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In wavefront-driven vision correction, ocular aberrations are often measured on the pupil plane and the correction is applied on a different plane. The problem with this practice is that any changes undergone by the wavefront as it propagates between planes are not currently included in devising customized vision correction. With some valid approximations, we have developed an analytical foundation based on geometric optics in which Zernike polynomials are used to characterize the propagation of the wavefront from one plane to another. Both the boundary and the magnitude of the wavefront change after the propagation. Taylor monomials were used to realize the propagation because of their simple form for this purpose. The method we developed to identify changes in low-order aberrations was verified with the classical vertex correction formula. The method we developed to identify changes in high-order aberrations was verified with ZEMAX ray-tracing software. Although the method may not be valid for highly irregular wavefronts and it was only proven for wavefronts with low-order or high-order aberrations, our analysis showed that changes in the propagating wavefront are significant and should, therefore, be included in calculating vision correction. This new approach could be of major significance in calculating wavefront-driven vision correction whether by refractive surgery, contact lenses, intraocular lenses, or spectacles. OCIS codes: 170.1020, 170.4460, 220.2740, 330.4460, 120.3890.

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, rectangular, and square pupils, due to their lack of orthogonality over such pupils. We emphasize the use of orthonormal polynomials for such pupils, but we show how to obtain the Zernike coefficients correctly. We illustrate that the wavefront fitting with a set of orthonormal polynomials is identical to the fitting with a corresponding set of Zernike polynomials. This is a consequence of the fact that each orthonormal polynomial is a linear combination of the Zernike polynomials. However, since the Zernike polynomials do not represent balanced aberrations for a noncircular pupil, the Zernike coefficients lack the physical significance that the orthonormal coefficients provide. We also analyze the error that arises ifZernike polynomials are used for noncircular pupils by treating them as circular pupils and illustrate it with numerical examples. OCIS codes: 010.1080, 010.7350, 220.1010, 220.3180, 220.0220, 330.4460.

Presbyopia, the gradual loss of accommodation that accompanies aging, can be corrected by creating asphericity in the optical path of the eye. Bifocal and aspheric contact lenses, intraocular lenses, spectacle lenses, and laser refractive surgery are all widely used to alleviate the symptoms of presbyopia. These types of corrective surfaces try to concentrate vision in limited peaks over the full range of vergences. The methodology described in this paper is designed to correct presbyopia by optimizing vision over the entire target range of near to distant. A corrective surface was created by employing an iterative function minimization algorithm to optimize an optical metric. In most cases, it is possible to obtain an optical surface that will optically compensate for presbyopia. OCIS codes: 170.4460, 170.4470, 220.1250, 330.1800, 330.4060, 330.4460.

A study was conducted for the purpose of improving the designs of the next generation of refractive surgical laser systems. Two common refractive laser systems, variable-spot scanning (type A) and small-spot scanning (type B), are discussed by identifying sources of error that could adversely affect the capability of these lasers to accurately produce complex, customized wavefront guided ablations. A mathematical model was used to construct a laser simulator that models the two common laser systems in terms of the root-mean-square error. Error sources from ablation profile fitting, ablation registration, eye tracking, and the laser delivery system are compared, and the relative contribution of each to the overall system error is analyzed. This system-level analysis can be helpful to the improvement of both laser systems. OCIS codes: 140.2180, 170.1020, 170.3890, 170.4460, 170.4470.

The conventional grid-point approach for calculating regional coverage of satellite constellation is time-consuming and inefficient. Based on sampling theory, this paper proposed a sampling grid-point simulation approach, and presented sampling grid-point approach for calculating coverage in two different types of accuracy requirements. Moreover, it proposed the error estimation approach for calculating coverage, which made it possible to quantitatively adjust the grid size to control the computing time and calculation error according to confidence and accuracy requirements and avoid resource waste due to aimless adjustment. Simulation results show that apply the sampling approach to the grid-point approach is feasible and effective. In addition, compared with traditional grid-point approach, the computational efficiency of the proposed algorithm is 81 times faster without decreasing the computational accuracy, which significantly improves the computational efficiency of regional cove-rage. [ABSTRACT FROM AUTHOR]

This paper proposed a new robust evaluation way based on slope which was computed by the three-order inverse distance square weight difference algorithm. Slope index reflected effectively the trend and smoothness of the benchmark functions. Then it designed a multi-objective evolutionary algorithm to solve the robust optimization problems. Simulation experiments verify its effectiveness. The experiments also show the advantages of the method in the distribution and the distinction of solution. [ABSTRACT FROM AUTHOR]

In the later stage of multi-objective evolutionary algorithm, the traditional genetic operation may be invalid, thus the performance of the algorithm will be reduced, while at the early stage of probabilistic modeling, the search direction of the sampling new individuals may be differ from the exact direction for the lack of distribution rule of the population. The paper proposed an entropy-based multi-objective evolutionary algorithm ( EB-MOEA),it used the phenomenon that the population went from disorder to order in the process of evolution. It designed a distribution calculation method and used as the criteria which could guide the switching time of genetic operation and probabilistic modeling operation. The new algorithm adopted ZDT, DTLZ test suits to conduct the comparison experiment with NSGA- II and RM-MEDA, results show that the effectiveness of the new criterion and the proposed algorithm has better optimization performance. [ABSTRACT FROM AUTHOR]

Without taking the heterogeneous grid characteristics into account, Min-Min heuristic can lead to load imbalance. A novel mapping heuristic based on resource's serviceability is proposed in this work. The mapping process is as follows. First, the serviceability of resources to meta-task is calculated and then the meta-task is divided into two groups-prior group and secondary group. Two groups of meta-task are mapped by use of classical Min-Min heuristic, respectively. Under the condition of simulated heterogeneous grid environment with fixed meta- task and resources, the experiments of using classical heuristic and proposed heuristic were conducted to obtain meta-task' makespans. The results show that novel mapping algorithm based on resource's serviceability has shorter makespan under heterogeneous grid environment. [ABSTRACT FROM AUTHOR]