Biomedical subjects

Guang-Ming Dai

Publications and source records attributed to Guang-Ming Dai.

6 recordsLinked to original sources

PubMed2007

Nonrecursive determination of orthonormal polynomials with matrix formulation.

A general theoretical approach has been developed for the determination of orthonormal polynomials over any integrable domain, such as a hexagon. This approach is better than the classical Gram-Schmidt orthogonalization process because it is nonrecursvie and can be performed rapidly with matrix transformations. The determination of the orthonormal hexagonal polynomials is demonstrated as an example of the matrix approach.

Journal Article↗

PubMed2007

Zernike annular polynomials and atmospheric turbulence.

Imaging through atmospheric turbulence by systems with annular pupils is discussed using the Zernike annular polynomials. Fourier transforms of these polynomials are derived analytically to facilitate the calculation of variance and covariance of the aberration coefficients. Zernike annular shape functions are derived and used to calculate the Strehl ratio and the residual phase structure and mutual coherence functions when a certain number of modes are corrected using, say, a deformable mirror. Special cases of long- and short-exposure images are also considered. The results for systems with a circular pupil are obtained as a special case of the annular pupil.

Journal Article↗

PubMed2006

Optical surface optimization for the correction of presbyopia.

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.

Animals↗

PubMed2006

System performance evaluation of refractive surgical lasers: a mathematical approach.

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.

Computer Simulation↗

PubMed2006

Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation.

The set of Fourier series is discussed following some discussion of Zernike polynomials. Fourier transforms of Zernike polynomials are derived that allow for relating Fourier series expansion coefficients to Zernike polynomial expansion coefficients. With iterative Fourier reconstruction, Zernike representations of wavefront aberrations can easily be obtained from wavefront derivative measurements.

Journal Article↗

PubMed2006

Comparison of wavefront reconstructions with Zernike polynomials and Fourier transforms.

PURPOSE: To make a direct comparison between Fourier and Zernike reconstructions of ocular wavefronts using a newly available analytical theory by which Fourier coefficients can be converted to Zernike coefficients and vice versa. METHODS: Noise-free random wavefronts were simulated with up to the 15th order of Zernike polynomials. For each case, 100 random wavefronts were simulated separately. These wavefronts were smoothed with a low-pass Gaussian filter to remove edge effects. Wavefront slopes were calculated, and normally distributed random noise was added within the circular area to simulate realistic Shack-Hartmann spot patterns. Three wavefront reconstruction methods were performed. The wavefront surface error was calculated as the percentage of the input wavefront root mean square. RESULTS: Fourier full reconstruction was more accurate than Zernike reconstruction from the 6th to the 10th orders for low-to-moderate noise levels. Fourier reconstruction was found to be approximately 100 times faster than Zernike reconstruction. Fourier reconstruction always makes optimal use of information. For Zernike reconstruction, however, the optimal number of orders must be chosen manually. The optimal Zernike order for Zernike reconstruction is lower for smaller pupils than larger pupils. CONCLUSIONS: Fourier full reconstruction is faster and more accurate than Zernike reconstruction, makes optimal use of slope information, and better represents ocular aberrations of highly aberrated eyes.

Corneal Topography↗