Abstract

Theoretical models of the signal detected by a CCD camera during hyperspectral imaging with an integrating sphere are derived using Markov chains with absorbing states. The models provide analytical expressions that describe the real reflectance of the sample as a function of the detected signal at each pixel of the image. Validation of the models was done by using reflectance standards and tissue phantoms. The models provide accurate analytical solutions for samples and spheres that are near-Lambertian reflectors.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. G. Goebel, "Generalized integrating-sphere theory," Appl. Opt. 6, 125-128 (1967).
    [CrossRef] [PubMed]
  2. J. W. Pickering, C. J. M. Moes, H. J. C. M. Sterenborg, S. A. Prahl, and M. J. C. van Gemert, "Two integrating spheres with an intervening scattering sample," J. Opt. Soc. Am. A 9, 621-631 (1992).
    [CrossRef]
  3. J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, "Double-integrating-sphere system for measuring the optical properties of tissue," Appl. Opt. 32, 399-410 (1993).
    [CrossRef] [PubMed]
  4. J. S. Dam, T. Dalgaard, P. E. Fabricius, and S. Andersson-Engels, "Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements," Appl. Opt. 39, 1202-1209 (2000).
    [CrossRef]
  5. L. M. Hanssen, "Effects of non-Lambertian surfaces on integrating sphere measurements," Appl. Opt. 35, 3597-3606 (1996).
    [CrossRef] [PubMed]
  6. B. G. Crowther, "Computer modeling of integrating spheres," Appl. Opt. 35, 5880-5886 (1996).
    [CrossRef] [PubMed]
  7. A. V. Prokhorov, S. N. Mekhontsev, and L. M. Hanssen, "Monte Carlo modeling of an integrating sphere reflectometer," Appl. Opt. 42, 3832-3842 (2003).
    [CrossRef] [PubMed]
  8. D. L. Isaacson and R. W. Madsen, Markov Chains: Theory and Applications (Wiley, New York, 1976).
  9. A. Kienle, L. Lilge, I. A. Vitkin, M. S. Patterson, B. C. Wilson, R. Hibst, and R. Steiner, "Why do veins appear blue? A new look at an old question," Appl. Opt. 35, 1151-1160 (1996).
    [CrossRef] [PubMed]
  10. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
    [CrossRef] [PubMed]
  11. C. M. Gardner, S. L. Jacques, and A. J. Welch, "Fluorescence spectroscopy of tissue: recovery of intrinsic fluorescence from measured fluorescence," Appl. Opt. 35, 1780-1792 (1996).
    [CrossRef] [PubMed]
  12. J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
    [CrossRef]
  13. M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
    [CrossRef] [PubMed]
  14. M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
    [CrossRef]
  15. T. E. Dielman, Applied Regression Analysis (Duxbury, 2001).

2003 (1)

2002 (1)

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

2001 (1)

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

2000 (1)

1996 (5)

1993 (1)

1992 (1)

1967 (1)

Andersson-Engels, S.

Beek, J. F.

Colombo, A.

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

Cornelissen, F.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Crowther, B. G.

Dalgaard, T.

Dam, J. S.

Dev, A.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Dielman, T. E.

T. E. Dielman, Applied Regression Analysis (Duxbury, 2001).

Fabricius, P. E.

Farina, B.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

Gardner, C. M.

Geerts, H.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Geusebroek, J. M.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Goebel, D. G.

Hanssen, L. M.

Hibst, R.

Isaacson, D. L.

D. L. Isaacson and R. W. Madsen, Markov Chains: Theory and Applications (Wiley, New York, 1976).

Jacques, S. L.

Kienle, A.

Lilge, L.

Lualdi, M.

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

Madsen, R. W.

D. L. Isaacson and R. W. Madsen, Markov Chains: Theory and Applications (Wiley, New York, 1976).

Marchesini, M.

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

Marchesini, R.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

Mari, A.

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

Mekhontsev, S. N.

Moes, C. J. M.

Patterson, M. S.

Pickering, J. W.

Prahl, S. A.

Prokhorov, A. V.

Smeulders, A. W. M.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Steiner, R.

Sterenborg, H. J. C. M.

Tomatis, S.

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

van den Boomgaard, R.

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

van Gemert, M. J. C.

van Wieringen, N.

Vitkin, I. A.

Welch, A. J.

Wilson, B. C.

Appl. Opt. (9)

D. G. Goebel, "Generalized integrating-sphere theory," Appl. Opt. 6, 125-128 (1967).
[CrossRef] [PubMed]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, "Double-integrating-sphere system for measuring the optical properties of tissue," Appl. Opt. 32, 399-410 (1993).
[CrossRef] [PubMed]

J. S. Dam, T. Dalgaard, P. E. Fabricius, and S. Andersson-Engels, "Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements," Appl. Opt. 39, 1202-1209 (2000).
[CrossRef]

B. G. Crowther, "Computer modeling of integrating spheres," Appl. Opt. 35, 5880-5886 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, I. A. Vitkin, M. S. Patterson, B. C. Wilson, R. Hibst, and R. Steiner, "Why do veins appear blue? A new look at an old question," Appl. Opt. 35, 1151-1160 (1996).
[CrossRef] [PubMed]

C. M. Gardner, S. L. Jacques, and A. J. Welch, "Fluorescence spectroscopy of tissue: recovery of intrinsic fluorescence from measured fluorescence," Appl. Opt. 35, 1780-1792 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[CrossRef] [PubMed]

L. M. Hanssen, "Effects of non-Lambertian surfaces on integrating sphere measurements," Appl. Opt. 35, 3597-3606 (1996).
[CrossRef] [PubMed]

A. V. Prokhorov, S. N. Mekhontsev, and L. M. Hanssen, "Monte Carlo modeling of an integrating sphere reflectometer," Appl. Opt. 42, 3832-3842 (2003).
[CrossRef] [PubMed]

J Laser Appl. (1)

M. Lualdi, A. Colombo, A. Mari, S. Tomatis, and M. Marchesini, "Development of simulated pigmented lesions in an optical skin-tissue phantom: experimental measurements in the visible and near infrared," J Laser Appl. 14, 122-127 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

Lasers Surg. Med. (1)

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, "A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine," Lasers Surg. Med. 28, 237-243 (2001).
[CrossRef] [PubMed]

Other (3)

T. E. Dielman, Applied Regression Analysis (Duxbury, 2001).

D. L. Isaacson and R. W. Madsen, Markov Chains: Theory and Applications (Wiley, New York, 1976).

J. M. Geusebroek, A. Dev, R. van den Boomgaard, A. W. M. Smeulders, F. Cornelissen, and H. Geerts, "Color invariant edge detection," in Scale-Space Theories in Computer Vision, LNCS (Springer, 1999), Vol. 1682, pp. 459-464.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Diagram of the imaging setup.

Fig. 2
Fig. 2

Measured (solid curve) and modeled (dotted curve) image values of the 75% reflectance standard. R 2 = 0.999, maximum error = 5%, mean error = 1.1%.

Fig. 3
Fig. 3

Measured (solid curve) and modeled (dotted curve) reflectance spectra of two uniform skinlike phantoms. (a) R 2 = 0.995, maximum error = 8%, mean error = 2.4%; (b) R 2 = 0.993, maximum error = 2%, mean error = 0.84%.

Fig. 4
Fig. 4

Reflectance spectra of the phantom containing black melanin lesions. (a) Reflectance of the phantom surrounding the lesions (R 2 = 0.984, maximum error = 7%, mean error = 3.5%); (b) mean reflectance of the phantom including both the lesions and the surrounding tissue (R 2 = 0.994, maximum error = 7%, mean error = 1.9%).

Fig. 5
Fig. 5

Reflectance spectra of the phantom containing a red blood lesion. (a) Reflectance of the phantom surrounding the lesion (R 2 = 0.979, maximum error = 6%, mean error = 2.8%); (b) mean reflectance of the phantom including the lesion and the surrounding tissue (R 2 = 0.994, maximum error = 6.2%, mean error = 2.6%).

Equations (25)

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

[ I 0 R T ] ,
Q = ( I T ) 1 ,
A D A S A H A W R S R W A D 1 0 0 0 0 0 A S 0 1 0 0 0 0 A H 0 0 1 0 0 0 A W 0 0 0 1 0 0 R S d ( 1 r ) s h ( 1 w ) α r s w α R W d ( 1 r ) s h ( 1 w ) α r s w α .
T = [ r s w α r s w α ] ,
R = [ d ( 1 r ) s h ( 1 w ) α d ( 1 r ) s h ( 1 w ) α ] .
A D A S A H A W     R S d β s ( 1 r ) β h β α ( 1 w ) β    R W d β s ( 1 r ) β h β α ( 1 w ) β ,
M = d 1 r s w α .
r = m ( 1 w α ) d w m s .
T = [ 0 w α 1 s r s w α ] ,
R = [ d 1 s 0 h 1 s ( 1 w ) α 1 s d ( 1 r ) s h ( 1 w ) α ] .
m = d w [ 1 ( 1 r ) s ] 1 s w α [ 1 ( 1 r ) s ] .
r = ( 1 s ) [ d w + m ( 1 w α ) ] w s ( d + m α ) .
R = [ c 1 s 0 0 h 1 s ( 1 w ) α 1 s 0 c 1 s 0 h 1 s ( 1 w ) α 1 s 0 c ( 1 r ) s h ( 1 w ) α ] ,
T = [ 0 0 w α 1 s 0 0 w α 1 s r p r ( s p ) w α ] .
m = c p r w 1 s w α [ 1 ( 1 r ) s ] .
r = m ( 1 s ) ( 1 w α ) w ( m s α + c p ) .
R = [ 0 c 1 s h 1 s c 1 s 0 h 1 s 0 c h 0 0 ( 1 w ) α 1 s 0 0 ( 1 w ) α 1 s ( 1 r ¯ ) ( s p ) ( 1 r k ) p ( 1 w ) α ] ,
T = [ 0 0 w α 1 s 0 0 w α 1 s r ¯ ( s p ) r k p w α ] .
m k = c r k p w ( 1 s ) ( 1 w α ) r k p w α r ¯ w α ( s p ) .
r k = m k [ ( 1 s ) ( 1 w α ) r ¯ w α ( s p ) ] p w ( c + m k α ) .
r k = A k [ ( 1 s ) ( 1 w α ) r ¯ w α ( s p ) ] .
1 N k = 1 N r k = r ¯ ,
r ¯ = ( 1 s ) ( 1 w α ) k = 1 N A k N + w α ( s p ) k = 1 N A k .
e r = 100 | r meas r mod | r meas ,
c 50 = i 50 m 50 .

Metrics