In this letter we present a method to design the freeform surfaces of an off-axis unobscured two-mirror telescope by integration of a system of differential equations. The system is derived from the differentiation of the Fermat path's principle and is integrated as an ordinary differential equation problem. The method is used to design the freeform surfaces of a telescope whose performance is verified in off-the-shelf optical design software (Zemax).
Optical design relies on ray tracing to evaluate and optimize the performance of optical systems. Differential ray tracing, in which the ray properties are calculated together with their derivatives, has been shown to be of interest to improve the accuracy and speed of common optical design tasks. We present in this paper an algorithm capable of performing differential ray tracing in the general case. This algorithm is not constrained by a specific optical system geometry such as rotational symmetry or restricted to a set of surface definitions (e.g., conics, polynomial aspheres).
In this paper we propose a new method to jointly design a sensor and its neural-network based processing. Using a differential ray tracing (DRT) model, we simulate the sensor point-spread function (PSF) and its partial derivative with respect to any of the sensor lens parameters. The proposed ray tracing model makes no thin lens nor paraxial approximation, and is valid for any field of view and point source position. Using the gradient backpropagation framework for neural network optimization, any of the lens parameter can then be jointly optimized along with the neural network parameters. We validate our method for image restoration applications using three proves of concept of focus setting optimization of a given sensor. We provide here interpretations of the joint optical and processing optimization results obtained with the proposed method in these simple cases. Our method paves the way to end-to-end design of a neural network and lens using the complete set of optical parameters within the full sensor field of view.
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