This paper explores the use of Spherical Harmonics to represent the reflectance function of a 3D surface with known geometry. It is shown that reflectance can be conceived of as a convolution in the angular domain. Spherical Harmonics are used to define a frequency domain in which convolution in the angular domain is equivalent to multiplication in the spherical harmonic frequency domain. This ...

purpose: to report the results of photorefractive keratectomy (prk) with mitomycin-c (mmc) to correct myopia and astigmatism in patients who had previously undergone penetrating keratoplasty (pkp). methods: thirty-eight eyes of 32 patients underwent prk with mmc to correct astigmatism and myopia following pkp. result: mean spherical equivalent (se) was -5.2±4.7 d (diopter) and mean astigmatism ...

In the framework of the teleparallel equivalent of general relativity, we obtain the evolution equation of the neutrino oscillation in vacuum. A comparison with the equivalent result of general relativity case, shows that the Dirac equation in Riemann and Weitzenböck spacetimes is equivalent in the spherical symmetric Schwarzschild spacetime, but turns out to be different in the case of the axi...

We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...

METHODS: In this consecutive case series, patients underwent phacoemulsification and bilateral or unilateral IOL implantation with the M-flex T IOL (Rayner Intraocular Lenses Ltd.). All underwent refractive assessment and corneal topography preoperatively and postoperatively. Outcome measures included uncorrected distance VA, spherical and cylindrical refraction, and spherical equivalent (SE) (...

We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...

This paper is concerned with proving the existence of solutions to an underdetermined system of equations and with the application to existence of spherical t-designs with (t+ 1)2 points on the unit sphere S2 in R3. We show that the construction of spherical designs is equivalent to solution of underdetermined equations. A new verification method for underdetermined equations is derived using B...

AIMS To report the results of a series of patients who were treated with LASIK to correct post penetrating keratoplasty ametropia. METHODS 26 eyes of 24 patients underwent LASIK to correct astigmatism and myopia after corneal transplantation; 14 eyes also received arcuate cuts in the stromal bed at the time of surgery. The mean preoperative spherical equivalent was -5.20D and the mean preoper...

PURPOSE The purpose of this study was to assess predictability, efficacy, safety and stability in patients who received a toric implantable collamer lens to correct moderate to high myopic astigmatism. METHODS Forty-three eyes of 23 patients underwent implantation of a toric implantable collamer lens (STAAR Surgical Inc) for astigmatism correction. Mean spherical refraction was -4. 98 ± 3.49 ...