Representing the retinal line spread shape with mathematical functions

Abstract

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.

Fig. 1

(a) Example of an optical section retinal image obtained in one subject. An intensity profile was derived from the area of interest outlined by the rectangular box; (b) Example of an intensity profile, obtained from the area outlined in (a). The left and right peaks coincide with the vitreoretinal and chorioretinal interfaces, respectively. The line spread function was derived by mirroring the left side of the intensity distribution about its peak

Fig. 2

Examples of the same normalized double-pass line spread function fitted with (a) Lorentzian function, (b) Gaussian function, and (c) exponential function

Fig. 2

Examples of the same normalized double-pass line spread function fitted with (a) Lorentzian function, (b) Gaussian function, and (c) exponential function

Fig. 2

Examples of the same normalized double-pass line spread function fitted with (a) Lorentzian function, (b) Gaussian function, and (c) exponential function

Fig. 3

The relationship between the full width at half maximum (FWHM) of the Lorentzian function and age. The error bars represent the standard error (SE) of the means

Fig. 4

The mean root mean square error (RSME) for fitting the double-pass line spread function to each of the three fitted functions. Error bars represent the standard deviations (SD)

Fig. 5

The mean root mean square error (RMSE) for fitting of the line spread function to the Lorentzian function in younger subjects (age range (28±5) years; N=8) and older subjects (age range (57±8) years; N=13). The error bars represent the standard deviations (SD)