Objective Simultaneous modulation of beam intensity and wavefront with freeform surfaces is widely used in illumination optics and imaging optics. The current method of simultaneous modulation of beam intensity and wavefront is generally aimed at vertical-axis optical systems. However, the optical system generally has an off-axis layout to achieve a compact optical structure. In this paper, we proposed a method to design freeform surfaces to realize simultaneous modulation of beam intensity and wavefront on the tilted target plane.
Methods Firstly, a virtual observation plane perpendicular to the optical axis is set up, and the mapping relationship between the specific irradiance distribution on the target off-axis observation plane and the corresponding irradiance distribution on the vertical axis virtual observation plane is established. Then the Monge–Ampère (MA) equation with nonlinear boundary conditions for the vertical virtual plane is established according to Snell's law, local energy conservation law, and optical path conservation constraints. Then the finite difference method is used to solve the beam control model of vertical axis layout, and the numerical solutions of beam intensity and wavefront modulation of freeform surface on the off-axis observation plane are obtained. Finally, the Monte Carlo ray tracing method is used to verify the effectiveness of the designed freeform surface.
Results and Discussion The design example is to use two freeform surfaces to shape a Lambertian point source into a uniform square irradiance distribution on an off-axis target plane, the shaped beam is a divergent spherical wave, and the off-axis target surface has an inclination angle of 30 degrees. The obtained surfaces are intricate but smooth, continuous, and easy to fabricate. Researchers use 10 million rays for Monte Carlo tracing to verify the effectiveness of the designed lens. The irradiance distribution on the target plane demonstrates the effectiveness of the modulation of beam intensity, with the irradiance error RMS=0.0117. The analysis of the outgoing wavefront and the simulation results at different distances verify the effectiveness of the modulation of the beam wavefront.
Conclusion Simultaneous modulation of beam intensity and wavefront is a challenging but worth exploring problem. In this paper, the efficient and accurate modulation of beam intensity and wavefront under an inclined optical path layout is realized by establishing the mapping transformation of off-axis irradiance distribution to vertical irradiance distribution. This method breaks the restriction of vertical optical path layout and obtains a flexible optical path layout, which plays an active role in promoting the wide application of freeform surface beam modulation. This method uses only two freeform surfaces to realize efficient and flexible modulation of beam intensity and wavefront, which will promote the beam control system towards the direction of comprehensive function and compact system.
DownLoad: