Wavefront Aberration Coefficients Research Articles

Optical Quality Variation of Different Intraocular Lens Designs in a Model Eye: Lens Placed Correctly and in an Upside-Down Position

Introduction: Intraocular lenses (IOLs) may lose their optical quality if they are not correctly placed inside the capsular bag once implanted. One possible malpositioning of the IOL could be the implantation in an upside-down position. In this work, three aspheric IOLs with different spherical aberration (SA) have been designed and numerically tested to analyse the optical quality variation with the IOL flip, and misalignments, using a theoretical model eye. Methods: Using the commercial optical design software OSLO, the effect of decentration and tilt was evaluated by numerical ray tracing in two conditions: in their designed position and flipped with respect to the planned position (IOL is implanted upside down). The theoretical model eye used was the Atchison model eye. Seven IOL designs of +27.00 diopters were used: a lens with negative SA to correct the corneal SA, a lens to partially correct the corneal SA, and a lens to not add any SA to the cornea (aberration-free IOL). These lenses were designed with the aspherical surface located on the anterior and posterior IOL surface. A lens with no aspherical surfaces was also included. For the optical quality analysis, the modulation transfer function (MTF) was used, together with the Zernike wavefront aberration coefficients of defocus, astigmatism, and primary coma. Results: Off-centring and tilting the IOL reduced overall MTF values and increased wavefront aberration errors. With the IOL correctly positioned within the capsular bag, an aberration-free IOL is the best choice for maintaining optical quality. When the IOL is flipped inside the capsular bag, the optical quality changes, with the aberration-free IOL and the IOL without aspheric surfaces providing the worst results. With the lens in an upside-down position, an IOL design to partially correct corneal SA shows the best optical quality results in decentration and tilt, in terms of MTF and wavefront aberrations. Conclusion: The aberration-free IOL is the best choice when minimal postoperative errors of decentration or tilt are predicted. With IOL flip, the negative SA lens design is the best choice, regarding the root mean square wavefront aberrations. However, in a proper IOL implantation, the IOL designed to partially compensate the corneal SA including asphericity on its posterior surface is the better possible option, even in the presence of decentration or tilt.

Structural Topology Optimization of Reflective Mirror Based on Objective of Wavefront Aberration

Due to the increasing requirements for the imaging quality of optical systems, the design method for optical–mechanical structures has become a research hotspot in recent decades. To improve the imaging performance of the reflective system, it is often necessary to increase the aperture of the mirror. To meet the imaging quality and lightweightedness requirements of the mirror, the topology optimization method aiming at the minimization of wavefront aberration is proposed. The optical–mechanical coupling relationship is established by ray tracing of the deformed mirror surface fitted by orthogonal bases. The topology optimization model is established by the solid isotropic material with penalization model (SIMP). Additionally, the adjoint method is used to analyze the sensitivity of the objective and the constraints. To illustrate the rationality and effectiveness of the method, the mirrors of the Cassegrain system have been optimized under the action of gravity with the objective of the weighted sum of squares of wavefront aberration coefficients under the constraints of the mass of the design domain, the rigid body displacement of the mirror surface, and the residual of deformation fitting. The results show that the proposed method can effectively improve imaging performance under the condition of satisfying the constraints. In addition, the optimization method with wavefront aberration as the objective is a concrete application of the idea of opto-mechanical integration, which can improve optical performance more directly and effectively.

Alternative method for computing primary wavefront aberrations using Taylor series expansion of optical path length

This work proposes a methodology for computing the primary wavefront aberration coefficients of axis-symmetrical optical systems by expanding the optical path length of a general ray using the Taylor series expansion. The obtained values of the wavefront aberration coefficients are compared with those determined from Zemax simulations. It is shown that the corresponding numerical results are in excellent agreement with those obtained from Zemax simulations.

Modal-based nonlinear optimization algorithm for wavefront measurement with under-sampled data.

The aliasing effect in the discrete Fourier transform inherent will impose a serious detrimental effect on conventional phase retrieval measurement accuracy with under-sampled intensity. In this Letter, we describe a modal-based nonlinear optimization phase retrieval approach that is capable of retrieving wavefront measurements using under-sampled intensities. The extended Nijboer-Zernike theory is introduced to establish an analytic solution between wavefront phase and intensity image, and then nonlinear optimization is further utilized to solve wavefront aberration coefficients from under-sampled intensity data. The feasibility and accuracy of the algorithm are verified by simulations and experiments. This is a promising method that is especially suitable for full field phase recovery of optical systems with a relatively high numerical aperture.

Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey–Chrétien telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

Geometrical irradiance changes in a symmetric optical system

The concept of the aberration function is extended to define two functions that describe the light irradiance distribution at the exit pupil plane and at the image plane of an axially symmetric optical system. Similar to the wavefront aberration function, the irradiance function is expanded as a polynomial, where individual terms represent basic irradiance distribution patterns. Conservation of flux in optical imaging systems is used to derive the specific relation between the irradiance coefficients and wavefront aberration coefficients. It is shown that the coefficients of the irradiance functions can be expressed in terms of wavefront aberration coefficients and first-order system quantities. The theoretical results—these are irradiance coefficient formulas—are in agreement with real ray tracing.

Zernike phase spatial filter for measuring the aberrations of the optical structures of the eye

To measure directly the wavefront aberration coefficients, we propose to use the multi-order diffractive element fitted with the set of Zernike polynomials. Polynomials of lowest degree describe defocusing (ametropy) and astigmatism. Coefficients of highest degree correspond to the spherical aberration of oblique rays that occurs as a consequence of misalignment of the crystalline lens and foveola, as well as deflection at the periphery of the crystalline lens. Multi-order elements allow several tens of expansions coefficients to be measured simultaneously, which will enable to investigate insufficiently known high-order aberrations for the differentiated diagnostics of eye diseases.

Pupil scaling for the estimation of aberrations in natural pupils.

This study aimed to validate the mathematical Zernike pupil size scaling from bigger pupils to smaller pupils, and vice versa, by comparing the estimates of the Zernike coefficients with corresponding clinical measurements obtained at different pupil sizes. The i.Profiler Plus (Carl Zeiss Vision, Inc, USA) was used to obtain measures of wavefront aberrations for two pupil sizes (3 mm and the maximum natural pupil size) from the right eyes of 28 visually normal subjects (mean [±SD] age, 57 [±7] years) whose maximum pupil size was greater than or equal to 5 mm without pharmacological dilation. Zernike coefficients were estimated for a 3-mm pupil size scaling down from the measured data of the maximum natural pupil size and, similarly, for the maximum pupil size scaling up from the measured data of the 3-mm pupil. The differences between the estimated and measured values were not significantly different (repeated-measures analysis of variance; p > 0.05) over the range of pupil sizes examined, irrespective of whether the estimates were made by scaling up from a small pupil or scaling down from a large pupil. However, the difference between the measured and estimated coefficients was more variable and less systematic when scaling to a larger pupil size when compared with scaling to a smaller pupil size. Estimation of ocular wavefront aberration coefficients either scaling down from large to smaller pupils or scaling up from smaller to large pupils provides estimates that are not significantly different from clinically measured values. However, when scaling up to a larger pupil size, the estimates are more variable. These findings have implications for pupil scaling on an individual basis, such as in cases of refractive surgery or when using pupil scaling to examine a clinical cohort.

Aberration analysis and efficiency improvement of a bidirectional optical subassembly

An approach to improve the coupling efficiency of bidirec- tional optical subassembly BOSA modules is proposed and experimen- tally demonstrated. We analyzed the wavefront aberration coefficients of a typical BOSA. It was found that the 45-deg wavelength filter induces coma and astigmatism, and then it further deteriorates the laser diode to fiber coupling. We measured the BOSA efficiencies based on a series of different filters. For a typical 0.5-mm filter, 25% coupling efficiency im- provement was achieved by optimizing the filter parameters. © 2009 Soci-

Wave-front measurement errors from restricted concentric subdomains.

In interferometry and optical testing, system wave-front measurements that are analyzed on a restricted subdomain of the full pupil can include predictable systematic errors. In nearly all cases, the measured rms wave-front error and the magnitudes of the individual aberration polynomial coefficients underestimate the wave-front error magnitudes present in the full-pupil domain. We present an analytic method to determine the relationships between the coefficients of aberration polynomials defined on the full-pupil domain and those defined on a restricted concentric subdomain. In this way, systematic wave-front measurement errors introduced by subregion selection are investigated. Using vector and matrix representations for the wave-front aberration coefficients, we generalize the method to the study of arbitrary input wave fronts and subdomain sizes. While wave-front measurements on a restricted subdomain are insufficient for predicting the wave front of the full-pupil domain, studying the relationship between known full-pupil wave fronts and subdomain wave fronts allows us to set subdomain size limits for arbitrary measurement fidelity.

Analytical expressions for the wave-front aberration coefficients of a tilted plane-parallel plate

An expression is given for the aberration imparted by a tilted plane-parallel plate to a converging or diverging pencil of rays. Analytical expressions for the wave-front aberration coefficients up to the sixth order are derived. These expressions, among others, are of importance when reading an optical disk through its substrate or when using a plane-parallel plate as a beam splitter. Differences with previous expressions from the literature are noted.

Aberrations of holographic toroidal grating systems

Expressions are derived for the sixteen wave front aberration coefficients of a single grating. These give the wave aberrations to the fourth order for a plane symmetric grating system. The contributions from each mirror and grating can be added to give the aberrations in the final image. Problems encountered with intermediate astigmatic images are overcome by defining the wave front aberration with respect to an astigmatic reference surface. There is one field variable describing displacement of the object point from the symmetry plane. The aperture stop may be placed anywhere in the system, and equations are given for the aberration changes produced by shifting this position.

A New Derivation of Third-Order Aberration Coefficients

The Feder expressions for four third-order aberration coefficients, namely, B for spherical aberration, F for coma, C for astigmatism, E for distortion, and the Petzval curvature P, are derived by a new and direct method based on the wavefront concept and with the use of rather elementary means of geometry and algebra. Their relation with the wavefront aberration coefficients is given.