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Nodal aberration theory (NAT) is a vectorized aberration theory that was developed to describe systems without rotational symmetry. NAT predicts non-rotationally symmetric aberration field dependences for third-order astigmatism and in particular a “binodal” behavior in which there are two points in the field of view where astigmatism vanishes. This study serves to demonstrate an alignment technique based on an understanding of this binodal behavior using a custom Ritchey-Chretien telescope. A method involving a commercial Shack-Hartmann compact-format wavefront sensor was developed to rapidly measure densely sampled full-field displays of the telescope, which has its secondary mirror mounted on a precision hexapod to allow for repeatable control of the telescope alignment. Real ray-based simulations were carried out on a model of the telescope and were consistent with the observed experimental results for both aligned and misaligned states of the telescope. We then provide guidelines on how to interpret Fringe Zernike astigmatism full-field displays for use during optical system alignment. This method is particularly relevant for freeform systems, which often have asymmetric field dependencies for multiple aberration types including astigmatism. 

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. 

We report the simulation of an adaptive interferometric null test using a high-definition phase-only spatial light modulator (SLM) to measure form and mid spatial frequencies of a freeform mirror with a sag departure of 150 μm from its base sphere. A state-of-the-art commercial SLM is modeled as a reconfigurable phase computer generated hologram (CGH) that generates a nulling phase function with close to an order of magnitude higher amplitude than deformable mirrors. The theoretical uncertainty in form measurement arising from pixelation and phase quantization of the SLM is 50.62 nm RMS. The calibration requirements for hardware implementation are detailed. © 2019 Optical Society of America https://doi.org/10.1364/OL.44.002000 

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. 

Freeform optical components enable significant advances for optical systems. A major challenge for freeform optics is the current lack of metrology methods with measurement uncertainty on the order of tens of nanometers or less. Towards addressing this challenge, optical coherence tomography (OCT) is a viable technique. In the context of low uncertainty metrology, the design requirements pertaining to the sample arm of an OCT metrology system are explicitly addressed in this paper. Two telecentric, broadband, diffraction limited, custom objective lens designs are presented with their design strategies. One objective lens was fabricated and experimentally tested for wavefront performance and telecentricity. This lens demonstrates near diffraction limited performance and a maximum deviation from telecentricity of 8.7 arcseconds across the full field of view, correlating to measurement uncertainty of less than 12 nm in simulation. The telecentricity test method developed completes the loop with respect to the design requirements and strategies presented and provides further intuition for telecentric lens designs in general. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 

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 

Freeform optical surfaces offer significant design opportunities but pose new challenges in metrology and manufacturing. Evolution in optics manufacturing processes have changed the surface spatial frequencies that must be measured. Optical surface definition is expected to be with respect to fiducials and datums which must be realizable at all stages of manufacture; uncertainty in that realization becomes important in some cases. Concurrent engineering is required, but appropriate data has not been collated for use by optical designers. One approach to providing such data is described.