世界の地上太陽光学望遠鏡とDST 飛騨天文台 上野 From 花岡さん資料 この資料中で紹介する地上太陽望遠鏡 1) Sac Peak DST (1969 -- ) 2) VTT (1989 -- ) & GREGOR (201X --) 3) SST (2002 -- ) 4) BBSO: NST (1969, 2008 -- ) 5) Hida DST (1979 -- ) Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) 入射窓径76cm 焦点面太陽径51cm 67m 250トンの全光学系を水 銀で浮かせるタイプの ベアリングで支えている 41.5m Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Solar Adaptive Optics Project Since the late 1990s the National Solar Observatory has been advancing the ShackHartmann technique. We divide the solar image into subapertures then deform a flexible mirror so each subaperture matches one reference subaperture. In 1998 we applied a low-order AO system to the Dunn Solar Telescope, thus allowing it to operate near its diffraction limit under moderately good atmospheric conditions. This technology now is applied at several solar telescopes around the world. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for imaging A unique instrument at the focus of the Dunn Solar Telescope is the Universal Birefringent Filter, or UBF. (Lyot type filter with rotating crystal elements using quarter waveplates and linear polarizers to tune.) It can be tuned to look at any particular visible color in the Sun's spectrum. A picture can then be taken of that region of the sun. This allows scientists to observe different altitudes and temperatures on the sun, as each chemical element emits or absorbs its own color of light. In order to record images or spectra, an electronic camera called a CCD is often used. The pictures are read by a computer and stored either on disk or magnetic tape for later analysis. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for imaging IBIS: Interferometric Bidimensional Spectrometer The Interferometric Bidimensional Spectrometer (IBIS) is a Solar Research Instrument on the DST. (ファブリペローフィルタによる2次元フィルタ分光) Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy HSG: the Horizontal Spectrograph The Horizontal Spectrograph (HSG) is a high spectral and spatial resolution instrument. The spectrograph consists of a rectangular slit, of fixed width, a collimator lens, plane grating, camera lenses, and CCD detectors. Component Description Grating: 316 lines/mm reflection type by Bausch and Loumb 206mm x 128 mm ruled area Blazed at 63.4333 degrees (63 degrees, 26 minutes) Blaze wavelength - all Resolution 472,596 (2/3 of theoretical) at 5000 A, 11th order, resolving power 7mA Slit: Adjustable Scale at slit = 7.5arcsec/mm, Maximum FOV = 170 x 170 arcsec 1 arcsec = 133.3 microns Collimating Lens: 3 meter focal length for f36 setup, 1.5 meter focal length for f72 Camera Lenses: 3 meter focal length singlets or 1.5 meter focal length singlets Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy 4種類の分光偏光装置 Advanced Stokes Polarimeter (ASP) : This uses a horizontally-mounted spectrograph to study complex magnetic fields, such as are common in sunspots. The ASP can also be used with the UBF to produce simultaneous, coordinated data sets. Cf. Elmore et al. 1992 SPIE, 1746, 22E Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy The Diffraction-Limited Spectro-Polarimeter (DLSP) built in collaboration with the HAO and operated at the NSO Dunn Solar Telescope is an innovative and contempo grating polarimeter specifically designed to meet the high requirements pursued in solar spectropolarimetry. With the excellent imaging properties of the instrument and the efficient performance of the high-order adaptive optics system we achieve a spatial resolution of 0.4 arcsec on a regular basis. The spectrograph is in an autocollimated configuration (Littrow mount) with an off-axis parabola (P). The dispersive element is a 79 grooves/mm Echelle grating (G) working in high order (36th order). The aperture slit (S) has a width of 12 micron. The detector (CCD) is a high speed, backside illuminated split-frame transfer sensor (652 x 494 pixel) manufactured by PixelVision. The DLSP uses two ferro-electric liquid crystals upfront right after the exit port to modulate the light beam. A polarizing beam splitter (PBS) right in front of the detector acts as an analyzer. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy The DLSP has two operation modes coined high- and low-resolution mode. In high resolution the diffraction limit of the DST @630.2 nm is critically sampled with 0.09 arcsec/pixel covering 59 arcsec along the slit. In low resolution the spatial sampling is 0.25 arcsec/pixel allowing for a larger FOV of 163 arcsec. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy FIRS: the Facility IR Spectropolarimeter The Facility Infrared Spectrapolarimeter for the Dunn Solar Telescope is an advanced imaging spectropolarimeter developed by the Institute for Astronomy - University of Hawai'i (P.I. Haosheng Lin) and the National Solar Observatory. This instrument provides simultaneous spectral coverage at visible and infrared wavelengths through the use of a unique dual-armed spectrograph design. The geometry of the spectrograph has been specially designed to capture the Fe I 6302 Å and 15648 Å lines with maximum efficiency. In addition, the spectrograph operates in a multiple slit mode. By using narrow band filters, the spectra from four consecutive slit positions can be imaged at once on the same detector. This feature greatly reduces the time necessary to scan across a large area on the sun, making it an ideal instrument for the study of quickly developing active regions. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy SPINOR: Spectro-Polarimeter for Infrared and Optical Regions SPINOR is an instrument developed for the NSO by HAO. Polarization Optics All the optical mounts built for the Advanced Stokes Polarimeter are used for SPINOR as well. Every ASP optical element is replaced by a new achromatic one. Entrance Window Calibration Polarizer The entrance window calibration polarizer is an array of 13 VersaLight wafers. The wafer diameter is approximately 150mm (with a flat on one side aligned to the polarization direction). The mechanical mount developed for DST calibration that fits over the entrance window of the telescope has been modified to accept these achromatic Versalight polarizers. Calibration Linear Polarizer The calibration linear polarizer is VersaLight selected for good performance over a 50mm aperture and AR coated for 450nm to 1600nm. The location of the calibration Linear polarizer is the stage closest to the exit port of the telescope in the Calibration Modulation Unit. Calibration Retarder The calibration retarder is a 50mm diameter bi-crystalline achromat of the design shown in the plot, but with thicknesses scaled for quarter wave retardance between 450nm to 1600nm and AR coated for the same range. The location of the calibration retarder is the stage just above the calibration linear polarizer in the Calibration Modulation Unit where the light beam is f/72. Sacramento Peak, National Solar Observatory Richard B. Dunn Solar Telescope (DST) Instruments for spectroscopy SPINOR: Spectro-Polarimeter for Infrared and Optical Regions Polarization Modulator The polarization modulator is a 50mm diameter bi-crystalline achromat with thicknesses scaled for 0.35 wave retardance from 450nm to 1600nm and AR coated for the same range. The location of the polarization modulator is just after the fast mirror near the exit of the Calibration Modulation Unit where the beam is f/36. This retarder design includes positive and negative birefringent crystals has a low variation of retardance vs. angle. It is likely that the temperature will need to be monitored as there is a small variation of retardance vs temperaturethat diminishes with wavelength. Polarizing Beam Splitter The polarizing beam splitter uses a VersiLight beam splitting cube, is 16.5mm per side and is the same design as that developed for the ASP. As with the ASP, the image of the slit is split into two beams separated vertically. Each beam is polarized at 45º to the orientation of the rulings on the grating. The polarizing beam splitter is just behind the entrance slit of the Horizontal spectrograph. Gratings Since SPINOR operates over a much wider wavelength range compared to ASP, different grating choices are appropriate. Depending upon the spectral line of interest and spectral resolution desired different gratings might be selected. Higher blaze angle gives higher spectral resolution for the same spatial sample size. Since SPINOR will operate with AO, its design should tend towards higher spatial resolution than the ASP, but since it is a research instrument and cannot be optimized for a single line, not as high as DLSP. These spectrograph issues lead to a spectrograph using a 40 mm slit and 1000mm camera lens.The Infrared Triplet is of special interest for SPINOR as the three lines are inaccessible to ASP both due to the calibration optics and the performance of the 316 line/mm grating at these wavelengths. Four possible SPINOR gratings have good performance for near infrared lines. Teide Observatory, Tenerife Vacuum Tower Telescope (VTT) 38m It is operated under the leadership of the KIS (60%) in cooperation with AIP (20%) and MPS (20%). It is a classical solar telescope: two celeostat morrors feed the sunlight into the telescope. It has a 70 cm diameter primary mirror and a focal length of 46 m. Thanks to an adaptive optics system, in operation since spring 2000, it is able to resolve details down to 0.2 arcsec. Teide Observatory, Tenerife Vacuum Tower Telescope (VTT) - Diameter of primary mirrorl: 70 cm - Focal length: 45.640 m - Aperture ratio f/D: 65.7 - Resolving power at 543.4 nm: 0.196" - Image scale in primary focu: 4.59"/mm Teide Observatory, Tenerife Vacuum Tower Telescope (VTT) An adaptive-optics system Is permanently installed and available to all instruments; this leads to a substantial improvement of the image quality. On good days, this provides a spatial resolution of about 0.2 arcsec at 500 nm for short exposures, and of some 0.5 arcsec for exposures as long as 10 seconds. - 35 actuators, 50mm illuminated pupil diameter, 100mm total diameter - Minimum radius of curvature (maximum voltage (±400V) applied to all actuators): ca ± 20m - First resonance frequency: 900 Hz Teide Observatory, Tenerife Vacuum Tower Telescope (VTT) Instruments for Imaging TESOS/VIP is a 2D spectrometer based on three Fabry-Pérot interferometers with a telecentric design and a spectral resolution of 250,000. It covers the visible part of the spectrum and can be operated in intensity mode, to record Stokes-I line profiles of 2D images, and in polarization mode, to measure the full polarization state of the light along line profiles (I, Q, U, and V). HELLRIDE (HELioseismic Large Region Interferometric Device) is a Fabry-Pérot spectrometer that can scan 16 different solar lines, with 20 wavelength steps each, at a cadence of 60 seconds, in a field-of-view as large as 100×100 arcsec2. This instrument is outstanding as it provides unique data to study atmospheric waves, and will help to understand how the chromosphere is heated by shock waves. Teide Observatory, Tenerife Vacuum Tower Telescope (VTT) Instruments for Spectroscopy Echelle spectrograph; a grating spectrograph with a predisperser, which allows to measure up to three different spectral bands at a spectral resolution of about 1 million. A reliable interaction with the telescope and the AO-Tip-Tilt system ensures that maps of solar regions-of-interest can be scanned. Data acquisition is performed with up to three of the following CCDs: PCO 1, PCO 2, & Sensicam (more details on CCDs below). On the slit (focal plane of telescope), the image scale is 4.49 arcsec/mm. The image scale in the focal pane of the spectrograph is 8.98 arcsec/mm. TIP-II (Tenerife Infrared Polarimeter) is a near-infrared spectropolarimeter which is used together with the Echelle spectrograph to measure the Stokes profiles of near infrared spectral lines (1.0-1.8 μm) with high spectral and spatial resolution. The solar surface can be scanned using a scanning unit LARS (Absolute Reference Spectrograph) introduces a laser-frequency reference comb into the spectral images through a fibre optics system. Line positions can, consequently, be measured on an absolute wavelength scale. Teide Observatory, Tenerife GREGOR (under preparing) GREGOR is the new 1.5 m solar telescope currently assembled on Tenerife, Spain, by the German consortium of the KiepenheuerInstitut für Sonnenphysik, the Leibniz Institute for Astrophysics Potsdam, the Institut für Astrophysik Göttingen, the Max-Planck-Institut für Sonnensystemforschung and other international partners. Teide Observatory, Tenerife GREGOR (under preparing) The telescope is designed for high-precision measurements of the magnetic field and the gas motion in the solar photosphere and chromosphere with a resolution of 70 km on the Sun, and for high resolution stellar spectroscopy. The new Gregory type telescope with open telescope structure, alt-azimuth mount, complete retractable dome, adaptive optics and a pool of well established and new developed post focus instruments will replace the 45 cm Gregory Coudé telescope at the Teide Observatory on Tenerife which will be retired after 40 years of service. Teide Observatory, Tenerife GREGOR (under preparing) - 1500mm free aperture - Gregory configuration with additional tertiary mirror (M3) - light weighted optics - integrated adaptive optics - Image de-rotatornominal field of view 150" (max. 300") - effective focal length: 55.6m (F/38) - low instrumental polarisation - polarisation and calibration unit in symmetric beam - wavelength range from 350nm to several µm - night time observations possible - mirrors made from silicon carbide (Cesic) - primary mirror (D=1,5m) active thermally controlled - M2 (D=0.43m) and M3 (D=0,36m) passive cooled Teide Observatory, Tenerife GREGOR (under preparing) Hochauflösendes, zweidimensionales Spektro-Polarimeter (高分解能2次元フィルタ偏光分光観測装置) Als eines der ersten wissenschaftlichen Instrumente wird ein Spektrometer mit zwei Fabry-Perot-Interferometern (FPI) im kollimierten Strahlengang zur Verfügung stehen. Für Polarisationsmessungen kann ein Full-Stokes-Polarimter in den Strahlengang eingefügt werden. CCD Kameras mit 1376 x 1040 Pixeln aufgenommen. Bei der gewählten Auflösung ergibt dies ein maximales Bildfeld von 52 Bogensekunden x 40 Bogensekunden. Die Kameras werden mit 12 Bit digitalisiert. Der spektraler Bereich reicht von 530 nm bis 960 nm, die spektrale Auflösung ist etwa 250 000. 52秒角×40秒角 カメラ:12ビット 530nmのから960 nmのスペクトル範囲 スペクトル分解能:250 000 最大視野時フレームレート:毎秒約10フレーム Teide Observatory, Tenerife GREGOR (under preparing) Nacht-Spektrograph(UV・可視2波長同時分光観測装置) Als eines der wenigen Sonnenteleskope kann GREGOR auch regelmäßig für Nachtbeobachtungen eingesetzt werden. Dazu wird es mit einem fiberoptischen Doppelspektrographen ausgestattet. Die spektrale Auflösung beträgt etwa 100 000. Mit diesem Spektrographen sollen sonnenähnliche Sterne parallel im visuellen und blauem Spektralbereich beobachtet werden. Der Betrieb soll möglichst vollständig robotisch erfolgen. Teide Observatory, Tenerife GREGOR (under preparing) POLIS (可視・近紫外の2波長同時分光偏光観測装置) Mit einem Nachbau des Polarimetric Littrow Spectrometer (POLIS) Instrumentes am VTT können gleichzeitige, polarimetrische Beobachtungen bei zwei bestimmten Wellenlängenbereich des sichtbaren und nahen ultravioletten Spektrums gemacht werden. Die spektrale Auflösung beträgt etwa 250 000. Die Installation des Instruments wird nach der Inbetriebnahme des Teleskops erfolgen. Teide Observatory, Tenerife GREGOR (under preparing) Infrarot Spaltspektrograph Für Beobachtungen im Wellenlängenbereich von etwa 1µm bis 1.8µm wird das GREGOR Teleskop mit einem Spaltspektrographen ausgestattet. Mit einer Kamera mit 1020 x 1024 Pixeln erhält man ein Bildfeld von etwa 136 Bogensekunden x 137 Bogensekunden. Die spektrale Auflösung beträgt zwischen 380 000 bis etwa 570 000. Mit einem Polarimeter hinter dem Eintrittsspalt können die verschiedenen Polarisationszustände des Sonnenlichtes gemessen werden. Für die Zukunft ist geplant, den Spektrographen auch für parallele Beobachtungen im optischen Wellenlängenbereich zu erweitern. 赤外線スリット分光装置の立体概略図 黄色の5階にある光学ベンチ(青色)に 偏光モジュレータと入射スリット。 スリットを通った太陽光は4階(グレー)の スペクトルカメラミラーによって捕らえ、 回折格子上にコリメートさせる。 Roque de los Muchachos Observatory, La Palma Swedish Solar Telescope (SST) The Swedish 1-m Solar Telescope (SST) is a refracting solar telescope at Roque de los Muchachos Observatory, La Palma in the Canary Islands. It is run by the Institute for Solar Physics of the Royal Swedish Academy of Sciences. The primary element is a single fused silica lens, making it the second largest optical refracting telescope in use in the world. The 110-cm lens has a clear aperturediameter of 98 cm. The SST is most often used as a Schupmann telescope, thereby correcting the chromatic aberrations of the singlet primary. The SST is a vacuum telescope, meaning that it is evacuated internally to avoid disruption of the image from air inside. This is a particular problem with solar telescopes because of the heating from the large amounts of light collected being passed on to any air causing image degradation. As of 2005 it has produced the highest resolution images on the Sun of any Roque de los Muchachos Observatory, La Palma Swedish Solar Telescope (SST) Currently, the SST is operating with an adaptive optics system with a 37-actuatordeformable mirror from AOPTIX, although upgrades are underway. Roque de los Muchachos Observatory, La Palma Swedish Solar Telescope (SST) A. Details of the box holding the field mirror and field lens. B. The Schupman corrector with one lens and one mirror. C. The re-imaging optics, located on the optical table and consisting of a tip-tilt mirror, an adaptive mirror and a re-imaging lens. Roque de los Muchachos Observatory, La Palma Swedish Solar Telescope (SST) Instruments The SST has two modes of operation. One mode is a spectrograph mode, using the TRI-Port Polarimetric EchelleLittrow (TRIPPEL) spectrograph with a resolution of R = 230 000 (corresponding to 1.3 km/s at the solar surface). TRIPPEL is a Littrow spectrograph using a 79 grooves/mm echelle grating with a blaze angle of 63.43 degrees. Roque de los Muchachos Observatory, La Palma Swedish Solar Telescope (SST) Instruments The other mode is an imaging mode, where imaging is split up in a red and a blue beam by a dichroic beamsplitter. The red beam has a tunable filter called CRisp Imaging SpectroPolarimeter (CRISP) which operates from 510 to 860 nm and is able to measure polarization by using liquid crystal modulation combined with a polarizing beamsplitter. The total system uses three 1k × 1k Sarnoff CCDs, two are used for direct observations and the third is used in aiding the MOMFBD image reconstruction method. The blue beam is a setup with a total of 4 MegaPlus II es4020 cameras. Big Bear Solar Observatory * Built by the California Institute of Technology in 1969. * In 1997, transferred to the New Jersey Institute of Technology (NJIT). * The surface of Big Bear Lake is about 2,055 meters (6,742 ft) abovesea level. * The main observatory building is in the open waters of the lake. The original main solar telescopes: a 65 cm (26 in) vacuum reflector Its Main purpose was studies of sunspots on the solar surface. Big Bear Solar Observatory The New Solar Telescope (NST) -In early 2007, The New Solar Telescope (NST) was began building. - December 2008, first engineering light at the Nasmyth focus - January 2009, solar observations began. - The telescope is set on an equatorial mount. - 1.6 m (63 in) clear aperture open frame, off-axis Gregorian telescope. - new ventilated dome Big Bear Solar Observatory The New Solar Telescope (NST) -In early 2007, The New Solar Telescope (NST) was began building. - December 2008, first engineering light at the Nasmyth focus - January 2009, solar observations began. - The telescope is set on an equatorial mount. - 1.6 m (63 in) clear aperture open frame, off-axis Gregorian telescope. - new ventilated dome Big Bear Solar Observatory The New Solar Telescope (NST) - f/2.4 primary mirror (M1) - 83.2m effective focal length (f/52 at Gregorian focus) - Telescope optics (PM,SM) made of Zerodur (ドイツ・ショット社が開発した低膨張率光学ガラス). - Plate scale 2.48 arcsec/mm - Diffraction limited resolution of 0.06" at 500nm and 0.2" at 1,565nm (with AO) - Computer controlled pointing and tracking - Real-time systems for maintaining telescope alignment - Temperature monitoring at many points on the telescope - Active optics & Adaptive optics - Gregory-Coudé focus => 2 arcmin FOV Wavelength range from 0.39-1.6μm with AO - Nasmyth focus => All wavelengths > 0.39μm also at with tip/tilt but without AO Big Bear Solar Observatory The New Solar Telescope (NST) Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for imaging 開発中のものも含め、現在以下の4種類の焦点面装置がある ・BFIs ・VIS ・IRIM ・NIRIS Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for imaging 光球撮像用 Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for imaging 彩層観測用 Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for imaging 光球の赤外磁場偏光観測 Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for imaging IRIMの後継機:視野拡大、スループット増大、彩層ラインも Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for Spectroscopy(いずれも開発中) Fast Imaging Solar Spectrograph (FISS) collaborative work between Seoul National University (SNU) and Korean Astronomy and Space Science Institute (KASI) Concept of two-mirrored field scanner. Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for Spectroscopy (いずれも開発中) Fast Imaging Solar Spectrograph (FISS) As of now, FISS is undergoing lab tests at KASI. Alignment test on a horizontal optical table was successful. The FWHM at the focal plane was 2.5 pixels and this can be regarded as moderate sampling. Still imaging test using coelostat is ongoing. Finally, it should undergo the same procedure on a vertical optical table, which is the same environment at the Coudé lab of NST. →現在既にNSTに設置して観測を開始している が、空間分解能の点で本来の性能が出ていないようで、要調整。(11月のSolar-C会 議で本件についての講演の予定あり。) Big Bear Solar Observatory The New Solar Telescope (NST) Instruments for Spectroscopy (いずれも開発中) 低温赤外対応多波長スペクトログラフ Hida Observatory Domeless Solar Telescope (DST) 1次焦点面 クーデ鏡ユニット 1次焦点面ユニット PG部 PGセンサ コーン・ダイアフラム ターレット 垂直分光器 Gバンドの撮像 を行なう場合は、 ここにダイクロ イックミラーを 置く (1)1979年~1996年: 撮像データは写真フィルムに記録。 (2)1995年 ~2000年: PULNiX製アナログビデオカメラの 画像を、レーザービデオディスク メディアに記録。 (3)2001年~現在: デジタルCCDカメラ KODAK MegaPlux4.2iにて直接デジタル画像とし て記録。 垂直分光器焦点面におけるHαリオフィルタによるフィルタグラフ観測データ例 垂直分光器 垂直分光器を用いた偏光分光観測による 光球マグネトグラフのデータ例 現VMGC 現ircam2PC 現ircamPC 現dstraid 垂直分光器を用いたCa II K線スペクトロヘリオグラフ 観測による彩層ジェットの観測例 (Morita et al. 2010) 水平分光器 水平分光器 水平分光器を用いた3波長同期スペクトロヘリオグラフの観測例 分光器・回折格子の性能について (ツェルニー・ターナー型) 太陽像の焦点面 スペクトルの焦点面 回折格子 (グレーティング) コリメータ鏡 カメラ鏡 グレーティング(回折格子)の基本公式 d A α B C β 光の波が強め合う入反射角度の関係式: mλ = AB+BC = d(sinα+sinβ) ・・・(1) ここで、m:干渉の次数(整数) 波長分散 dβ/dλ = 1/(dβ/dλ)= m / dcosβ ・・・(2) 波長分解能 λ/Δλ = Nm/1.22 ・・・(3) ここで、N;有効な溝の全本数 (なぜなら、 Δβ = 1.22λ/D = 1.22λ/Ndcosβ D;反射光の口径 かつ、 Δβ =(m/dcosβ)Δλ ) Nd D β ドームレス太陽望遠鏡 垂直分光器を用いた場合の例 回折格子の溝の密度 :632本/mm 観測する波長と入反射角(例):6302.5Å、 α=54.29°、β=51.38° (必ずαーβ=2.907°) 観測するスペクトルの次数(例):4 (1)式左辺 mλ=4×6302.5=25210 (1)式右辺 d(sinα+sinβ)=107/632×(sin(54.29°)+sin(51.38°)=25210 ここで、(2)式より 分散: dβ/dλ = m / d cosβ = 4 /(107/632) cos(51.38°) = 4.05×10-4 [rad/Å] = 5.689 [mm/Å] また、 有効口径内の溝の全本数:N = (632本/mm×400 mm) なので、(3)式より、 波長分解能:λ/Δλ = Nm/1.22 = 632×400 × 4 / 1.22 = 828852 よって、Δλ= λ/828852 = 6302.5 Å/828852 = 0.00760 Å ドームレス太陽望遠鏡 水平分光器6番ポートを用いた場合の例 回折格子の溝の密度 :1201本/mm 観測する波長と入反射角 :7773Å、 β=32.98°、α=22.90° (必ずβーα=10.08° for port-6) 観測するスペクトルの次数:1 (1)式左辺 mλ=1×7773=7773 (1)式右辺 d(sinα+sinβ)=107/1201×(sin(22.90°)+sin(32.98°) ~ 7773 ここで、(2)式より 分散: dβ/dλ = m / d cosβ = 1 /(107/1201) cos(32.98°) = 1.432×10-4 [rad/Å] = 1.430 [mm/Å] = 0.699 [Å/mm] (焦点距離9.985mとして) また、有効口径内の溝の全本数:N = (1201本/mm×160 mm÷cosα) なので(3)式より 波長分解能:λ/Δλ = Nm =(1201×160/cos(22.90°))× 1 = 208601 よって、Δλ= λ/208601 = 7773 Å/208601 ~ 0.0372 Å ここまで