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2.5 Reimaging and the scale at the detectorThe camera reimages the collimated beams onto the detector/CCD. The camera has toaccept the collimated beam so it hasD cam = D pupil .In practice, D cam should be slightly greater to avoid vignetting off-axis beams. (This diameteris really the size of the camera’s entrance pupil, not the physical size of a lens.) Thus thef-number of the camera isN cam = f cam /D pupil = N telf camf coll.Because the camera focal length is usually fairly short to get demagnification of the focalplane onto a small detector, the camera typically has to be fast (small N cam ). As drawn inFigure 3, the beam converges with a wider (faster) angle at the detector, compared to thebeam delivered by the telescope.An off-axis beam is reimaged at distance from the detector center ofSo this means thatD ccd /2 = θ offaxis f cam .D ccd = D fieldf camf coll,s ccd = s telf collf cam,s ccd = 206265”f telf collf cam.The focal plane and plate scale have been demagnified by the ratio of collimator to camerafocal lengths. If the collimator is 3x longer than the camera, the detector can be 3x smallerthan the field size in the telescope focal plane. Large telescopes have big focal planes, whiledetectors are usually smaller, so reimaging systems with demagnification allow us to get areasonable field of view, and can make the pixel scale a better match to the typical seeing.3 SpectroscopyNow consider putting a grating or grism in the collimated beam to do spectroscopy. Theimportant choice for spectroscopy is the lines/mm of the grating, call this M grating , whichgoverns the spectral resolution. Typical numbers for large astronomical gratings range from100-1200 lines/mm (apart from echelle gratings, which are used at a different rangle ofincident angles and in more complex spectrographs).6
3.1 Angles of diffraction: the grating equationfromcollimatorgratingnormalαβreflectiongratingtocameraFigure 4: A collimated beam incident from the left on a reflection gratingand the outgoing diffracted beams (red and blue). The incident and diffractedangles α and β are governed by the grating equation and depend on wavelengthand the lines/mm of the grating.A transmission grating deviates light of wavelength λ by an angle α,sin α = k order λ/l grating ,where l grating = interline spacing, and k order is an integer ≥ 1. Equivalently,sin α = k order λM grating .Let’s work in first order where k order = 1. For a reflection grating the grating equation issin α + sin β = k order λM gratingwhere α and β are the angles of incident and diffracted rays with respect to the gratingnormal, shown in Figure 4. The diffracted beams are shown as red and blue. Light from asingle point source produces one incident collimated beam. The diffracted beam of a singlepoint source at a single wavelength (e.g. the blue lines) is still collimated and will be imagedat a single point on the detector, while the red lines will be imaged at a different point. Thefact that wavelengths are separated in angle, but each single wavelength stays collimated, iswhy we want to have the disperser in the collimated beam.The zeropoint of the diffracted angle β depends on the incident angle and grating normal,but the change in β with λ governs the resolution of the spectrograph.We’re not directly concerned with the zeropoint of β, assuming we have tilted the grating soas to get light into the camera, but with the change in β per wavelength and the resulting7
Page 1 and 2: Scaling relations for telescopes, s
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