The proposed Survey and Time-domain Astrophysical Research eXplorer mission contains multiple subassemblies including the X-Ray Telescope. This paper discusses the optical design of that telescope, detailing the requirements, telescope architecture and performance analysis.
The High Energy X-ray Probe (HEX-P) is a probe-class mission concept that combines high spatial resolution x-ray imaging and broad spectral coverage to enable revolutionary new insights into the important astrophysical questions of the next decade. HEX-P will fly a complement of two Hard Energy Mirror Assemblies (HEMA) and one Low Energy Mirror Assembly (LEMA), all of which will have a focal length of 20 meter. Ir/C has been chosen as the baseline coating for the LEMA, and a combination of Pt/C and W/Si multilayers for the HEMA. We present here the mirror design, optimization of coating recipes, and estimated performance.
The far-infrared imager and polarimeter (FIP) for the Origins Space Telescope (Origins) is a basic far-infrared imager and polarimeter. The camera will deliver continuum images and polarization measurements at 50 and 250 μm. Currently available detector technologies provide sufficient sensitivity for background limited observations from space, at least on a single pixel basis. FIP incorporates large next-generation superconducting detector arrays and our technology development plan will push the pixel numbers for the arrays to the required size of 8000. Two superconducting detector technologies are currently candidates for the instrument: transition edge sensors or microwave kinetic inductance devices. Using these detectors and taking advantage of the cryogenic telescope that is provided by Origins, FIP will achieve mapping speeds of up to eight orders of magnitude faster than what has been achieved by existing observatories. The science drivers for FIP include observations of solar system objects, dust properties, and magnetic field studies of the nearby interstellar medium, and large scale galaxy surveys to better constrain the star formation history of the universe to address one of the main themes of Origins: “How does the Universe work?” In addition to the science, the FIP instrument plays a critical functional role in aligning the mirrors during on orbit observatory commissioning.
KEYWORDS: Space telescopes, Telescopes, James Webb Space Telescope, Mirrors, Optical instrument design, Astronomy, Space operations, Cryogenics, Aerospace engineering, Cryocoolers
The Origins Space Telescope will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did galaxies evolve from the earliest galactic systems to those found in the universe today? How do habitable planets form? How common are life-bearing worlds? We describe how Origins was designed to answer these alluring questions. We discuss the key decisions taken by the Origins mission concept study team, the rationale for those choices, and how they led through an exploratory design process to the Origins baseline mission concept. To understand the concept solution space, we studied two distinct mission concepts and descoped the second concept, aiming to maximize science per dollar and hit a self-imposed cost target. We report on the study approach and describe the concept evolution. The resulting baseline design includes a 5.9-m diameter telescope cryocooled to 4.5 K and equipped with three scientific instruments. The chosen architecture is similar to that of the Spitzer Space Telescope and requires very few deployments after launch. The cryo-thermal system design leverages James Webb Space Telescope technology and experience.
The Origins Survey Spectrometer (OSS) is a multi-purpose far-IR spectrograph for Origins. Operating at the photon background limit, OSS covers the 25- to 588-μm wavelength range instantaneously at a resolving power (R) of 300 using six logarithmically spaced grating modules. Each module couples at least 30 and up to 100 spatial beams simultaneously, enabling true [three-dimensional (3D)] spectral mapping. In addition, OSS provides two high-resolution modes. The first inserts a long-path Fourier-transform spectrometer (FTS) into a portion of the incoming light in advance of the grating backends, enabling R up to 43 , 000 × [ λ / 112 μm ] , while preserving the grating-based sensitivity for line detection. The second incorporates a scanning etalon in series with the FTS to provide R up to 300,000 for the 100-to 200-μm range.
The Origins Space Telescope (Origins) study team prepared and submitted a Mission Concept Study Report for the 2020 Decadal Survey in Astrophysics. During the study, a Materials Working Group was formed to evaluate materials for Origins. The Materials Working Group identified material candidates and evaluated the candidates using driving requirements and key material considerations. The evaluation resulted in several options to aid the study team in making a materials selection for the mission concept. Our paper details the approach to the materials evaluation and the results.
Our paper discusses the optical design of the Origins Space Telescope. Origins is one of four large missions under study in preparation for the 2020 Decadal Survey in Astronomy and Astrophysics. Sensitive to the mid- and far-infrared spectrum (between 2.8 and 588 μm), Origins sets out to answer a number of important scientific questions by addressing NASA’s three key science goals in astrophysics. The Origins telescope operates at f / 14. The design includes a 5.9-m-diameter primary mirror. The large on-axis primary consists of 18 “keystone” segments of two different prescriptions arranged in two annuli (six inner and twelve outer segments) that together form a circular aperture in the goal of achieving a symmetric point spread function. To accommodate the 46 × 15 arc min full field of view (FOV) of the telescope at the design wavelength of λ = 30 μm, a three-mirror anastigmat configuration is used. The design is diffraction-limited across its instruments’ FOV. A brief discussion of each of the three baselined instruments within the Instrument Accommodation Module is presented: (1) Origins Survey Spectrometer, (2) Mid-infrared Spectrometer, Camera transit spectrometer channel, and (3) Far-Infrared Polarimeter/Imager. In addition, the upscope options for the observatory are laid out as well including a fourth instrument: the Heterodyne Receiver for Origins.
The Heterodyne Receiver for Origins (HERO) is the first detailed study of a heterodyne focal plane array receiver for space applications. HERO gives the Origins Space Telescope the capability to observe at very high spectral resolution (R = 107) over an unprecedentedly large far-infrared (FIR) wavelengths range (111 to 617 μm) with high sensitivity, with simultaneous dual polarization and dual-frequency band operation. The design is based on prior successful heterodyne receivers, such as Heterodyne Instrument for the Far-Infrared /Herschel, but surpasses it by one to two orders of magnitude by exploiting the latest technological developments. Innovative components are used to keep the required satellite resources low and thus allowing for the first time a convincing design of a large format heterodyne array receiver for space. HERO on Origins is a unique tool to explore the FIR universe and extends the enormous potential of submillimeter astronomical spectroscopy into new areas of astronomical research.
The Origins Space Telescope will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did galaxies evolve from the earliest galactic systems to those found in the Universe today? How do habitable planets form? How common are life-bearing worlds? To answer these alluring questions, Origins will operate at mid- and far-infrared (IR) wavelengths and offer powerful spectroscopic instruments and sensitivity three orders of magnitude better than that of the Herschel Space Observatory, the largest telescope flown in space to date. We describe the baseline concept for Origins recommended to the 2020 US Decadal Survey in Astronomy and Astrophysics. The baseline design includes a 5.9-m diameter telescope cryocooled to 4.5 K and equipped with three scientific instruments. A mid-infrared instrument (Mid-Infrared Spectrometer and Camera Transit spectrometer) will measure the spectra of transiting exoplanets in the 2.8 to 20 μm wavelength range and offer unprecedented spectrophotometric precision, enabling definitive exoplanet biosignature detections. The far-IR imager polarimeter will be able to survey thousands of square degrees with broadband imaging at 50 and 250 μm. The Origins Survey Spectrometer will cover wavelengths from 25 to 588 μm, making wide-area and deep spectroscopic surveys with spectral resolving power R ∼ 300, and pointed observations at R ∼ 40,000 and 300,000 with selectable instrument modes. Origins was designed to minimize complexity. The architecture is similar to that of the Spitzer Space Telescope and requires very few deployments after launch, while the cryothermal system design leverages James Webb Space Telescope technology and experience. A combination of current-state-of-the-art cryocoolers and next-generation detector technology will enable Origins’ natural background-limited sensitivity.
OSS on Origins is designed to decode the cosmic history of nucleosynthesis, star formation, and supermassive black hole growth with wide-area spatial-spectral 3-D surveys in the 30 to 670 micron band. Six wideband grating modules combine to cover the full band at R=300, each couples a long slit with at least 30 beams on the sky. Two high-resolution modes are provided: one incorporates an interferometer in front of the gratings providing R of more than 40,000 at 112 microns, the other adds an etalon for R>300,000 at 112 microns. The full system design is presented, including optics, detector arrays, readouts, and the thermal design.
As the optical performance requirements of space telescopes get more stringent, the need to analyze all possible error sources early in the mission design becomes critical. One large telescope with tight performance requirements is the Large Ultraviolet / Optical / Infrared Surveyor (LUVOIR) concept. The LUVOIR concept includes a 15-meter-diameter segmented-aperture telescope with a suite of serviceable instruments operating over a range of wavelengths between 100nm to 2.5um. Using an isolation architecture that involves no mechanical contact between the telescope and the host spacecraft structure allows for tighter performance metrics than current space-based telescopes being flown. Because of this separation, the spacecraft disturbances can be greatly reduced and disturbances on the telescope payload contribute more to the optical performance error. A portion of the optical performance error comes from the disturbances generated from the motion of the Fast Steering Mirror (FSM) on the payload. Characterizing the effects of this disturbance gives insight into FSM specifications needed to achieve the tight optical performance requirements of the overall system. Through analysis of the LUVOIR finite element model and linear optical model given a range of input disturbances at the FSM, the optical performance of the telescope and recommendations for FSM specifications can be determined. The LUVOIR observatory control strategy consists of a multi-loop control architecture including the spacecraft Attitude Control System (ACS), Vibration Isolation and Precision Pointing System (VIPPS), and FSM. This paper focuses on the control loop containing the FSM disturbances and their effects on the telescope optical performance.
This paper discusses the optical design of the Origins Space Telescope. Origins is one of four large missions under study in preparation for the 2020 Decadal Survey in Astronomy and Astrophysics. Sensitive to the mid- and far-infrared spectrum (between 2.8 and 588 μm), Origins sets out to answer a number of important scientific questions by addressing NASA’s three key science goals in astrophysics. The Origins telescope has a 5.9 m diameter primary mirror and operates at f/14. The large on-axis primary consists of 18 ‘keystone’ segments of two different prescriptions arranged in two annuli (six inner and twelve outer segments) that together form a circular aperture in the goal of achieving a symmetric point spread function. To accommodate the 46 x 15 arcminute full field of view of the telescope at the design wavelength of λ = 30 μm, a three-mirror anastigmat configuration is used. The design is diffraction-limited across its instruments’ fields of view. A brief discussion of each of the three baselined instruments within the Instrument Accommodation Module (IAM) is presented: 1) Origins Survey Spectrometer (OSS), 2) Mid-infrared Spectrometer, Camera (MISC) transit spectrometer channel, and 3) Far-Infrared Polarimeter/Imager (FIP). In addition, the upscope options for the observatory are laid out as well including a fourth instrument: the Heterodyne Receiver for Origins (HERO).
The Large Ultraviolet/Optical/Infrared Surveyor (LUVOIR) is a large-scale space telescope being submitted for review to the 2020 Decadal Survey in Astronomy and Astrophysics. Its science objectives include both direct imaging and spectral characterization of habitable exoplanets around sun-like stars, the study of planet, star, and galaxy formation, the transfer of matter between different galaxies, and the remote sensing of objects within the Solar System. Two architectures have been designed: a 15 m diameter on-axis telescope (LUVOIR-A) and an 8 m off-axis telescope (LUVOIR-B).
This paper discusses the opto-mechanical design of the three LUVOIR instruments: the High Definition Imager (HDI), the LUVOIR UV Multi-object Spectrograph (LUMOS), and the Extreme Coronagraph for Living Planetary Systems (ECLIPS). For both the LUVOIR-A and LUVOIR-B variants of each instrument, optical design specifications are presented including first-order constraints, packaging requirements, and optical performance metrics. These factors are used to illustrate the final design of each instrument and LUVOIR as a whole. While it is desirable to have the two variants of each instrument be as similar to one another as possible to reduce engineering design time, this was not possible in a number of instances which are described in this paper along with the resulting tradeoffs. In addition to the optical designs, mechanical models are presented for each instrument showing the optical mounts, mechanisms, support structure, etc.
The Origins Space Telescope will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did galaxies evolve from the earliest galactic systems to those found in the universe today? How do habitable planets form? How common are life-bearing worlds? To answer these alluring questions, Origins will operate at mid- and far-infrared wavelengths and offer powerful spectroscopic instruments and sensitivity three orders of magnitude better than that of Herschel, the largest telescope flown in space to date. After a 3 ½ year study, the Origins Science and Technology Definition Team will recommend to the Decadal Survey a concept for Origins with a 5.9-m diameter telescope cryocooled to 4.5 K and equipped with three scientific instruments. A mid-infrared instrument (MISC-T) will measure the spectra of transiting exoplanets in the 2.8 – 20 μm wavelength range and offer unprecedented sensitivity, enabling definitive biosignature detections. The Far-IR Imager Polarimeter (FIP) will be able to survey thousands of square degrees with broadband imaging at 50 and 250 μm. The Origins Survey Spectrometer (OSS) will cover wavelengths from 25 – 588 μm, make wide-area and deep spectroscopic surveys with spectral resolving power R ~ 300, and pointed observations at R ~ 40,000 and 300,000 with selectable instrument modes. Origins was designed to minimize complexity. The telescope has a Spitzer-like architecture and requires very few deployments after launch. The cryo-thermal system design leverages JWST technology and experience. A combination of current-state-of-the-art cryocoolers and next-generation detector technology will enable Origins’ natural backgroundlimited sensitivity.
The large UV/optical/IR surveyor (LUVOIR) is a concept for a highly capable, multiwavelength space observatory with ambitious science goals. Finding and characterizing a wide range of exoplanets, including those that might be habitable, is a major goal of the study. The ambitious science goals drive the challenges of optical design. This paper will present how the optical design meets the unique challenges for coronagraphs on large telescopes to achieve high contrast for a wide wavelength range from 200 to 2000 nm. Some of these unique challenges include the position and size of occulter masks, deformable mirror placement and separation, tight tolerances on the optical system and each element, and finally, packaging all instruments in a limited space. Three types of modules are designed after the coronagraph to explore the exoplanets and analyze the spectrum of detected exoplanet signals: two imaging cameras, two integral field spectrographs, and one high-resolution spectrometer. All of them work together to provide information to meet scientific challenges in searching for habitable planets. The optical designs, unique challenges, and the solutions for all coronagraph and spectral modules are presented. Their specifications derived from science goals are also presented.
The OSS on the Origins Space Telescope is designed to decode the cosmic history of nucleosynthesis, star formation, and supermassive black hole growth with wide-area spatial-spectral 3-D surveys across the full 25 to 590 micron band. Six wideband grating modules combine to cover the full band at R=300, each couples a long slit with 60-190 beams on the sky. OSS will have a total of 120,000 background-limited detector pixels in the six 2-D arrays which provide spatial and spectral coverage. The suite of grating modules can be used for pointed observations of targets of interest, and are particularly powerful for 3-D spectral spectral surveys. To chart the transition from interstellar material, particularly water, to planetary systems, two high-spectral-resolution modes are included. The first incorporates a Fourier-transform spectrometer (FTS) in front of the gratings providing resolving power of 25,000 (δv = 12 km/s) at 179 µm to resolve water emission in protoplanetary disk spectra. The second boosts the FTS capability with an additional etalon (Fabry-Perot interferometer) to provide 2 km/s resolution in this line to enable detailed structural studies of disks in the various water and HD lines. Optical, thermal, and mechanical designs are presented, and the system approach to the detector readout enabling the large formats is described.
The Origins Space Telescope (OST) is a NASA study for a large satellite mission to be submitted to the 2020 Decadal Review. The proposed satellite has a fleet of instruments including the HEterodyne Receivers for OST (HERO). HERO is designed around the quest to follow the trail of water from the ISM to disks around protostars and planets. HERO will perform high-spectral resolution measurements with 2x9 pixel focal plane arrays at any frequency between 468GHz to 2,700GHz (617 to 111 μm). HERO builds on the successful Herschel/HIFI heritage, as well as recent technological innovations, allowing it to surpass any prior heterodyne instrument in terms of sensitivity and spectral coverage.
The Origins Space Telescope (OST) is the mission concept for the Far-Infrared Surveyor, one of the four science and technology definition studies of NASA Headquarters for the 2020 Astronomy and Astrophysics Decadal survey. "Concept-1" is a cold (4 K) 9 m space telescope with five instruments, while "concept 2" consists of a cold 5.9 m telescope and four instruments, providing imaging and spectroscopic capabilities between 5μm and 600μm. The sensitivity provided by the observatory will be a three to four orders of magnitude improvement over currently achieved observational capabilities, allowing to address a wide range of new and so far inaccessible scientific questions, ranging from bio-signatures in the atmospheres of exo-planets to the production of the first metals in the universe right after the end of re-ionization. Here we present the Far Infrared Imager and Polarimeter (FIP) for OST. The camera will cover four bands, 50μm, 100μm, 250μm, and 500μm. In the "concept 1" version of the instrument, FIP will allow for differential polarimetry with the ability to observe two colors simultaneously, while all four bands can be observed simultaneously in total power mode. The confusion limit in the total power mode will be reached in only 8 ms at 500μm, while at 50μm the source density in the sky is so low that at OST's angular resolution of (see manuscript for symbol) 2" in this band the source confusion limit will only be reached after about two hours of integration with the "concept-2" version of FIP ("concept-1" FIP will not be confusion limited at 50m, no matter how long it integrates). Science topics that can be addressed by the camera include, but are not limited to, galactic and extragalactic magnetic field studies, deep galaxy surveys, and outer Solar System objects.
The Origins Space Telescope (OST) will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did the universe evolve in response to its changing ingredients? How common are life-bearing planets? To accomplish its scientific objectives, OST will operate at mid- and far-infrared wavelengths and offer superlative sensitivity and new spectroscopic capabilities. The OST study team will present a scientifically compelling, executable mission concept to the 2020 Decadal Survey in Astrophysics. To understand the concept solution space, our team studied two alternative mission concepts. We report on the study approach and describe both of these concepts, give the rationale for major design decisions, and briefly describe the mission-enabling technology.
NASA commissioned the study of four large mission concepts, including the Large Ultraviolet / Optical / Infrared (LUVOIR) Surveyor, to be evaluated by the 2020 Decadal Survey in Astrophysics. In response, the Science and Technology Definition Team (STDT) identified a broad range of science objectives for LUVOIR that include the direct imaging and spectral characterization of habitable exoplanets around sun-like stars, the study of galaxy formation and evolution, the exchange of matter between galaxies, star and planet formation, and the remote sensing of Solar System objects. To meet these objectives, the LUVOIR Study Office, located at NASA’s Goddard Space Flight Center (GSFC), completed the first design iteration of a 15-m segmented-aperture observatory that would be launched by the Space Launch System (SLS) Block 2 configuration. The observatory includes four serviceable instruments: the Extreme Coronagraph for Living Planetary Systems (ECLIPS), an optical / near-infrared coronagraph capable of delivering 10−10 contrast at inner working angles as small as 2 λ/D; the LUVOIR UV Multi-object Spectrograph (LUMOS), which will provide low- and medium-resolution UV (100 – 400 nm) multi-object imaging spectroscopy in addition to far-UV imaging; the High Definition Imager (HDI), a high-resolution wide-field-of-view NUV-Optical-NIR imager; and Pollux, a high-resolution UV spectro-polarimeter being contributed by Centre National d’Etudes Spatiales (CNES). The study team has executed a second design iteration to further improve upon the 15-m concept, while simultaneously studying an 8-m concept. In these proceedings, we provide an update on these two architectures.
This work presents updates to the coronagraph and telescope components of the Segmented Aperture Interferometric Nulling Testbed (SAINT). The project pairs an actively-controlled macro-scale segmented mirror with the Visible Nulling Coronagraph (VNC) towards demonstrating capabilities for the future space observatories needed to directly detect and characterize a significant sample of Earth-sized worlds around nearby stars in the quest for identifying those which may be habitable and possibly harbor life. Efforts to improve the VNC wavefront control optics and mechanisms towards repeating narrowband results are described. A narrative is provided for the design of new optical components aimed at enabling broadband performance. Initial work with the hardware and software interface for controlling the segmented telescope mirror is also presented.
A design study is compiled for a VIS-SWIR dual band 3X zoom lens. The initial first order design study investigated zoom motion, power in each lens group, and aperture stop location. All designs were constrained to have both the first and last lens groups fixed, with two middle moving groups. The first order solutions were filtered based on zoom motion, performance, and size constraints, and were then modified to thick lens solutions for the SWIR spectrum. Successful solutions in the SWIR were next extended to the VIS-SWIR. The resulting nine solutions are all nearly diffraction limited using either PNNP or PNPZ (“Z” indicating the fourth group has a near-zero power) design forms with two moving groups. Solutions were found with the aperture stop in each of the four lens groups. Fixed f-number solutions exist when the aperture stop is located at the first and last lens groups, while varying f-number solutions occur when it is placed at either of the middle moving groups. Design exploration included trade-offs between parameters such as diameter, overall length, back focal length, number of elements, materials, and performance.
Gradient-index (GRIN) zoom lenses are shown to offer superior imaging performance to homogenous designs over the visible spectrum. For a given element count, copolymer GRIN designs are better corrected for axial and lateral color than homogeneous aspheric designs.
Gradient-index (GRIN) zoom lenses are shown to offer superior imaging performance to homogenous designs over the visible spectrum. For a given element count, copolymer GRIN designs are better corrected for axial and lateral color than homogeneous aspheric designs. A macro was developed in CODE V® to calculate the surface contributions to both axial and lateral color for a radial GRIN lens. This macro confirms the improved color correction of the GRIN systems over the homogeneous ones.
High-performance eyepiece designs have been carried out using both spherical and radial gradient-index (GRIN)
elements. Eyepiece designs of both geometries are shown to offer superior imaging performance with fewer elements
when compared to purely homogeneous systems. These GRIN lenses are formed from monomer diffusion between
polymethyl methacrylate (PMMA) and polystyrene (PSTY) during the polymerization process, resulting in a copolymer
of the two homogeneous materials.
A process for fabricating spherical GRIN elements is discussed where copolymer axial GRIN blanks are thermally
compressed using spherical surface molds. This process curves the nominally-straight isoindicial surfaces of the axial
GRIN rod to be consistent with the shape found during optimization of the design. Once compressed, the spherical
blanks are diamond-turned for final surface figure and finish. Measurement of the GRIN profile is carried out using the
Schmidt immersion technique in a Mach-Zehnder interferometer. Tolerances specific to GRIN elements are identified
and determined to be readily achievable using the aforementioned manufacturing process.
Radial and spherical polymer gradient-index (GRIN) eyepiece designs are presented. The chromatic behavior of GRIN profiles is constrained to real material properties of a polymethyl methacrylate polystyrene copolymer gradient-index system. Single-element, two-element, and multielement eyepiece design configurations each demonstrate significant spot diameter and modulation transfer function performance improvements with the use of a GRIN element. A high-performance spherical GRIN eyepiece design, with 48-deg full field-of-view and 3% distortion, is compared to a similar homogeneous glass solution.
A 40-deg full field-of-view high-performance eyepiece design utilizing a polymer spherical gradient-index (GRIN) optical element is presented. In the design process, the GRIN lens material is constrained to current manufacturing capabilities. Several spherical GRIN lens blanks are fabricated from a thermoformable axial GRIN polymethyl methacrylate polystyrene copolymer material. One is diamond turned into a lens for the eyepiece, and the additional blanks are used to characterize the fabrication process. The spherical GRIN profile is evaluated in the original design, and a tolerance analysis is provided.
The ability of gradient index (GRIN) materials to correct color in the infrared is explored. An overview of GRIN materials is provided, including a review of the most common index profiles (axial, radial, and spherical). Due to the high potential for color correction, a design study is carried out to compare a single ZnS/ZnSe GRIN element’s imaging performance to that of homogeneous singlets and doublets. A radial GRIN element is able to correct axial color and provide superior performance over an aspheric homogeneous singlet and offer a reduction in weight when compared to a homogeneous doublet. The ZnS/ZnSe GRIN is also shown to be superior to other infrared GRIN materials between 3 and 5 μm.
The article explores the possibility of athermalizing a gradient-index (GRIN) lens so that the effective focal length (EFL) of the element remains constant over a change in temperature. This is accomplished by designing the lens so that the surface curvatures and index profile compensate for one another over a change in temperature to maintain constant optical power. The means to determine how the lens geometry and index profile change with temperature for both a homogeneous and radial GRIN are explained. An analytic model for the purpose of identifying athermalized GRIN singlets is described and validated against the previous work in this field. The model is used to identify an athermalized polymer radial GRIN element and compare it with four other polymer elements of the same focal length but different index profiles, including a homogeneous one. Comparison of these singlets in CODE V® optical design software shows that the athermalized GRIN element maintains its nominal EFL over a temperature change the best of the five in the group while the homogeneous element (having no GRIN profile to counteract the effect of temperature on the surface curvatures) has the poorest performance. A numerical model to analyze more complicated GRIN systems is discussed.
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