Abstract
This work presents a compact statistical model of the retinal image quality in a large population of human eyes following two objectives. The first was to develop a general modal representation of the optical transfer function (OTF) in terms of orthogonal functions and construct a basis composed of cross-correlations between pairs of complex Zernike polynomials. That basis was not orthogonal and highly redundant, requiring the application of singular value decomposition (SVD) to obtain an orthogonal basis with a significantly lower dimensionality. The first mode is the OTF of the perfect system, and hence the modal representation, is highly compact for well-corrected optical systems, and vice-versa. The second objective is to apply this modal representation to the OTFs of a large population of human eyes for a pupil diameter of 5 mm. This permits an initial strong data compression. Next, principal component analysis (PCA) is applied to obtain further data compression, leading to a compact statistical model of the initial population. In this model each OTF is approximated by the sum of the population mean plus a linear combination of orthogonal eigenfunctions (eigen-OTF) accounting for a selected percentage (90%) of the population variance. This type of models can be useful for Monte Carlo simulations among other applications.
Highlights
Among the different optical and image quality functions, wavefront aberration W is the most extensive way to objectively characterize the optical performance of the human eye
A more direct estimation of visual performance, would require analyzing the retinal image quality by means of the frequency response given by the Optical Transfer Function optical transfer function (OTF) [13] or the impulse response given by the Point Spread Function PSF [14,15]
Another work proposed an orthogonal expansion in which the first function was the OTF of the perfect system [19], causing OTFs close to the diffraction limit to be highly compressed, whereas OTFs of low-quality optical systems would require a large number of modes
Summary
Among the different optical and image quality functions, wavefront aberration W is the most extensive way to objectively characterize the optical performance of the human eye. Non-linear relationship between wavefront aberration and retinal image, these studies showed a reasonable overall correlation between wavefront-based metrics, typically calculated with the coefficients of a Zernike polynomial expansion [12], and clinical Rx or visual acuity. A more direct estimation of visual performance, would require analyzing the retinal image quality by means of the frequency response given by the Optical Transfer Function OTF [13] or the impulse response given by the Point Spread Function PSF [14,15]. Another work proposed an orthogonal expansion in which the first function was the OTF of the perfect system [19], causing OTFs close to the diffraction limit to be highly compressed, whereas OTFs of low-quality optical systems would require a large number of modes (basis functions)
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