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When using freeform surfaces in optical design, the field dependence of the aberrations can become quite complex, and understanding these aberrations facilitates the design process. Here we calculate the field dependence of low-order Zernike astigmatism (Z5/6) up to the eighth order in nodal aberration theory (NAT). Expansion of NAT astigmatism terms to the eighth order facilitates a more accurate fit to the Zernike astigmatism data. We then show how this estimated field dependence can be used to quantitatively analyze a freeform telescope design. This analysis tool adds to the optical designer’s arsenal when up against the challenge of designing with freeform optics. ©2019 Optical Society of America https://doi.org/10.1364/JOSAA.36.002115 

The invention of new design techniques for unobscured reflective systems using freeform surfaces has expanded the optical design space for these system types. We illustrate how the use of freeform surfaces can expand the design space of the Three Mirror Compact design type to allow both better performance at a given system volume and smaller volumes for a given performance target. By evolving designs using conventional off-axis asphere type surfaces to ever smaller volumes and then converting these off-axis asphere descriptions to centered Zernike descriptions, we show that the wavefront error improves by up to 69% in this case by allowing the surfaces to break rotational symmetry. In addition, we show that evolving designs from the same starting point as the off-axis asphere designs but instead using a centered Zernike description can produce a design with a 39% smaller volume in this case while maintaining the same diffraction-limited performance. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 

CubeSats are a type of miniaturized satellites that consist of 10×10×10 cm cubic units (1U), which is established as a standard by Jordi Puig-Suari and Robert Twiggs in 1999 to push low-cost educational and industrial space experimentation [1]. In recent years the CubeSat format has gained popularity for research and industrial purposes including Earth imaging, communication and technology demonstration. High performing optical systems such as spectrometers and imagers that can be contained in CubeSat format are also desired in many space missions. In this paper, a design study is conducted for a 3-mirror spectrometer based on the reflective triplet design form that is fully contained in 1U space. As shown in Fig. 1, the spectrometer consists of three mirrors and a plane grating serving as the aperture stop. Light from a slit enters the system and travels through the three mirrors to the grating where it is dispersed and reflected. The light then travels back through the system in reverse to the detector near the slit which results in a 2D image (or spectrum). To show the freeform advantage, we compared two designs of this spectrometer - one designed with freeform surfaces and the other with off-axis aspheres. 

Refractive eyepiece design forms are often limited by chromatic aberrations and require a mix of glass types to achieve sufficient correction, thus they are not conducive to manufacture in volume. Reflective surfaces are inherently achromatic and can be produced in volume, but rotationally symmetric reflective surfaces are either used with lossy obscurations or are incapable of correcting rotationally variant aberrations when used in an unobscured form. Freeform optics enable unobscured reflective design forms with excellent image quality. Here, we document the design, fabrication, and assembly of an all-reflective high-end electronic viewfinder that shows the applicability of freeform surfaces to eyepiece design forms. 

When leveraging orthogonal polynomials for describing freeform optics, designers typically focus on the computational efficiency of convergence and the optical performance of the resulting designs. However, to physically realize these designs, the freeform surfaces need to be fabricated and tested. An optimization constraint is described that allows on-the-fly calculation and constraint of manufacturability estimates for freeform surfaces, namely peakto- valley sag departure and maximum gradient normal departure. This constraint’s construction is demonstrated in general for orthogonal polynomials, and in particular for both Zernike polynomials and Forbes 2D-Q polynomials. Lastly, this optimization constraint’s impact during design is shown via two design studies: a redesign of a published unobscured three-mirror telescope in the ball geometry for use in LWIR imaging and a freeform prism combiner for use in AR/VR applications. It is shown that using the optimization penalty with a fixed number of coefficients enables an improvement in manufacturability in exchange for a tradeoff in optical performance. It is further shown that, when the number of coefficients is increased in conjunction with the optimization penalty, manufacturability estimates can be improved without sacrificing optical performance. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement