Ophthalmic system for shape determination and modification

A system for modifying an eye, comprising:

• a light source comprising a plurality of light elements;
• a photodetector;
• an optical system for directing light from the light elements reflected by a surface of the eye onto the photodetector, the photodetector configured to produce a signal comprising a plurality of images of at least some of the plurality of light elements, each image corresponding to a location on the surface of the eye, the plurality of images not forming a uniform grid;
• a memory including programming code for processing the signal produced by the photodetector;
• and
• a processor for executing the programming code and outputting shape data for use in calculating a treatment plan for a corneal refractive procedure on the eye;
• wherein the programming code comprises instructions for determining the shape data based on a combination of zonal reconstruction and polynomial fitting using the plurality of images, the zonal reconstruction comprising:
• determining a light pattern from the plurality of images, the light pattern representing the surface of the eye;
• forming a plurality of neighborhoods of vertices based on the light pattern comprising a Delaunay triangulation of the vertices;
• and
• fitting a polynomial to each neighborhood of the plurality of neighborhoods;
• and
• wherein the programming code is further programmed to perform the operations of:
• (a) determining an initial surface location on the cornea for each of the plurality of images;
• (b) calculating initial values for one or more derivatives for each initial surface location;
• (c) forming a plurality of neighborhoods, each neighborhood comprising a set of vertices corresponding to a set of initial surface locations;
• (d) forming a system matrix including all vertices contained in each neighborhood;
• (e) characterizing each vertex contained in each neighborhood by a mathematical relationship including a plurality of parameter coefficients;
• (f) calculating values for each of the plurality of parameter coefficients based on the mathematical relationships of the vertices for all the neighborhoods;
• (g) based on the system matrix and the values for the parameter coefficients, calculating one or more new surface values for at least some of the vertices and new values for at least some of the one or more derivatives for each new surface value;
• (h) comparing one or more of the new values for at least some of the one or more derivatives with the initial values for one or more derivatives and the one or more new surface values with the initial surface values;
• and
• (i) if the comparison meets a predetermined criteria, outputting the shape data, the shape data comprising one or more of:
• at least some of the initial surface values, at least some of the initial values for one or more derivatives, at least some of the one or more new surface values, and at least some of the new values for at least some of the one or more derivatives;
• or if the comparison does not meet the predetermined criteria:
• replacing one or more of the initial surface values with one or more of the one or more new surface values and replacing the one or more initial values for one or more derivatives with one or more of the new values for at least some of the one or more derivatives;
• and
• repeating instructions (e), (f), (g), (h), and (i).