Justo Arines

Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils

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.

Minimum variance centroid thresholding.

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 techniques performance are given. The direct extension of these results to Shack-Hartmann wave-front sensors is also shown.

Measurement and compensation of optical aberrations using a single spatial light modulator

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.

Influence of thresholding on centroid statistics: full analytical description

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.

Least-squares modal estimation of wrapped phases: application to phase unwrapping

Phase unwrapping continues to be an important step in those techniques that obtain the phase from Fourier transforms. We propose a fast two-dimensional phase-unwrapping algorithm that has been specially designed to be used as part of an iterative algorithm. It can be used also as a final step of a phase retrieval process with other unwrapping techniques. The algorithm consists of a modal least-squares estimation of the wrapped phase by using as inputs to the linear estimation the derivative of the wrapped phase. A theoretical description of the method, simulations, and experimental validations are presented.

Direct and inverse discrete Zernike transform

An invertible discrete Zernike transform, DZT is proposed and implemented. Three types of non-redundant samplings, random, hybrid (perturbed deterministic) and deterministic (spiral) are shown to provide completeness of the resulting sampled Zernike polynomial expansion. When completeness is guaranteed, then we can obtain an orthonormal basis, and hence the inversion only requires transposition of the matrix formed by the basis vectors (modes). The discrete Zernike modes are given for different sampling patterns and number of samples. The DZT has been implemented showing better performance, numerical stability and robustness than the standard Zernike expansion in numerical simulations. Non-redundant (critical) sampling along with an invertible transformation can be useful in a wide variety of applications.

Effective noise in thresholded intensity distribution: influence on centroid statistics

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.

Fabrication and characterization of microlens arrays on soda-lime glass using a combination of laser direct-write and thermal reflow techniques

We describe a hybrid technique for fabricating microlens arrays on soda-lime glass substrates composed by a direct-laser write and a post thermal treatment. In particular we use a nanosecond Q-Switch Nd: YVO4 laser and a mufla Heraeus furnace working in the range of 620 °C−670 °C. An improvement in the quality of the microlens arrays were obtained as temperature increases, reducing their optical aberrations, surface roughness and increasing their resemblance. In particular at 670 °C we obtain high quality microlens array with diameter 47.89 ± 6.65 μm; focal length 510 ± 10 μm; focal spot size 2.82 ± 0.02 μm; a root mean square of the total aberration λ/28 ± λ/77, strehl ratio 0.9475 ± 0.0352 and depth of focus 16.438 ± 5.762 μm. Our results show the reliability of the combination of the Laser-direct writing technique with thermal treatment for fabricating high quality microlens arrays.

Changes of ocular aberrations with gaze

The dependence of the ocular aberrations on gaze has been studied in three eyes using a fast‐acquisition, Hartmann–Shack wavefront sensor. Although there were some trends in the change of some aberration terms with gaze, the changes of most Zernike coefficients were smaller than their variability at each individual gaze position, due to the combined effects of microfluctuations of accommodation, eye movements, tear film dynamics, and measurement noise. For our particular experimental dataset, the confidence level at which the null hypothesis (i.e. that the aberrations do not change significantly with gaze) can be rejected is very low. Further advances in the study of the dependence of eye aberrations with gaze will require a tighter control of the sources of aberration variability at each individual gaze position.

Impact of Liquid Crystals in Active and Adaptive Optics

Active and dynamic modulation of light has been one of major contributions of liquid crystals to Optics. The spectrum of application range from signposting panels to high resolution imaging. The development of new materials is the key to continued progress in this field. To promote this we will present in this paper recent uses of liquid crystals as active or adaptive modulators of light. Besides, we will reflect on their current limitations. We expect with this to contribute to the progress in the field of liquid crystals and thus the development of new useful tools for Active and Adaptive Optics.