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.
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.
Rectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.
The Scanning Long-wave Optical Test System (SLOTS) is a slope measuring deflectometry system that provides accurate measurements on ground surfaces. As it uses a thermal source, we can measure an optic during the grinding phase which allows us to correct figure errors when material removal is much faster. We have made improvements in SLOTS, such as the step-and-stare method, the ceramic rod, and the Gaussian fitting processing software, so that this system supports higher accuracy and resolution. As a result, SLOTS is an optical testing system that covers a huge portion of the fabrication process from the grinding to the figuring. It is a complementary solution for other metrology systems such as the laser tracker, SCOTS, and null interferometry. SLOTS can reduce the manufacturing time by producing ground aspheres that have low errors of the surface figure when polishing begins.
A new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called G polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind – a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.
Large optic fabrication is a delicate and time consuming process. Obtaining a large prime optic is often in the critical path of a project and poses a serious risk to both the schedule and budget. The Optical Engineering and Fabrication Facility (OEFF) at the College of Optical Sciences, the University of Arizona, has developed a new way of optimizing its large optic fabrication process for maximum efficiency in convergence. The new process optimization takes the amount of stock material removal, tool characteristics, metrology uncertainty, optic prescription, optic material properties, and resource availability as input parameters and provides an optimized process along with an achievable convergence. This paper presents technical details of the new process optimization and demonstrates performance on 6.5m mirror fabrication at the University of Arizona. Two case studies for an 8.4m GMT off-axis primary mirror segment and a 3.1m TMT convex secondary mirror fabrication are also presented.
One of the major challenges of optical fabrication is measurement of the surface when first polished out, before its figure is within the capture range of interferometry. A high dynamic range instrument with good accuracy is needed to efficiently guide the processing. Our approach is to use the Software Configurable Optical Test System (SCOTS), a deflectometry technique that uses a camera and liquid crystal display to measure the surface slope. We describe the use of SCOTS in the fabrication of a 6.5 m on-axis mirror and an 8.4 m off-axis mirror segment (Giant Magellan Telescope primary). SCOTS has the dynamic range to measure high slope errors early in the mirror figuring process, with sufficient accuracy to corroborate later interferometric measurements. Accurately measuring low order figure errors with SCOTS requires careful calibration of the system geometry. Details of the data collection and processing, and comparison to interferometry measurements are presented.
The Optical Engineering and Fabrication Facility (OEFF) at the College of Optical Sciences, University of Arizona has successfully fabricated a 6.5m primary mirror and conducted integration and testing (I & T) of the primary mirror and telescope cell assembly for the University of Tokyo Atacama Observatory. The mirror has been fabricated using a new facility and advanced technologies developed by the group, including fabrication process optimization, a super-stable optical metrology support, infrared and visible metrology with high accuracy, and interferometry. Fabrication process optimization has simulated the entire fabrication process from the initial grinding to final polishing to specification, and optimized the tooling, frequency of metrology, and estimated convergence. Through the project the new process optimization successfully demonstrated the performance and guided the process in a deterministic way.
The 6.5m primary mirror is made of E6 bolo-silicate glass with a honeycomb structure. Due to the scale it requires a mechanically and thermally stable metrology support to ensure highly accurate metrology. The new metrology support has demonstrated its extremely stable force stability and thermal stability over the project period.
Metrology of large optics is always a challenge and the OEFF group has made outstanding advancement in IR and visible metrology and applied them seamlessly during the mirror fabrication with extremely low uncertainty.
By applying the newly developed facility and technologies, the OEFF group successfully fabricated the 6.5m primary mirror in less than 7months, which is about 3 times faster than past 6.5m mirror fabrication at UA.
After fabrication the mirror was integrated to the telescope cell and the primary mirror cell assembly has been tested using optical metrology to identify the static and dynamic behavior of the system. The testing includes support actuator influence functions, the nominal support force set, bending mode correction, and assessment of deliverable image quality.
This paper presents the technical aspects of the mirror fabrication, advancement of metrology and I & T of the 6.5m primary mirror assembly.
Modern large telescopes such as TAO, LSST, TMT and EELT require 0.9m-4m monolithic convex secondary mirrors. The fabrication and testing of these large convex secondary mirrors of astronomical telescopes is getting challenging as the aperture of the mirror is getting bigger. The biggest challenge to fabricate these large convex aspheric mirrors is to measure the surface figure to a few nanometers, while maintaining the testing and fabrication cycle to be efficient to minimize the downtime. For the last a couple of decades there was huge advancement in the metrology and fabrication of large aspheric secondary mirrors. College of Optical Sciences in the University Arizona developed a full fabrication and metrology process with extremely high accuracy and efficiency for manufacturing the large convex secondary mirrors.
In this paper modern metrology systems including Swing-Arm Optical Coordinate Measuring System (SOCMM) which is comparable to Interferometry and a Sub-aperture stitching interferometry scalable to a several meters have been presented. Also a Computer Controlled Fabrication Process which produces extremely fine surface figure and finish has been demonstrated. These most recent development has been applied to the fabrication and testing of 0.9m aspheric convex secondary mirror for the Tokyo Atacama Observatory’s 6.5m telescope and the result has been presented.
Daniel K. Inouye Solar Telescope (formerly known as Advanced Technology Solar Telescope) will be the largest optical solar telescope ever built to provide greatly improved image, spatial and spectral resolution and to collect sufficient light flux of Sun. To meet the requirements of the telescope the design adopted a 4m aperture off-axis parabolic primary mirror with challenging specifications of the surface quality including the surface figure, irregularity and BRDF. The mirror has been completed at the College of Optical Sciences in the University of Arizona and it meets every aspect of requirement with margin. In fact this mirror may be the smoothest large mirror ever made.
This paper presents the detail fabrication process and metrology applied to the mirror from the grinding to finish, that include extremely stable hydraulic support, IR and Visible deflectometry, Interferometry and Computer Controlled fabrication process developed at the University of Arizona.
Several next generation astronomical telescopes or large optical systems utilize aspheric/freeform optics for creating a segmented optical system. Multiple mirrors can be combined to form a larger optical surface or used as a single surface to avoid obscurations. In this paper, we demonstrate a specific case of the Daniel K. Inouye Solar Telescope (DKIST). This optic is a 4.2 m in diameter off-axis primary mirror using ZERODUR thin substrate, and has been successfully completed in the Optical Engineering and Fabrication Facility (OEFF) at the University of Arizona, in 2016. As the telescope looks at the brightest object in the sky, our own Sun, the primary mirror surface quality meets extreme specifications covering a wide range of spatial frequency errors. In manufacturing the DKIST mirror, metrology systems have been studied, developed and applied to measure low-to-mid-to-high spatial frequency surface shape information in the 4.2 m super-polished optical surface. In this paper, measurements from these systems are converted to Power Spectral Density (PSD) plots and combined in the spatial frequency domain. Results cover 5 orders of magnitude in spatial frequencies and meet or exceed specifications for this large aspheric mirror. Precision manufacturing of the super-polished DKIST mirror enables a new level of solar science.
Subaperture stitching is a popular method for extending small, subaperture interferometer measurements to cover largeaperture optics. The method is simple in that there are only two steps: 1) make multiple measurements across the surface and 2) use well-established software techniques to merge the individual measurements into one surface estimate. Because parts of the system must move between measurements, small misalignments between subapertures are unavoidable, but easily accommodated within the software. Unfortunately this process has the potential to introduce errors. In this work, we show how random noise in a circular ring of subapertures creates artifacts in low-order surface shape estimates. The magnitude of these errors depends on setup parameters such as the number of subapertures and their overlap, as well as the measurement noise within a single subaperture. Understanding the relationships between subaperture stitching configuration and surface artifacts is important when designing high-accuracy metrology systems which rely on subaperture stitching. This work will help metrology system designers incorporate subaperture stitching into error budgets and tolerances.
Deflectometry is a powerful metrology technique that uses off-the-shelf equipment to achieve nanometer-level accuracy surface measurements. However, there is no portable device to quickly measure eyeglasses, lenses, or mirrors. We present an entirely portable new deflectometry technique that runs on any Android™ smartphone with a front-facing camera. Our technique overcomes some specific issues of portable devices like screen nonlinearity and automatic gain control. We demonstrate our application by measuring an amateur telescope mirror and simulating a measurement of the faulty Hubble Space Telescope primary mirror. Our technique can, in less than 1 min, measure surface errors with accuracy up to 50 nm RMS, simply using a smartphone.
Subaperture stitching extends measurements such as interferometry by combining several overlapping measurements into a single, high-accuracy estimate of the overall image. In designing a subaperture measurement regimen, there are several tradeoffs related to size, quantity and locations of subapertures within the full aperture of the test optic. Understanding how individual subaperture measurement noise couples through these parameters into errors in the final stitched map is important for estimating overall system performance. In this work, we explore parametric rules for estimating the accuracy of stitched results based on subaperture geometry parameters and noise characteristics for a self-calibrating system where both a test optic and reference optic are simultaneously determined. From these rules, we examine types of errors introduced by stitching which enables confidence estimates for the final stitched map surface quality.
KEYWORDS: Data conversion, Optical engineering, Finite element methods, Surface finishing, Visualization, Data analysis, Visual analytics, Data modeling, Polishing, Optical testing
SAGUARO is open-source software developed to simplify data assimilation, analysis, and visualization by providing a
single framework for disparate data sources from raw hardware measurements to optical simulation output. Developed
with a user-friendly graphical interface in the MATLABTM environment, SAGUARO is intended to be easy for the enduser
in search of useful optical information as well as the developer wanting to add new modules and functionalities. We
present here the flexibility of the SAGUARO software and discuss how it can be applied to the wider optical engineering
community.
We present a fast and ambiguity-free method for slope measurement of reflective optical elements based on
reflectometry. This novel reflectometric method applies triangulation to compute the slope based off projected
patterns from an LCD screen, which are recorded by a camera. Accurate, ambiguity-free measurements can be
obtained by displaying one pixel at a time on the screen and retrieving its unique image. This process is typically
accelerated by scanning lines of pixels or encoding the information with phase using sinusoidal waves. Various
classes of solutions exist, centroiding and phase-shifting being the most accepted, but their sensitivities vary with
experimental conditions. This paper demonstrates solutions based on various parameters such as accuracy or
efficiency. The results are presented in a decision matrix and merit function. Additionally, we propose a new class of
solutions – Binary Square screens – in an attempt to address system limitations and compare current systems to our
solutions using the decision matrix. Several test conditions are proposed along with the best suited solution.
Algorithms for polarization ray tracing biaxial materials and calculating the directions of ray propagation and
energy flow, the refractive indices, and the coupling coefficients for all four resultant reflected and transmitted
rays are presented. Examples of polarization state maps, retardance maps and diattenuation maps are generated
as a function of angle of incidence for comparing plane parallel plate systems with uniaxial and biaxial
materials.
Understanding the interaction of polarized light with materials is critical to applications such as remote
sensing, laser radar, and quality control. The availability of angular and spatial information add additional dimensions
to this understanding.
A facility is constructed for Mueller Matrix Bidirectional Reflectance Distribution (MMBRDF) imaging.
Polarized light at near infrared and visible wavelengths is scattered from samples ranging from bare metals to complex
organic structures with various textures and orientations. The resulting scattered polarized light is measured with a
Mueller matrix active imaging polarimeter.
The in-plane MMBRDF is measured for a sanded aluminum sample as a demonstration of the facility. The
aluminum is found to be a weak depolarizer, with a somewhat higher depolarization index at specular angles.
Retardance is dominated by its linear component and is close to 180° for the majority of angles. Diattenuation is weak,
especially in the specular region, and increases in the region further away from specular angles.
The in-plane Mueller matrix bidirectional reflectance distribution function (MMBRDF) is measured for a Spectralon
calibration target with a reflectance of 99%. Measurements are acquired using a Mueller matrix active imaging,
goniometric polarimeter operated in the near infrared at 1550nm. The Spectralon is measured for both incident and
scattering angles from -80 degrees to 80 degrees to within 20 degrees of retro-reflection. A range of polarization states
is generated and scattered polarization states are analyzed by means of a dual rotating retarder Mueller matrix
polarimeter. Complete Mueller matrix data is measured with a high-resolution camera in image form.
Polarization scatter data is presented in Mueller matrix angular arrays. As expected the Spectralon is a strong
depolarizer and weak s-plane oriented diattenuator. It was also a weak retarder. Diattenuation and retardance are
strongest at horizontal and vertical polarizations, and weakest for circular polarization states.
We have implemented a continuous measurement of the mean magnetic moment of an ensemble of atoms trapped in a far-off-resonance optical lattice, by detecting the Faraday rotation of one of the lattice beams after it has passed through the atom cloud. In a first demonstration experiment we have observed Larmor precession with high signal-to-noise ratio, and compared the performance of the measurement with a simple theory. Faraday spectroscopy offers an ideal method to monitor the atomic dynamics and will be applied to the study of quantum chaos in magneto-optical lattices. In principle the measurement sensitivity can be increased to the point where quantum backaction becomes significant, thereby opening the door to studies of quantum feedback, spin squeezing and the role played by quantum measurement in quantum/classical correspondence.
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