Fig. 1. Reverse ray-tracing model of simplified FOA system

Fig. 2. Structure of crystal. (a) Cutting orientation of KDP crystal; (b) optical axis direction of KDP crystal

Fig. 3. Reverse ray-tracing process of KDP crystal

Fig. 4. Simulation of ray-tracing. (a) Forward ray-tracing; (b) reverse ray-tracing

Fig. 5. System simulation results after removing the first four terms of Zernike polynomials without additional surface shapes. (a) Wavefront aberration for forward ray-tracing of o light; (b) wavefront aberration for reverse ray-tracing of o light; (c) difference between Figs.5(a) and (b); (d) wavefront aberration result for forward ray-tracing of e light; (e) wavefront aberration result for reverse ray-tracing of e light; (f) difference between Figs.5 (d) and (e)

Fig. 6. Simulated crystal surface shapes and coordinate distributions of o and e light at exit surface. (a) Front surface shape of crystal; (b) rear surface shape of crystal; (c) coordinate distribution before introducing surface shape; (d) coordinate distribution after introducing surface shape

Fig. 7. System simulation results after removing the first four terms of Zernike polynomials with additional surface shapes. (a) Wavefront aberration for forward ray-tracing of o light; (b) wavefront aberration for reverse ray-tracing of o light; (c) difference between Figs.7(a) and (b); (d) wavefront aberration result for forward ray-tracing of e light; (e) wavefront aberration result for reverse ray-tracing of e light; (f) difference between Figs.7 (d) and (e)

Fig. 8. Experimental setup

Fig. 9. Experimental images. (a) Unloaded fringe pattern; (b) distorted fringe pattern; (c) crystal birefringence pattern

Fig. 10. Simulation and theoretical results of system after removing the first four terms of Zernike polynomials. (a) Simulated wavefront aberration of o-light; (b) simulated wavefront aberration of e-light; (c) theoretical wavefront aberration of o-light; (d) theoretical wavefront aberration of e-light

Fig. 11. Experimental and simulation results of system after removing the first four terms of Zernike polynomials. (a) Experimental wavefront aberration of o light; (b) experimental wavefront aberration of e light; (c) simulated wavefront aberration of o light; (d) simulated wavefront aberration of e light

Fig. 12. Wavefront aberration of single lens and surface shapes of frequency doubling crystal. (a) Wavefront aberration of lens after removing the first four terms of Zernike polynomials; (b) front surface shape; (c) rear surface shape