Full Text:   <1487>

CLC number: Q81

On-line Access: 

Received: 2008-06-05

Revision Accepted: 2008-08-17

Crosschecked: 2008-10-29

Cited: 2

Clicked: 3506

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE B 2008 Vol.9 No.12 P.996~1002


Representing the retinal line spread shape with mathematical functions

Author(s):  Yi-rong YANG, Justin WANEK, Mahnaz SHAHIDI

Affiliation(s):  Department of Bioengineering, University of Illinois at Chicago, IL 60607, USA; more

Corresponding email(s):   yyang19@uic.edu

Key Words:  Retina, Double-pass line spread function (LSF), Lorentzian, Gaussian, Exponential

Share this article to: More <<< Previous Article|

Yi-rong YANG, Justin WANEK, Mahnaz SHAHIDI. Representing the retinal line spread shape with mathematical functions[J]. Journal of Zhejiang University Science B, 2008, 9(12): 996~1002.

@article{title="Representing the retinal line spread shape with mathematical functions",
author="Yi-rong YANG, Justin WANEK, Mahnaz SHAHIDI",
journal="Journal of Zhejiang University Science B",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Representing the retinal line spread shape with mathematical functions
%A Yi-rong YANG
%A Justin WANEK
%J Journal of Zhejiang University SCIENCE B
%V 9
%N 12
%P 996~1002
%@ 1673-1581
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.B0820184

T1 - Representing the retinal line spread shape with mathematical functions
A1 - Yi-rong YANG
A1 - Justin WANEK
A1 - Mahnaz SHAHIDI
J0 - Journal of Zhejiang University Science B
VL - 9
IS - 12
SP - 996
EP - 1002
%@ 1673-1581
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.B0820184

Objective: To report a mathematical function that characterizes the double-pass line spread function (LSF) of the human eye. Determining analytical functions that represent the double-pass LSF is important because it allows modeling the optical performance of the eye. Methods: Optical section retinal images, generated in normal human eyes using a modified slit-lamp biomicroscope, were analyzed to derive the double-pass LSF by plotting the intensity distribution of laser light reflected/ scattered from the vitreoretinal interface. Three mathematical functions (lorentzian, gaussian, exponential) were fitted to the double-pass LSF and the root mean square error (RMSE) was calculated to provide a measure of the goodness of fit. Results: The lorentzian function provided the best representation of the double-pass LSF of normal human eyes. The full width at half maximum (FWHM) of the lorentzian fitted curve was positively correlated with age, indicating that the double-pass LSF broadens with age. Furthermore, the goodness of fit of the lorentzian function was significantly better in younger subjects as compared with older subjects, suggesting that the fitted function to the double-pass LSF may vary according to age. Conclusion: The results demonstrate an age-related change in the double-pass LSF width and the goodness of fit of the lorentzian function.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Amano, S., Amano, Y., Yamagami, S., Miyai, T., Miyata, K., Samejima, T., Oshika, T., 2004. Age-related changes in corneal and ocular higher-order wavefront aberrations. Am. J. Ophthalmol., 137(6):988-992.

[2] Artal, P., Iglesias, I., Lopez-Gil, N., Green, D.G., 1995a. Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 12(10):2358-2366.

[3] Artal, P., Marcos, S., Navarro, R., Williams, D.R., 1995b. Odd aberrations and double-pass measurements of retinal image quality. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 12(2):195-201.

[4] Artal, P., Berrio, E., Guirao, A., Piers, P., 2002. Contribution of the cornea and internal surfaces to the change of ocular aberrations with age. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 19(1):137-143.

[5] Artal, P., Guirao, A., Berrio, E., Piers, P., Norrby, S., 2003. Optical aberrations and the aging eye. Int. Ophthalmol. Clin., 43:63-77.

[6] Beckman, C., Nilsson, O., Paulsson, L.E., 1994. Intraocular light-scattering in vision, artistic painting, and photography. Appl. Optics., 33:4749-4753.

[7] Brunette, I., Bueno, J.M., Parent, M., Hamam, H., Simonet, P., 2003. Monochromatic aberrations as a function of age, from childhood to advanced age. Invest. Ophthalmol. Vis. Sci., 44(12):5438-5446.

[8] Calver, R.I., Cox, M.J., Elliott, D.B., 1999. Effect of aging on the monochromatic aberrations of the human eye. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 16(9):2069-2078.

[9] Campbell, F.W., Gubisch, R.W., 1966. Optical quality of the human eye. J. Physiol., 186:558-578.

[10] Chen, L., Singer, B., Guirao, A., Porter, J., Williams, D.R., 2005. Image metrics for predicting subjective image quality. Optom. Vis. Sci., 82(5):358-369.

[11] Collins, M.J., Buehren, T., Iskander, D.R., 2006. Retinal image quality, reading and myopia. Vision Res., 46(1-2):196-215.

[12] David, C.C., 1996. Lasers and Electro-Optics: Fundamentals and Engineering. Cambridge University Press, New York, NY.

[13] Diaz-Douton, F., Benito, A., Pujol, J., Arjona, M., Guell, J.L., Artal, P., 2006. Comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument. Invest. Ophthalmol. Vis. Sci., 47(4):1710-1716.

[14] Flamant, M.F., 1955. Etude de la repartition de lumiere dans l'image retinienne d'une fente. Rev. Opt., 34:433-459.

[15] Fujikado, T., Kuroda, T., Ninomiya, S., Maeda, N., Tano, Y., Oshika, T., Hirohara, Y., Mihashi, T., 2004. Age-related changes in ocular and corneal aberrations. Am. J. Ophthalmol., 138(1):143-146.

[16] Guirao, A., Gonzalez, C., Redondo, M., Geraghty, E., Norrby, S., Artal, P., 1999. Average optical performance of the human eye as a function of age in a normal population. Invest. Ophthalmol. Vis. Sci., 40:203-213.

[17] Hammond, C.J., Snieder, H., Spector, T.D., Gilbert, C.E., 2000. Factors affecting pupil size after dilatation: the Twin Eye Study. Br. J. Ophthalmol., 84(10):1173-1176.

[18] Hennelly, M.L., Barbur, J.L., Edgar, D.F., Woodward, E.G., 1998. The effect of age on the light scattering characteristics of the eye. Ophthalmic Physiol. Opt., 18(2):197-203.

[19] Iglesias, I., Berrio, E., Artal, P., 1998. Estimates of the ocular wave aberration from pairs of double-pass retinal images. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 15(9):2466-2476.

[20] Ijspeert, J.K., Dewaard, P.W.T., van den Berg, T.J.T.P., Dejong, P.T.V.M., 1990. The intraocular straylight function in 129 healthy-volunteers: dependence on angle, age and pigmentation. Vision Res., 30(5):699-707.

[21] Jones, R.C., 1958. On the point and line spread functions of photographic images. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 48(12):934-937.

[22] Karbassi, M., Magnante, P.C., Wolfe, J.K., Chylack, L.T.Jr., 1993. Objective line spread function measurements, Snellen acuity, and LOCS II classification in patients with cataract. Optom. Vis. Sci., 70:956-962.

[23] Krauskopf, J., 1962. Light distribution in human retinal images. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 52(9):1046-1050.

[24] Kuroda, T., Fujikado, T., Ninomiya, S., Maeda, N., Hirohara, Y., Mihashi, T., 2002. Effect of aging on ocular light scatter and higher order aberrations. J. Refract. Surg., 18:598-602.

[25] Liang, J., Westheimer, G., 1995. Optical performances of human eyes derived from double-pass measurements. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 12(7):1411-1416.

[26] Navarro, R., Losada, M.A., 1995. Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 12(11):2385-2392.

[27] Peng, Y., Lu, R., 2005. Modeling multispectral scattering profiles for prediction of apple fruit firmness. Transactions of the Asae, 48:235-242.

[28] Röhler, R., Howland, H.C., 1979. Merits of the Gaussian moment in judging optical line spread width—coment on a paper by W.N. Charman and J.A.M. Jennings. Vision Res., 19(7):847-849.

[29] Shahidi, M., Yang, Y., 2004. Measurements of ocular aberrations and light scatter in healthy subjects. Optom. Vis. Sci., 81(11):853-857.

[30] Shahidi, M., Blair, N.P., Mori, M., Zelkha, R., 2004. Optical section retinal imaging and wavefront sensing in diabetes. Optom. Vis. Sci., 81(10):778-784.

[31] Siik, S., Airaksinen, P.J., Tuulonen, A., 1992. Light scatter in aging and cataractous human lens. Acta Ophthalmol. (Copenh), 70:383-388.

[32] van den Berg, T.J., 1995. Analysis of intraocular straylight, especially in relation to age. Optom. Vis. Sci., 72(2):52-59.

[33] Westheimer, G., 1963. Optical and motor factors in the formation of the retinal image. J. Opt. Soc. Am., 53(1):86-93.

[34] Westheimer, G., Campbell, F.W., 1962. Light distribution in the image formed by the living human eye. J. Opt. Soc. Am., 52(9):1040-1045.

[35] Westheimer, G., Liang, J., 1994. Evaluating diffusion of light in the eye by objective means. Invest. Ophthalmol. Vis. Sci., 35:2652-2657.

[36] Westheimer, G., Liang, J., 1995. Influence of ocular light scatter on the eye’s optical performance. J. Opt. Soc. Am. A: Opt. Image Sci. Vis., 12(7):1417-1424.

[37] Whitaker, D., Steen, R., Elliott, D.B., 1993. Light scatter in the normal young, elderly, and cataractous eye demonstrates little wavelength dependency. Optom. Vis. Sci., 70:963-968.

[38] Yin, S., Gardner, T.W., Thomas, T.O., Kolanda, K., 2003. Light scatter causes the grayness of detached retinas: implications for vision loss in retinal detachment. Arch. Ophthalmol., 121(7):1002-1008.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE