Cascade optical coherence tomography (C-OCT).

Significant advances for optical systems in terms of both performance and packaging are enabled by freeform optical components. Yet, surface form metrology for freeform optics remains a challenge. We developed and investigated a point-cloud cascade optical coherence tomography (C-OCT) technique to address this metrology challenge. The mathematical framework for the working principle of C-OCT is presented. A novel detection scheme is developed to enable high-speed measurements. Experimental results validate the C-OCT technique with the prototype setup demonstrating single-point precision of ±26 nm (∼λ/24 at the He-Ne wavelength), paving the way towards full surface measurements on freeform optical components.

Off-axis conics as base surfaces for freeform optics enable null testability.

When conducting interferometric tests of freeform optical surfaces, additional optical components, such as computer-generated holograms or deformable mirrors, are often necessary to achieve a null or quasi-null. These additional optical components increase both the cost and the difficulty of interferometric tests of freeform optical surfaces. In this paper, designs using off-axis segments of conics as base surfaces for freeforms are explored. These off-axis conics are more complex base surfaces than typically-used base spheres but remain null-testable. By leveraging off-axis conics in conjunction with additional orthogonal polynomial departures, designs were found with up to an order-of-magnitude of improvement in testability estimates relative to designs that use base spheres. Two design studies, a three-mirror telescope and a wide field-of-view four-mirror telescope, demonstrate the impact of using off-axis conics as the base surface.

Experimental investigation in nodal aberration theory (NAT) with a customized Ritchey-Chrétien system: third-order coma.

Nodal aberration theory (NAT) describes the aberration properties of optical systems without symmetry. NAT was fully described mathematically and investigated through real-ray tracing software, but an experimental investigation is yet to be realized. In this study, a two-mirror Ritchey-Chrétien telescope was designed and built, including testing of the mirrors in null configurations, for experimental investigation of NAT. A feature of this custom telescope is a high-precision hexapod that controls the secondary mirror of the telescope to purposely introduce system misalignments and quantify the introduced aberrations interferometrically. A method was developed to capture interferograms for multiple points across the field of view without moving the interferometer. A simulation result of Fringe Zernike coma was generated and analyzed to provide a direct comparison with the experimental results. A statistical analysis of the measurements was conducted to assess residual differences between simulations and experimental results. The interferograms were consistent with the simulations, thus experimentally validating NAT for third-order coma.

Design, fabrication, and testing of convex reflective diffraction gratings.

The convex reflective diffraction grating is an essential optical component that lends itself to various applications. In this work, we first outline the design principles of convex diffraction gratings from wavefront quality and efficiency perspectives. We then describe a unique fabrication method that allows for the machining of convex diffraction gratings with variable groove structure, which is extendable to rotationally non-symmetric convex diffraction grating substrates. Finally, we demonstrate two quantitative wavefront measurement methods and respective experimental validation.