Abstract

The purposes of the study were to compare the performance of ten representative focus measures in the presence of nondefocus aberrations and to evaluate their applicability to the eye. For fixed amounts of nondefocus aberrations, the amount of defocus was changed to generate a series of blurred images from which focus measure curves were derived. In the presence of small amounts of nondefocus aberrations, all focus measures showed unimodal and monotonic behavior, although there were large differences in their sensitivity to defocus and effective ranges. There were breakdowns in monotonicity and unimodality for some focus measures when applied to data from human eyes, while other focus measures could detect the shift in the best-focus plane in the blurred image series resulting from spherical aberration.

© 2007 Optical Society of America

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References

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  1. K. Choi, J. Lee, and S. Ko, "New auto-focusing technique using the frequency selective weighted median filter for video cameras," IEEE Trans. Consumer Electron. 45, 820-826 (1999).
    [CrossRef]
  2. S. Jutamulia, T. Asakura, R. Bahuguna, and P. De Guzman, "Autofocusing based on power-spectra analysis," Appl. Opt. 33, 6210-6212 (1994).
    [CrossRef] [PubMed]
  3. J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, "A new wavelet-based measure of image focus," Pattern Recogn. Lett. 23, 1785-1794 (2002).
    [CrossRef]
  4. A. Lohmann and D. Mendlovic, "Digital method for measuring the focus error," Appl. Opt. 36, 7204-7209 (1997).
    [CrossRef]
  5. M. Subbarao, T. Choi, and A. Nikzad, "Focusing techniques," Opt. Eng. (Bellingham) 32, 2824-2836 (1993).
    [CrossRef]
  6. Y. Tian, H. Feng, and Z. Xu, "A new autofocusing technique based on analysing the RGB components of color images," Acta Photon. Sinica 31, 363-366 (2002).
  7. Y. Tian, H. Feng, Z. Xu, and J. Huang, "Dynamic focus window selection strategy for digital cameras," Proc. SPIE 5678, 219-229 (2005).
    [CrossRef]
  8. R. Schachar, "The mechanism of accommodation and presbyopia," Int. Ophthalmology Clinics 46, 39-61 (2006).
    [CrossRef]
  9. F. Toates, "Accommodation function of the human eye," Physiol. Rev. 52, 828-863 (1972).
    [PubMed]
  10. C. Wildsoet, "Active emmetropization--evidence for its existence and ramifications for clinical practice," Ophthalmic Physiol. Opt. 17, 279-290 (1997).
    [CrossRef] [PubMed]
  11. C. Schor and J. Kotulak, "A computational model of the error detector of human visual accommodation," Biol. Cybern. 54, 189-194 (1986).
    [CrossRef] [PubMed]
  12. L. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
    [CrossRef]
  13. Y. Tian and C. Wildsoet, "Diurnal fluctuations and developmental changes in ocular dimensions and optical aberrations in young chicks," Invest. Ophthalmol. Visual Sci. 47, 4168-4178 (2006).
    [CrossRef]
  14. X. Cheng, A. Bradley, and L. Thibos, "Predicting subjective judgment of best focus with objective image quality metrics," J. Vision 4, 310-321 (2004).
    [CrossRef]
  15. F. Groen, I. Young, and G. Ligthart, "A comparison of different focus functions for use in autofocus algorithms," Cytometry 6, 81-91 (1985).
    [CrossRef]
  16. Y. Zhang, Y. Zhang, and C. Wen, "A new focus measure method using moments," Image Vis. Comput. 18, 959-965 (2000).
    [CrossRef]
  17. Y. Tian, "Monte Carlo evaluation of ten focus measures," Proc. SPIE 6502, 65020C (2007).
    [CrossRef]
  18. Y. Tian, K. Shieh, and C. Wildsoet, "Do focus measures apply to retinal images?" Proc. SPIE 6492, 64920P (2007).
    [CrossRef]
  19. Y. Tian, "Dynamic focus window selection using a statistical color model," Proc. SPIE 6069, 60690A (2006).
    [CrossRef]
  20. S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
    [CrossRef]
  21. J. Porter, A. Guirao, I. Cox, and D. Williams, "Monochromatic aberrations of the human eye in a large population," J. Opt. Soc. Am. A 18, 1793-1803 (2001).
    [CrossRef]
  22. J. Castejon-Mochon, N. Lopez-Gil, A. Benito, and A. Artal, "Ocular wave-front aberration statistics in a normal young population," Vision Res. 42, 1611-1617 (2002).
    [CrossRef] [PubMed]
  23. J. Liang, B. Grimm, S. Goelz, and J. Bille, "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor," J. Opt. Soc. Am. A 11, 1949-1957 (1994).
    [CrossRef]
  24. L. Thibos, R. Applegate, J. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," J. Refract. Surg. 18, S652-660 (2002).
    [PubMed]
  25. L. Thibos, M. Ye, X. Zhang, and A. Bradley, "The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans," Appl. Opt. 31, 3594-3600 (1992).
    [CrossRef] [PubMed]
  26. B. Winn, D. Whitaker, and D. Elliott, "Factors affecting light-adapted pupil size in normal human subjects," Invest. Ophthalmol. Visual Sci. 35, 1132-1137 (1994).
  27. S. Burns, S. Wu, J. He, and A. Elsner, "Variations in photoreceptor directionality across the central retina," J. Opt. Soc. Am. A 14, 2033-2040 (1997).
    [CrossRef]
  28. F. Campbell, "The depth of field of the human eye," J. Mod. Opt. 4, 157-164 (1957).
  29. G. Legge, K. Mullen, G. Woo, and F. Campbell, "Tolerance to visual defocus," J. Opt. Soc. Am. A 4, 851-863 (1987).
    [CrossRef] [PubMed]
  30. J. Tarrant and C. Wildsoet, "Interactions between the Zernike modes, spherical aberration, and defocus during accommodation and effects of multifocal soft contact lenses," Invest. Ophthalmol. Visual Sci. 47, ARVO E-abstract 1510 (2007).
  31. T. Oshika, S. Klyce, R. Applegate, H. Howland, and M. El Danasoury, "Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis," Am. J. Ophthalmol. 127, 1-7 (1999).
    [CrossRef] [PubMed]
  32. J. Marsack, L. Thibos, and R. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
    [CrossRef]
  33. A. Watson and A. Ahumada, "Human optical image quality and the spatial standard observer," J. Vision 4, 2a (2004).
    [CrossRef]
  34. I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992).
    [CrossRef]

2007 (3)

Y. Tian, "Monte Carlo evaluation of ten focus measures," Proc. SPIE 6502, 65020C (2007).
[CrossRef]

Y. Tian, K. Shieh, and C. Wildsoet, "Do focus measures apply to retinal images?" Proc. SPIE 6492, 64920P (2007).
[CrossRef]

J. Tarrant and C. Wildsoet, "Interactions between the Zernike modes, spherical aberration, and defocus during accommodation and effects of multifocal soft contact lenses," Invest. Ophthalmol. Visual Sci. 47, ARVO E-abstract 1510 (2007).

2006 (3)

Y. Tian, "Dynamic focus window selection using a statistical color model," Proc. SPIE 6069, 60690A (2006).
[CrossRef]

R. Schachar, "The mechanism of accommodation and presbyopia," Int. Ophthalmology Clinics 46, 39-61 (2006).
[CrossRef]

Y. Tian and C. Wildsoet, "Diurnal fluctuations and developmental changes in ocular dimensions and optical aberrations in young chicks," Invest. Ophthalmol. Visual Sci. 47, 4168-4178 (2006).
[CrossRef]

2005 (1)

Y. Tian, H. Feng, Z. Xu, and J. Huang, "Dynamic focus window selection strategy for digital cameras," Proc. SPIE 5678, 219-229 (2005).
[CrossRef]

2004 (4)

J. Marsack, L. Thibos, and R. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

A. Watson and A. Ahumada, "Human optical image quality and the spatial standard observer," J. Vision 4, 2a (2004).
[CrossRef]

X. Cheng, A. Bradley, and L. Thibos, "Predicting subjective judgment of best focus with objective image quality metrics," J. Vision 4, 310-321 (2004).
[CrossRef]

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

2002 (5)

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, "A new wavelet-based measure of image focus," Pattern Recogn. Lett. 23, 1785-1794 (2002).
[CrossRef]

J. Castejon-Mochon, N. Lopez-Gil, A. Benito, and A. Artal, "Ocular wave-front aberration statistics in a normal young population," Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

L. Thibos, R. Applegate, J. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," J. Refract. Surg. 18, S652-660 (2002).
[PubMed]

Y. Tian, H. Feng, and Z. Xu, "A new autofocusing technique based on analysing the RGB components of color images," Acta Photon. Sinica 31, 363-366 (2002).

L. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
[CrossRef]

2001 (1)

2000 (1)

Y. Zhang, Y. Zhang, and C. Wen, "A new focus measure method using moments," Image Vis. Comput. 18, 959-965 (2000).
[CrossRef]

1999 (2)

T. Oshika, S. Klyce, R. Applegate, H. Howland, and M. El Danasoury, "Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis," Am. J. Ophthalmol. 127, 1-7 (1999).
[CrossRef] [PubMed]

K. Choi, J. Lee, and S. Ko, "New auto-focusing technique using the frequency selective weighted median filter for video cameras," IEEE Trans. Consumer Electron. 45, 820-826 (1999).
[CrossRef]

1997 (3)

1994 (3)

1993 (1)

M. Subbarao, T. Choi, and A. Nikzad, "Focusing techniques," Opt. Eng. (Bellingham) 32, 2824-2836 (1993).
[CrossRef]

1992 (1)

1987 (1)

1986 (1)

C. Schor and J. Kotulak, "A computational model of the error detector of human visual accommodation," Biol. Cybern. 54, 189-194 (1986).
[CrossRef] [PubMed]

1985 (1)

F. Groen, I. Young, and G. Ligthart, "A comparison of different focus functions for use in autofocus algorithms," Cytometry 6, 81-91 (1985).
[CrossRef]

1972 (1)

F. Toates, "Accommodation function of the human eye," Physiol. Rev. 52, 828-863 (1972).
[PubMed]

1957 (1)

F. Campbell, "The depth of field of the human eye," J. Mod. Opt. 4, 157-164 (1957).

Acta Photon. Sinica (1)

Y. Tian, H. Feng, and Z. Xu, "A new autofocusing technique based on analysing the RGB components of color images," Acta Photon. Sinica 31, 363-366 (2002).

Am. J. Ophthalmol. (1)

T. Oshika, S. Klyce, R. Applegate, H. Howland, and M. El Danasoury, "Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis," Am. J. Ophthalmol. 127, 1-7 (1999).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Biol. Cybern. (1)

C. Schor and J. Kotulak, "A computational model of the error detector of human visual accommodation," Biol. Cybern. 54, 189-194 (1986).
[CrossRef] [PubMed]

Cytometry (1)

F. Groen, I. Young, and G. Ligthart, "A comparison of different focus functions for use in autofocus algorithms," Cytometry 6, 81-91 (1985).
[CrossRef]

IEEE Trans. Consumer Electron. (1)

K. Choi, J. Lee, and S. Ko, "New auto-focusing technique using the frequency selective weighted median filter for video cameras," IEEE Trans. Consumer Electron. 45, 820-826 (1999).
[CrossRef]

Image Vis. Comput. (1)

Y. Zhang, Y. Zhang, and C. Wen, "A new focus measure method using moments," Image Vis. Comput. 18, 959-965 (2000).
[CrossRef]

Int. Ophthalmology Clinics (1)

R. Schachar, "The mechanism of accommodation and presbyopia," Int. Ophthalmology Clinics 46, 39-61 (2006).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (3)

Y. Tian and C. Wildsoet, "Diurnal fluctuations and developmental changes in ocular dimensions and optical aberrations in young chicks," Invest. Ophthalmol. Visual Sci. 47, 4168-4178 (2006).
[CrossRef]

B. Winn, D. Whitaker, and D. Elliott, "Factors affecting light-adapted pupil size in normal human subjects," Invest. Ophthalmol. Visual Sci. 35, 1132-1137 (1994).

J. Tarrant and C. Wildsoet, "Interactions between the Zernike modes, spherical aberration, and defocus during accommodation and effects of multifocal soft contact lenses," Invest. Ophthalmol. Visual Sci. 47, ARVO E-abstract 1510 (2007).

J. Mod. Opt. (1)

F. Campbell, "The depth of field of the human eye," J. Mod. Opt. 4, 157-164 (1957).

J. Opt. Soc. Am. A (5)

J. Refract. Surg. (1)

L. Thibos, R. Applegate, J. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," J. Refract. Surg. 18, S652-660 (2002).
[PubMed]

J. Vision (3)

J. Marsack, L. Thibos, and R. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

A. Watson and A. Ahumada, "Human optical image quality and the spatial standard observer," J. Vision 4, 2a (2004).
[CrossRef]

X. Cheng, A. Bradley, and L. Thibos, "Predicting subjective judgment of best focus with objective image quality metrics," J. Vision 4, 310-321 (2004).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

C. Wildsoet, "Active emmetropization--evidence for its existence and ramifications for clinical practice," Ophthalmic Physiol. Opt. 17, 279-290 (1997).
[CrossRef] [PubMed]

Opt. Eng. (Bellingham) (1)

M. Subbarao, T. Choi, and A. Nikzad, "Focusing techniques," Opt. Eng. (Bellingham) 32, 2824-2836 (1993).
[CrossRef]

Pattern Recogn. Lett. (1)

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, "A new wavelet-based measure of image focus," Pattern Recogn. Lett. 23, 1785-1794 (2002).
[CrossRef]

Physiol. Rev. (1)

F. Toates, "Accommodation function of the human eye," Physiol. Rev. 52, 828-863 (1972).
[PubMed]

Proc. SPIE (4)

Y. Tian, H. Feng, Z. Xu, and J. Huang, "Dynamic focus window selection strategy for digital cameras," Proc. SPIE 5678, 219-229 (2005).
[CrossRef]

Y. Tian, "Monte Carlo evaluation of ten focus measures," Proc. SPIE 6502, 65020C (2007).
[CrossRef]

Y. Tian, K. Shieh, and C. Wildsoet, "Do focus measures apply to retinal images?" Proc. SPIE 6492, 64920P (2007).
[CrossRef]

Y. Tian, "Dynamic focus window selection using a statistical color model," Proc. SPIE 6069, 60690A (2006).
[CrossRef]

Vision Res. (1)

J. Castejon-Mochon, N. Lopez-Gil, A. Benito, and A. Artal, "Ocular wave-front aberration statistics in a normal young population," Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

Other (1)

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Illustration of the principle of a focus measure. (a) With increasing defocus, PSFs increase in size, and images appear increasingly blurred. (b) Hypothetical focus measure (FM, solid curve) and its first-order derivative [diff(FM): dashed curve]. The extreme-focus measure value of 1 corresponds to the best-focused image, which in return corresponds to zero defocus in ideal optical systems. The more an optical system is out of focus, the smaller the focus measure value.

Fig. 2
Fig. 2

Imaging targets used in simulations. (a) An eye chart. Letters in the row with the single-line mark are 20/20 letters. (b) A natural image (Yosemite Falls).

Fig. 3
Fig. 3

Comparison of the computational efficiency of the focus measures, expressed in terms of the time needed to obtain an output from a Matlab simulation run on a personal computer. The input image (focus window) is square-shaped, and the pixel number given on the x coordinate is the one-dimensional size of the image. For each of four pairs of focus measures (AIG and EIG, based on gradient; SBR and EOS, based Fourier transform; AIL and EIL, based on Laplacian; WBR and EOW, based on wavelet transform), the underlying computations and thus computational efficiencies were very similar; in these cases, the result for only one of each pair is shown.

Fig. 4
Fig. 4

Comparison of the average noise sensitivity of the focus measures. Three noise types (Gaussian, salt and pepper, and speckle noise) were tested. Because the type of noise did not affect the relative sensitivity to noise of the focus measures, only the results of speckle noise are shown. For each focus measure, its value for a given level of noise divided by its noise-free value gives the noise sensitivity (so noise sensitivity for the noise-free condition is always 1); at each given noise level, 100 simulations were repeated and averaged to give the average noise sensitivity.

Fig. 5
Fig. 5

Comparison of the performance of ten focus measures in low-noise and low-aberration conditions (noise level <1%; Zernike coefficients generated from Gaussian functions with zero means, standard deviations < 0.02 μ m , and pupil diameter 3.5 mm ). Relative focus measures are plotted as a function of defocus; only the results of positive defocus are shown here, the results for negative defocus being their mirror image, just as expected for an ideal optical system, which the conditions closely approximate. The extreme-focus measure value of 1 corresponds to the best-focused image. The more an optical system is out of focus, the smaller the focus measure value.

Fig. 6
Fig. 6

The performance of the focus measures tested using data representing twenty different human eyes; each curve represents one eye. (a) Image variance (VAR) and energy of spectrum (EOS). (b) Centered Fourth-order image moments (M22). (c) Absolute image gradient (AIG). (d) Energy of image gradient (EIG). (e) Spectrum band ratio (SBR). (f) Absolute image Laplacian (AIL). (g) Energy of image Laplacian (EIL). (h) Wavelet band ratio (WBR). (i) Energy of wavelets (EOW). The extreme-focus measure value of 1 corresponds to the best focused image. The more an optical system is out of focus, the smaller the focus measure value.

Fig. 7
Fig. 7

Relative focus measures plotted against defocus for four different amounts of spherical aberration. (a) Image variance (VAR) and energy of spectrum (EOS). (b) Centered fourth-order image moments (M22). (C) Energy of image gradient (EIG). (d) Absolute image gradient (AIG). (e) Wavelet band ratio (WBR). (f) Energy of wavelets (EOW). Adding spherical aberration shifts the best-focus plane; that is, the best-focus plane; is at nonzero Zernike defocus (if there were no nondefocus aberrations, the best-focus plane would be at zero Zernike defocus); all of the focus measures shown here are able to detect these shifts in best focus, as evidenced by the leftward displacement of the curves with increasing spherical aberration.

Fig. 8
Fig. 8

Shifts in the best-focus plane as a function of total nondefocus aberrations and spherical aberration of human eyes. “Shifts in the best-focus plane” means that the best-focus plane is at nonzero Zernike defocus (if there were no nondefocus aberrations, the best-focus plane would be at zero Zernike defocus). Each data point represents one eye; its value shown in the two graphs is the mean of the shifts in best-focus plane calculated from the seven focus measures (SBR, AIL, EIL excluded because of their poor performance); total nondefocus aberrations and spherical aberration are expressed in terms of equivalent defocus power (EDP). For spherical aberration, the direction of the shift in the best focus-plane is sign-dependent.

Tables (3)

Tables Icon

Table 1 Means and Standard Deviations of the Nondefocus Second- to Fourth-order Zernike Coefficients for 100 Sets Randomly Generated and 20 Sets from Human Eyes a

Tables Icon

Table 2 Coefficients of Variations (Standard Deviations Divided by Means, Unitless) of the Ten Focus Measures at 2% and 4% Noise Levels (Speckle Noise) a

Tables Icon

Table 3 Coefficients of Variations (Standard Deviations Divided by Means, Unitless) of the Ten Focus Measures at 0.5, 1.0, and 1.5 D Defocus Levels Simulated Using the 100 Sets of Generated Aberrations Shown in Table 1 a

Equations (17)

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W ( x , y ) x = Δ x f , W ( x , y ) y = Δ y f ,
W ( x , y ) = n , m c n m Z n m ( x , y ) ,
EDP = 4 3 RMS r 2 ,
p ( x , y ) = c ( x , y ) exp [ i 2 π W ( x , y ) λ ] ,
PSF ( ξ , ψ ) = p ( x , y ) exp [ i 2 π ( ξ x + ψ y ) ] d x d y
f = [ i ( x , y ) i ¯ ( x , y ) ] 2 d x d y ,
f ( p , q ) = ( x x ¯ ) p ( y y ¯ ) q i ( x , y ) d x d y , p > 0 , q > 0 ,
f = i ( x , y ) d x d y .
f = i ( x , y ) 2 d x d y .
f = 2 i ( x , y ) d x d y .
f = 2 i ( x , y ) 2 d x d y .
F = ( u 2 + v 2 ) I 2 ( u , v ) d u d v ,
F = ( u 2 + v 2 ) 2 I 2 ( u , v ) d u d v ,
f = ( u 3 , v 3 ) ( u 4 , v 4 ) I 2 ( u , v ) d u d v ( u 1 , v 1 ) ( u 2 , v 2 ) I 2 ( u , v ) d u d v ,
f = ( 0 + , 0 + ) ( , ) I 2 ( u , v ) d u d v .
f = k = 2 4 c k 2 ( u , v ) d u d v c 1 2 ( u , v ) d u d v ,
f = k = 1 4 c k 2 ( u , v ) d u d v

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