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1. Alignment of a Ritchey-Chrétien telescope with primary mirror figure error guided by the rapid measurement of binodal astigmatism

   https://doi.org/10.1364/OE.541050  

   Romer, N; Zhao, N; Karci, Ö; Rolland, J (December 2024, Optics Express)

   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. 

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2. Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope

   https://doi.org/10.1364/OE.502744  

   Yeşiltepe, Meltem; Bauer, Aaron; Karcı, Özgür; Rolland, Jannick P. (December 2023, Optics Express)

   Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where “local” refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations. 

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3. Effect of freeform surfaces on the volume and performance of unobscured three mirror imagers in comparison with off-axis rotationally symmetric polynomials

   https://doi.org/10.1364/OE.27.021750  

   Schiesser, e; Bauer, a; Rolland, j (July 2019, Optics express)

   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 

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4. On-the-fly surface manufacturability constraints for freeform optical design enabled by orthogonal polynomials

   https://doi.org/10.1364/OE.27.006129  

   Takaki, N; Bauer, A; Rolland, J (March 2019, Optics express)

   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 

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5. Variable extended depth of field imaging using freeform optics

   https://doi.org/10.1117/12.2568723  

   Moein, Sara; Suleski, Thomas J. (August 2020, SPIE Optical Engineering + Applications, 2020, Online Only)

   Hahlweg, Cornelius F.; Mulley, Joseph R. (Ed.)

   Increasing depth of field in imaging systems can be beneficial, particularly for systems with high numerical apertures and short depth of field, such as microscopy. Extending depth of field has been previously demonstrated, for example, using non-rotationally symmetric (freeform) components such as cubic and logarithmic phase plates. Such fixed phase plates are generally designed for a specific optical system, so a different phase plate is required for each system. Methods that enable variable extended depth of field for multiple optical systems could provide benefits by reducing the number of required components and costs. In this paper, we explore the design of a single pair of transmissive freeform surfaces to enable extended depth of field for multiple lenses with different numerical apertures through relative translation of the freeform components. This work builds on the concept of an Alvarez lens, in which one pair of transmissive XY-polynomial freeform surfaces generates variable optical power through lateral relative shifts between the surfaces. The presented approach is based on the design of multiple fixed phase plates to optimize the through-focus Modulation Transfer Function (MTF) for imaging lenses of given numerical apertures. The freeform surface equation for the desired variable phase plate pair is then derived and the relative shift amounts between the freeform surfaces are calculated to enable extended depth of field for multiple imaging lenses with different numerical aperture values. Design approaches and simulation results will be discussed. © (2020) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only. Citation Download Citation Sara Moein and Thomas J. Suleski "Variable extended depth of field imaging using freeform optics", Proc. SPIE 11483, Novel Optical Systems, Methods, and Applications XXIII, 114830G (21 August 2020); https://doi.org/10.1117/12.2568723 

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