Optimizing Freeform Optics

VALERIE C. COFFEY, SCIENCE WRITER

Astronomical imaging from both ground and space provides precise data, and each has its pros and cons. Ground-based observation benefits from flexible infrastructure with large telescopes and instruments but suffers from atmospheric turbulence and light pollution, whereas observation from space is free of turbulence, but the telescopes must meet onerous size, weight, and cost restrictions for launch. The size and weight of space telescopes continue growing while costs must be reduced.

Concave detector array prototypes stand to improve the efficiency of freeform optics. Courtesy of French National Centre for Scientific Research and Curve-One.

One part of space-based imaging with room for optimization is the optics. For over a century, manufacturers have used nearly the same grinding and lap polishing techniques to create the optics in imaging systems, but recent revolutionary fabrication advancements mean optical designers have room to extemporize. Enter freeform optics: asymmetric mirrors defined simply by having at least one surface with no translational or rotational symmetry about any axis normal to the observational plane. In less than a decade, a flurry of research has made great strides in freeform design, with fabrication and testing not far behind.

Telescopes have conventionally used spherical, aspherical, or conic mirrors — optics that are rotationally symmetric about their center. Recent systems tend to use off-axis optics for more compactness, complicating fabrication and test and integration. However, new computer-controlled fabrication techniques such as subaperture polishing, diamond turning, ion-beam figuring, and others can create precision freeform mirror shapes, giving additional degrees of freedom in the design to enable system miniaturization, fewer components, and better optical performance. In addition, surface measurement techniques such as computer-generated holograms have enabled precise control of the surface shape. Freeform design optimization can enable folding of the optical path in three dimensions to reduce telescope volume while increasing the field of view (FOV), correcting aberrations, and reducing the number of surfaces. Whereas optical design was previously hampered by the inability to fabricate conflated designs, today’s freeform optics designs can consider various surface shapes, symmetries, obscurations, and states of correction, all of which can be combined to greatly improve imaging performance.

Joseph Howard, an optical engineer at NASA’s Goddard Space Flight Center in Bethesda, Md., and colleagues are exploring the ways in which freeform optics enable high-performance systems while keeping the cost and manufacturing obstacles to a minimum. The most common freeform optical designs at NASA look like most other mirrors at first glance, according to Howard (Figure 1). But one or more of the mirrors actually has a subtle, slightly asymmetric shape designed to provide a larger, usable FOV. The challenge to designers is to compensate for the asymmetry throughout the system. In a series of recently published papers, Howard and colleagues defined the starting points for various designs. For example, in a freeform four-mirror imaging system, the starting design must compensate for first-, second-, and third-order aberrations¹.

Figure 1. Conventional telescopes feature mirrors and lenses with rotational symmetry (top). Freeform optics uses asymmetrical deviations such as a potato chip or saddle shape, greatly magnified here for illustrative purposes, to improve image quality and larger FOV while enabling smaller packaging in space-based instruments (bottom). Courtesy of NASA.

Jannick Rolland, the Brian J. Thompson Professor of Optical Engineering at the University of Rochester (U of R) in Rochester, N.Y., is a co-author on that series of papers and many others. A pioneer in freeform optics, Rolland has taken that design goal to the next level by founding the Center for Freeform Optics (CeFO) in Rochester, a research collaboration between the U of R, the University of North Carolina (UNC) at Charlotte, and 18 companies and research institutions. Along with National Science Foundation funding through 2023, several other foundations and institutions provide fellowships and donations, including NASA. The goal of CeFO is to advance design and fabrication of freeform lenses and mirrors that can correct the aberrations that limit FOV and resolution. Her hope is that the work at CeFO will lead to smaller devices with fewer optics that actually offer improved imaging over conventional imaging systems.

Part of the challenge in developing freeform optics is that most commercially available optical design programs are limited in their ability to optimize the types of surfaces involved in freeform optical systems. So freeform design often requires the development of custom optical design code, optimized using the mathematical properties of the freeform optical surfaces.

One of Rolland’s protégés, Aaron Bauer, who was her doctoral student at the U of R, is now a senior research scientist at CeFO. Bauer is the lead designer of a next-generation freeform telescope that consists of three mirrors with a 250-mm aperture, working with precision manufacturing experts at UNC Charlotte to ensure the design will work — not a trivial task. The design uses complex mathematical functions called Zernike polynomials to define the surface shape. After using the function to determine the optimal folded design of a three-mirror anastigmat (TMA), the group used an iterative process of adjusting variables to correct aberrations². The final optimized design could provide diffraction-limited imaging better than any commercially available sensor that can detect it, leaving room to back off the performance in favor of realistic manufacturing tolerances (Figure 2).

Figure 2. The folded optical design of a 250-mm-aperture, three-mirror telescope conceived at CeFO enables diffraction-limited imaging at 550 nm. Courtesy of A. Bauer/University of Rochester.

Next, Bauer sent the design to Nick Horvath, a UNC Charlotte doctoral candidate in mechanical engineering. Horvath fabricated a novel aluminum mirror mount designed to address the difficulties inherent in the precision assembly tolerances. The aluminum was designed as a prototype for the eventual identical silicon carbide optics and housing that the imaging system design specifies³. The optical cell acts as a mirror mount and stays with the mirror all the way through system integration via matching kinematic mounts during manufacturing and testing. The goal of the work is to develop a repeatable assembly procedure to produce the high-performance optics while minimizing cost and time. The project sets a precedent in concurrent collaboration between optical design, mechanical fabrication, and metrology that allows for volume scaling in production and a reduction in costly design changes. The process itself helped define key constraints of future designs.

“Freeform optics is a game-changing technology for astronomical optics,” said Bauer. “Our results have been tangible and persuasive, which we hope will motivate the expansion of investment in freeform optics R&D.”

Curved detectors

Another obstacle to freeform optical systems is that a typical flat detector limits the performance over the FOV and nullifies the full benefits of freeform optics to correct higher-order aberrations. Research led by professors Emmanuel Hugot and Marc Ferrari at the Laboratoire d’Astrophysique de Marseille (LAM) in Marseille, France, explored how curved detectors could help. Curved detectors offer new parameters for optimization in freeform optical systems, enabling direct compensation of the field curvature aberration in the focal plane while keeping the small system size that is desirable for astronomical imaging. The LAM group proposed applying active and deformable optics technology to fabricate deformable detectors with concave, convex, or toroidal shapes⁴. Ultimately, the group proposed curved detectors as part of several European Space Agency space-based freeform optics TMA telescope proposals⁵ (Figure 3).

Figure 3. Layout in the symmetry plane shows a freeform TMA design for a space-based telescope (left) involving anamorphic primary (M1), flat secondary (M2), and spherical tertiary (M3) mirrors. 3D view reveals the placement of a curved detector in the center of the flat secondary mirror (right). Reproduced with permission from Reference 5. Courtesy of A. Bauer/University of Rochester.

The LAM group recently developed prototypes of the curved detectors that may have potential in freeform astronomical applications⁶ (opening image, page 40). The CMOS detectors show promising performance, slightly besting flat sensors in terms of dark current and readout noise. A telescope combining freeform surfaces with a curved detector could enable enhanced performance over a FOV up to 9.4× that of a classical Ritchey-Chrétien telescope scheme.

Curved detectors offer new parameters for optimization in freeform optical systems.

Furthermore, co-author and previous LAM colleague Wilfried Jahn, now a postdoctoral researcher in the aerospace department at the California Institute of Technology (Caltech), is developing a carbon fiber mirror technology that will significantly save weight and cost on the telescope manufacturing. The objective is to combine freeform optics, curved sensors, and carbon fiber technology for imaging on the ground and in space, a concept that may interest government agencies and commercial entities involved in new smaller CubeSat missions. In addition, the curved sensor technology has spun out into its own wide-field camera company, Curve-One, located in Paris, with potential applications far beyond telescopes, including augmented and virtual reality, autonomous vehicles, smartphones, cameras, medical imaging, and drones.

According to Jahn, a growing cadre of researchers and engineers believes that freeform optics technology can enable new optical functionality that could profoundly affect optics, from illumination to detecting faraway Earth-like planets.

“Developing new technologies to more precisely observe our environment and the universe is essential to really understand our ecosystem and behave appropriately,” said Jahn. “Advancing imaging systems via freeform optics could help scientists address crucial topics, from fundamental research to the protection of our planet and exploration of others.”

References

1. J. Papa et al. (2018). Starting point designs for freeform four-mirror systems. Opt Eng, Vol. 57, Issue 1, p. 101705, https://doi.org/10.1117/1.OE.57.10.101705.

2. A. Bauer et al. (May 14, 2019). Concurrent engineering of a next-generation freeform telescope: optical design. Proc SPIE, Vol. 10998, Advanced Optics for Imaging Applications: UV through LWIR IV, 109980W, https://doi:10.1117/12.2519174.

3. N. Horvath and M. Davies (May 14, 2019). Concurrent engineering of a next-generation freeform telescope: mechanical design and manufacture. Proc SPIE, Vol. 10998, Advanced Optics for Imaging Applications: UV through LWIR IV, 109980X, https://doi:10.1117/12.2518954.

4. E. Muslimov et al. (2017). Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture. Opt Express, Vol. 25, Issue 13, p. 14598, https://doi.org/10.1364/OE.25.014598.

5. G. Lemaitre et al. (2019). Active optics in astronomy: freeform mirror for the MESSIER telescope proposal. Math Comput Appl, Vol. 24, Issue 2, https://doi:10.3390/mca24010001.

6. S. Lombardo et al. (March 13, 2019). Curved detectors for astronomical applications: characterization results on different samples. Appl Opt, Vol. 58, Issue 9, p. 2174, https://doi.org/10.1364/AO.58.002174.