Optical modelling for uncorrected and corrected myopia using ray tracing technique

Current trend shows that the eye modelling is based on the emmetropic eye taken its ocular optical components value from the population-based studies. However, no studies have been done to study the effect of aberration of myopic refractive error by modelling the eye using the parameters from ocular biometrics and ray tracing method. The objective of the present study was to assess the aberrations quality of myopic refractive error using eye modelling and ray tracing technique. Five eye models had been successfully modelled in Zemax software, namely, Emsley’s Reduced Eye, Gullstrand-Emsley, emmetropic Liou and Brennan, myopic Liou and Brennan, corrected myopic Liou and Brennan. The optical performance of the eye models were tested using the merit functions in Zemax, namely, modulation transfer function (MTF), spot diagram (SPD), ray fan plot, point spread function (PSF), and diffraction image analysis. From the MTF analysis at 100 cycles/mm, the tangential and sagittal rays of Liou and Brennan had the highest optical performance from sharpness ability and contrast behaviour among the emmetropic models. In contrast, the Emsley produced the lowest optical performance for both components. As the MTF value indicates the threshold of the image contrast of sinusoidal pattern, the higher the value will enable higher image recognition. On further analysis, the MTF value for myopic Liou and Brennan eye was the lowest compared to the other emmetropic models. Also, it was found out that the MTF value of the corrected myopic Liou and Brennan model was higher compared to the previous uncorrected myopic model. Furthermore, in comparison with the emmetropic models, the MTF values for corrected myopic Liou and Brennan was also higher compared to both emmetropic Emsley and Gullstrand-Emsley models. However, the corrected myopic model produced lower MTF values for both tangential and sagittal MTF compared with the emmetropic model of Liou and Brennan. For the SPD, the emmetropic Liou and Brennan model had the lowest root mean square (RMS) value and Airy disc diameters among the three emmetropic models as this model had collective aberration corrections from the multiple ocular optical components. In contrast, the emmetropic Emsley model had the highest RMS value as its single refracting surface produced higher diffraction effect. On further analysis, the ray distribution from the analysis of SPD of myopic Liou and Brennan eye was larger compared to the emmetropic model. In comparison with the emmetropic Liou and Brennan model, for the blue wavelength, the RMS spot radius for the corrected version was increased. However, the RMS values were decreased for green and red wavelengths. The large difference at longer wavelength specifically at green and red were due to chromatic aberration of the lens medium. For the corrected myopic version of Liou and Brennan, in comparison with its emmetropic model, the Airy disc diameter increased with the increment of wavelengths. Although the corrective lenses had been used to correct the myopia, the refractive correction is not at the optimum state. This was because the corrective lens power was calculated in the spherical equivalent refraction (SER) forms that sums up the spherical and cylindrical components. For the ray fan plot, as the chromatic aberration is highly dependent on light wavelength, this had caused the myopic Liou and Brennan model to contain more spherical aberration effect in comparison to emmetropic eye models. Furthermore, in comparison with the emmetropic Liou and Brennan model, the corrected version of myopic Liou and Brennan model had more diffraction-limited effect, thus the marginal rays were less aberrated. The green wavelength had almost no aberration as the corrective lenses refractive index was calculated at the wavelength closer to the green wavelength itself. For the PSF, the Strehl ratio for all the three wavelengths for the Liou and Brennan model were the highest among the emmetropic models. Whereas, in comparison with emmetropic eye models, the Strehl ratio value of myopic Liou and Brennan was much lower, thus did not producing a diffraction-limited system. On further analysis, in comparing with the emmetropic model, it was found out that the Strehl ratio values for all wavelengths of corrected myopic Liou and Brennan were much higher except for the blue wavelength. Finally, for the diffraction image analysis, the image quality from Liou and Brennan model was at the upmost quality among the emmetropic models. On the other hand, the image quality of the myopic Liou and Brennan model was at the lowest quality. On further analysis, in comparison with the emmetropic Liou and Brennan model, the image quality of the corrected myopic version was slightly lower. In this study, the accuracy of the merit functions for the myopia correction and emmetropia using the Liou and Brennan (1997) model were calculated. It was found that the accuracy of the MTF value at tangential and sagittal rays was lower. In contrast, for the Airy disc diameter, the accuracy were higher for the blue, green and red wavelengths. Although the accuracy values were in a positive sign, for Airy disc diameter, the smaller value indicates a diffraction-limited condition. Finally, for the Strehl ratio, the accuracy for the blue wavelength was lower. On the other hand, the green and red wavelengths had higher accuracy.

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