Rafael Navarro

OFF-AXIS ABERRATIONS OF A WIDE-ANGLE SCHEMATIC EYE MODEL

A schematic eye model based on anatomical data, which had been previously designed to reproduce image quality on axis, has been transformed into a wide-angle model by simply adding a spherical image surface that plays the role of the retina. This model captures the main features of the wide-angle optical design of the human eye with minimum complexity: four conic optical surfaces plus a spherical image surface. Seidel aberrations (spherical aberration, coma, astigmatism, field curvature, and distortion), longitudinal and transverse chromatic aberrations, and overall monochromatic spot diagrams have been computed for this eye model and for field angles ranging from 0 degree to 60 degrees by both finite and third-order ray tracing. The modulation transfer function for each field angle has been computed as well. In each case our results have been compared with average experimental data found in the literature, showing a reasonably good agreement. The agreement between the model and experimental data is better off axis, mainly at moderate (10 degrees-40 degrees) field angles, than on axis. The model has been applied to simulate a variety of experimental methods in which image aberrations are estimated from measurements taken in the object space. Our results suggest that for some types of aberration, these methods may yield biased estimates.

The depth-of-field of the human eye from objective and subjective measurements

The depth-of-field (DOF) measured through psychophysical methods seems to depend on the targets characteristics. We use objective and subjective methods to determine the DOF of the eye for different pupil diameters and wavelengths in three subjects. Variation of image quality with focus is evaluated with a double-pass technique. Objective DOF is defined as the dioptric range for which the image quality does not change appreciably, based on optical criteria. Subjective DOF is based on the accuracy of focusing a point source. Additional DOFs are obtained by simulation from experimental wavefront aberration data from the same subjects. Objective and subjective measurements of DOF are only slightly affected by pupil size, wavelength and spectral composition. Comparison of DOF from double-pass and wavefront aberration data allows us to evaluate the role of ocular aberrations and Stiles-Crawford effect.

Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions

Gabor schemes of multiscale image representation are useful in many computer vision applications. However, the classic Gabor expansion is computationally expensive due to the lack of orthogonality of Gabor functions. Some alternative schemes, based on the application of a bank of Gabor filters, have important advantages such as computational efficiency and robustness, at the cost of redundancy and lack of completeness. In a previous work we proposed a quasicomplete Gabor transform, suitable for fast implementations in either space or frequency domains. Reconstruction was achieved by simply adding together the even Gabor channels. We develop an optimized spatial-domain implementation, using one-dimensional 11-tap filter masks, that is faster and more flexible than Fourier implementations. The reconstruction method is improved by applying fixed and independent weights to the Gabor channels before adding them together. Finally, we analyze and implement, in the spatial domain, two ways to incorporate a high-pass residual, which permits a visually complete representation of the image.

A new approach to the study of ocular chromatic aberrations.

We measured the ocular wavefront aberration at six different visible wavelengths (between 450 and 650 nm) in three subjects, using a spatially resolved refractometer. In this technique, the angular deviation of light rays entering the pupil at different locations is measured with respect to a target viewed through a centered pupil. Fits of the data at each wavelength to Zernike polynomials were used to estimate the change of defocus with wavelength (longitudinal chromatic aberration, LCA) and the wavelength-dependence of the ocular aberrations. Measured LCA was in good agreement with the literature. In most cases the wavefront aberration increased slightly with wavelength. The angular deviations from the reference stimulus measured using a magenta filter allowed us to estimate the achromatic axis and both optical and perceived transverse chromatic aberration (TCA), (including the effect of aberrations and Stiles-Crawford effect). The amount of TCA varied markedly across subjects, and between eyes of the same subject. Finally, we used the results from these experiments to compute the image quality of the eye in polychromatic light.

Monochromatic aberrations and point-spread functions of the human eye across the visual field

The monochromatic aberrations of the human eye along the temporal meridian are studied by a novel laser ray-tracing method. It consists of delivering a narrow laser pencil into the eye through a given point on the pupil and recording the aerial image of the retinal spot with a CCD camera. The relative displacement of this image is proportional to the geometrical aberration of the ray (laser pencil) at the retina. We scanned the pupils of four observers in steps of 1 mm (effective diameter, 6.7 mm) and for five field angles (0 degree, 5 degrees, 10 degrees, 20 degrees, and 40 degrees). In addition, the aerial image for each chief ray is a low-pass-filtered version of the retinal point-spread function corresponding to a fully dilated pupil. The resulting spot diagrams, displaying the distribution of ray aberrations, are highly correlated with these point-spread functions. We have estimated the wave-front error by fitting Zernike polynomials (up to the fifth order). Despite the large variation found among observers, the overall rms wave-front error is relatively homogeneous. At the fovea, the average rms value was 1.49 microns when the second-order terms (defocus and astigmatism) were considered; this was reduced to 0.45 micron when the second-order terms were ignored. The rms values increase slowly, in a roughly linear fashion with eccentricity, such that at 40 degrees they are approximately double. These results are consistent with previous findings on the off-axis optical quality of the eye.

Laser Ray Tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye

A comparison and validation study of Laser Ray Tracing (LRT) and Hartmann-Shack wave-front-sensor (to be referred to as H-S) methods was carried out on both artificial and human eyes. The aim of this work was double. First, we wanted to verify experimentally the equivalence of single- and double-pass measurements for both H-S and LRT. This interest is due to the impossibility of making single-pass measurements in human eyes. In addition, we wanted to validate the LRT technique by comparing it with the H-S wave-front sensor, currently used in many physiological optics laboratories. Comparison of the different methods and configurations carried out in the artificial eye yielded basically the same results in all cases, which means a reciprocal validation of both LRT and H-S, in either single- or double-pass configurations. Other aspects, such as robustness against speckle noise or the influence of the size of the entrance (H-S) or exit (LRT) pupil were studied as well. As a global reference, the point-spread function (PSF) of the artificial eye was recorded directly on a CCD camera and compared with simulated PSFs computed from the experimental aberration data. We also applied these two methods to real eyes (double pass), finding again a close match between the resulting aberration coefficients and also between the standard errors for two normal subjects. However, for one myopic eye with an especially low optical quality (RMS wave-front error >2 microm) and asymmetric aberrations, the array of spots recorded with the H-S sensor was highly distorted and too difficult to analyze.

Detection of local defects in textile webs using Gabor filters

A method of image analysis is proposed for detection of local defects in materials with periodic regular texture. A general improvement and enlargement of vision system capabilities for versatility, full automa- tism, computational efficiency, and robustness in their application to the industrial inspection of periodic textured materials is pursued. In the pro- posed method, a multiscale and multiorientation Gabor filter scheme that imitates the early human vision process is applied to the sample under inspection. The designed algorithm automatically segments defects from the regular texture. A variety of examples of fabric inspection are pre- sented. In all of them defects are successfully segmented from the tex- ture background.

Phase plates for wave-aberration compensation in the human eye

We present a method for manufacturing phase plates to compensate for the wave aberration in the human eye. The wave aberration of the eye is measured in vivo by a new laser ray-tracing method and then compensated for by a phase plate placed in front of the eye. This plate is made from a gray-level single-mask photosculpture in photoresist. Two experiments were carried out, first with an artificial eye and then with a human eye: 80% compensation for the wave aberration was achieved in both cases.

Laser ray-tracing method for optical testing

We have developed a novel laser ray-tracing method to measure aberrations in optical systems. It consists of delivering narrow laser pencils (by a laser scanner), recording the spots that are formed on the image plane (with a CCD camera), and computing the position of each centroid. This approach could be considered an experimental (approximate) implementation of standard numerical ray tracing. Several tests and experiments, including a direct comparison with a Hartmann-Shack wave-front sensor, provided highly satisfactory results that confirmed the validity of the method and revealed potential advantages.

Nonlinear image representation for efficient perceptual coding

Image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized. The success of such a system depends on two properties of the representation. First, the coding rate is minimized only if the elements of the representation are statistically independent. Second, the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent. We argue that linear transforms cannot achieve either of these goals and propose, instead, an adaptive nonlinear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood. We then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements. We develop an efficient method of inverting this transformation, and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images.