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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. 

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.