J. Eur. Opt. Society-Rapid Publ. 2026, 22, 42 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026024 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Automatic search for cemented doublets using the saddle point construction method Hugo Maurey 1, 2,*
, Patrice Twardowski 1, Robin Pierron 2, Philippe Gérard 1, and Manuel Flury 1 1 ICube, Université de Strasbourg, CNRS, INSA, F-67000 Strasbourg, France 2 Optiive, 300 Boulevard Sebastien Brant, 67400 Illkirch-Graffenstaden, France
Received 4 December 2025 / Accepted 8 March 2026
Abstract. Conventional optical design relies on iterative and time-consuming optimization methods. Finding the right starting system facilitates the design of relevant optical systems. It has been demonstrated that Saddle Point Construction Method( SPCM) can be used to design innovative optical systems based on pre-existing systems, or from scratch. This paper presents the results of a Python program using Code V’ s Application Programming Interface( API) and applying the special version of SPCM to automatically design optical systems using a reduced glass map. To illustrate its robustness, cemented doublets have been automatically designed. A reduced glass map with thirty-four Schott glasses was combined with the SPCM for the design of 68 achromatic cemented doublets. They were then compared with achromatic cemented doublets from well-known manufacturers and with those described in the literature using a semi-analytical approach. The achromatic cemented doublets were first designed with a total field of view( FOV) of 0 ° and were subsequently designed with a FOV of 5 °. The best achromatic cemented doublets obtained performed better or as well as existing achromatic cemented doublets.
Keywords: Optical Design, Optimization method, Saddle Point Construction Method, CODE V, Python, Reduced Glass Map.
1 Introduction
The design of an optical imaging system combines a set of optical constraints( focal length, numerical aperture, used wavelengths, etc.), a set of mechanical constraints( total system dimensions, minimum lens center thicknesses, etc.) and a set of variables( radii of curvature, center thicknesses, distances between lenses, optical materials, etc.). To characterize the system, a relevant merit function that includes optical and mechanical constraints and evaluates one or more optical performance parameters useful for solving the design problem must be defined( e. g. geometric image spot diameter, Modulation Transfer Function( MTF) modulus values at certain spatial frequencies, etc.). The design objective is then to find the set of variables that minimizes the merit function. However, the merit function is a non-convex function and is therefore very sensitive to the chosen initial system or starting point. The development of increasingly powerful computers and commercial optical design software, such as Code V and Zemax with local and global optimization procedures, has accelerated the pace of optical design
* Corresponding author: hugo. maurey @ etu. unistra. fr with increasingly complex and high-performance systems. The optimization of optical systems is a non-linear problem, and as a result, searching for one or several local minima in the design landscape becomes a challenge [ 1 ]. A lens design method from scratch has been suggested by H. Sun [ 2 ], but this method is iterative and time-consuming. Having a good starting point facilitates the design of a relevant system. The selected or created starting point differs depending on the constraints and the designer’ s strategies. The most common way to find a starting point is to use a previous design close to the constraints of the system through patents, articles, or databases. When none of these approaches is feasible, the designer must create a starting system from scratch based on their own experience, knowledge or wisely chosen algorithm for its creation. For instance a method to automatically generate an initial configuration without a starting point based on the Delano diagram was proposed in [ 3 ]. A method using a Deep Neural Network( DNN) framework has been proposed for automatically generating an initial starting system [ 4 ]. A drawback of deep learning is that it requires large databases for training. An overview of AI techniques used in optical design has been carried out by Yow et al. [ 5 ]. However, these methods have been mainly developed for spherical systems. New design methods taking
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