Light patterns for corneal topography

A method, comprising:

• determining, by one or more processors of a control unit for a head-mounted assembly, an illumination pattern to be projected over a sequence of frames onto an eye of a user wearing the head-mounted assembly, wherein:
• the sequence of frames includes a first frame and a second frame;
• the first frame includes a first pattern of dots;
• the second frame includes a second pattern of dots;
• the first pattern and the second pattern are non-rectilinear patterns configured to become substantially rectilinear approximations of one or more corresponding reference patterns when reflected off an eye-shaped surface, wherein each reference pattern comprises dots arranged according to a two-dimensional grid having straight lines that define rows and columns in which the dots are arranged, and wherein each non-rectilinear pattern represents a transformation of a corresponding reference pattern to distort the lines of the two-dimensional grid;
• and
• the first pattern differs from the second pattern with respect to a wavelength of light used to project one or more dots, a position of one or more dots, or both;
• after determining the illumination pattern, causing, by the control unit, one or more illuminators in the head-mounted assembly to project the illumination pattern over the sequence of frames and onto the eye of the user;
• and
• calculating, by the one or more processors, an eye model based on reflections of the illumination pattern as projected over the sequence of frames and onto the eye of the user, wherein the eye model characterizes a topography of a cornea of the eye of the user.