Ophthalmic method for shape determination and modification
Systems and methods for modifying an eye including a light source with light elements, a photodetector producing a signal representing images of the light elements and corresponding to locations on an ocular surface, an optical system directing light from the light elements reflected by the ocular surface onto the photodetector, a memory including code for processing the signal, and a processor for executing the code and outputting shape data for use in calculating a treatment plan for the eye. The code includes instructions for determining the shape data based on a combination of zonal reconstruction and polynomial fitting using the plurality of images.
1. A method of shape determination for a surface of an eye, the method comprising the steps of:
directing a pattern of light, from a light source, onto the eye
sensing a light pattern, by a photodetector, based on a plurality of images reflected from the surface of the eye, each image corresponding to a location on the surface of the eye; and
determining, by a processor, shape data corresponding to the surface of the eye based on a combination of zonal reconstruction and polynomial fitting using the light pattern having the plurality of images,
wherein determining shape data comprises:
(a) determining an initial surface location 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 which is a polynomial function 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 locations for at least some of the vertices and new values for at least some of the one or more derivatives for each new surface location;
(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 locations with the initial surface locations; 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 locations, at least some of the initial values for one or more derivatives, at least some of the one or more new surface locations, 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 locations with one or more of the one or more new surface locations 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 steps (e), (f), (g), (h), and (i).
2. The method of claim 1 , further comprising filtering unwanted neighborhoods from the plurality of neighborhoods after step (c) and before step (d).
3. The method of claim 2 , wherein each neighborhood of the plurality of neighborhoods comprises a triangle of vertices, and wherein the filtering unwanted neighborhoods comprises:
determining a subset of neighborhoods of the plurality of neighborhoods that have an angle less than a predetermined angle; and
replacing at least some of the neighborhoods of the subset of neighborhoods with a different neighborhood, the different neighborhood lacking the angle less than the predetermined angle.
4. The method of claim 1 , wherein the forming a plurality of neighborhoods comprises a Delaunay triangulation of the vertices.