In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.

To evaluate and compare the effect of misalignment and tilt on the optical performance of different aspheric intraocular lens (IOL) designs. Methods Three aspheric IOLs with a different quantity of spherical aberration (SA) have been designed and the effect of IOL misalignment and tilt on the imaging quality of an eye model has been numerically assessed using a commercial optical design software. The prototypes have been manufactured by lathe turning and tested in vitro using the same optical bench (PMTF, Lambda-X) that complies with International Organization for Standardization standard 11979-2 requirements. Image quality was evaluated from the modulation transfer functions (MTFs), through-focus modulation transfer functions (TF-MTFs), root mean square (RMS) values of defocus, astigmatism and coma, and images of the United States Air Force (USAF) target were taken. A comparison with the optical performance of spherical IOLs has also been performed. Results Intraocular lens misalignment and tilt increased wavefront aberrations; the effect of misalignment on root mean square (RMS) astigmatism and coma was positively correlated with the spherical aberration of the IOL. Aberration-free IOLs showed the highest MTF for all misalignment values and for IOLs with negative SA correction the MTF decays below 0.43 when they are decentered 0.50 mm. Conclusions Aspherical IOLs are more sensitive than spherical IOLs to misalignment or tilt, depending on their SA correction. The optical degradation caused by IOL misalignment had a greater effect on IOL designs with a higher amount of negative spherical aberration. In contrast, the effect of tilt on the optical performance was less sensitive to the IOL design.

The results show the usefulness of the proposed approach and point out the need for developing further adapted optimizations.

The use of a Shack-Hartmann wave-front sensor as a position-sensing device is proposed and demonstrated. The coordinates of a pointlike object are determined from the modal Zernike coefficients of the wave fronts emitted by the object and detected by the sensor. The position of the luminous centroid of a moderately extended incoherent flat object can also be measured with this device. Experimental results with off-the-shelf CCD cameras and conventional relay optics as well as inexpensive diffractive microlens arrays show that axial positioning accuracies of 74 microm rms at 300 mm and angular accuracies of 4.3 microrad rms can easily be achieved.

Image-processing thresholding algorithms are extended segmentation tools that are suitable for tracking applications. The centroid of the tracked image distribution is a good point of reference for the location of the image. We describe a new thresholding technique that is based on the estimation of the optimum threshold for achieving minimal variance in the centroid of the processed image. Experimental proofs for evaluating the technique's performance are given. The direct extension of these results to Shack-Hartmann wave-front sensors is also shown.

The centroid method is a common procedure for subpixel location that is applied to a large number of optical sensors. In practice, it is always accompanied by thresholding algorithms used to eliminate undesirable background that may decrease precision. We present a full analytical description of the interaction between centroiding and thresholding applied over an intensity distribution corrupted by additive Gaussian noise. An in depth analysis of the most outstanding statistical properties of this relation (mean and variance) is also presented by means of simulated and experimental data. This work provides fundamental concepts to the designers of sensors that are based on centroid measurements to allow them to use thresholding correctly before centroid computation.

We describe a compact adaptive optical system using a spatial light modulator (SLM) as a single element to both measure and compensate optical aberrations. We used a low-cost, off-the-shelf twisted nematic liquid-crystal display (TNLCD) optimally configured to achieve maximum phase modulation with near constant transmittance. The TNLCD acts both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensation element. This adaptive setup is easy to implement and offers great versatility.

It is usual to preprocess data before reduction, but it is not so common to study how this operation affects the final results. Determination of the centroid is a relevant task for many optical measurement devices, and the centroid is very often calculated over thresholded data. The influence of preprocessing thresholding algorithms on the statistical properties of intensity data affected by additive Gaussian noise is described as a different effective additive signal perturbation. Theoretical, simulated, and experimental analyses of the model of the effective noise were performed, and good agreement among the analyses was obtained. Direct extension of the analyses from the influence of preprocessing to centroid determination is also presented.