Signal-to-noise ratio and aberration statistics in ocular aberrometry
ABSTRACT We define a signal-to-noise ratio (SNR) for eye aberrometry in terms of the sensor geometry, measurement noise, and population statistics. The overall estimation error is composed of three main contributions: the bias in the estimated modes, the truncation error, and the error due to the noise propagation. This last term can be easily parametrized by the proposed SNR. We compute the overall error as well as the magnitude of its three components for a typical sensor configuration, population statistics, and different SNR. We show that there are an optimum number of Zernike aberration modes to be retrieved in each case.
Article: Synthetic aperture wavefront sensing[Show abstract] [Hide abstract]
ABSTRACT: We propose the synthetic aperture wavefront sensing approach. It is based on acquiring several sets of measurements of the wavefront slopes by displacing sequentially the microlens array with respect to the unknown wavefront. These measurements are stacked together and processed as if obtained with a single-sampling array with an effective number of subpupils equal to the product of the number of microlenses by the number of displacements. We analyze and compare the performance of this approach with the method of modal coefficient averaging. The comparison is made in terms of the squared wavefront reconstruction error, spatially averaged over the pupil and statistically averaged over the noise and the aberrations of the population. We focused our attention on its applications to eye aberrometry. Our numerical results were obtained for a population statistics consistent with a wide sample of young adult eyes using different sampling grids and with several signal-to-noise ratios. They indicate that the synthetic aperture wavefront sensing is affected by less bias and noise propagation than the averaging method, providing smaller mean-squared estimation error. The number of complete Zernike radial orders that can be estimated using the synthetic aperture approach is consistently higher than that allowed by the conventional method. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)Optical Engineering 06/2013; 53(6):061703. DOI:10.1117/1.OE.53.6.061703 · 0.96 Impact Factor
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ABSTRACT: In order to work in a consistent way with Zernike aberration coefficients estimated in different pupils, it is necessary to refer them to a common pupil size. Two standard approaches can be used to that end: to rescale algebraically the coefficients estimated in the original pupil or to refit them anew using the wavefront slope measurements available within the new one. These procedures are not equivalent; they are affected by different estimation errors that we address in this work. Our results for normal eye populations show that in case of reducing the pupil size it is better to rescale the original coefficients than to refit them using the measurements contained within the smaller pupil. In case of enlarging the pupil size, as it can a priori be expected, the opposite holds true. We provide explicit expressions to quantify the errors arising in both cases, including the expected error incurred when extrapolating the Zernike estimation beyond the radius where the measurements were made.Journal of the Optical Society of America A 01/2014; 31(1):114-23. DOI:10.1364/JOSAA.31.000114 · 1.45 Impact Factor
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ABSTRACT: This Letter studies the statistics of wavefront aberrations in a sample of eyes with normal vision. Methods relying on the statistics of the measured wavefront slopes are used, not including the aberration estimation stage. Power-law aberration models, an extension of the Kolmogorov one, are rejected by χ 2 -tests performed on fits to the slope structure function data. This is due to the large weight of defocus and astigmatism variations in normal eyes. Models of only second-order changes are not ruled out. The results are compared with previous works in the area.Optics Letters 06/2014; 39(11):3197-200. DOI:10.1364/OL.39.003197 · 3.18 Impact Factor