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Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994)
Vision Res. Vol.34, No. 10, pp. 1251 1253,1994
Pergamon
0042-6989(93)E0021-X
Copyright© 1994ElsevierScienceLtd Printedin GreatBritain.All rightsreserved 0042-6989/94$7.00+ 0.00
Letter to the Editor Discrepancies in High Frequency Optical Modulation Transfer of the Human Eye, Reply to Drasdo, Thompson and Charman (1994) T. J. T. P. VAN D E N BERG,*t J. K. IJSPEERT,*t H. SPEKREIJSE*t Receh~ed 8 March 1993; in revised form 14 May 1993
Recently an improved mathematical description was developed for the foveal point spread function with parameters for age, pupil size and pigmentation (IJspeert, van den Berg & Spekreijse, 1993). A mathematical formalism was chosen to yield analytically equivalent expressions for the optical modulation transfer function, the point spread function as well as the line spread function. The formalism describes the presently available data for visual function (including directional sensitivity of the retina) from Campbell and Green (1965) and from IJspeert, de Waard, van den Berg and de Jong (1990) on light scattering, measured with the direct compensation method (van den Berg, 1986; van den Berg & Spekreijse, 1987). The result was compared to one proposal for the point spread function (Vos, 1984) and to two proposals for the modulation transfer function (MTF) (Geisler, 1984; Drasdo, Cox & Thompson, 1987; which is an adapted version of Jennings & Charman, 1974). The latter two proposals show much more high frequency fall off than our proposal. Regrettably, an error was made plotting Figs 2 and 3 in IJspeert et al. (1993), exaggerating the difference (at 50 c/deg the plot is a factor 1.35 too high). The formula's etc. are correct though. Figure 1 shows the MTFs again (IJvdBS), plotted correctly, for two pupil diameters, 2 mm (thin lines) and 4 mm (heavy lines). The solid lines give our model curves for age 35 yr and mean caucasian pigmentation (pigmentation parameter m = 0.142). The dotted lines represent the diffraction limit for a wavelength of 555 nm. Drasdo, Thompson and Charman (1994) discuss this discrepancy at the high frequency side. They use another adapted version of the Jennings and Charman (1974) proposal including effects of pupil diameter (Deeley, Drasdo & Charman, 1991), which result in the dashed
line curves of Fig. 1 (DDC). Because of their discussion two questions arise. (a) Is the high frequency side better described by the Jennings and Charman (or adapted) proposal? (b) In other respects, how does this alternative compare to our description? To start with (b) we need to reiterate some starting points for our description formula, none of which apply to the alternative. (i) Our formula is useful for both the frequency and angular domains. The alternative is defined for the frequency domain only. (ii) Our formula is applicable to the full range of the frequency and angular domains, including light scattering. The alternative does not include (larger angle) light scattering. (iii) Our formula includes age and pigmentation effects. Since these effects are only well documented for light scattering, it is implicit in (ii) that these effects are not included in the alternative. (iv) Our formula is valid for visual function, including directional sensitivity of the retina. That is why we based it on the Campbell and Green (1965) data, and not on the double pass data as the alternative.
Admittedly, an important charm of the alternative is its simplicity; but at the cost of the above points. Now question (a): is the high frequency side better described by the alternative? The answer to this question depends partly on how one feels toward point (iv) above, since there is a difference between visual and optical modulation transfer: Artal, Navarro, Brainard, Galvin and Williams (1992) have found that the functional high frequency modulation transfer is about twice as high as the double pass derived high frequency modulation *Laboratory of Medical Physics and Informatics, Universityof Amtransfer. Also others have stressed that functional modusterdam, Amsterdam, The Netherlands. ?The Netherlands Ophthalmic Research Institute, Meibergdreef 15, lation transfer is higher (Campbell & Gubish, 1966; 1105AZ Amsterdam, The Netherlands. Jennings & Charman, 1974). The difference might be 1251
1252
LETTER TO THE EDITOR 1
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FIGURE 1. Model optical modulation transfer functions of the human eye for pupil diameters 2 and 4 mm. Abbreviations: diff. lim., diffraction limited; IJvdBS, IJspeert, van den Berg and Spekreijse (1993); DDC, Deeley, Drasdo and Charman (1991).
caused b y the d i r e c t i o n a l sensitivity o f the retina a n d the m o d u l a t i o n t r a n s f e r o f the reflection process o f the fundus. T h e reflection o f the fundus, is n o t l o c a t e d at one site. D e p t h s differing b y a few tens o f a m i l l i m e t e r m a y c o n t r i b u t e d e p e n d i n g on w a v e l e n g t h [retina, p i g m e n t e p i t h e l i u m , c h o r o i d , see e.g. v a n B l o k l a n d a n d van N o r r e n (1986), van N o r r e n a n d T i e m e y e r (1986) a n d D e l o r i a n d Pflibsen (1989)]. This induces a s p r e a d i n g t h a t is o n l y p a r t l y o f f u n c t i o n a l i m p o r t a n c e because o f the d i r e c t i o n a l sensitivity o f the retina. A n o t h e r p r o b l e m using d o u b l e pass d a t a as basis is the i n h e r e n t u n c e r t a i n t y . This results in very different m o d u l a t i o n transfer values, as has been discussed by Jennings a n d C h a r m a n (1974). Especially at the high f r e q u e n c y side u n c e r t a i n t i e s are large, since the noise in the m e a s u r e m e n t s is relatively m o r e i m p o r t a n t at frequencies with low transfer values. This p o i n t is clearly illustrated in Fig. 2 o f Jennings a n d C h a r m a n (1974). A r t a l et al. (1992) r e p o r t e d significantly higher values for high f r e q u e n c y transfer as c o m p a r e d to those o f J e n n i n g s a n d C h a r m a n (1981). E r r o r b e h a v i o u r s h o u l d be c o n s i d e r e d if differences between m o d e l s are discussed a n d d e m o n s t r a t e d in plots. I f no e r r o r b a r s are included, scaling s h o u l d be such t h a t no suggestive differences result. T h a t is why m o s t a u t h o r s p l o t m o d u l a t i o n t r a n s f e r figures f r o m d o u b l e pass e x p e r i m e n t s on a linear scale as we d i d (Fig. 1). D r a s d o et al. (1994) however, e x t r a p o l a t e d their m o d e l b e y o n d the limits set b y the d a t a base a n d e r r o r b e h a v i o u r . This results in an e x a g g e r a t i o n o f the discrepancies. A d m i t t e d l y , also the d a t a base used by us c o n t a i n s errors. A n i m p o r t a n t p o t e n t i a l flaw in the technique o f C a m p b e l l a n d G r e e n (1965) is t h a t the m o d u l a t i o n o f the interference fringes o n the retina is n o t c o m p l e t e l y i n d e p e n d e n t o f the optics o f the eye. F o r m o r e p o t e n t i a l sources o f e r r o r see D r a s d o et al. (1994). A t present, insufficient insight exists to correct for these errors.
But since we a i m e d at f u n c t i o n a l relevance we used C a m p b e l l a n d G r e e n ' s d a t a base. In conclusion, we do n o t agree with D r a s d o et al. (1994) that present k n o w l edge p o i n t s to their p r o p o s a l . But they rightfully p o i n t e d t o w a r d s p o t e n t i a l flaws in p a r t o f the d a t a base used by us.
REFERENCES
Artal, P., Navarro, R., Brainard, D. H., Galvin, S. J. & Williams, D. R. (1992). Off axis optical quality of the eye and retinal sampling. Investigative Ophthalmology and Visual Science (Suppl.), 33, 3241. van den Berg, T. J. T. P. (1986). Importance of pathological intraocular scatter for visual disability. Documenta Ophthalmologica, 61, 327-333. van den Berg, T. J. T. P. & Spekreijse, H. (1987). Measurement of the straylight function of the eye in cataract and other optical media disturbances by means of a direct compensation method. Investigative
Ophthalmology
and Visual Science (Suppl.), 28,
397. van Blokland, G. J. & van Norren, D. (1986). Intensity and polarization of light scattered at small angles from the human fovea. Vision Research, 26, 485-494. Campbell, F. W. & Green, D. C. (1965). Optical and retinal factors affecting visual resolution. Journal of Physiology, 181, 576 593. Campbell, F. W. & Gubisch, R. W. (1966). Optical quality of the human eye. Journal of Physiology, 186, 558-578. Deeley, R. J., Drasdo, N. & Charman, W. N. (1991). A simple parametric model of the human ocular modulation transfer function. Ophthalmology and Physiological Optics, 11, 9143. Delori, F. C. & Pfiibsen, K. P. (11989). Spectral reflectance of the human ocular fundus. Applied Optics, 28, 1061 1077. Drasdo, N., Cox, W. & Thompson, D. A. (1987). The effects of image degradation on retinal ilIuminance and pattern responses to checkerboard stimuli. Documenta Ophthalmologica, 66, 267-275. Drasdo, N., Thompson, C. M. & Charman, W. N. (1994). Inconsistencies in models of the human ocular modulation transfer function. Vision Research, 34, 1247-1249. Geisler, W. S. (1984). Physical limits of acuity and hyperacuity. Journal of the Optical Society of America A, 1, 755-782. IJspeert, J. K., van den Berg, T. J. T. P. & Spekreijse, H. (1993). An
LETTER TO THE EDITOR improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation. Vision Research, 33, 15~0. IJspeert, J. K., de Waard, P. W. T., van den Berg, T. J. T. P. & de Jong, P. T. V. M. (1990). The intraocular straylight function in 129 healthy volunteers; dependence on angle, age and pigmentation. Vision Research, 30, 699-707. Jennings, J. A. M. & Charman, W. N. (1974). An analytical approxi-
1253
mation for the modulation transfer function of the eye. British
Journal of Physiological Optics, 29, 64-72. Jennings, J. A. M. & Charman, W. N. (1981). Off-axis image quality in the human eye. Vision Research, 21, 445-455. van Norren, D. & Tiemeyer, L. F. (1986). Spectral reflectance of the human eye. Vision Research, 26, 313-320. Vos, J. J. (1984). Disability glare--a state of the art report. CIEJournal, 3/2, 39-53.
Pergamon
0042-6989(93)E0021-X
Copyright© 1994ElsevierScienceLtd Printedin GreatBritain.All rightsreserved 0042-6989/94$7.00+ 0.00
Letter to the Editor Discrepancies in High Frequency Optical Modulation Transfer of the Human Eye, Reply to Drasdo, Thompson and Charman (1994) T. J. T. P. VAN D E N BERG,*t J. K. IJSPEERT,*t H. SPEKREIJSE*t Receh~ed 8 March 1993; in revised form 14 May 1993
Recently an improved mathematical description was developed for the foveal point spread function with parameters for age, pupil size and pigmentation (IJspeert, van den Berg & Spekreijse, 1993). A mathematical formalism was chosen to yield analytically equivalent expressions for the optical modulation transfer function, the point spread function as well as the line spread function. The formalism describes the presently available data for visual function (including directional sensitivity of the retina) from Campbell and Green (1965) and from IJspeert, de Waard, van den Berg and de Jong (1990) on light scattering, measured with the direct compensation method (van den Berg, 1986; van den Berg & Spekreijse, 1987). The result was compared to one proposal for the point spread function (Vos, 1984) and to two proposals for the modulation transfer function (MTF) (Geisler, 1984; Drasdo, Cox & Thompson, 1987; which is an adapted version of Jennings & Charman, 1974). The latter two proposals show much more high frequency fall off than our proposal. Regrettably, an error was made plotting Figs 2 and 3 in IJspeert et al. (1993), exaggerating the difference (at 50 c/deg the plot is a factor 1.35 too high). The formula's etc. are correct though. Figure 1 shows the MTFs again (IJvdBS), plotted correctly, for two pupil diameters, 2 mm (thin lines) and 4 mm (heavy lines). The solid lines give our model curves for age 35 yr and mean caucasian pigmentation (pigmentation parameter m = 0.142). The dotted lines represent the diffraction limit for a wavelength of 555 nm. Drasdo, Thompson and Charman (1994) discuss this discrepancy at the high frequency side. They use another adapted version of the Jennings and Charman (1974) proposal including effects of pupil diameter (Deeley, Drasdo & Charman, 1991), which result in the dashed
line curves of Fig. 1 (DDC). Because of their discussion two questions arise. (a) Is the high frequency side better described by the Jennings and Charman (or adapted) proposal? (b) In other respects, how does this alternative compare to our description? To start with (b) we need to reiterate some starting points for our description formula, none of which apply to the alternative. (i) Our formula is useful for both the frequency and angular domains. The alternative is defined for the frequency domain only. (ii) Our formula is applicable to the full range of the frequency and angular domains, including light scattering. The alternative does not include (larger angle) light scattering. (iii) Our formula includes age and pigmentation effects. Since these effects are only well documented for light scattering, it is implicit in (ii) that these effects are not included in the alternative. (iv) Our formula is valid for visual function, including directional sensitivity of the retina. That is why we based it on the Campbell and Green (1965) data, and not on the double pass data as the alternative.
Admittedly, an important charm of the alternative is its simplicity; but at the cost of the above points. Now question (a): is the high frequency side better described by the alternative? The answer to this question depends partly on how one feels toward point (iv) above, since there is a difference between visual and optical modulation transfer: Artal, Navarro, Brainard, Galvin and Williams (1992) have found that the functional high frequency modulation transfer is about twice as high as the double pass derived high frequency modulation *Laboratory of Medical Physics and Informatics, Universityof Amtransfer. Also others have stressed that functional modusterdam, Amsterdam, The Netherlands. ?The Netherlands Ophthalmic Research Institute, Meibergdreef 15, lation transfer is higher (Campbell & Gubish, 1966; 1105AZ Amsterdam, The Netherlands. Jennings & Charman, 1974). The difference might be 1251
1252
LETTER TO THE EDITOR 1
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-=~.
.
O.8- L- ...,~...¢~....... :~::-.............. ~.=:::.................~......................................... \DlgC4rrkn "'-.. i .......... i ~, ,. \ : "-.. : .... ~di~ rn 4mmi 0.6-
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g
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................. :\
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0.4 .......... "~" ....... ~ - - - ~
0
"+.: ................. ! "-.,
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10
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i ............. ::'::',:.,--.::: ! ! ........ . . . . . . . . . . . . .
i
::
',
..
....
................... :'~,i,ff--luzl,-2mmi' ' ....................
20 30 spatial frequency q (cpd)
40
50
FIGURE 1. Model optical modulation transfer functions of the human eye for pupil diameters 2 and 4 mm. Abbreviations: diff. lim., diffraction limited; IJvdBS, IJspeert, van den Berg and Spekreijse (1993); DDC, Deeley, Drasdo and Charman (1991).
caused b y the d i r e c t i o n a l sensitivity o f the retina a n d the m o d u l a t i o n t r a n s f e r o f the reflection process o f the fundus. T h e reflection o f the fundus, is n o t l o c a t e d at one site. D e p t h s differing b y a few tens o f a m i l l i m e t e r m a y c o n t r i b u t e d e p e n d i n g on w a v e l e n g t h [retina, p i g m e n t e p i t h e l i u m , c h o r o i d , see e.g. v a n B l o k l a n d a n d van N o r r e n (1986), van N o r r e n a n d T i e m e y e r (1986) a n d D e l o r i a n d Pflibsen (1989)]. This induces a s p r e a d i n g t h a t is o n l y p a r t l y o f f u n c t i o n a l i m p o r t a n c e because o f the d i r e c t i o n a l sensitivity o f the retina. A n o t h e r p r o b l e m using d o u b l e pass d a t a as basis is the i n h e r e n t u n c e r t a i n t y . This results in very different m o d u l a t i o n transfer values, as has been discussed by Jennings a n d C h a r m a n (1974). Especially at the high f r e q u e n c y side u n c e r t a i n t i e s are large, since the noise in the m e a s u r e m e n t s is relatively m o r e i m p o r t a n t at frequencies with low transfer values. This p o i n t is clearly illustrated in Fig. 2 o f Jennings a n d C h a r m a n (1974). A r t a l et al. (1992) r e p o r t e d significantly higher values for high f r e q u e n c y transfer as c o m p a r e d to those o f J e n n i n g s a n d C h a r m a n (1981). E r r o r b e h a v i o u r s h o u l d be c o n s i d e r e d if differences between m o d e l s are discussed a n d d e m o n s t r a t e d in plots. I f no e r r o r b a r s are included, scaling s h o u l d be such t h a t no suggestive differences result. T h a t is why m o s t a u t h o r s p l o t m o d u l a t i o n t r a n s f e r figures f r o m d o u b l e pass e x p e r i m e n t s on a linear scale as we d i d (Fig. 1). D r a s d o et al. (1994) however, e x t r a p o l a t e d their m o d e l b e y o n d the limits set b y the d a t a base a n d e r r o r b e h a v i o u r . This results in an e x a g g e r a t i o n o f the discrepancies. A d m i t t e d l y , also the d a t a base used by us c o n t a i n s errors. A n i m p o r t a n t p o t e n t i a l flaw in the technique o f C a m p b e l l a n d G r e e n (1965) is t h a t the m o d u l a t i o n o f the interference fringes o n the retina is n o t c o m p l e t e l y i n d e p e n d e n t o f the optics o f the eye. F o r m o r e p o t e n t i a l sources o f e r r o r see D r a s d o et al. (1994). A t present, insufficient insight exists to correct for these errors.
But since we a i m e d at f u n c t i o n a l relevance we used C a m p b e l l a n d G r e e n ' s d a t a base. In conclusion, we do n o t agree with D r a s d o et al. (1994) that present k n o w l edge p o i n t s to their p r o p o s a l . But they rightfully p o i n t e d t o w a r d s p o t e n t i a l flaws in p a r t o f the d a t a base used by us.
REFERENCES
Artal, P., Navarro, R., Brainard, D. H., Galvin, S. J. & Williams, D. R. (1992). Off axis optical quality of the eye and retinal sampling. Investigative Ophthalmology and Visual Science (Suppl.), 33, 3241. van den Berg, T. J. T. P. (1986). Importance of pathological intraocular scatter for visual disability. Documenta Ophthalmologica, 61, 327-333. van den Berg, T. J. T. P. & Spekreijse, H. (1987). Measurement of the straylight function of the eye in cataract and other optical media disturbances by means of a direct compensation method. Investigative
Ophthalmology
and Visual Science (Suppl.), 28,
397. van Blokland, G. J. & van Norren, D. (1986). Intensity and polarization of light scattered at small angles from the human fovea. Vision Research, 26, 485-494. Campbell, F. W. & Green, D. C. (1965). Optical and retinal factors affecting visual resolution. Journal of Physiology, 181, 576 593. Campbell, F. W. & Gubisch, R. W. (1966). Optical quality of the human eye. Journal of Physiology, 186, 558-578. Deeley, R. J., Drasdo, N. & Charman, W. N. (1991). A simple parametric model of the human ocular modulation transfer function. Ophthalmology and Physiological Optics, 11, 9143. Delori, F. C. & Pfiibsen, K. P. (11989). Spectral reflectance of the human ocular fundus. Applied Optics, 28, 1061 1077. Drasdo, N., Cox, W. & Thompson, D. A. (1987). The effects of image degradation on retinal ilIuminance and pattern responses to checkerboard stimuli. Documenta Ophthalmologica, 66, 267-275. Drasdo, N., Thompson, C. M. & Charman, W. N. (1994). Inconsistencies in models of the human ocular modulation transfer function. Vision Research, 34, 1247-1249. Geisler, W. S. (1984). Physical limits of acuity and hyperacuity. Journal of the Optical Society of America A, 1, 755-782. IJspeert, J. K., van den Berg, T. J. T. P. & Spekreijse, H. (1993). An
LETTER TO THE EDITOR improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation. Vision Research, 33, 15~0. IJspeert, J. K., de Waard, P. W. T., van den Berg, T. J. T. P. & de Jong, P. T. V. M. (1990). The intraocular straylight function in 129 healthy volunteers; dependence on angle, age and pigmentation. Vision Research, 30, 699-707. Jennings, J. A. M. & Charman, W. N. (1974). An analytical approxi-
1253
mation for the modulation transfer function of the eye. British
Journal of Physiological Optics, 29, 64-72. Jennings, J. A. M. & Charman, W. N. (1981). Off-axis image quality in the human eye. Vision Research, 21, 445-455. van Norren, D. & Tiemeyer, L. F. (1986). Spectral reflectance of the human eye. Vision Research, 26, 313-320. Vos, J. J. (1984). Disability glare--a state of the art report. CIEJournal, 3/2, 39-53.