1. Zero field The 25 ‑ m f /0.7 primary mirror for the Giant Magellan Telescope (GMT) is made of seven 8.4 ‑ m segments in a close packed array. Each of the off-axis mirror segments has 14 mm of aspheric departure, which makes the fabrication and testing of the segments challenging The pentaprism test is based on the property of a paraboloidal surface where all rays parallel to the optical axis will be reflected to go through the focal point. We have developed a scanning pentaprism system that exploits this geometry to measure off-axis paraboloidal mirrors such as those for the Giant Magellan Telescope primary mirror. Extension of the pentaprism test to off- axis mirrors requires special attention to field effects that can be ignored in the measurement of an axisymmetric mirror. The test was demonstrated on a 1.7-m diameter off-axis mirror and matched an interferometric test of this surface to 32 nm rms. This paper gives detailed performance results for the measurement of the 1.7-m mirror, and designs and analysis for the test of the GMT segments. Scanning pentaprism measurements of off-axis aspherics Peng Su a, James H. Burge a,b, Brian Cuerden b, Hubert M. Martin b a College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA b Steward Observatory, University of Arizona, Tucson, AZ 85721, USA GMT The scanning prism is moved across different diameters of the off axis mirror. As a result, the scans do not have symmetry of the parent Contributions to in-scan motionContributions to cross-scan motion Beam projector pitchBeam projector yaw (Prism yaw) 2 Prism yaw (Prism yaw) x (beam projector yaw)Prism roll (Prism roll) x (beam projector yaw)(Prism roll) x (beam projector pitch) (Detector roll) x (cross-scan motion)(Prism yaw) x (beam projector pitch) Table 1 Contributions to line-of-sight error from prism, beam projector, and determination of in-scan direction Scanning pentaprism system layout Flow diagram for data collection and processing In-scan spot displacements at CCD after subtracting motion of the reference spot. The fit to the Zernike polynomials is shown. Fig.9 Residuals after removing the polynomial fit and field aberrations Pentaprism measurement Interferometric test aberration interferometerpentaprism nm rms surface astigmatism 0° 8 9 ± 23 astigmatism 45° 0 -2 ± 23 coma 0°-87-98 ± 12 coma 90° -4 16 ± 12 trefoil 0°-50-32 ± 35 trefoil 30° 9 23 ± 30 spherical-32-35 ± 8 Table 2. Surface coefficients from pentaprism test and interferometric test for the 1.7-m NST mirror Issue with testing off-axis mirror If the parabolic mirror is illuminated with collimated light that is parallel to its axis, all reflected rays go through the focal point of the parabola. If these rays are not parallel to the axis, the rays will shift away from the focal point and they no longer intersect at a point. For a full axially symmetric mirror, this appears as well-known coma. The off-axis segment covers part of the comatic pattern, which appears as a combination of astigmatism and coma in the wavefront. The magnitude of this aberration is linear with the misalignment. The pentaprism test for an off-axis parabola has some special characteristics when compared with the test for a rotationally symmetric surface. One of the four scans is in the plane containing the optical axis of the parent. Plane symmetry is not available for scans 2, 3 and 4. Moreover, as an off- axis part of a parabolic surface, the mirror suffers field aberrations. For the case of the GMT test, there is a 2.3:1 ratio between the image location (chief ray) shift and the coma blur in the tangential direction. The mirror acts as if the focal length depends on position. Because of the two features mentioned above, the in-scan and cross-scan directions of the test in the detector plane change orientation at different pupil locations during a single scan. An intuitive way to understand this is shown below. A cross scan error would generally shift the image to the right, but because of the field aberration, the light from different portions of the pupil are shifted by different amounts and they have a component in the orthogonal direction. The red dots below show this effect for a linear scan at 45° for the off axis segment. Changes in field angle will linearly shift and scale the spot diagram. The cross-scan direction depends on pupil position. Wave aberrations due to 0.001° field of views Test for GMT mirror segment Pentaprism rail lies in plane perpendicular to parent axis. Hub rotates rail to scan different diameters. Scanning pentaprism test as implemented for GMT off-axis segments. Pentaprism rail is suspended from tower. Table 3. Performance estimate: Monte Carlo analysis of 1 μrad rms random error in wavefront slope for NST test as performed, NST test with 40 points/scan uniform sampling, and the GMT test sampled the same way aberration rms surface error (nm) As sampled as in NST measurement rms surface error (nm) NST mirror (40 points/scan) rms surface error (nm) GMT segment (40 points/scan) Focus15944 Sine Astigmatism231784 Cosine Astigmatism231784 Sine Coma12630 Cosine Coma12630 Sine Trefoil352099 Cosine Trefoil352099 Spherical aberration8420 RSS5836180 The scanning prism is translated across the mirror diameter while the fixed prism is held stationery. Variations in the pitch direction are insensitive to errors in the prism or motion. The prism is actively controlled in roll and yaw based on feedback from an autocollimator and from the CCD at the focus So one component of mirror slope errors (defined by the pitch direction of the prism) can be measured to < 1 µrad accuracy Basic Concept An ideal parabolic mirror will focus rays parallel to the axis to a point at the focus. One can measure errors in the surface by sending parallel rays into the mirror and measuring where they intercept the focal plane. The scanning pentaprism system uses a collimated light source and a pentaprism to create parallel beams that are scanned over the surface, as shown above. For an off-axis mirror, several scans across different diameters are used to determine the low- order aberrations in the system. We used four pentaprism scans at 45° to provide sampling of low order surface errors. Variations in tilt of the collimated source, or beam projector, also cause spot motion. We remove this error by using a stationary pentaprism in addition to the scanning pentaprism. Common motion of both spots is due to changes in the beam projector, while the differential motion is a measure of the slope error at the pupil position of the scanning beam. The pentaprism test works because the deflection of the beam in the pitch direction, defined in the figure above, is independent of rotation. The corresponding direction on the mirror surface and in the focal plane is called the in-scan direction, and the perpendicular direction is the cross-scan direction. The scanning pentaprism system measures slope errors in the in-scan direction with high accuracy. Rotation of the prism about its other axes (roll and yaw) causes first- order deflection of the beam in the cross-scan direction, so we do use the cross-scan information only as a guide to align the system, not as a measurement of surface slopes. The only direct coupling to in-scan spot motion is a change in pitch of the beam projector, and this is removed by the differential measurement with two pentaprisms. There are second-order effects, however, that must be considered. Table 1 lists sources of line-of-sight error, to second order. Prism yaw will introduce quadratic motions in the in-scan direction, and yaw of the beam projector couples with prism rotations to cause in-scan motion. Finally, there is uncertainty in determining the in-scan direction in the focal plane. This error is called detector roll. An error of in determining the in-scan direction will cause a coupling of cross-scan motion into the in-scan measurement. Demonstration for a 1.7-m off-axis paraboloid A scanning pentaprism system was configured for the measurement of a 1.7-m off axis paraboloid. This off-axis parabola is the primary mirror for the New Solar Telescope at Big Bear Solar Observatory. As an off axis part of an f/0.7 paraboloid, it is a 1/5 scale prototype for the GMT segments. The linear stage that moves the scanning prism was supported above the mirror such that it was tilted 13.5° to align the scanning beam to the optical axis of the parent paraboloid. A CCD camera was placed at the focal point. The measurements were performed according to the sequence below. The data were fit to low order aberration. Alignment aberrations were subtracted from the data leaving the figure error. This test was performed during a phase of fabrication when the mirror had considerable error of 106 nm rms. The scanning pentaprism data matched the data from an interferometrr with CGH null corrector to 32 nm rms. CCD image The scanning pentaprism test is important for GMT because it provides confirmation that the off-axis mirrors are made correctly. This demonstration at 1/5 scale is an important milestone for GMT. The scanning pentaprism system for measuring the GMT primary mirror segments now being built. We us a single rail supported at the center by a bearing tilted 13.5°. To perform different scans, the rail is rotated and locked at different angles. This system will be integrated into the new large test tower at Steward Observatory Mirror Lab. The rail assembly stows alongside the test tower to allow access for the other optical measurements. A CCD camera is located at the focal point, 18 meters above the mirror nm 106 nm rms113 nm rms