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We report studies on the mitigation of optical effects of bright low-Earth-orbit (LEO) satellites on Vera C. Rubin Observatory and its Legacy Survey of Space and Time (LSST). These include options for pointing the telescope to avoid satellites, laboratory investigations of bright trails on the Rubin Observatory LSST camera sensors, algorithms for correcting image artifacts caused by bright trails, experiments on darkening SpaceX Starlink satellites, and ground-based follow-up observations. The original Starlink v0.9 satellites are g ~ 4.5 mag, and the initial experiment "DarkSat" is g ~ 6.1 mag. Future Starlink darkening plans may reach g ~ 7 mag, a brightness level that enables nonlinear image artifact correction to well below background noise. However, the satellite trails will still exist at a signal-to-noise ratio ~ 100, generating systematic errors that may impact data analysis and limit some science. For the Rubin Observatory 8.4-m mirror and a satellite at 550 km, the full width at half maximum of the trail is about 3" as the result of an out-of-focus effect, which helps avoid saturation by decreasing the peak surface brightness of the trail. For 48,000 LEOsats of apparent magnitude 4.5, about 1% of pixels in LSST nautical twilight images would need to be masked., Originally 16 pages, 11 figures, submitted to AAS Journals. Revised to 18 pages, 12 figures, accepted for publication in AJ; v2 addresses referee comments with revised figures, text updates, and additional references. Finally 17 pages, 12 figures, published in AJ; v3 includes final proofing edits and updated metadata

POLARBEAR-2 is a ground based cosmic microwave background (CMB) radiation experiment observing from Atacama, Chile. The science goals of POLARBEAR-2 are to measure the CMB polarization signals originating from the inflationary gravity-wave background and weak gravitational lensing. In order to achieve these science goals, POLARBEAR-2 employs 7588 polarization sensitive transition edge sensor bolometers at observing fre­ quencies of 95 and 150 GHz with 5.5 and 3.5 arcmin beam width, respectively. The telescope is the off-axis Gregorian, Huan Tran Telescope, on which the POLARBEAR-1 receiver is currently mounted. The polarimetry is based on modulation of the polarized signal using a rotating half-wave plate and the rotation of the sky. We present the developments of the optical and polarimeter designs including the cryogenically cooled refractive optics that achieve the overall 4 degrees field-of-view, the thermal filter design, the broadband anti-reflection coating, and the rotating half-wave plate.

BigBOSS is a proposed ground-based dark energy experiment to study baryon acoustic oscillations (BAO) and the growth of structure with a 14,000 square degree galaxy and quasi-stellar object redshift survey. It consists of a 5,000- fiber-positioner focal plane feeding the spectrographs. The optical fibers are separated into ten 500 fiber slit heads at the entrance of ten identical spectrographs in a thermally insulated room. Each of the ten spectrographs has a spectral resolution (λ/Δλ) between 1500 and 4000 over a wavelength range from 360 - 980 nm. Each spectrograph uses two dichroic beam splitters to separate the spectrograph into three arms. It uses volume phase holographic (VPH) gratings for high efficiency and compactness. Each arm uses a 4096x4096 15 μm pixel charge coupled device (CCD) for the detector. We describe the requirements and current design of the BigBOSS spectrograph. Design trades (e.g. refractive versus reflective) and manufacturability are also discussed.

BigBOSS is a proposed ground-based dark energy experiment to study baryon acoustic oscillations (BAO) and the growth of large scale structure. It consists of a fiber-fed multi-object spectrograph designed to be installed on the Mayall 4-meter telescope at Kitt Peak, Arizona. BigBOSS includes an optical corrector assembly and 5000-fiber-positioner focal plane assembly that replace the existing Mayall prime focus hardware. 40-meter long optical fiber bundles are routed from the focal plane, through the telescope declination and right ascension pivots, to spectrographs in the thermally insulated FTS Laboratory, immediately adjacent to the telescope. Each of the ten spectrographs includes three separate spectral bands. The FTS Laboratory also houses support electronics, cooling, and vacuum equipment. The prime focus assembly includes mounts for the existing Mayall f/8 secondary mirror to allow observations with Cassegrain instruments. We describe the major elements of the BigBOSS instrument, plans for integrating with the Telescope, and proposed modifications and additions to existing Mayall facilities.

BigBOSS is a Stage IV dark energy experiment based on proven techniques to study baryon acoustic oscillations and the growth of large scale structure. The 2010 Astronomy and Astrophysics Decadal Survey labeled dark energy as a key area of exploration. BigBOSS is designed to perform a 14,000 square degree survey of 20 million galaxies and quasi-stellar objects. The project involves installation of a new instrument on the Mayall 4m telescope, operated by the National Optical Astronomy Observatory. The instrument includes a new optical widefield corrector, a 5,000 fiber actuator system, and a multi-object spectrometer. Systems engineering flowdown from data set requirements to instrument requirements are discussed, along with the trade considerations and a pre-conceptual baseline design of the widefield optical corrector, spectrometer and fiber positioner systems.

The BigBOSS instrument is a proposed multi-object spectrograph for the Mayall 4m telescope at Kitt Peak, which will measure the redshift of 20 million galaxies and map the expansion history of the universe over the past 8 billion years, surveying 10-20 times the volume of existing studies. For each 20 minute observation, 5000 optical fibers are individually positioned by a close-packed array of 5000 robotic positioner mechanisms. Key mechanical constraints on the positioners are: o12mm hardware envelope, o14mm overlapping patrol zones, open-loop targeting accuracy ≤ 40μm, and step resolution ≤ 5μm, among other requirements on envelope, power, stability, and speed. This paper describes the design and performance of a newly-developed fiber positioner with R-θ polar kinematics, in which a flexure-based linear R-axis is stacked on a rotational θ-axis. Benefits over the usual eccentric parallel axis θ-φ kinematic approach include faster repositioning, simplified anti-collision schemes, and inherent anti-backlash preload. Performance results are given for complete positioner assemblies as well as sub-component hardware characterization.

BigBOSS is a proposed DOE-NSF Stage IV ground-based dark energy experiment designed to study baryon acoustic oscillations (BAO) and the growth of large scale structure with a 14,000 square degree survey of the redshifts of galaxies and quasi-stellar objects. The project involves modification of existing facilities operated by the National Optical Astronomy Observatory (NOAO). Design and systems engineering of a preliminary 3 degree field of view refractive corrector, atmospheric dispersion corrector (ADC), and 5000 actuator fiber positioning system are presented.

It is well known that a telescope with an unobstructed circular pupil delivers a smaller diffraction pattern than one centrally obstructed by its secondary mirror. Spaceborne dark energy investigations require measuring targets over a wide range of redshifts, with the most distant galaxies being the reddest, faintest, and smallest. For any given signal-to-noise (SNR) requirement, these highest redshift targets are the most demanding in terms of mission cost (time, aperture, etc), not only because they are faint but also because the diffraction pattern is largest at the longest wavelengths being observed. At the same time, a telescope's field of view must be large -- the order of a square degree -- to survey the entire extragalactic sky in reasonable time. The large field of view imposes a minimum requirement on the size of the secondary mirror baffle. For a centrally obstructed telescope, an enlarged secondary mirror baffle further enlarges the diffraction pattern. Previously published JDEM telescopes were centrally obstructed. Here, we explore unobstructed telescope designs because these can have a nearly ideal Airy diffraction pattern, avoiding both the central obstruction and the supporting spider legs, limited only by optical manufacturing and alignment errors. They therefore can deliver the best possible SNR for a given aperture. Simulations show that a 1.1m unobstructed aperture can deliver about the same cosmological constraints as a 1.4m aperture that has a 50% linear central obstruction.

We investigate practical implementations of the Korsch 1 (1977) annular field three mirror anastigmat (AFTMA) telescope. This TMA offers a wide, diffraction-limited field of view (FOV) suitable for space-based survey missions. The advantages of this configuration include superior stray light baffling (distinct exit pupil) and the wide range of available focal lengths available from geometrically similar configurations. Key in the design of an AFTMA is the location of the Cassegrain focus (CF) and the exit pupil (EP). We investigate the effects of telescope geometry and optimization constraints on the location of the CF and EP, and suggest a family of geometries suitable for practical and vignetting-free AFTMA designs. The space of practical designs is generalized in terms of mirror diameter, telescope focal ratio and field of view for an annular, detector-tiled focal plane. Focal ratios between roughly f/10 and f/25 produce a geometric blur of less than 0.1arcsec. For this range of f/numbers, the focal plane should be less than ½ the primary mirror (PM) diameter, and the cross-axis should be located roughly 0.6 PM diameters behind the PM vertex.

We compare and contrast the Korsch (1972) full-field three-mirror anastigmat telescope (TMA) to the Korsch (1977) annular-field TMA. Both TMAs offer flat fields with comparably good aberration correction and comparably good telephoto advantage. Both offer good accessibility of the focal plane. The advantages of the FFTMA are its extremely uniform focal length over its field, its nearly telecentric final focus, and the fact that there is no hole in the center of its field. The advantages of the AFTMA are its complete accessible cold stop (essential if a warm telescope is to be used to image the sky at near-IR wavelengths) and its low sensitivity to mirror location error. Either alternative can deliver diffraction-limited visible-wavelength images over a one degree diameter field with a two meter aperture.

SNAP is a proposed space-based experiment designed to quantify dark energy by measuring the redshift-magnitude diagram of supernovae and to quantify the growth of structure in the universe by measuring weak gravitational lensing over cosmological distances. The baseline SNAP telescope is an ambient temperature three-mirror anastigmat (TMA). The goal of the stray light design is to ensure that stray light in the 0.4 to 1.7 micron wavelength range does not exceed a small fraction of Zodiacal radiation within the mission's target field near the North ecliptic pole. At visible wavelengths, we expect the primary source of stray light will be starlight scattered by the primary mirror. In our longest wavelength NIR band we expect thermal emission from the mirrors and structure will dominate. Scattered stray light is mitigated by an internal field stop, and a cold (140K) internal aperture stop. Stray light scattered by mirror roughness and particulate contamination, as well as scattering from the telescope baffles are modeled and quantified. The baseline design and analyses contained herein ensure that stray light will be less than 10% of Zodiacal in all bands.

SNAP is a proposed space-based experiment designed to study dark energy and alternate explanations of the acceleration of the universe's expansion by performing a series of complementary systematic-controlled astrophysical measurements. The principal mission activities are the construction of an accurate Type Ia supernova Hubble diagram (the supernova program) and conducting a wide-area weak gravitational lensing (WL) survey. WL measurements require highly constant point spread function (PSF) second moments (ellipticity), and the aim of this study is to expand on the 2005 Sholl, et al. preliminary work, specifically via use of the Ball Aerospace integrated modeling tool, EOSyM (End-to-end Optical System Model). This modeling environment combines thermal, structural and optical effects, including alignment errors, manufacturing residuals and diffraction, in an integrated model of the telescope. Thermo-mechanically induced motions and deformations of the mirrors are modeled as well as other disturbances, and corresponding ellipticity variations of the PSF are quantified for typical operational scenarios. In this study, the effects of seasonal variations in solar flux, transients introduced when pointing the body-fixed Ka-band antenna toward Earth, 90° roll maneuvers (planned every three months of operations) and structure dimensional changes associated with composites desorption are quantified and introduced into the optical system. Uncertainty in the telescope ellipticity distribution may be reduced by examination of foreground stars within the field of view. Reference is made to ongoing work on the use of foreground stars in quantifying the PSF.

SNAP is a proposed space-based experiment designed to study dark energy and alternate explanations of the acceleration of the universe's expansion by performing a series of complementary systematic-controlled astrophysical measurements. The principal mission activities are the construction of an accurate Type Ia supernova Hubble diagram (the supernova program), and conducting a wide-area weak gravitational lensing (WL) survey. WL measurements benefit from a highly constant point spread function (PSF). The goal of this study is to quantify the anticipated variations in PSF arising from on-orbit thermal variations and and shrinkage associated with dryout of the composite telescope metering structure. A combined thermo-mechanical-optical analysis tool was developed, and WL metrics whisker and effective anisotropy quantified for thermal and composite structure dryout effects. Stability limits necessary for WL are defined, and compared to stability tolerances defined for the supernova program. The mission is designed for operations at at the Earth-Sun L2 Lagrange point, where thermal disturbances from Earth are minimal. In this study, the effects of seasonal variations in solar flux, transients introduced when pointing the body-fixed Ka-band antenna toward Earth and 90° roll maneuvers (planned every three months of operations) are quantified, and introduced into the optical system. Whisker and effective anisotropy were computed, and found to be well below the WL requirement for stability. The effects of composite structure shrinkage due to on-orbit H 2 O desorption are discussed, and estimated to be below WL limits for daily observations, at the beginning of the WL phase of the mission.

SNAP is a candidate for the Joint Dark Energy Mission (JDEM) that seeks to place constraints on the dark energy using two distinct methods. The first, Type Ia SN, is discussed in a companion white paper. The second method is weak gravitational lensing, which relies on the coherent distortions in the shapes of background galaxies by foreground mass structures. The excellent spatial resolution and photometric accuracy afforded by a 2-meter space-based observatory are crucial for achieving the high surface density of resolved galaxies, the tight control of systematic errors in the telescope's Point Spread Function (PSF), and the exquisite redshift accuracy and depth required by this project. These are achieved by the elimination of atmospheric distortion and much of the thermal and gravity loads on the telescope. The SN and WL methods for probing dark energy are highly complementary and the error contours from the two methods are largely orthogonal., 17 pages, 6 figures; White paper to the Dark Energy Task Force

We present the baseline telescope design for the telescope for the SuperNova/Acceleration Probe (SNAP) space mission. SNAP’s purpose is to determine expansion history of the Universe by measuring the redshifts, magnitudes, and spectral classifications of thousands of supernovae with unprecedented accuracy. Discovering and measuring these supernovae demand both a wide optical field and a high sensitivity throughout the visible and near IR wavebands. We have adopted the annular-field three-mirror anastigmat (TMA) telescope configuration, whose classical aberrations (including chromatic) are zero. We show a preliminary optmechanical design that includes important features for stray light control and on-orbit adjustment and alignment of the optics. We briefly discuss stray light and tolerance issues, and present a preliminary wavefront error budget for the SNAP Telescope. We conclude by describing some of the design tasks being carried out during the current SNAP research and development phase.

A wide field space-based imaging telescope is necessary to fully exploit the technique of observing dark matter via weak gravitational lensing. This first paper in a three part series outlines the survey strategies and relevant instrumental parameters for such a mission. As a concrete example of hardware design, we consider the proposed Supernova/Acceleration Probe (SNAP). Using SNAP engineering models, we quantify the major contributions to this telescope's Point Spread Function (PSF). These PSF contributions are relevant to any similar wide field space telescope. We further show that the PSF of SNAP or a similar telescope will be smaller than current ground-based PSFs, and more isotropic and stable over time than the PSF of the Hubble Space Telescope. We outline survey strategies for two different regimes - a ``wide'' 300 square degree survey and a ``deep'' 15 square degree survey that will accomplish various weak lensing goals including statistical studies and dark matter mapping., 25 pages, 8 figures, 1 table, replaced with Published Version

The proposed SuperNova/Acceleration Probe (SNAP) mission will have a two-meter class telescope delivering diffraction-limited images to an instrumented 0.7 square degree field in the visible and near-infrared wavelength regime. The requirements for the instrument suite and the present configuration of the focal plane concept are presented. A two year R&D phase, largely supported by the Department of Energy, is just beginning. We describe the development activities that are taking place to advance our preparedness for mission proposal in the areas of detectors and electronics.