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A6525 - Lec. 03 Stops, Pupils, Field Optics and Cameras Astronomy 6525 Lecture 03 Outline Stops Étendue Pupils and Windows Vignetting The periscope, and field lenses A simple camera Supplemental Material Stops and aberrations: Examples Field lenses and the PMT Stops, Pupis, etc. 2 A6525 - Lecture 03 1 A6525 - Lec. 03 Stops A stop is something in the optical system that limits the Aperture diameter of the beam of light. Aperture Stop: Like an iris in a camera or your eye. Limits the size of the primary optic. Field Stop: Limits the size of the field of view – the amount of “sky” that reaches the detector, as in the photomultiplier tube below, or for CCD arrays, it is the physical size of a pixel or of the array in the focal plane. Stop Field Stop PMT Stops, Pupis, etc. 3 A6525 - Lecture 03 Etendue: Stops & Throughput The étendue, or area – solid angle product, AΩ, (also called the throughput) of an optical system is determined by the combination of the aperture and field stops. Pupils A is limited by the aperture stop Ω is limited by the field stop The entrance pupil is the image of the aperture stop through the optical system from the front The exit pupil is the image of the aperture stop from the back Aberrations The position of stops can affect system aberrations. Stops, Pupis, etc. 4 A6525 - Lecture 03 2 A6525 - Lec. 03 Stop at mirror – causes aberations Consider a spherical mirror with an aperture stop at mirror There is now an axis defined by the line from the center of the stop (center of the mirror) to the center of curvature. The location of the aperture stop controls aberrations. Off-axis coma Stops, Pupis, etc. 5 A6525 - Lecture 03 Stop at center of curvature: control aberrations Consider a spherical mirror with an aperture stop at the center of curvature The “on-axis” and “off-axis” beams pass around the center of curvature and hit the mirror. There is no “optical axis” for a sphere so there are no “off-axis” rays. No off-axis aberrations -- just spherical aberration! Stops, Pupis, etc. 6 A6525 - Lecture 03 3 A6525 - Lec. 03 Pupils and Windows in Optical Systems: I 2f 2f 2f 2f f f Exit pupil Chief Rays Boyd, page 73 Entrance pupil and aperture stop Entrance pupil – the image of the aperture stop in object space Exit pupil – the image of the aperture stop in image space All the light transmitted by the optical system must pass through the entrance and exit pupils Chief Ray – any ray that passes through the center of the aperture stop. It will also pass through the center of the entrance and exit pupils. Different chief rays will correspond to different object and image points Stops, Pupis, etc. A6525 - Lecture 03 7 Pupils and Windows in Optical Systems: 2 2f Entrance window 2f 2f 2f f f Exit pupil Chief Rays Entrance pupil and aperture stop Field stop and exit window Boyd, page 73 The maximum cone of light defined by the chief rays corresponding to different object and image points defines the field stop Entrance window – the image of the field stop in object space Exit window – the image of the field stop in image space Stops, Pupis, etc. 8 A6525 - Lecture 03 4 A6525 - Lec. 03 Vignetting Aperture image in object space A P object plane exit Last optical pupil surface st entrance 1 optical surface pupil As we move off-axis, all the rays from a point in the object plane may not make it through the optical system. For example, due to an undersized mirror, represented by “A”, not all the rays from point P make it through the entrance pupil. This phenomena is called vignetting. Stops, Pupis, etc. image plane Exit pupil Bundle of rays that are passed A6525 - Lecture 03 9 A Simple Periscope 2f 2f 2f 2f lens 2 lens 1 object image 2 C A E B D entrance window (image of lens 2 by lens 1) image 1 The optical system above transfers an upright, one-to-one image Either lens 1, or lens 2 may be thought of as the aperture stop, since both define the same cone as seen from the image point A Lens 2 defines the field stop One can show that the diameter of the entrance window is 1/3 the diameter of each lens, d, therefore, AE/AD =(d/6)/CD, so that the field of view (FOV) of the object is given by: 2AE =AD/CD⋅(d/3) = d/2, since CD =4/3 ⋅f, and AD = 2f. The maximum image size is ½ the size of the lens that is used! Stops, Pupis, etc. 10 A6525 - Lecture 03 5 A6525 - Lec. 03 Field Lenses object lens 1 lens 3 lens 2 aperture 3' apertures 1' & 2' image 1 image 2 Inserting lens 3 (which has the same focal length and aperture of lenses 1 and 2) into the system doubles the field of view The entrance pupils are all the same size (imaged to locations 1', 2', and 3' above). The entrance window is now the image of lens 3 (aperture 3') which has the same diameter as the image. Lens 3 is called a field lens. When the entrance window coincides with the object, there is no vignetting, and the illumination over the whole field of view is uniform Stops, Pupis, etc. A6525 - Lecture 03 11 A Simple Camera: 1 primary lens or mirror Lyot stop (at pupil) telescope image plane detector image plane filter relay lens or mirror Simple optical/infrared imaging systems will contain four major elements: 1. Relay lens 2. Lyot stop 3. Filters 4. Detector Stops, Pupis, etc. 12 A6525 - Lecture 03 6 A6525 - Lec. 03 primary lens or mirror A Simple Camera: 2 Lyot stop (at pupil) telescope image plane detector image plane filter relay lens or mirror Relay lens – reimages telescope focal plane onto the detector focal plane. Reimaging f/# chosen to match physical size of the pixels Lyot stop – a stop (baffle) on which the secondary (or primary for a refractor) is imaged by the relay lens. For thermal IR systems, this stop is a cold baffle that prevents unwanted thermal radiation (such as from the ground) from reaching the detector. Stops, Pupis, etc. primary lens or mirror A6525 - Lecture 03 13 A Simple Camera: 3 telescope image plane Lyot stop (at pupil) detector image plane filter relay lens or mirror Filters limit the range of wavelengths that can reach the detector so as to obtain the best sensitivity, and photometry or spectroscopy. Filters are often put at the Lyot stop for a variety of reasons, including Small imperfections in the filter will have a small effect on all pixels – if in the image plane, get spots in the image! Resonant filters (e.g. Fabry-Perot etalons) may require near normal incidence to function properly Pupils often have the smallest requirements for filter size – especially good for wide field cameras Stops, Pupis, etc. 14 A6525 - Lecture 03 7 A6525 - Lec. 03 Matching to the Focal Plane primary lens or mirror relay lens or mirror telescope image plane Dc Lyot stop (at pupil) Dp detector image plane filter i o Dc = diameter of relay (camera) Dp = diameter of primary Matching to the focal plane Suppose the focal plane has 18 micron pixels (xp) and we wish map these to 0.5′′ (θs) on the sky which covers a distance (xt) in the telescope focal plane. = = but # = # or = # Stops, Pupis, etc. # = & # = A6525 - Lecture 03 15 The Power of Étendue conservation Looking at our last equation, we have = # # = or Squaring both sides of the second equation shows that the étendue of the system is conserved Except for certain circumstances (such as broadening of the beam in optical fibers) étendue conservation defines the properties of the beam at any element in the optical system (in terms of AΩ). Ω = AΩ irrespective of any intervening optical elements! To match detector to sky you only need to look at the (final) camera f-number. Stops, Pupis, etc. 16 A6525 - Lecture 03 8 A6525 - Lec. 03 primary lens or mirror Collimating the Beam Lyot stop (at pupil) telescope image plane detector image plane filter collimator camera Typically one wants a collimated beam to fall upon the filter or dispersive element Otherwise there can be aberrations and/or degradation of spectral resolution Since étendue is conserved, an angle, , on the sky corresponds to an angle = / at the filter. We have as before the camera Stops, Pupis, etc. 17 # is set by # # = / A6525 - Lecture 03 Diffraction Limited Observations Starting with the equation that defines the focal plane camera fnumber # Under diffraction limited observations: = / Let assume we want 2 pixels across the diffraction disk, then the f-number of the camera is given by # = = 2 And hence, the size of the telescope does not matter Stops, Pupis, etc. 18 A6525 - Lecture 03 9 A6525 - Lec. 03 Example: FORCAST Faint Object Infrared Camera for the Sofia Telescope 5 to 38 μm 2 color facility camera that employs 256 × 256 pixel Si:As, and Si:Sb BIB arrays Pixel size: 50 µm, wish to fully sample at shortest diffraction limited wavelength of 2.5 m SOFIA telescope: 15 µm For full sampling, we have f#⋅λ/2 = 50 μm f# = 2⋅50/15 = 6.7 at the focal plane For a 2.5 m telescope, θdiffraction ~ λ/D = λ/10, so at 15 μm, θdiffraction = 1.5” pixel size on sky is 1.5”/2 = 0.75” Heavily over sampled at the longest wavelengths: 5 pixels per beam at 38 µm For more info see: "First Science Observations with SOFIA/FORCAST: Field of view: 3.2’ × 3.2’ The FORCAST Mid-infrared Camera," Herter et al. 2012, ApJ, 749, L18 Stops, Pupis, etc. 19 A6525 - Lecture 03 Supplemental Material References Stop and aberration examples Field lens example: Photomultiplier tubes (PMT) Stops, Pupis, etc. 20 A6525 - Lecture 03 10 A6525 - Lec. 03 Some References Telescope Optics: Evaluation and Design Astronomical Optics R. N. Wilson Optics Daniel Schroeder Reflecting Telescope Optics Harrie Rutten and Martin van Venrooij Hecht and Zajac Principles of Optics Born and Wolf Stops, Pupis, etc. 21 A6525 - Lecture 03 Stops and Distortion The position of a stop can affect distortion. Stops, Pupis, etc. 22 A6525 - Lecture 03 11 A6525 - Lec. 03 Stops and Distortion (cont’d) Placing the stop symmetrically eliminates distortion (and coma). Stops, Pupis, etc. 23 A6525 - Lecture 03 Stops and Vignetting If your eye is placed next to the eyepiece (E0), you don’t see the whole field. This FOV is vignetted. Put your eye at E (the exit pupil) to see the whole field. But eyepiece must be large! Stops, Pupis, etc. 24 A6525 - Lecture 03 12 A6525 - Lec. 03 Stop and Field Lens exit pupil Field lens Place a lens at L3 (common focus) which reimages L1 onto L2. The field lens does not change the intermediate image In practice, don’t put exactly at focus (dust, etc.) Now your eye can be next to the eyepiece. Stops, Pupis, etc. A6525 - Lecture 03 25 Field Optics and the PMT: 1 Consider a device such as the photomultiplier tube drawn below, that is designed to accurately measure the flux from faint stars The star is imaged directly onto the face of the PMT, which at first glance appears OK. However, due to atmospheric seeing, the star’s image will wander about on the surface of the PMT Since the sensitivity of the PMT is not strictly uniform, the output signal varies: Field Stop PMT Hot spot This is not photon noise! Signal Dead spot Time Stops, Pupis, etc. 26 A6525 - Lecture 03 13 A6525 - Lec. 03 Field Lenses and the PMT: 2 To mitigate this problem, one can use a field lens, that makes an image of the objective, matched in size to fill the aperture stop. field lens aperture stop PMT field stop objective lens Any light that leaves the objective and hits the field lens will go through the aperture stop. The PMT does not have an image of the star, but rather an image of the objective. So, if the star wanders around in the field stop, the PMT will remain uniformly illuminated (but from different angles). Stops, Pupis, etc. A6525 - Lecture 03 27 Field Lenses and the PMT: 3 For example: star in center PMT star at the edge PMT Note: It is best not to place the field lens exactly in the focus of the primary, because small imperfections (e.g. dust, finger prints, scratches, etc…) can scatter a significant amount of light. Stops, Pupis, etc. 28 A6525 - Lecture 03 14