We consider a schematic human eye with four centered aspheric surfaces. We show that by introducing recent experimental average measurements of cornea and lens into the Gullstrand-Le Grand model, the average spherical aberration of the actual eye is predicted without any shape fitting. The chromatic dispersions are adjusted to fit the experimentally observed chromatic aberration of the eye. The polychromatic point-spread function and modulation transfer function are calculated for several pupil diameters and show good agreement with previous experimental results. Finally, from this schematic eye an accommodation-dependent model is proposed that reproduces the increment of refractive power of the eye during accommodation. The variation of asphericity with accommodation is also introduced in the model and the resulting optical performance studied.

A method for the determination of the bidimensional optical transfer function (OTF) and the point-spread function of human eyes is presented. Aerial short-term images of a point source are directly recorded with a TV camera and fed into a digital image-processing system that allows one to determine and display such functions. The method has been implemented in such a way that recording and computation can be carried out on a routine basis with minimum discomfort for the observer. A detailed description of the method and typical aerial and retinal images of a point source as well as the OTF's results are presented in this paper.

The enhancement and detection of elongated structures in noisy image data are relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores U : R 2 × S 1 → C were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores U : R 3 ×S 2 → C. First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. Here we introduce two types of cake wavelets: the first uses a discrete Fourier transform, and the second is designed in the 3D generalized Zernike basis, allowing us to calculate analytical expressions for the spatial filters. Second, we propose a nonlinear diffusion flow on the 3D roto-translation group: crossing-preserving coherence-enhancing diffusion via orientation scores (CEDOS). Finally, we show two applications of the orientation score transformation. In the first application we apply our CEDOS algorithm to real medical image data. In the second one we develop a new tubularity measure using 3D orientation scores and apply the tubularity measure to both artificial and real medical data.

The wave aberration of human eyes is retrieved from actual point-spread-function (PSF) data and the modulus of the pupil function. The PSF had been obtained previously by application of a hybrid optical-digital method developed recently. The retrieval is done by using a bidimensional Gerchberg-Saxton phase-retrieval algorithm joined to an iterative phase-unwrapping algorithm. To obtain an adequate convergence, the initial wave aberration for starting the retrieval-unwrapping algorithm is estimated with a nonlinear least-squares algorithm. The resulting wave aberrations for several subjects show irregular aberrations superimposed upon the regular wave-aberration components, with astigmatism being the most important asymmetric aberration.

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