We previously proposed an iterative wavefront tailoring (IWT) method [Optics Letters 44(9): 2274-2277] to solve the freeform lens design problem for irradiance tailoring, where the entrance surface can be predefined as a spherical, aspherical or freeform surface. Here, this method is adapted to address a more challenging design problem where the exit surface is predefined. We design a freeform lens with a fixed aspherical exit surface to demonstrate the effectiveness of the modified method.
High-precision phase reconstruction is crucial for beam analysis and control. In a previous work, we proposed a phase retrieval method based on the Monge-Ampère equation (MAE). Similar to the commonly-used transport of intensity equation (TIE), the MAE is also a partial differential equation (PDE) that describes the relationship between irradiance and phase. However, in the framework of geometric optics, the MAE could be a more accurate and general method for solving the phase retrieval problem compared to the TIE. In this paper, we apply the MAE to reconstruct the field of a laser beam. By capturing two irradiance distributions at two different planes that are perpedicular to the propagation direction, the complex amplitude distribution at the first plane can be retrieved based on the MAE method. The angular spectrum method is employed to determine the complex amplitude distributions at different positions along the beam propagation direction. The factor of the laser beam is calculated based on the reconstructed beam field. Results show that the factor values computed based on the MAE method have small deviations from that tested with a commercial beam profiler.
We previously optimized the freeform surfaces using extended polynomials in stereographic projection coordinates based on an automated workflow linking the optimization engine, 3D modeling software and ray tracing software [Optics Express 29(9), 13469–13485 (2021)]. However, this method is time consuming as it needs thousands of irradiance evaluations. Here, we speed up the optimization of spherical-freeform lenses for uniform illumination based on differentiable ray tracing. The freeform surface is still parameterized with the ‘uv’ extended polynomials under stereographic projection coordinates, which is suitable for generating simple illumination patterns. We implement differentiable ray tracing based on computation graph in MindSpore framework, which is efficient and effective by calculating derivatives of the surface parameters during a single backpropagation. We provide two design examples for generating uniform irradiance distributions with a point-like source and an extended light source, respectively.
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