1957

A. W. Agar, “The measurement of the thickness of thin carbon films,” Br. J. Appl. Phys. 8, 35–36 (1957).
[CrossRef]

Agar, A. W.

A. W. Agar, “The measurement of the thickness of thin carbon films,” Br. J. Appl. Phys. 8, 35–36 (1957).
[CrossRef]

Aggarwal, M.

M. Aggarwal, H. Hua, and N. Ahuja, “On cosine-fourth and vignetting effects in real lenses,” in Proceedings of Eighth IEEE International Conference Computer Vision, 2001. ICCV 2001 (2001), Vol. 1, pp. 472–479.
[CrossRef]

Ahuja, N.

M. Aggarwal, H. Hua, and N. Ahuja, “On cosine-fourth and vignetting effects in real lenses,” in Proceedings of Eighth IEEE International Conference Computer Vision, 2001. ICCV 2001 (2001), Vol. 1, pp. 472–479.
[CrossRef]

Alius, H.

H. Alius and R. Schmidt, “Interference method for monitoring the refractive index and the thickness of transparent films during deposition,” Rev. Sci. Instrum. 61, 1200–1203 (1990).
[CrossRef]

Arda, E.

Ö. Pekcan, E. Arda, K. Kesenci, and E. Piskin, “Photon transmission technique for studying film formation from polystyrene latexes prepared by dispersion polymerization using various steric stabilizers,” J. Appl. Polym. Sci. 68, 1257–1267(1998).
[CrossRef]

Ö. Pekcan and E. Arda, “Effect of molecular weight on latex film formation: photon transmission study,” J. Appl. Polym. Sci. 70, 339–351 (1998).
[CrossRef]

Ö. Pekcan, F. Kemeroglu, and E. Arda, “Measuring backbone activation energy at polymer-polymer interfaces during latex film formation by using a photon transmission method,” Eur. Polym. J. 34, 1371–1378 (1998).
[CrossRef]

Ashford, R. D.

R. D. Ashford, “Beta gauge mechanism,” U.S. patent 4,324,136 (13 April 1982).

Bautz, M. W.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Boddeke, F. R.

J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

Brusewitz, G. H.

N. Kotwaliwale, P. R. Weckler, and G. H. Brusewitz, “X-ray attenuation coefficients using polychromatic x-ray imaging of pecan components,” Biosyst. Eng. 94, 199–206 (2006).
[CrossRef]

Burke, B. E.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Chow, S.

M. L. Parker, S. Chow, P. R. Steiner, and L. A. Jozsa, “Application of x-ray densitometry to determine density profile in waferboard: relationship of density to thickness expansion and internal bond strength under various cycles,” Wood Sci. 11, 48–55 (1978).

Cox, G.

G. Cox and C. J. R. Sheppard, “Measurement of thin coatings in the confocal microscope,” Micron 32, 701–705 (2001).
[CrossRef] [PubMed]

Dasa, N. C.

R. P. Shukla, D. V. Udupaa, N. C. Dasa, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38, 552–557 (2006).
[CrossRef]

Dierks, F.

F. Dierks, “Sensitivity and image quality of digital cameras,” (2004, cited 16 Sept. 2009), http://www.baslerweb.com/downloads/9835/Image_Quality_of_Digital_Cameras.pdf.

Doran, S. J.

S. J. Doran and N. Krstajic, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45–57 (2006).
[CrossRef]

Ducote, J.

S. Molloi, T. Xu, J. Ducote, and C. Iribarren, “Quantification of breast arterial calcification using full field digital mammography,” Med. Phys. 35, 1428–1439 (2008).
[CrossRef] [PubMed]

Flook, W. M.

W. M. Flook and C. B. Moore, “Automatic control apparatus for maintaining transverse thickness uniformity of extruded material,” U.S. patent 3,212,127 (19 October 1965).

Flournoy, P. A.

Françon, M.

Goodman, T. M.

G. R. Hopkinson, T. M. Goodman, and S. R. Prince, A Guide to the Use and Calibration of Detector Array Equipment (SPIE Press, 2004).

Gregory, J. A.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Griffiths, R. E.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Heavens, O. S.

O. S. Heavens, “Optical properties of thin films,” Rep. Prog. Phys. 23, 1–65 (1960).
[CrossRef]

Hopkinson,

G. R. Hopkinson, T. M. Goodman, and S. R. Prince, A Guide to the Use and Calibration of Detector Array Equipment (SPIE Press, 2004).

Horn, B. K. P.

B. K. P. Horn, Robot Vision (MIT Press1986).

Hua, H.

M. Aggarwal, H. Hua, and N. Ahuja, “On cosine-fourth and vignetting effects in real lenses,” in Proceedings of Eighth IEEE International Conference Computer Vision, 2001. ICCV 2001 (2001), Vol. 1, pp. 472–479.
[CrossRef]

Iribarren, C.

S. Molloi, T. Xu, J. Ducote, and C. Iribarren, “Quantification of breast arterial calcification using full field digital mammography,” Med. Phys. 35, 1428–1439 (2008).
[CrossRef] [PubMed]

Jarrett, J.

J. Jarrett, “High-temperature and engineering films in the marketplace,” IAPD Magazine , 40–41 (2003).

Johnson, J. T.

J. T. Johnson, “Defect and thickness inspection system for cast thin films using machine vision and full-field transmission densitometry,” M.S. thesis (George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 2009).

Jones, B. T.

B. T. Jones and J. D. Winefordner, “Molecular fluorescence in thin liquid films,” Anal. Chem. 58, 2870–2872 (1986).
[CrossRef] [PubMed]

Jozsa, L. A.

M. L. Parker, S. Chow, P. R. Steiner, and L. A. Jozsa, “Application of x-ray densitometry to determine density profile in waferboard: relationship of density to thickness expansion and internal bond strength under various cycles,” Wood Sci. 11, 48–55 (1978).

Kemeroglu, F.

Ö. Pekcan, F. Kemeroglu, and E. Arda, “Measuring backbone activation energy at polymer-polymer interfaces during latex film formation by using a photon transmission method,” Eur. Polym. J. 34, 1371–1378 (1998).
[CrossRef]

Kemerolu, F.

Ö. Pekcan and F. Kemerolu, “Photon transmission method for studying void-closure kinetics during coalescence of hard latex particles,” J. Appl. Polym. Sci. 72, 981–988 (1999).
[CrossRef]

Kesenci, K.

Ö. Pekcan, E. Arda, K. Kesenci, and E. Piskin, “Photon transmission technique for studying film formation from polystyrene latexes prepared by dispersion polymerization using various steric stabilizers,” J. Appl. Polym. Sci. 68, 1257–1267(1998).
[CrossRef]

Kirov, A. S.

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
[CrossRef] [PubMed]

Kotwaliwale, N.

N. Kotwaliwale, P. R. Weckler, and G. H. Brusewitz, “X-ray attenuation coefficients using polychromatic x-ray imaging of pecan components,” Biosyst. Eng. 94, 199–206 (2006).
[CrossRef]

Kraft, R. L.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Krstajic, N.

S. J. Doran and N. Krstajic, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45–57 (2006).
[CrossRef]

Kwok, H. L.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Larena, A.

A. Larena, F. Millán, and G. Pinto, “Iterative method for the optical characterization of biaxially oriented poly(ethyleneterephthalate) films,” Opt. Mater. 28, 1013–1019 (2006).
[CrossRef]

A. Larena, G. Pinto, and F. Millán, “Using the Lambert-Beer law for thickness evaluation of photoconductor coatings for recording holograms,” Appl. Surf. Sci. 84, 407–411 (1995).
[CrossRef]

Lumb, D. H.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Mantravadi, M. V.

R. P. Shukla, D. V. Udupaa, N. C. Dasa, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38, 552–557 (2006).
[CrossRef]

McClure, R. W.

Meigooni, A. S.

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
[CrossRef] [PubMed]

Millán, F.

A. Larena, F. Millán, and G. Pinto, “Iterative method for the optical characterization of biaxially oriented poly(ethyleneterephthalate) films,” Opt. Mater. 28, 1013–1019 (2006).
[CrossRef]

A. Larena, G. Pinto, and F. Millán, “Using the Lambert-Beer law for thickness evaluation of photoconductor coatings for recording holograms,” Appl. Surf. Sci. 84, 407–411 (1995).
[CrossRef]

Mishra, V.

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
[CrossRef] [PubMed]

Molloi, S.

S. Molloi, T. Xu, J. Ducote, and C. Iribarren, “Quantification of breast arterial calcification using full field digital mammography,” Med. Phys. 35, 1428–1439 (2008).
[CrossRef] [PubMed]

Moore, C. B.

W. M. Flook and C. B. Moore, “Automatic control apparatus for maintaining transverse thickness uniformity of extruded material,” U.S. patent 3,212,127 (19 October 1965).

Mullikin, J. C.

J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

Netten, H.

J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

Nousek, J. A.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

Parker, M. L.

M. L. Parker, S. Chow, P. R. Steiner, and L. A. Jozsa, “Application of x-ray densitometry to determine density profile in waferboard: relationship of density to thickness expansion and internal bond strength under various cycles,” Wood Sci. 11, 48–55 (1978).

Pekcan, Ö.

Ö. Pekcan and F. Kemerolu, “Photon transmission method for studying void-closure kinetics during coalescence of hard latex particles,” J. Appl. Polym. Sci. 72, 981–988 (1999).
[CrossRef]

Ö. Pekcan and E. Arda, “Effect of molecular weight on latex film formation: photon transmission study,” J. Appl. Polym. Sci. 70, 339–351 (1998).
[CrossRef]

Ö. Pekcan, E. Arda, K. Kesenci, and E. Piskin, “Photon transmission technique for studying film formation from polystyrene latexes prepared by dispersion polymerization using various steric stabilizers,” J. Appl. Polym. Sci. 68, 1257–1267(1998).
[CrossRef]

Ö. Pekcan, F. Kemeroglu, and E. Arda, “Measuring backbone activation energy at polymer-polymer interfaces during latex film formation by using a photon transmission method,” Eur. Polym. J. 34, 1371–1378 (1998).
[CrossRef]

Pickenpaugh, T.

F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
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[CrossRef]

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J. F. Power, “Inverse problem theory in the optical depth profilometry of thin films,” Rev. Sci. Instrum. 73, 4057–4141(2002).
[CrossRef]

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F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
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F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
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[CrossRef]

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F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

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S. Tolansky, Multiple Beam Interferometry of Surface and Films (Clarendon, 1948), pp. 147–150.

Udupaa, D. V.

R. P. Shukla, D. V. Udupaa, N. C. Dasa, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38, 552–557 (2006).
[CrossRef]

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J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
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Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
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[CrossRef] [PubMed]

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J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

Zhu, Y.

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
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[CrossRef] [PubMed]

Appl. Opt.

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A. Larena, G. Pinto, and F. Millán, “Using the Lambert-Beer law for thickness evaluation of photoconductor coatings for recording holograms,” Appl. Surf. Sci. 84, 407–411 (1995).
[CrossRef]

Biosyst. Eng.

N. Kotwaliwale, P. R. Weckler, and G. H. Brusewitz, “X-ray attenuation coefficients using polychromatic x-ray imaging of pecan components,” Biosyst. Eng. 94, 199–206 (2006).
[CrossRef]

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[CrossRef]

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Ö. Pekcan, F. Kemeroglu, and E. Arda, “Measuring backbone activation energy at polymer-polymer interfaces during latex film formation by using a photon transmission method,” Eur. Polym. J. 34, 1371–1378 (1998).
[CrossRef]

IAPD Magazine

J. Jarrett, “High-temperature and engineering films in the marketplace,” IAPD Magazine , 40–41 (2003).

Invest. Ophthalmol. Visual Sci.

W. A. H. Rushton, “Densitometry of pigments in rods and cones of normal and color defective subjects,” Invest. Ophthalmol. Visual Sci. 5, 233–241 (1966).

J. Appl. Polym. Sci.

Ö. Pekcan and F. Kemerolu, “Photon transmission method for studying void-closure kinetics during coalescence of hard latex particles,” J. Appl. Polym. Sci. 72, 981–988 (1999).
[CrossRef]

Ö. Pekcan, E. Arda, K. Kesenci, and E. Piskin, “Photon transmission technique for studying film formation from polystyrene latexes prepared by dispersion polymerization using various steric stabilizers,” J. Appl. Polym. Sci. 68, 1257–1267(1998).
[CrossRef]

Ö. Pekcan and E. Arda, “Effect of molecular weight on latex film formation: photon transmission study,” J. Appl. Polym. Sci. 70, 339–351 (1998).
[CrossRef]

J. Phys. Conf. Ser.

S. J. Doran and N. Krstajic, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45–57 (2006).
[CrossRef]

Med. Phys.

Y. Zhu, A. S. Kirov, V. Mishra, A. S. Meigooni, and J. F. Williamson, “Quantitative evaluation of radiochromic film response for two-dimensional dosimetry,” Med. Phys. 24, 223–231 (1997).
[CrossRef] [PubMed]

S. Molloi, T. Xu, J. Ducote, and C. Iribarren, “Quantification of breast arterial calcification using full field digital mammography,” Med. Phys. 35, 1428–1439 (2008).
[CrossRef] [PubMed]

Micron

G. Cox and C. J. R. Sheppard, “Measurement of thin coatings in the confocal microscope,” Micron 32, 701–705 (2001).
[CrossRef] [PubMed]

Opt. Laser Technol.

R. P. Shukla, D. V. Udupaa, N. C. Dasa, and M. V. Mantravadi, “Non-destructive thickness measurement of dichromated gelatin films deposited on glass plates,” Opt. Laser Technol. 38, 552–557 (2006).
[CrossRef]

Opt. Mater.

A. Larena, F. Millán, and G. Pinto, “Iterative method for the optical characterization of biaxially oriented poly(ethyleneterephthalate) films,” Opt. Mater. 28, 1013–1019 (2006).
[CrossRef]

Proc. SPIE

J. C. Mullikin, L. J. van Vliet, H. Netten, F. R. Boddeke, G. van der Feltz, and I. T. Young, “Methods for CCD camera characterization,” Proc. SPIE 2173, 73–84 (1994).
[CrossRef]

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[CrossRef]

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[CrossRef]

J. F. Power, “Inverse problem theory in the optical depth profilometry of thin films,” Rev. Sci. Instrum. 73, 4057–4141(2002).
[CrossRef]

Wood Sci.

M. L. Parker, S. Chow, P. R. Steiner, and L. A. Jozsa, “Application of x-ray densitometry to determine density profile in waferboard: relationship of density to thickness expansion and internal bond strength under various cycles,” Wood Sci. 11, 48–55 (1978).

Other

D. J. Ryan, “Film thickness measuring method and apparatus,” U.S. patent 3,860,820 (14 January 1975).

W. M. Flook and C. B. Moore, “Automatic control apparatus for maintaining transverse thickness uniformity of extruded material,” U.S. patent 3,212,127 (19 October 1965).

ExxonMobil Chemical, “Optical density” (2001, cited 25 Aug. 2009), http://www.polyprint.com/faq_optical.htm.

G. R. Hopkinson, T. M. Goodman, and S. R. Prince, A Guide to the Use and Calibration of Detector Array Equipment (SPIE Press, 2004).

Tobias Associates, Transmission Densitometers (cited 25 August 2009), http://www.densitometers.net/transmission.asp.

X-Rite, “500 Series Family: Measure any Density Status Quickly and Reliably” (cited 25 August 2009), http://www.xrite.com/product_overview.aspx?ID=278.

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F. Schuermeyer, T. Pickenpaugh, M. R. Squillante, K. S. Shah, J. A. Nousek, M. W. Bautz, B. E. Burke, J. A. Gregory, R. E. Griffiths, R. L. Kraft, H. L. Kwok, and D. H. Lumb, “Photometry and radiometry,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press, 1999).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Thickness profilometry schematic.

Fig. 2
Fig. 2

Block diagram of the mathematical pixel model from [33].

Fig. 3
Fig. 3

Theoretical thickness error from camera noise versus extinction coefficient for a 400 μm sample.

Fig. 4
Fig. 4

(a) Calibration sheet in gray scale and (b) resulting thickness contour plot.

Fig. 5
Fig. 5

Comparisons of the measurements using the direct method (left) and the calibrated densitometer (right).

Fig. 6
Fig. 6

Error in the calibrated densitometer.

Fig. 7
Fig. 7

Theoretical density error from camera noise versus sample density.

Fig. 8
Fig. 8

Complications with density measurements. Image width is approximately 6 cm .

Fig. 9
Fig. 9

True thickness (from the micrometer) versus densitometer thickness.

Tables (1)

Tables Icon

Table 1 Error Results for the Densitometry Test

Equations (17)

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

D = a t ,
T = Φ e Φ i ,
D = log 10 T .
D = log ( Φ e Φ i ) .
E [ n p ] = μ p Φ · t int ,
μ z = K ( η μ p + μ e _ dark ) ,
t = 1 a log ( μ p _ efflux μ p _ influx ) 1 a log ( K ( η μ p _ efflux + μ e _ dark _ efflux ) K ( η μ p _ influx + μ e _ dark _ influx ) ) = 1 a log ( μ z _ efflux μ z _ influx ) ,
t 1 a [ log μ z _ influx known log z efflux measured ] .
σ z _ temporal 2 = K 2 η μ p photo _ induced + σ z _ dark 2 ,
SNR = μ z μ z _ dark σ z ,
n e = λ n e , λ λ η λ n p , λ ,
n e = λ n e ( λ ) d λ = λ η ( λ ) n p ( λ ) d λ ,
log 10 ( n e , e n e , i ) = a t ,
log 10 ( λ η ( λ ) n p , e ( λ ) d λ λ η ( λ ) n p , i ( λ ) d λ ) = λ a ( λ ) t d λ .
n p , e ( λ ) = T ( λ ) n p , i ( λ ) .
t = 1 λ a ( λ ) d λ log 10 ( λ η ( λ ) n p , i ( λ ) T ( λ ) d λ λ η ( λ ) n p , i ( λ ) d λ ) .
P ( D ) = log ( P ( z efflux ) q = 1 M P ( z influx ) ) log ( μ z _ efflux _ photo _ induced + Norm ( μ z _ dark , σ z _ temporal _ efflux ) μ z _ influx _ photo _ induced + Norm ( μ z _ dark , σ z _ temporal _ influx M ) ) .

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