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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.

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 field corrector to compensate the aberrations from the primary mirror and present seeing limited imaged to the pickoffs for the fiber-fed spectrographs. The requirements for this system pose several challenges, including optical fabrication of the aspheric mirrors, system alignment, and operational mechanical stability. This paper presents current status of the program which covers fabrication of mirrors and structures and pretest result from the alignment of the system.

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 the natural and laser guide stars, to calibrate and verify the performance of the AO system. We present an optical design for this calibration source, and discuss the expected accuracy based on the tolerance analysis.

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 precludes conventional alignment methods. For the WFC system alignment a “center reference fixture” has been used as the reference for each mirror’s vertex and optical axis. The center reference fixtures have both a CGH and sphere mounted retroreflector (SMR) nests. The CGH is aligned to the mirror’s optical axis to provide a reference for mirror decenter and tilt. The vertex of each mirror is registered to the SMR nests on the center reference fixtures using a laser tracker. The spacing between the mirror vertices is measured during the system alignment using these SMR nest locations to determine the vertex locations. In this paper we present the procedures and results from creating and characterizing these center reference fixtures. As a verification of our alignment methods we also present results from their application in the WFC system alignment are also presented.

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 integrated circuit production. Surface measurements with nanometer level precision can be performed using accurately wellcalibrated equipment. This paper provides a systematic analysis of all significant sources of error for CGH metrology, including encoding error, pattern distortion, substrate irregularity and calibration, and system alignment.

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.

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 for full surface measurements of a wide range of convex and concave aspheric surfaces. For measuring off-axis and freeform aspheric surfaces, the holograms include features that provide references for alignment. Very high spatial resolution is achieved with subaperture interferometric measurements which can be stitched together to provide a full-aperture map. Scanning systems complement the capabilities of interferometry by achieving larger dynamic range and providing independent corroboration. Optical coordinate measurement machines (CMMs) provide non-contact measurements of surfaces in their ground state to guide figuring, as well as highly accurate measurements of finished optics. Scanning systems for measuring flat mirrors provide excellent resolution and absolute accuracy. The performance and practical issues for this full array of measurement techniques are presented to show the relative strengths of each method.

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 Southwell integration method and a modal approach leveraging Zernike curvature basis, that reconstruct the surface 3-dimensional profiles from the curvature data. The performance of suggested methods and the sensitivity to noise is diagnosed for various SNR (Signal-to-Noise Ratio) cases.

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 phase shift from etching and the duty cycle of the binary pattern. The system is capable of measuring variations that cause 1 nm PV phase errors in the wavefront created by the CGH. The measurements will be used primarily for quality control CGHs, but the data can also be used to provide a lookup table for corrections that allow calibration of the lithography errors. Such calibration may be necessary for us to achieve our goal of measuring freeform aspheric surfaces with 1 nm RMS accuracy.

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, swing arm optical CMM with different type of sensors, slope measurements with SCOTS, the Software Configurable Optical Test System (SCOTS) and interferometry with computer generated holograms. We summarize the test methods and provide comparison of the relative strengths and weaknesses.

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 a honeycomb sandwich configuration, currently in production at The University of Arizona’s Steward Observatory Mirror Lab. We will provide an update to the status of the mirrors and metrology systems, which have advanced from concepts to hardware in the past two years. In addition to the normal requirements for smooth surfaces of the appropriate prescriptions, the alignment of the two surfaces must be accurately measured and controlled in the production lab, reducing the degrees of freedom needed to be controlled in the telescope. The surface specification is described as a structure function, related to seeing in excellent conditions. Both the pointing and centration of the two optical axes are important parameters, in addition to the axial spacing of the two vertices. This paper details the manufacturing process and metrology systems for each surface, including the alignment of the two surfaces. M1 is a hyperboloid and can utilize a standard Offner null corrector, whereas M3 is an oblate ellipsoid, so it has positive spherical aberration. The null corrector is a phase-etched computer-generated hologram (CGH) between the mirror surface and the center-of-curvature. Laser trackers are relied upon to measure the alignment and spacing as well as rough-surface metrology during looseabrasive grinding.

Aspheric surfaces are often measured using interferometers with null correctors. The null corrector creates a wavefront that matches the surface under test, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations cause high frequency features in the surface under test to be filtered out and create artifacts at edges. We provide a concise methodology for analyzing these effects using field curvatures, and showing how they couple with diffraction as represented by the Talbot effect and Fresnel edge diffraction.

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 measurements together to provide a full map. This paper explores the application of this measurement technique for very large mirrors, and discusses issues for measuring large flat or convex mirrors.

Aspheric surfaces are measured using standard interferometers coupled with computer generated holograms (CGHs) that compensate the aspheric wavefronts. Such systems can measure complex aspheric shapes with accuracy of a few nanometers. However, the imaging properties of the interferometer-CGH combination can provide limitations for data mapping, resolution, and accuracy. These effects are explored, with an emphasis on the diffraction effects that are unique to interferometry.

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 a honeycomb sandwich configuration, currently in production at The University of Arizona’s Steward Observatory Mirror Lab. In addition to the normal requirements for smooth surfaces of the appropriate prescriptions, the alignment of the two surfaces must be accurately measured and controlled in the production lab. Both the pointing and centration of the two optical axes are important parameters, in addition to the axial spacing of the two vertices. This paper describes the basic metrology systems for each surface, with particular attention to the alignment of the two surfaces. These surfaces are aspheric enough to require null correctors for each wavefront. Both M1 and M3 are concave surfaces with both non-zero conic constants and higher-order terms (6 th order for M1 and both 6 th and 8 th orders for M3). M1 is hyperboloidal and can utilize a standard Offner null corrector. M3 is an oblate ellipsoid, so has positive spherical aberration. We have chosen to place a phase-etched computer-generated hologram (CGH) between the mirror surface and the center-of-curvature (CoC), whereas the M1 null lens is beyond the CoC. One relatively new metrology tool is the laser tracker, which is relied upon to measure the alignment and spacings. A separate laser tracker system will be used to measure both surfaces during loose abrasive grinding and initial polishing.

Large aspheric primary mirrors are proposed that use hundreds segments that all must be aligned and phased to approximate the desired continuous mirror. We present a method of measuring these concave segments with a Fizeau interferometer where a spherical convex reference surface is held a few millimeters from the aspheric segment. The aspheric shape is accommodated by a small computer generated hologram (CGH). Different segments are measured by replacing the CGH. As a Fizeau test, nearly all of the optical elements and air spaces are common to both the measurement and reference wavefront, so the sensitivities are not tight. Also, since the reference surface of the test plate is common to all tests, this system achieves excellent control for the radius of curvature variation from one part to another. This paper describes the test system design and analysis for such a test, and presents data from a similar 1.4-m test performed at the University of Arizona.

The Giant Magellan Telescope has a 25 meter f/0.7 near-parabolic primary mirror constructed from seven 8.4 meter diameter segments. Several aspects of the interferometric optical test used to guide polishing of the six off-axis segments go beyond the demonstrated state of the art in optical testing. The null corrector is created from two obliquelyilluminated spherical mirrors combined with a computer-generated hologram (the measurement hologram). The larger mirror is 3.75 m in diameter and is supported at the top of a test tower, 23.5 m above the GMT segment. Its size rules out a direct validation of the wavefront produced by the null corrector. We can, however, use a reference hologram placed at an intermediate focus between the two spherical mirrors to measure the wavefront produced by the measurement hologram and the first mirror. This reference hologram is aligned to match the wavefront and thereby becomes the alignment reference for the rest of the system. The position and orientation of the reference hologram, the 3.75 m mirror and the GMT segment are measured with a dedicated laser tracker, leading to an alignment accuracy of about 100 microns over the 24 m dimensions of the test. In addition to the interferometer that measures the GMT segment, a separate interferometer at the center of curvature of the 3.75 m sphere monitors its figure simultaneously with the GMT measurement, allowing active correction and compensation for residual errors. We describe the details of the design, alignment, and use of this unique off-axis optical test.

The primary mirror of the Giant Magellan Telescope consists of seven 8.4 m segments which are borosilicate honeycomb sandwich mirrors. Fabrication and testing of the off-axis segments is challenging and has led to a number of innovations in manufacturing technology. The polishing system includes an actively stressed lap that follows the shape of the aspheric surface, used for large-scale figuring and smoothing, and a passive "rigid conformal lap" for small-scale figuring and smoothing. Four independent measurement systems support all stages of fabrication and provide redundant measurements of all critical parameters including mirror figure, radius of curvature, off-axis distance and clocking. The first measurement uses a laser tracker to scan the surface, with external references to compensate for rigid body displacements and refractive index variations. The main optical test is a full-aperture interferometric measurement, but it requires an asymmetric null corrector with three elements, including a 3.75 m mirror and a computer-generated hologram, to compensate for the surface's 14 mm departure from the best-fit sphere. Two additional optical tests measure large-scale and small-scale structure, with some overlap. Together these measurements provide high confidence that the segments meet all requirements.

Aspheric surfaces, such as telescope mirrors, are commonly measured using interferometry with computer generated hologram (CGH) null correctors. The interferometers can be made with high precision and low noise, and CGHs can control wavefront errors to accuracy approaching 1 nm for difficult aspheric surfaces. However, such optical systems are typically poorly suited for high performance imaging. The aspheric surface must be viewed through a CGH that was intentionally designed to introduce many hundreds of waves of aberration. The imaging aberrations create difficulties for the measurements by coupling both geometric and diffraction effects into the measurement. These issues are explored here, and we show how the use of larger holograms can mitigate these effects.

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 HET uses an 11-m fixed elevation segmented spherical primary mirror, with pointing and tracking performed by moving the prime focus instrument package (PFIP) such that it rotates about the virtual center of curvature of the spherical primary mirror. 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 field corrector to compensate the aberrations from the primary mirror and present seeing limited imaged to the pickoffs for the fiber-fed spectrographs. The requirements for this system pose several challenges, including optical fabrication of the aspheric mirrors, system alignment, and operational mechanical stability.

Coddington Equations are used to calculate the astigmatic images of a small bundle of rays centered on a ray commonly known as the principal ray. Some authors generalize it such that for a refractive or reflective surface of any shape to the 2nd order, and an incident wavefront of any shape to the 2nd order, the refracted or reflected wavefront can be calculated to the 2nd order. We extend it further such that it applies to the diffractive surface as well. The derivation is based on the general Snell's law and differential ray tracing approach. We present these generalized Coddington Equations in two forms: matrix formalism and explicit expressions. The equations are verified with explicit ray tracing using a commercial lens design program. The relations are applied to evaluate the imaging performance for null testing of aspheric surfaces using computer generated holograms.

New developments in fabrication and testing techniques at th e College of Optical Sciences, University of Arizona have allowed successful completion of 1.4-m diameter convex off-axis aspherics. The optics with up to 300 µm aspheric departure were finished using a new method of computer controlled polishing and measured with two new optical tests: the Swingarm Optical CMM (SOC) and a Fi zeau interferometer using a spherical reference surface and CGH correction. This paper shows the methods and equipment used for manufacturing these surfaces. Keywords: Optical fabrication, aspheres, optical testing, large optics 1. INTRODUCTION Fabrication of large optical surfaces is difficult because of the complicated tooling needed for all stages of handling, manufacturing, and measuring. Aspheric surfaces are especia lly difficult because the polishing tools need to conform to a non-spherical shape, and the measurement cannot rely on the symmetry provided by spherical shapes. Off-axis aspheres cannot even use the axisymmetry of more common aspheric shapes, which are figures of revolution. The unique difficulty for convex surfaces arises from the difficulty performing optical tests – reflection from a concave surface causes light to converge, allowing the test system to be smaller than the optic being measures. Reflection from a convex surface causes the light to diverge, requiring auxiliary optics that are larger then the surface being measured. We present the successful completion of such surfaces that are la rge (1.4 meters in diameter), non-symmetric aspheres (off axis portions of a paraboloid or OAP, having up to 300 µm aspheric departure), and convex (requiring new optical test methods). This paper summarizes the manufacturing for these OAPs, emphasizing the techniques developed at University of Arizona that are novel and interesting on their own. The po lishing of the aspherical surf aces was performed with a new class of computer controlled polishing machines that use the swing arm geometry to provide robust motion control. The measurement of the optical surface was performed using two methods: x Swing arm Optical CMM SOC: A new machine was constructed that provide two-dimensional shape information from a series of scans that use swing arm geometry and utilize an interferometric, non-contact measurement. These measuremen ts are accurate to ~6 nm rms.

We developed a complete and orthonormal set of vector polynomials defined over a unit circle. One application of these vector polynomials is for fitting the mapping distortions in an interferometric null test. This paper discusses the source of the mapping distortions and the approach of fitting the mapping relations, and justifies why the set of vector polynomials is the appropriate choice for this purpose. Examples are given to show the excellent fitting results with the polynomials.

Optical testing of a large convex aspheric surface, such as the secondary of a Ritchey-Chretien telescope, can be performed with a Fizeau interferometer that utilizes subapertur e aspheric reference plates, each providing a null test of a subaperture of the larger mirror. The subaperture data can be combined or stitched together to create a map of the full surface. The region of the secondary mirror surface under test in each sub-aperture is an off-axis segment of the parent aspheric surface, therefore, the Fizeau reference requires a non-axi-symmetric aspheric surface to match it. Misalignment of the Fizeau reference relative to the parent in each sub-aperture will then result in aberrations in the measurements other than the ordinary terms of piston and tilt. When stitching sub-aperture measurements together, the apparent aberrations due to the null lens misalignment need to be fitted and subtracted. This paper presents an algorithm to perform this particular type of stitching. Keywords: optical testing, stitching, aspheric optics

We describe methods to correct both symmetric and asymmetric distortion mapping errors induced by null testing elements such as holograms or null lenses. We show experimental resu lts for direct measurement and correction of symmetric mapping distortion, as well as an example result for analytical mapping performed using an orthogonal set of vector polynomials for asymmetric correction. The empirical determination of symmetric distortion is made via calculation from predicted and measured changes to aberrations induced via known changes to the testing point. 1. INTRODUCTION Aspheric primary mirrors are popular for astronomical telescope systems. These mirrors are polished to aspheric shapes to help minimize the overall length of the telescope system and provide additional optical correction for improved telescope performance. Optical testing with high accuracy is necessary, from as early a point in the fabrication process as is feasible, to efficiently converge to the proper finished optical surface. One potential obstacle encount ered when fabricating aspheric su rfaces is distortion present when imaging through null elements in the optical test. Dist ortion arises due to imperfect imaging through a null lens system and other optics in an interferometer or through a transmission CGH. The presence of distortion diminishes accuracy by mapping surface features to incorrect radial positions on the image plane. In this paper, we describe a method used to determine symmetric distortion which may prove practical for large asphere testing, as well as a more general correction method for asymmetric distortion. These techniques can be used to enable efficien t testing of aspheric optical surfaces.

To test an aspheric surface, usually a null lens is designed to create an aspheric wavefront that matches the surface. The null lens also relays the image of the surface under test to the interferometer. The effect of image distortion from the null lens is well known, and is accommodated by remapping the data. Imaging aberrations created by the null lens also affect the measurement by smoothing out wavefront errors which correspond to ripples in the surface. This leads to data that does not faithfully represent the surface. We characterize this smoothing using a measurement transfer function, which is analogous to the modulation transfer function used to quantify the performance of imaging systems. In this paper we present a technique and tools for predicting the transfer function for a null test.

Computer generated holograms (CGHs) have been successfully used for wavefront correction for measuring aspheric surfaces. Features on the CGHs have assisted the alignment of the optical test equipment. CGHs can also be used to provide alignment references for other complex optical systems. This paper discusses the types of CGHs that can be used for optical alignment and gives some examples.

Laser trackers have been developed that project laser beams and use optical systems to provide three dimensional coordinate measurements. The laser trackers incorporate a servo system to steer a laser beam so that it tracks a retroreflector, such as a corner cube. The line of sight gimbal angles and the radial distance to the retroreflector are used to determine the coordinates of the retroreflector relative to the tracker. In this paper, we explore the use of the laser tracker to define the metrology for aligning optical systems, including the use of mirrors and windows. We discuss how to optimize the geometry to take advantage of the tracker’s most accurate measurements. We show how to use the tracker for measuring angles as well as points.

Large flat mirrors can be measured by using subaperture Fizeau interferometer and stitching the data. We have implemented such a system that can efficiently and accurately measure flat mirrors several meters in diameter using a 1 meter sub-aperture instantaneous Fizeau interferometer, coupled with sophisticated analysis software. The 1-m aperture optical system uses a fused silica test plate, reflective collimator, and commercial instantaneous interferometer. Collimator errors, mapping distortion, surface errors in the test plate, and other systematic effects were measured and compensated for individual measurements. Numerous individual maps were stitched together to determine the global shape of a 2-m class flat.

The Giant Magellan Telescope (GMT) uses seven 8.4-m diameter segments to create a giant primary mirror, 25 meters across with focal ratio f /0.7. The off-axis segments will be difficult to measure accurately, as they have 14.5 mm departure from the nearest fitting sphere! The test configuration adopted uses a large 3.75-m powered mirror to fold the light path and provide most of the aspheric correction, with a smaller mirror and computer generated hologram (CGH) providing the additional correction. These optics will be aligned to a vibration-insensitive interferometer using a combination of optical references created by the CGH and metrology with a laser tracker. Some key challenges for this system are presented here including, the system alignment, the large fold mirror, and the mechanical structure. Analysis of the optical test shows that it will meet GMT specifications, including the difficult requirement that the separate segments have matching radius of curvature. Additional corroborative testing will be performed to assure that the mirror segments are correctly figured.

Large diameter, non-axisymmetric aspheric mirrors can be measured interferometrically using null correctors that employ computer generated holograms (CGHs). The testing of off axis segments for the new class of giant telescopes pose requirements that beyond the state of the art for CGHs alone. The long radius of curvature and the magnitude of the aspheric departure require other lenses and mirrors to be used along with the CGH. The alignment of these systems is very sensitive and the absolute accuracy of the alignment is critical to the system performance. We have developed techniques that use diffracted light from patterns on the CGH to accurately define the alignment of multi-element null correctors. We will present results from the null test of the 1.7-m New Solar Telescope primary mirror. The optical shape of this mirrors is an off-axis paraboloid from an f/0.7 parent.

The primary mirror for the 25-m Giant Magellan Telescope is made of seven circular segments, each of 8.4-m diameter. The lack of axisymmetry and the steep aspheric departure present significant technical challenges for the metrology. These segments will be measured interferometrically using a complex system of mirrors and holograms to give a null test with high spatial resolution. While analysis predicts this system will meet requirements, an additional set of measurements will be used to corroborate the principal interferometric measurement. The set of tests, including these alternate surface measurements, assures that all aspects of the mirror surface are measured completely and redundantly. The corroboration tests discussed in this paper are: x Direct surface profile using metrology system based on a laser tracker, measuring low order shape errors x Shear testing with full aperture interferometer, separating small scale errors in the null test from those in the mirror x Slope testing with scanning pentaprism, measuring low order shape errors and sampling small scale errors

We have nearly completed the manufacture of a 1.7 m off-axis mirror as part of the technology development for the Giant Magellan Telescope. The mirror is an off-axis section of a 5.3 m f/0.73 parent paraboloid, making it roughly a 1:5 model of the outer 8.4 m GMT segment. The 1.7 m mirror will be the primary mirror of the New Solar Telescope at Big Bear Solar Observatory. It has a 2.7 mm peak-to-valley departure from the best-fit sphere, presenting a serious challenge in terms of both polishing and measurement. The mirror was polished with a stressed lap, which bends actively to match the local curvature at each point on the mirror surface, and works for asymmetric mirrors as well as symmetric aspheres. It was measured using a hybrid reflective-diffractive null corrector to compensate for the mirror's asphericity. Both techniques will be applied in scaled-up versions to the GMT segments.

A scanning pentaprism system may be used as an absolute test for an optical flat. Such a system was built and used to test a 2-meter flat mirror. This system uses light from an autocollimator that is reflected from 2 pentaprisms to project reference beams of light onto the flat mirror. The light reflected from the mirror back through the pentaprisms provides information on low order optical aberrations in the flat mirror. We report results of the test on a 2-meter flat.

Interferometers that use different states of polarization for the reference and test beams can modulate the relative phase shift using polarization optics in the imaging system. This allows the interferometer to capture simultaneous images that have a fixed phase shift, which can be used for phase shifting interferometry. Since all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have advantage over Twyman-Green type systems because the optics are in the common path of both the reference and test wavefronts, therefore errors in these optics affect both wavefronts equally and do not limit the system accuracy. However, this is not strictly true for the polarization interferometer when both wavefronts are transmitted an optic that suffers from birefringence. If some of the components in the common path of the reference and test beams have residual birefringence, the two beams see different phases. Therefore, the interferometer is not strictly common path. As a result, an error can be introduced in the measurement. In this paper, we study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically for small amount of birefringence if the reference and test beams are circularly polarized rather than linearly polarized.

Aberrations of imaging systems can be described using a polynomial expansion of the dependence on field position. Aberrations on axis and those with linear field dependence can be calculated and controlled using Fermat's principle and the Abbe Sine Condition. We now present a powerful new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations, derived using Hamilton's characteristic functions, which we call the Pupil Astigmatism Criteria, use on-axis behavior to evaluate and control all aberrations with quadratic field dependence and arbitrary dependence on the pupil. These relations are explained, validated, and applied to design optical systems that are free of all quadratic field dependent aberrations.

We will present a system to perform closed-loop optical tests of the 64 cm diameter, 336 actuator adaptive secondary made at the Steward Observatory Mirror Laboratory. Testing will include Shack-Hartmann wavefront sensing and modal correction of static and dynamic aberrated wavefronts. The test optical system is designed so that experiments can be made with both the focal plane instrument and secondary installed in their normal configuration at the MMT, or with the same 9 m spacing in a laboratory test tower. The convex secondary will be illuminated at normal incidence through two 70 cm diameter lenses mounted just below. The artificial, aberrated star is projected from near the wavefront sensor in the Cassegrain focus assembly. Computer generated holograms correct for spherical aberration in the really optics at the test wavelengths of 0.594 and 1.5 micrometers . Atmospheric turbulence is reproduced by two spinning transmission plates imprinted with Kolmogorov turbulence. The Shimmulator will give us the opportunity to test fully the adaptive optics system before installation at the new MMT, hence saving much precious telescope time.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.