PubMed HealthSearch

PubMed · 9323740

Expressions for aberration coefficients using nonlinear transforms.

Abstract

A matrix method to do nonlinear calculations is described. This is possible only under the special condition when a transformation maps a zero vector onto a zero vector. Geometrical optics conform to this condition and hence matrix methods can be applied to calculate aberrations. Methods to reduce computational complexities using symmetry arguments are provided. The formalism is applied to study refraction by a conic surface. Aberration coefficients, up to fifth order, are obtained as functions of eccentricity and the latus rectum of the conic surface. The method can be used to model corneal aberrations.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

V Lakshminarayanan, S Varadharajan. 1997. Expressions for aberration coefficients using nonlinear transforms.. https://doi.org/10.1097/00006324-199708000-00030

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

Flap complications associated with lamellar refractive surgery.

PURPOSE: Corneal lamellar refractive surgery for myopia reduces the risk of corneal haze but adds to the risk of flap complications. We retrospectively determined the incidence of flap complications in the initial series of eyes undergoing lamellar refractive surgery by one surgeon. We assessed the incidence of flap complications overall, the trend in these complications during the surgeon's learning curve, and the impact of the complications on best spectacle-corrected visual acuity. METHODS: Charts of the first 1,019 eyes that underwent myopic keratomileusis in situ or laser in situ keratomileusis were reviewed for flap complications and visual outcome. RESULTS: Of the 1,019 eyes, 490 eyes underwent myopic keratomileusis in situ, and 529 eyes underwent laser in situ keratomileusis. Eighty-eight (8.6%) of 1,019 eyes had flap-related complications. Six eyes had two complications. Intraoperative complications included irregular keratectomy in nine eyes (0.9%), incomplete keratectomy in three eyes (0.3%), and a free cap in 10 eyes (1.0%). The incidence of intraoperative complications was six (6.0%) in the first 100 consecutive eyes, 14 (2.3%) in the next 600 consecutive eyes (P = .04, chi-square test), and one (0.3%) in the last 300 eyes (P = .03, chi-square test). Postoperative complications included displaced flaps that required repositioning in 20 eyes (2.0%), folds in the flap that required repositioning in 11 eyes (1.1%), diffuse lamellar keratitis in 18 eyes (1.8%), infectious keratitis in one eye (0.1%), and epithelial ingrowth that required removal in 22 eyes (2.2%). The incidence of flap displacement and folds in 200 eyes in which we irrigated under the flap and allowed it to settle without further manipulation averaged 8.5%, whereas the incidence in other groups of 100 consecutive eyes averaged 0.8% (P < .00001, chi-square test). The incidence of diffuse lamellar keratitis was 0.2% in eyes that had undergone myopic keratomileusis in situ and 3.2% in eyes treated by laser in situ keratomileusis (P = .0003, chi-square test). No eye lost 2 or more lines of best spectacle-corrected visual acuity because of flap complications. CONCLUSION: Flap complications after lamellar refractive surgery are relatively common but rarely lead to a permanent decrease in visual acuity. Physician experience with the microkeratome and with the handling of the corneal flap decreases the incidence of flap complications.

Cornea

Posterior corneal surface topographic changes after laser in situ keratomileusis are related to residual corneal bed thickness.

OBJECTIVE: To determine whether ectasia after laser in situ keratomileusis (LASIK) is related to residual corneal bed thickness. DESIGN: Retrospective noncomparative case series. PARTICIPANTS: Thirty-two eyes of 16 patients with refractive errors of -4.00 to -18.00 diopters were examined. INTERVENTION: LASIK was performed. The topography of the posterior corneal surface was examined with the Orbscan slit scanning corneal topography/pachymetry system. MAIN OUTCOME MEASURES: The difference in the elevation of posterior corneal surface regarding the best-fit sphere was measured. RESULTS: After surgery, mean bulge of 17.2 +/- 7.2 microns was found in eyes with residual corneal bed of 250 microns or greater, whereas 41.0 +/- 22.1 microns was seen in eyes with bed thickness less than 250 microns (t = 4.29; P = 0.000). CONCLUSION: Posterior corneal bulge is correlated with the residual corneal bed thickness. The risk of ectasia may be increased if the residual corneal bed is thinner than 250 microns.

Cornea