Abstract

Assessing how uniform the light distribution is throughout an illuminated target is important in many applications, but traditional methods do not quantify the variability of illuminance as the human visual system (HVS) does. Considering that most light patterns are intended for humans, I propose a simple metric that assesses the uniformity in a similar way as humans do. This uniformity indicator is based on the fact that the HVS is highly sensitive to spatial frequencies and then uses the Fourier transform and the contrast sensitivity function of the HVS in a practical way.

© 2010 Optical Society of America

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References

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2010 (2)

2009 (1)

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

2008 (3)

2006 (1)

2005 (1)

A. B. Watson and A. J. Ahumada, Jr., J. Vision 5, 717 (2005).
[CrossRef]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

2001 (1)

1999 (1)

A. Mahdavi and V. Pal, J. Illum. Eng. Soc. 28, 24 (1999).

Ahumada, A. J.

A. B. Watson and A. J. Ahumada, Jr., J. Vision 5, 717 (2005).
[CrossRef]

Avendaño-Alejo, M.

Berberidou, L.

A. Mahdavi, P. Prankprakma, and L. Berberidou, in Proceedings of the 1995 IESNA Annual Conference(Illuminating Engineering Society of North America, 1995).

Bergmans, J. W. M.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

Cassarly, W. J.

Chen, F.

Chien, W. T.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

Chu, K. K.

Chung, S. H.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

Daly, S.

S. Daly, in Digital Image and Human Vision, A.Watson, ed. (MIT, 1993).

Fournier, F.

Hsieh, C. T.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

Lim, D.

Linnartz, J. P. M. G.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

Liu, S.

Luo, X.

Mahdavi, A.

A. Mahdavi and V. Pal, J. Illum. Eng. Soc. 28, 24 (1999).

A. Mahdavi, P. Prankprakma, and L. Berberidou, in Proceedings of the 1995 IESNA Annual Conference(Illuminating Engineering Society of North America, 1995).

Mertz, J.

Moreno, I.

I. Moreno, J. Opt. Soc. Am. A 27, 1985 (2010).
[CrossRef]

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, Appl. Opt. 45, 2265 (2006).
[CrossRef] [PubMed]

Pal, V.

A. Mahdavi and V. Pal, J. Illum. Eng. Soc. 28, 24 (1999).

Peli, E.

Prankprakma, P.

A. Mahdavi, P. Prankprakma, and L. Berberidou, in Proceedings of the 1995 IESNA Annual Conference(Illuminating Engineering Society of North America, 1995).

Qin, Z.

Rietman, R.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

Rolland, J. P.

Schenk, T. C. W.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

Sun, C. C.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

Tzonchev, R. I.

Wang, K.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

Watson, A. B.

A. B. Watson and A. J. Ahumada, Jr., J. Vision 5, 717 (2005).
[CrossRef]

Yang, H.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

Yang, T. H.

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 1 (2004).

IEEE Trans. Signal Process. (1)

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, IEEE Trans. Signal Process. 57, 1044 (2009).
[CrossRef]

J. Illum. Eng. Soc. (1)

A. Mahdavi and V. Pal, J. Illum. Eng. Soc. 28, 24 (1999).

J. Opt. Soc. Am. A (2)

J. Soc. Inf. Disp. (1)

C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, J. Soc. Inf. Disp. 16, 519 (2008).
[CrossRef]

J. Vision (1)

A. B. Watson and A. J. Ahumada, Jr., J. Vision 5, 717 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (3)

S. Daly, in Digital Image and Human Vision, A.Watson, ed. (MIT, 1993).

IESNA, The Lighting Handbook, 9th ed. (Illuminating Engineering Society of North America, 2000).

A. Mahdavi, P. Prankprakma, and L. Berberidou, in Proceedings of the 1995 IESNA Annual Conference(Illuminating Engineering Society of North America, 1995).

Supplementary Material (1)

» Media 1: JPG (313 KB)     

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Figures (4)

Fig. 1
Fig. 1

Two examples where the illumination uniformity is usually characterized: (a) displays and projectors and (b) LED illumination.

Fig. 2
Fig. 2

CSF represents the contrast perceptibility of a periodic pattern in function of its spatial frequency. The two fringe patterns illustrate the contrast visibility for different frequencies.

Fig. 3
Fig. 3

Example 1: light patterns with different uniformities. U HVS is the uniformity based on human vision. Patterns (a) and (b) both have the same uniformities U 1 , U 2 , and U 3 ; however, (a) is perceived more uniform than (b). Distribution (d) is the sum of (a) and (c); although U 4 of (d) is higher than in (a), pattern (d) is perceived less uniform than (a). Patterns (e) and (f) both have the same uniformities U 1 to U 4 , and NU; however, (e) is perceived more uniform than (f). The parameters for U HVS calculation are the following: a pattern size of 5.4 cm × 5.0 cm , observed on a computer screen, and observation distance of 50 cm . A computation code is included (Media 1).

Fig. 4
Fig. 4

Example 2: experimental illumination patterns. Although the uniformity U 3 of (a) is quite lower than that of (b), the perceived uniformity of (a) is higher than in (b). The pattern size is intended to be 5.0 cm × 8.2 cm and is to be observed on a computer screen at 50 cm .

Equations (8)

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U 1 = E min E max ,
U 3 = E min E ¯ = E min ( 1 N i = 1 N E i ) 1 ,
NU = σ E E ¯ = [ 1 N 1 i = 1 N ( E i E ¯ E ¯ ) 2 ] 0.5 .
U 4 = E ¯ ( E ¯ + σ E ) 1 ,
U HVS = 100 1 + k · NU α · NU HVS β [ % ] ,
NU HVS = n F ( ω n ) CSF ( ω n ) C + n F ( ω n ) ,
CSF ( ω ) = min [ CSF 0 ( ω ) , CSF 0 ( ω r a r θ ) ] ,
CSF 0 ( ω ) = 0.9 A L ω e 0.9 B L ω [ 351.57 ( ω 2 A p ) 1.5 + 1 ] 0.2 [ 1 + 0.06 e 0.9 B L ω ] 0.5 .

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