Deflectometry is a versatile optical testing tool used in various fields, from astronomy to industrial applications, due to its non-null testing capability which facilitates precise measurement despite challenging optical surfaces and system layout constraints. In this manuscript, we present novel variational advancements to traditional deflectometry, towards universal functionality and system friendliness. Traditional dark-field illumination is an inspection technique that is sometimes used to detect particles on a specular surface. Problems arise in its repeatability, as an intensity-based measurement is vulnerably dependent on the testing conditions of time, limiting its ability to be used in automated fashion. The first advancement leverages phase algorithms commonly seen in deflectometry; by adding a secondary light source (normal to the surface) and modulating each source's intensity with a time-varying sinusoid. The phase-based information has a higher sensitivity to the light scattered from a defect producing a more robust computational image process method that is now insensitive to the environment. The second advancement is an alignment method to obtain lower-order shape. While deflectometry proves effective in measuring mid-to-high frequency surface shape, it faces challenges when assessing low-order shape measurements like power, astigmatism, and coma due to relative position and alignment error between the unit under test (UUT) and the deflectometry system. To avert the necessity of additional instruments like a coordinate measuring machine, laser trackers, or interferometers, we leveraged computational fiducials and sensitivity matrices to identify and address misalignments effectively. With enhanced capabilities and system-friendly features, our advanced deflectometry techniques provide powerful options in optical testing. By addressing the challenges in low-order shape measurements and incorporating dark field testing, our approaches extend the potential of deflectometry as a valuable tool in optical metrology across a broad spectrum of industries and scientific endeavors.
For any surface metrology system that obtains measurement with the aid of an imaging system, distortion must be carefully scrutinized. Both intrinsic lens distortion and perspective distortion embed surface error distributions that skew the interpretation of resultant surface maps. Either displaces acquired information due to the imaging process. Here, we quantify the origins of distortion, its modeling philosophy, and the effects of its digital correction procedure. This study includes simulation for lens-distorted systems such as interferometers and perspective-distorted systems such as monoscopic fringe projection profilometry and deflectometry. Summarily, this study hopes to clarify differences in low-order shape between surface metrology instrument measurements in which surface maps were not rectified for distortion.
OASIS (Orbiting Astronomical Satellite for Investigating Stellar Systems) is a space-based, MIDEX mission concept that employs a 14 meter inflatable aperture and cryogenic heterodyne receivers to perform high resolution (R<106) observations at terahertz frequencies. OASIS targets far-infrared transitions of H2O and its isotopologues, as well as HD and other molecular species from 660 to 63 μm that are otherwise obscured by the Earth’s atmosphere. OASIS will have <10x the collecting area and <4x the angular resolution of Herschel and complements the short wavelength capabilities of JWST. With its large collecting area and suite of terahertz heterodyne receivers, OASIS will have the sensitivity to follow the water trail from galaxies to oceans. OASIS represents a paradigm shift in the realization of large space apertures. Our paper will focus on how the development work for OASIS can be leveraged to realize a new generation of space telescopes.
The Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a 20-meter class proposed space terahertz observatory supported by an inflatable membrane architecture. To measure 150 mm and 1m models of the A1 reflective membrane antenna, two deflectometry configurations were designed. The smaller assembly and its corresponding deflectometer were simulated, built in our laboratory, and produce a reconstructable signal for clocked measurements of the highly-sloped pneumatic surface. We use non-sequential raytracing simulation to bound the maximum contributions of all shape errors and suggest the N-Rotations algorithm to remove the remaining radially asymmetric errors. Then, the 1m prototype assembly was tested inside a thermal vacuum chamber (TVAC). Differential deflectometry measurements tracked the 1m surface shape changes as it was subjected to a variety of environmental setpoints, cycled between three inflation gases, and also during controlled puncture. We summarize our development and results for absolute measurements as well as from TVAC testing.
The uninflated shape configurations of parabolic and spherical membrane mirrors were calculated by solving the inverse problem, i.e., given the design inflation pressure, the membrane material and geometric properties, what must be the initial uninflated shape such that on inflation to the design pressure, the exact desired surface of revolution is obtained. The resulting first order nonlinear differential equation was numerically integrated using the boundary conditions. The initial uninflated shape was then subjected to a forward transformation using FAIM, a proprietary geometric nonlinear membrane finite element code. FAIM has been validated against exact analytical solutions for both small and extremely large deformations that are up to eight orders of magnitude larger compared with the starting undeflected shape. Simulations reveal that to fabricate a very accurate and precise inflated membrane mirror relative to the design parameters, one must not only accurately measure and input the moduli in both meridional and hoop directions but an accurately measured Poisson’s ratio as well. The code was used to guide the membrane mirror design. For very small aperture diameters, the initial uninflated shape may be fabricated by thermo-forming the membrane. For aperture diameters exceeding one meter however, the membrane mirror is built with discrete gores that are joined together with tapes at the seams. This provided the impetus to write a companion computer code FLATE, to calculate the gore shapes using a slight modification of the solution to the inverse transformation equation to account for the presence of the seam tapes. After the gores were determined, the resulting final inflated shape was calculated and verified using FAIM. Sensitivity analyses can now be carried out to determine the resulting surface shape as a function of the different sources of error: gore width, gore length, perimeter attachment uncertainties, thermal effects, variation of material properties over the membrane continuum and inflation pressure changes. The code has been shown to be more robust than equivalent commercial analytical packages in so far as membrane, cable and space-frame element combinations are concerned. In particular, the analytical and finite element codes were used in the preliminary assessment of a membrane optic for the OASIS Mission (Orbiting Astronomical Satellite for Investigating Stellar Systems) [1]. The OASIS is a 20-meter class space observatory operating at high spectral resolution in the terahertz frequencies. Over its nominal 2-year mission it will probe conditions and search for biogenic molecules on hundreds of protoplanetary disks and other solar system objects.
Deformable reflector technology has mainly been used for observations at visible and infrared wavelengths but has yet to be utilized for terahertz wavefront correction. We present an actuator for deformable reflectors that overcomes challenges particular to this wavelength such as a millimeter-scale stroke requirement. Bending moment actuators are used in both the radial and tangential directions to correct low-order wavefront aberrations. Strong and flexible materials such as Delrin are used for the reflector material. Such a deformable antenna can be used to correct wavefronts on future large radio antennae such as the Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS). This antenna uses a 20-meter thin membrane as its primary radio wave collector. A deformable reflector may be added to this system to allow for looser tolerances on the primary antenna shape and correct for wavefront errors inherent in an inflatable optic. To predict the wavefront errors that may be expected when using this type of thin membrane primary reflector, TVAC (Thermal Vacuum Chamber) test methods are also presented in these proceedings.
Various ground-based and space-based future telescope technologies are currently being conceptualized, designed, prototyped and tested to perform next generation astronomical sciences. They include (1) the alignment of segmented multi-order diffractive elements for the Nautilus space observatory; (2) the inflatable terahertz OASIS space telescope primary mirror characterization metrology; (3) active alignment of the laser truss-based Large Binocular Telescope prime focus camera; (4) the modular cross-dispersion spectroscopy unit, MOBIUS, used at the prime focal plane of the Large Binocular Telescope; (5) pupil segmentation topological optimization for future high contrast imaging telescopes; and (6) the optical design of the long slit UV spectroscopy space telescope Hyperion. This suite of enabling optical technologies and concept designs will redefine how humans understand the genesis and future of our universe.
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.
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.
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.
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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.