| CPC G03H 1/0808 (2013.01) | 4 Claims |
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1. A method for calibrating substrate errors of computer-generated hologram c based on a ray propagation in three-dimensional model, comprising the following steps:
step 1, establishing three-dimensional ray propagation models according to different optical paths, comprising:
step 1.1, according to an optical path, confirming an F number of a standard spherical lens used and a radius of a curvature of a reference spherical surface of the standard spherical lens, a distance between a non-holographic surface of a computer-generated hologram and a focus of the standard spherical lens, a thickness and a refractive index of a substrate of the computer-generated hologram, and a distance between a holographic surface of the computer-generated hologram and an aspheric surface;
step 1.2, defining a mode of emitting rays wherein a rays emits from a focus O of the standard spherical lens, and the ray in a propagation process satisfies:
ri(x,y,p)=pNi(x,y)+Pi(xi,yi,pi);
where ray ri represents that in an ith segment of the ray, the ray propagates along a direction Ni(x,y) of the ith segment and passes through a point Pi; p is a distance in which the ray propagates in the optical path; x, y represents a spatial coordinate of the ray when propagating in a free space; and xi, yi, pi represents a spatial coordinate of the point Pi through which in the ith segment, the ray propagates in the free space;
step 1.3, calculating a propagation trajectory of the ray in the optical path;
after the ray is refracted through the non-holographic surface of the computer-generated hologram, a propagation direction is:
 where N0 is an incident direction of the ray; e is a ratio of the refractive indexes of an incident space and an emitting space; (α1, β1, γ1) is the cosine of an angle between a vector of a propagation direction of the ray and a Cartesian coordinate axis; and C0,f, D0,f are intermediate constants which satisfy the following relation:
 where dot represents a dot product between vectors;
Nf (x,y) is a surface normal of the non-holographic surface at (x, y), expressed as:
 where F is a surface equation indicating a surface at which a surface normal is obtained;
after the ray propagates to the holographic surface of the computer-generated hologram and is diffracted, the propagation direction of the diffracted ray of +1 level satisfies:
 where Nh(x,y) is a surface normal of the holographic surface at (x,y), Φ is an equivalent phase equation of the computer-generated hologram, and A is a wavelength; and C0,h, D0,h are intermediate constants, which satisfy the following relation:
 the propagation direction of the ray after reflection at the aspheric surface (x,y) satisfies:
N′(x,y)=N0−2[N0·N0(x,y)]N0(x,y);
where N′(x,y) represents the propagation direction of the ray after reflection at the aspheric surface; and Nα (x,y) is a surface normal of the aspheric surface at (x,y);
step 1.4, calculating a coordinate Pi of an intersection of the ray on a surface of an ith medium:
 where α1 and β1 are the cosine components of the propagation directions of the ray after passing through a previous surface, and xi-1, yi-1 is the coordinate of the intersection Pi-1 of the ray at the previous surface;
step 2, obtaining surface shape errors of a front surface and a rear surface of the substrate of the computer-generated hologram, and thickness uniformity of the substrate of the computer-generated hologram to calibrate substrate errors of the computer-generated hologram based on the three-dimensional ray propagation models, comprising:
step 2.1, obtaining shapes of the front and the rear surfaces and the thickness uniformity of the computer-generated hologram in a working condition;
step 2.2, according to the three-dimensional ray propagation models and the measurement results of the front and the rear surfaces and the thickness uniformity of the computer-generated hologram in step 1, calculating a propagation trajectory of the ray from any field of view coming from the focus of the standard spherical lens in the optical path, and calculating a difference from a propagation trajectory in an ideal condition to obtain an optical path difference ΔOPD caused by the substrate error of the computer-generated hologram; and meanwhile, recording the intersection of the ray in the computer-generated hologram;
step 2.3, according to the intersection of the ray in the computer-generated hologram, calculating an additional diffraction wave aberration ΔW caused by the deviation of the propagation trajectory of the ray on the holographic surface of the computer-generated hologram based on:
 where (x′1, y′1) represents an ideal position coordinate of the ray on the computer-generated hologram, and Δx1 and Δy1 are deviations of the ray between an actual position and a theoretical position of the computer-generated hologram;
step 2.4, calculating a measurement wave aberration ΔR caused by the substrate error of the computer-generated hologram based on:
 where ΔW and ΔW′ are additional diffraction wave aberrations caused by that the ray penetrates through the holographic surface of the computer-generated hologram for the first and second times respectively.
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