We introduce the design of a highly compact, non-planar illumination source for deflectometry. The source emits uniform and Lambertian light from a curved area resembling the inner bore of a cylinder. When equipped with motion hardware, the ring source behaves like a spatially modulated screen with a pixel pitch comparable to that of a typical LCD monitor. If this source, a detector, and test optic are coaxially aligned, then on-axis deflectometry measurements are possible for axicons and centrally obscured, convex optics. This paper highlights the illumination design behind a cylindrical ring source and its implementation as a prototype in the visible spectrum.
Accurate system calibration remains an area of active improvement in deflectometry. Since deflectometry requires the geometry information of all participating hardware to be well known, miscalibration can mar the accuracy of surface reconstruction especially in lower order shapes. To uphold reconstruction fidelity, extra measuring instruments (i.e. coordinate measuring machines, laser trackers, metering rods) or reference features (i.e. fiducial points or reference mirror) to find out the positions of a camera, a screen, and a unit under test are used. These methods provide reliable calibration but are resource-intensive. In this paper, we introduce an alignment algorithm to calibrate the geometry of a deflectometry configuration. We leverage the concept of alignment algorithm which uses a sensitivity model. With the aid of ray tracing simulation, the relationship between camera pixels and screen pixels of a deflectometer is quantitatively established. This pixel-to-pixel relationship enables us to generate computational imaging of screen and characterize the tendency of misalignments of the deflectometer. On top of that, we can calculate and make multiplexed patterns of screen which highlight the effect of misalignments. We set specific indices and corresponding screen patterns for each alignment parameters to build the sensitivity model. The initial simulation result shows that the algorithm can estimate misalignment status. We believe that this algorithm can be an alternative and efficient calibration process for the deflectometry system, especially when the usage of extra measuring devices is limited.
The ability of space telescopes to see into nascent protostellar systems and even further into our universe is driven by the size of their deployable light collection area. While large monolithic mirrors typically weigh tons, inflatable membrane mirrors present a scalable, ultralightweight alternative. Leveraging decades of advances in adaptive optics technology, the possibility of a well-corrected 20 meter-class space observatory such as the Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is strikingly feasible. However, with great aperture size, comes great metrology requirements. Membrane reflectors are characteristically structured as one transparent and one metallized polymer membrane sealed around a steel tensioning ring. The inflated surface does not naturally conform to a known or prescribed conic but an approximate Hencky surface. Furthermore, multiple internal reflections and polarization interactions between the dielectric and metal layers disturb coherent light that probes it. A non-contact, full-aperture testing method is needed and further, one that can test highly varying membranes after thermoforming too. We present our method in obtaining the absolute shape of thermally formed, inflatable reflectors for space telescopes. Our work measures a 1-meter prototype of the OASIS primary inflatable mirror. Evolving from laser distance scanning to photogrammetry to deflectometry, our survey of metrology techniques for inflatable membrane optics is discussed.
Reconfigurable freeform optical systems enable greatly enhanced imaging and focusing performance within nonsymmetric, compact, and ergonomic form factors. In this paper, several improvements are presented for the design, test, and data analysis with these systems. Specific improvements include definition of a modal G and C vector basis set based on Chebyshev polynomials for the design and analysis of non-circular optical systems. This framework is then incorporated into a parametric optimization process and tested with the Tomographic Ionized-carbon Mapping Experiment (TIME), a reconfigurable optical system. Beyond design, a reconfigurable deflectometry system enhances metrology to measure a fast, f/1.26 convex optic as well as an Alvarez lens. Further improvements in an infrared deflectometry system show accuracy around λ/10 of the notoriously difficult low-order power. Working together, the mathematical vector polynomial set, the programmatic optical design approach, and various deflectometry-based optical testing technologies enable more flexible and optimal utilization of freeform optical components and design configurations.