Automating optical design

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Optical design has traditionally required large amounts of complex calculations to be performed. This can now be automated.

(Image: Zhang et al.)

Optical imaging systems have been playing an essential role in scientific discovery and societal progress for several centuries. Since the early days of optical design, scientists and engineers have relied on aberration theory and performing large amounts of complex calculations to describe and quantify the deviation of light rays from the ideal focusing of an imaging system. Thus mathematical skills have previously been a very important requirement in the field of optical design.

Computers have since freed people from such heavy calculation tasks, and have helped realise fast ray tracing and the solving of complex aberration equations, leading to the application and development of optimisation algorithms, and software that greatly improve the speed and efficiency of optical design.

Today, the design of optical systems therefore relies largely on efficient ray tracing and optimisation algorithms. A successful and widely used optimisation-based optical design strategy thus consists of choosing a well-known optical system as a starting point, and steadily achieving incremental improvements. Such a ‘stepand-repeat’ approach to optical design, however, still requires considerable experience, intuition and guesswork, which is why optical design is sometimes referred to as both an art and a science. This applies especially to freeform optical systems.

Until recently, most imaging systems included spherical and aspherical refractive lenses or reflective mirrors, or a combination of both. With the introduction of new ultra-precise manufacturing methods, however, it has become possible to fabricate lenses and mirrors that lack the common translational or rotational symmetry about a plane or an axis. Such optical components are called freeform optical elements, and they can be used to greatly extend the functionalities, improve the performance, and reduce the volume and weight of optical imaging systems.

Lightening the load

Although there are an increasing number of automated tools emerging, optical design without human guidance is still generally considered impossible, according to a team of scientists from the Department of Precision Instruments at Tsinghua University, China.

For them, the future of optical design features three main aspects:

  • Firstly, human operators will no longer need to participate or make decisions in the design process. Only primary knowledge about optical design will be required, with the designer only needing to provide the system specifications and constraints.
  • Secondly, all the output results will satisfy the specifications and constraints given, and the imaging quality merits will meet the given requirements. A variety of optical systems of different types will be obtained to provide an overview of the solution space of the optical system under the given specifications and constraints.
  • And lastly, the main job of the designer will be to browse the output results, consider factors such as manufacturing and system structure comprehensively, and then select the preferred design.

Towards achieving this, in Light: Science & Applications, the team of scientists have reported their development of a result-diversified automatic design method for freeform optics. Using just the system’s specifications (field-of-view, focal length and entrance pupil diameter etc) as the only input, a variety of three-mirror freeform imaging systems can be obtained automatically.

The proposed method is able to perform a coarse search of the solution space of three-mirror freeform systems and design a wide variety of imaging systems, working in the visible and long-wavelength infrared bands. The user can then focus on specific designs and conduct finer searches to obtain solutions that are diffraction limited, or have optimal imaging quality.

Computing power

The design method is composed of five phases (detailed in the paper1 and summarised here):

  1. Construct a series of coaxial spherical systems with various optical power distributions.
  2. For every coaxial spherical system, find out a series of unobscured systems that meet the given constraints.
  3. Based on the unobscured off axis systems found, construct freeform systems and correct the optical power of the entire system.
  4. For every freeform system constructed, improve the system imaging quality to its highest value by calculating the shape of each optical surface and finding the optimal tilt angle for the image plane. 
  5. Calculate the system imaging quality metric (or other evaluation metrics) and output the systems that meet the given requirements.

According to the researchers, this is the first time such functionality has been realised in the field of optical design. Following the procedures above, they developed a program using MATLAB and deployed it on a highperformance computing cluster system. 

To demonstrate their method, the researchers sought after a freeform imaging system working in the visible band (420 to 680nm) with the primary system wavelength being 587.6nm. The object distance was set to infinity, the full field-of-view angle to 4°×4°, the focal length to 450mm, the entrance pupil diameter to 50mm and the F-number to 9. After 35.3hours of computation without human interaction, a total of 59 freeform systems were obtained, with the average time to obtain one system being 35.9 minutes. The curve of the number of running jobs versus the running time is shown in figure 1, as well as some of the output results. The number marked alongside each system is the average of the root-meansquare values of the wavefront error of the system with a unit of λ=587.6nm.

Figure 1: Some of the 59 outputs obtained by the researcher’s automated design program based on the input specifications, which took 35.3 hours to compute. Top left: The curve of the number of running jobs versus the running time. (Image: Zhang et al.)

The researchers provide an analysis of the figure 1 results as follows: ‘Systems V9-4, V39-3, and V11-3 have the three typical structures contained among the output results. Systems V10-1, V142-2 and V258-1 all have the same structure but have different volumes. Systems V773-4, V911-3 and V912-3 have similar structures but have different image plane positions. Systems V26-6, V27-5 and V452-3 have structures that are rarely seen and the volume of system V452-3 is relatively small. Systems V989-4 and V1006-3 both contain small tertiary mirrors with short back working lengths. In system V1014-4, the primary mirror and the tertiary mirror are located close together and can be fabricated on the same substrate. In system V144-5, the structure could be folded by placing planar mirrors in the middle of the light path to allow the structure to be more compact. Systems V789-3, V347-1 and V240-1 have smaller volumes and compact structures. V240-1 is possibly the best design among all the output results.’

Out of the five phases of the design method, the majority of the computing time is currently spent conducting phase four, according to the researchers, with the rest of the time typically spent by each phase being as follows: phases one and three generally take seconds of calculation, because phase one calculates the surface curvature radii and surface distances targeting at the focal length, and phase three only involves the calculation of freeform shape of three mirrors. Phase two takes hours of calculation to perform an exhaustive search of possible unobscured systems, depending on the number of computing jobs and searching density. In phase five, it takes minutes of calculation to evaluate the imaging qualities of the systems and output good design results. The rest of the time (the bottleneck of the time consumption) is in phase four.

A tool for both research and engineering

The method proposed in their work provides, according to the researchers, a new thought for the realisation of fully automatic optical design. It enables people to obtain a variety of high-quality systems with only basic knowledge of optical design.

‘In the field of scientific research, people can explore the solution space of optical systems and the boundaries of a system’s performance based on the results obtained, or conduct research on the disciplines of optical design,’ the researchers said, when announcing their research. ‘In the field of engineering applications, optical design tools based on the proposed method are expected to change the working mode and core content of optical design. People can focus on system specification, manufacturability and cost.’

Reference: [1] Light: Science & Applications volume 10, Benqi Zhang, Guofan Jin & Jun Zhu, ‘Towards automatic freeform optics design: coarse and fine search of the three-mirror solution space’, https://doi.org/10.1038/s41377-021-00510-z

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More information at: https://blogs.synopsys.com/optical-solutions/2021/02/11/top-5-tools-for-designing-freeform-surfaces-in-code-v