| 主权项 |
1. A method for designing a three-dimensional freeform surface, the method comprising:
step (S1), establishing an initial surface and a first three-dimensional rectangular coordinates system; step (S2), selecting a plurality of feature rays Ri (i=1, 2 . . . K); step (S3), calculating a plurality of feature data points Pi (i=1, 2 . . . K) of a first freeform surface point by point based on a given object-image relationship or a given light mapping relationship and a vector form of the Snell's law; step (S4), fitting the plurality of feature data points Pi (i=1, 2 . . . K) into a sphere in the first three-dimensional rectangular coordinates system; defining a feature data point (xo, yo, zo) corresponding to a chief ray of a central field angle among an entire field-of-view as a vertex of the sphere; and defining a second three-dimensional rectangular coordinates system by the vertex of the sphere as origin, and a line passing through a center of curvature and the vertex of the sphere as a Z′-axis; step (S5), transforming a plurality of first coordinates (xi, yi, zi) and a plurality of first normal vectors (αi, βi, γi), of the plurality of feature data points Pi (i=1, 2 . . . K), in the first three-dimensional rectangular coordinates system into a plurality of second coordinates (x′i, y′i, z′i) and a plurality of second normal vectors (a′i, β′i, γ′i) in the second three-dimensional rectangular coordinates system; fitting the plurality of feature data points Pi (i=1, 2 . . . K) into a conic surface in the second three-dimensional rectangular coordinates system; removing a plurality of third coordinates and a plurality of third normal vectors of the plurality of feature data points Pi (i=1, 2 . . . K), on the conic surface in the second three-dimensional rectangular coordinates system, from the plurality of second coordinates (x′i, y′i, z′i) and the plurality of second normal vectors (α′i, β′i, γ′i), to obtain a plurality of residual coordinates and a plurality of residual normal vectors; and surface fitting the plurality of residual coordinates and the plurality of residual normal vectors to obtain a second freeform surface; adding a first equation of the conic surface and a second equation of the second freeform surface to obtain a third equation of the first freeform surface; and step (S6), taking the first freeform surface as the initial surface for an iteration process, to obtain the three-dimensional freeform surface. |
