James H. Burge

• University of Arizona

In this paper, we present a modal data processing methodology, for reconstructing high resolution surfaces from measured slope data, over rectangular apertures. One of the primary goals is the ability to effectively reconstruct deflectometry measurement data for high resolution and freeform surfaces, such as telescope mirrors. We start by developin...

Interferometers using computer-generated holograms (CGHs) have become the industry standard to accurately measure aspheric optics. The CGH is a diffractive optical element that can create a phase or amplitude distribution and can be manufactured with low uncertainty using modern lithographic techniques. However, these CGHs have conventionally been...

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of onl...

A spherometer is often used to precisely measure the radius of curvature of a spherical surface. It can also measure the vertex radius of a more complex surface such as an off-axis parabola (OAP). This paper provides a reliable algorithm to find the vertex radius of an OAP by solving a few equations based on the test geometry. This algorithm can al...

The Hobby-Eberly Telescope (HET)†, located in West Texas at the McDonald Observatory, operates with a fixed segmented primary (M1) and has a tracker, which moves the prime-focus corrector and instrument package to track the sidereal and non-sidereal motions of objects. We have completed a major multi-year upgrade of the HET that has substantially i...

The Giant Magellan Telescope (GMT) primary mirror consists of seven 8.4 m light-weight honeycomb mirrors that are being manufactured at the Richard F. Caris Mirror Lab (RFCML), University of Arizona. In order to manufacture the largest and most aspheric astronomical mirrors various high precision fabrication technologies have been developed, resear...

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...

The Richard F. Caris Mirror Lab at the University of Arizona is responsible for production of the eight 8.4 m segments for the primary mirror of the Giant Magellan Telescope, including one spare off-axis segment. We report on the successful casting of Segment 4, the center segment. Prior to generating the optical surface of Segment 2, we carried ou...

The LSST M1/M3 combines an 8.4 m primary mirror and a 5.1 m tertiary mirror on one glass substrate. The combined mirror was completed at the Richard F. Caris Mirror Lab at the University of Arizona in October 2014. Interferometric measurements show that both mirrors have surface accuracy better than 20 nm rms over their clear apertures, in nearsimu...

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...

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...

Subaperture stitching is an economical way to extend small-region, high-resolution interferometric metrology to cover large-aperture optics. Starting from system geometry and measurement noise knowledge, this work derives an analytical expression for how noise in an annular ring of subapertures leads to large-scale errors in the computed stitched s...

SCOTS (Software Configurable Optical Test System) is a high-precision slope measurement technique based on deflectometry. It utilizes a well-calibrated commercial LCD screen and a diffraction-limited camera to provide high dynamic range, non-contact and full-field metrology of reflective/refractive optics of high accuracy but low cost. Recently, we...

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....

The Software Configurable Optical Test System (SCOTS) uses deflectometry to measure surface slopes of general optical shapes without the need for additional null optics. Careful alignment of test geometry and calibration of inherent system error improve the accuracy of SCOTS to a level where it competes with interferometry. We report a SCOTS surfac...

The classic Abbe sine condition relates pupil distortion to aberrations with linear field dependence such as coma. This paper provides a fully generalized form of the sine condition that does not use any symmetry. It accurately predicts the change in aberration in the presence of field independent and pupil aberrations. The definitions of the image...

Slope measuring deflectometry (SMD) systems are developing rapidly in testing freeform optics. They measure the surface slope using a camera and an incoherent source. The principle of the test is mainly discussed in geometric optic domain. The system response as a function of spatial frequency or instrument transfer function (ITF) has yet to be stu...

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 (TM) smartphone with a front-facing c...

Flexible Optical Ray Metrology (FORM) adds pupil diversity to phase measuring deflectometry enabling tomographic measurement of optical spaces containing multiple elements. When applied to conformal windows, FORM provides simultaneous measurement of both freeform aspheric surfaces. Article not available.

This paper presents the design of a synthetic extended source (SES) that reduces coherent noise in interferometric measurements. The SES uses a fully coherent source for data acquisition to preserve high-contrast interferograms. Multiple measurements are made while the point source is translated according to a prescribed trajectory. The average of...

The origin of the Optical Sciences Center (OSC) at the University of Arizona was closely tied to the need to expand the national capability for manufacturing large optics. This connection allowed OSC to grow quickly to become a truly unique place where new technologies are born and applied and where students have opportunities to apply academic les...

We present our analysis methodology for a 20.3 cm prototype optical tracker to determine why instabilities occur below 50 Hz and suggest improvements. The Navy Precision Optical Interferometer makes use of six small optical telescope stations spaced along a Y-array to synthesize an equivalent single larger telescope. Piezoelectric-driven optical tr...

The Steward Observatory Mirror Lab is nearing completion of the combined primary and tertiary mirrors of the Large Synoptic Survey Telescope. Fabrication of the combined mirror requires simulation of an active-optics correction that affects both mirror surfaces in a coordinated way. As is common for large mirrors, the specification allows correctio...

The Large Synoptic Survey Telescope (LSST) is a three-mirror wide-field survey telescope with the primary and tertiary mirrors on one monolithic substrate1. This substrate is made of Ohara E6 borosilicate glass in a honeycomb sandwich, spin cast at the Steward Observatory Mirror Lab at The University of Arizona2. Each surface is aspheric, with the...

Segment production for the Giant Magellan Telescope is well underway, with the off-axis Segment 1 completed, off-axis Segments 2 and 3 already cast, and mold construction in progress for the casting of Segment 4, the center segment. All equipment and techniques required for segment fabrication and testing have been demonstrated in the manufacture o...

Large telescope mirrors are typically measured using interferometry, which can achieve measurement accuracy of a few nanometers. However, applications of interferometry can be limited by small dynamic range, sensitivity to environment, and high cost. We have developed a range of surface measurement solutions using SCOTS, the Software Configurable O...

Large telescope mirrors have stringent requirements for surface irregularity on all spatial scales. Large scale errors, typically represented with Zernike polynomials, are relatively easy to control. Errors with smaller spatial scale can be more difficult because the specifications are tighter. Small scale errors are controlled with a combination o...

A 4-mirror prime focus corrector is under development to provide seeing-limited images for the 10-m aperture Hobby- Eberly Telescope (HET) over a 22 arcminute wide field of view. The images created by the spherical primary mirror are aberrated with 13 arcmin diameter point spread function. The University of Arizona is developing the 4-mirror wide f...

The Giant Magellan Telescope (GMT) is one of the extremely large telescopes of the next generation. The GMT adaptive optics (AO) system uses an adaptive secondary mirror and natural and laser guide stars to achieve diffraction-limited images. The AO calibration source provides sources at the telescope prime focus which replicate the properties of t...

We demonstrate micron-level alignment of SMR references to patterns written on computer generated holograms, allowing the use of a laser tracker for precision alignment of CGH metrology systems.

We show a design method for non axi-symmetric optical imaging systems that uses analytic conditions to constrain aberrations that have low order field dependence, but are corrected to all orders in the pupil.

Current methods to quantify transfer function of an interferometric test are limited to off-line characterization of interferometer itself. We propose an in situ technique for measuring instrument transfer function of a complete interferometric test system.

Advanced optical surfacing technologies are applied for the Advanced Technology Solar Telescope 4.2 m off-axis primary mirror fabrication. A newly developed Stressed lap and IR deflectometry system are demonstrated for a highly deterministic manufacturing process.

We present a new high resolution deflectometry technique for mid-to-high spatial frequency measurements of precision optical surfaces. This metrology technique was verified to be accurate to within 1 nm RMS, and repeatable to 300 nrad.

This paper expands on work previously presented that describes how to calculate the vertex radius of an off-axis parabolic segment using the sag measured by a three ball spherometer. An example of the vertex radius calculation is also presented.

The Slope-Measuring Portable Optical Test System (SPOTS) is a new, portable, high-resolution, deflectometry device that achieves mid to high (20 to 1000 cyc/m) spatial frequency optical surface metrology with very little filtering and very little noise. Using a proof of concept system, we achieved 1 nm RMS surface accuracy for mid to high spatial f...

We present a new device, the diffractive optics calibrator (DOC), for measuring etching variations of computer-generated holograms (CGHs). The intensity distribution of the far-field diffraction pattern is captured and fitted to a parametric model to obtain local etching parameters such as the duty cycle, etching depth, and grating period. The sens...

Continuing to develop the sine condition test (SCTest), we show how violations of the generalized sine condition can be used to align a three-mirror anastigmat (TMA). This paper shows how the linear aberrations measured using the sine condition, along with aberrations that have constant field dependence, can be used to align a system. We discuss th...

Deflectometry is widely used to accurately calculate the slopes of any specular reflective surface, ranging from car bodies to nanometer-level mirrors. This paper presents a new deflectometry technique using binary patterns of increasing frequency to retrieve the surface slopes. Binary Pattern Deflectometry allows almost instant, simple, and accura...

The camera lens effects for deflectometry surface measurements are analyzed. The evaluations of aberration induced errors are based on image simulation. Experiments for verification are undergoing.

Conventional design of imaging systems applies rules for low order aberration correction followed by numerical optimization. A different approach is shown that develops freeform surfaces directly to satisfy fundamental relations that underlie image formation.

Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal s...

One mathematical error from [ Appl. Opt. 50, 6391–6398 (2011)] is corrected in this erratum.

ITF is usually over looked during the deflectometry measurements, especially when low spatial frequency errors are the main test focus. However, real data shows that the effect of ITF cannot be ignored to reach high accuracy measurements of high spatial frequency features. We illustrated with simulation that ITF of SCOTS is proportional to the came...

The fabrication of computer-generated holograms (CGH) by e-beam or laser-writing machine specifically requires using polygon segments to approximate the continuously smooth fringe pattern of an ideal CGH. Wavefront phase errors introduced in this process depend on the size of the polygon segments and the shape of the fringes. In this paper, we prop...

A generalized model is developed to quantitatively describe the smoothing effects from different polishing tools used for optical surfaces. The smoothing effect naturally corrects mid-to-high spatial frequency errors that have features small compared to the size of the polishing lap. The original parametric smoothing model provided a convenient way...

The revolution in surface machining, testing and alignment of optical systems open new horizons for lens design. Imaging systems that are generally non axi-symmetric can be made. Freeform optical surfaces can be machined. In this paper we propose a method based on the generalized Sine condition for the design of aplanatic optical systems that are g...

Advanced fabrication and testing techniques produce freeform optical surfaces that lack symmetry. We summarize new methods for modeling and designing with these surfaces, as well as some practical issues with their manufacture and measurement.

By taking a new look at an old concept, we have shown in our previous work how the Abbe sine condition can be used to measure linearly field-dependent aberrations in order to verify the alignment of optical systems. In this paper, we expand on this method and discuss the design choices involved in implementing the sine condition test (SCTest). Spec...

Current metrology tools have limitations when measuring rough aspherical surfaces with 1–2 μm root mean square roughness; thus, the surface cannot be shaped accurately by grinding. To improve the accuracy of grinding, the scanning long-wave optical test system (SLOTS) has been developed to measure rough aspherical surfaces quickly and accurately wi...

High performance optical systems aiming for very low background noise from scattering or a sharp point spread function with high encircled energy often specify their beam wavefront quality in terms of a structure function or power spectral density function, which requires a control of mid-to-high spatial frequency surface errors during the optics m...

Interferometry with computer generated holograms (CGHs) has become the industry standard for accurate measurements of aspheric optical surfaces. The CGH is a diffractive optical element that can be designed to create virtually any phase or amplitude distribution, and can be accurately manufactured using methods and equipment developed for integrate...

The Hobby-Eberly Telescope (HET) Wide Field Corrector (WFC) is a four-mirror optical system which corrects for aberrations from the 10-m segmented spherical primary mirror. The WFC mirror alignments must meet particularly tight tolerances for the system to meet performance requirements. The system uses 1-m class highly aspheric mirrors, which precl...

Many scientific and industrial applications often require high performance optical systems utilizing spatially shaped illumination patterns of laser beams. Precisely shaped line illumination can be used for various line scanning systems or surface inspection devices. In order to achieve the highest resolution or superior signal to noise ratio limit...

We present a new device, the Diffractive Optics Calibrator (DOC), for measuring duty-cycle and etching depth for computer generated holograms (CGH). The system scans the CGH with a collimated laser beam, and collects the far field diffraction pattern with a CCD array. The relative intensities of the various orders of diffraction are used to fit the...

Modern advanced optical systems often require challenging high spatial frequency surface error control during their optical fabrication processes. While the large scale surface figure error can be controlled by directed material removal processes such as small tool figuring, surface finish (<<1mm scales) is controlled with the polishing process. Fo...

Refinements in computer controlled optical surfacing allow efficient grinding and polishing of meterclass optics to accuracy limited only by the surface metrology. We present a categorization of metrology methods and their implementation for meter-class optical components. Interferometry with computer generated holograms provides nanometer accuracy...

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. Un...

Increasing demand for highly accurate freeform aspheric surfaces requires accurate and efficient measurement techniques. One promising possibility uses a sub-aperture scanning system that measures local curvature variations across the part. In this paper, we develop and demonstrate two different data processing algorithms, a zonal approach using So...

The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength, incident angle and polarization. While measuring low frequency roughness is relatively easy, the correspondi...

SCOTS is a high precision slope measurement technology based on deflectometry. Light pattern on a LCD display illuminates the test surface and its reflected image is used to calculate the surface slope. SCOTS provides a high dynamic range full field measurement of the optics without null optics required. We report SCOTS tests on X-ray mirrors to nm...

A procedure that uses computer-generated holograms (CGHs) to align an optical system's meters in length with low uncertainty and real-time feedback is presented. The CGHs create simultaneous three-dimensional optical references, which are decoupled from the surfaces of the optics allowing efficient and accurate alignment even for systems that are n...

Absolute measurement with SCOTS/deflectometry is a calibration problem. We use a laser tracker to calibrate the test geometry. The performance id demonstrated with the initial measurement results from the Large Synoptic Survey Telescope tertiary mirror. Systematic errors from the camera are carefully controlled. Camera pupil imaging aberration is r...

A software configurable optical test system (SCOTS) based on deflectometry was developed at the University of Arizona for rapidly, robustly, and accurately measuring precision aspheric and freeform surfaces. SCOTS uses a camera with an external stop to realize a Hartmann test in reverse. With the external camera stop as the reference, a coordinate...

Computer-generated holograms are often used to test aspheric surfaces. This paper provides a parametric model for the CGH phase function using the exact geometric model. The phase function is then used to derive the sensitivity functions to alignment errors in testing. When using the CGH to test aspheric surface, it is important to separate the dif...

The Computer-controlled Large-tool such as the stressed-lap which firstly developed in the Steward Observatory Mirror Lab (SOML) [1]and the Computer controlled active lap which developed in the IOE (Institute of Optics and Electronics, Chinese Academy of Science), those large tools are controlled by computer to manufacturing large optics, especiall...

Several meter size steep aspheric optics, with aspheric departure ranging from 100μm to 2mm, have been successfully fabricated at the College of Optical Sciences at University of Arizona. Optical metrology systems have been developed for measuring the optical surfaces efficiently and accurately. These systems include laser tracker surface profiler,...

Previous works have shown the viability of using the Sine Condition Test (SCTest) to verify the alignment of optical systems. The SCTest uses the Abbe sine condition to measure the mapping between the entrance and exit pupils of an optical system. From this pupil mapping, the linearly-field dependent aberrations can be measured and used to verify t...

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...

We present the thermal sieve, which is a diffractive baffle that provides thermal isolation between an ambient collimator and a cryogenic optical system being measured. The baffle uses several parallel plates with holes in them. The holes are lined up to allow the collimated light to pass, but the view factor for thermal radiation is greatly reduce...

Production of segments for the Giant Magellan Telescope is well underway at the Steward Observatory Mirror Lab. We report on the completion of the first 8.4 m off-axis segment, the casting of the second segment, and preparations for manufacture of the remaining segments. The complete set of infrastructure for serial production is in place, includin...

A software configurable optical test system (SCOTS) based on fringe reflection was implemented for measuring the primary mirror segments of the Giant Magellan Telescope (GMT). The system uses modulated fringe patterns on an LCD monitor as the source, and captures data with a CCD camera and calibrated imaging optics. The large dynamic range of SCOTS...

Full aperture interferometric metrology has enabled fabrication and verification of large primary mirrors with nm precision. The measurement of mirrors that are several meters in diameter with flat or convex aspheric surfaces can be performed using interferometric measurements of overlapping subaperture regions, then stitching the date from these m...

As previously reported (at the SPIE Astronomical Instrumentation conference of 2010 in San Diego1), the Large Synoptic Survey Telescope (LSST) utilizes a three-mirror design in which the primary (M1) and tertiary (M3) mirrors are two concentric aspheric surfaces on one monolithic substrate. The substrate material is Ohara E6 borosilicate glass, in...

When defining surface irregularities more often than not it is useful to represent these as slope errors rather than surface errors. However, surface error specifications are more commonly used even though they do not accurately represent performance but simply physical characteristics. An example of slope measurement technique and specification is...

While the use of Zernike polynomials to represent simulated or measured data on a grid of points is common, the accuracy of the coefficients can be limited by the non-orthogonality of the functions over the pixelated domains. The Zernike polynomials are defined to be analytically orthogonal over a circular domain, but this breaks down for discrete...

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...

Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. Intended for practicing optical and mechanical engineers whose work involves both fields, this SPIE Field Guide describes how to mount optical components, as well as how to analyze a given design. Common issues involved with mounting...

The swing arm optical coordinate-measuring machine (SOC), a profilometer with a distance measuring interferometric sensor for in situ measurement of the topography of aspheric surfaces, has shown a precision rivaling the full aperture interferometric test. To further increase optical manufacturing efficiency, we enhance the SOC with an optical lase...

Control of mid-spatial-frequency errors on precision optical surfaces is very important for next-generation optical systems. We present results of smoothing experiments and of polishing runs utilizing figuring and smoothing for the 8.4m GMT off-axis segment.

The interferometric test for the 8.4m off-axis segment of the GMT primary mirror uses a complex null corrector that introduces a large amount of mapping distortion. This paper discusses the mapping correction for this test.

SAGUARO software is written for the optical engineer and designed to simplify data analysis and visualization. SAGUARO is easy for the end-user processing optical test information as well as the developer adding new functionalities.

Mixed-mode grinding occurs when a bound abrasive works in both brittle and ductile regimes simultaneously. Substrates ground in a mixed-mode behavior show reduced curvature induced by compressive surface forces than loose abrasives as demonstrated by observing the Twyman effect. This reduction in bending corresponds to reduced subsurface damage. Th...

Full aperture testing of large cryogenic optical systems has been impractical due to the difficulty of operating a large collimator at cryogenic temperatures. The Thermal Sieve solves this problem by acting as a thermal barrier between an ambient temperature collimator and the cryogenic system under test. The Thermal Sieve uses a set of thermally c...

In a previous paper, the University of Arizona (UA) has developed a measurement technique called: Software Configurable Optical Test System (SCOTS) based on the principle of reflection deflectometry. In this paper, we present results of this very efficient optical metrology method applied to the metrology of X-ray mirrors. We used this technique to...

The swing-arm optical coordinate measuring machine (SOC), a profilometer with a distance-measuring interferometric probe for in situ measurement of the topography of aspheric surfaces,has been used for measuring highly aspheric mirrors with a performance rivaling full aperture interferometric tests. Recently, we implemented a dual probe, self-calib...

We present a simple method to determine the relative distortion of axially symmetric lens systems. This method uses graphs to determine every parametric value instead of nonlinear minimization computation and is composed of an LCD screen to display a square grid pattern of pixel-wide spots and a set of analyzing processes for the spots in the image...

Rather than measuring aberrations across the field to quantify the alignment of an optical system, we show how a single, on-axis measurement of the pupil mapping can be used to measure the off-axis performance of the system and determine the state of alignment. In this paper we show how the Abbe sine condition can be used to relate the mapping betw...

An experimental test for violations of the sine condition is presented. This test is particularly useful for identifying the state of alignment of an imaging system because it provides a direct measurement of the linear astigmatism (astigmatism that varies linearly with field) in a system using only on axis measurements. The concept of the test is...

This paper outlines methods for dimensioning and tolerancing lens seats that mate with spherical lens surfaces. The two types of seats investigated are sharp corner and tangent contact. The goal is to be able to identify which seat dimensions influence lens tilt and displacement and develop a quantifiable way to assign tolerances to those dimension...

We characterize the precision of a low uncertainty alignment procedure that uses computer generated holograms as center references to align optics in tilt and centration. This procedure was developed for the alignment of the Wide Field Corrector for the Hobby Eberly Telescope, which uses center references to provide the data for the system alignmen...