Telescopes and Detectors

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Rodger Casey
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$Telescopes and Detectors 1 Reflection and Refraction Telescopes and lenses work because of te way ligt beaves at te interface between two different media.$ $Te ratio (1) is called te index of refraction. Because te ligt slows, te direction of travel canges. Tis is called refraction. t eac boundary, some of te ligt gets refracted and some gets reflected.$

1 Telescopes and Detectors 1 Reflection and Refraction Telescopes and lenses work because of te way ligt beaves at te interface between two different media. Te speed of ligt slows wen it passes from air to anoter denser medium. Tis is because ligt is an oscillating electromagnetic wave, and many molecules ave teir electric carge unevenly distributed. Te passing oscillating wave causes te molecules to oscillate, and tis slows te ligt down. Te speed of ligt is not constant in a medium, sorter radiation will be slowed te most. Te ratio (1) is called te index of refraction. Because te ligt slows, te direction of travel canges. Tis is called refraction. t eac boundary, some of te ligt gets refracted and some gets reflected. Te relation between te incident angle,, and te refracted angle,, is called Snell s Law: (2) Figure 1: Snell s law and te law of reflection. Te relation between te indicent and reflected waves, or te law of reflection, is tat tey are equal wit respect to te normal, i.e. =. 2 Telescopes 2.1 Image Formation & Focal Lengt mirror is described by a radius of curvature, and a focal point and te distance to te focal point, te focal lengt,. Te focal point is te point at wic incident parallel rays travelling toward te mirror will meet after reflection. Te distance from te mirror to te focal point is called te focal lengt. Rules of image formation: any incident ray traveling parallel to te principal axis of te mirror will pass troug te focal point any ray passing troug te focal point, will emerge parallel to te principal axis Figure 2: Formation of an image wit a concave mirror. If we are collecting ligt from an extended source, te amount of energy gatered by te mirror will be directly proportional to te area of te aperture (mirror), (were is te mirror diameter. Te incoming energy will be spread across a corresponding region of te image. Te amount of energy per unit area per unit time in te image will be inversely proportional to te image area. Te area of te image is proportional to te square of its lateral dimension,. Tus te flux density (or brigtness) of te image will be proportional to (D/f). Te term: (3) is called te f-number or f-ratio, and it is given by te focal lengt divided by te diameter of te primary mirror or lens. Te smaller te f-ratio, te faster te telescope (i.e. it concentrates more ligt in a small area). 2.2 Magnification Te main purpose of a telescope is to collect ligt. Tey can also magnify images (magnification is te ratio of te angular size of te object seen troug an instrument relative to te angular size witout te instrument). However, for most images in astronomy, magnification is not important. Te magnifying power,, is given by 1

!#"%$'&)(!#"+*-,* (4) were!#"+$.&)( is te focal lengt of te objective and!#"+*-,* is te focal lengt of te eyepiece.

Te most important criteria for most applications is te telescopes ligt gatering power, or ow many potons it collects. Tis is proportional to te area of te primary. 2.

) if te pat lengts of ligt from different regions is different, te waves can interfere wit eac oter and will be be eiter out of pase (in wic case tey cancel and no ligt is visible) or in pase

$Tus, altoug stars are so far away tat tey appear effectively as point sources, te image made at te telescope will ave a finite size because of tis penomenon of diffraction.$

2 !#"%$'&)(!#"+*-,* (4) were!#"+$.&)( is te focal lengt of te objective and!#"+*-,* is te focal lengt of te eyepiece. From tis equation it can be seen tat te greatest magnification is wit a long focal lengt telescope and sort focal lengt eyepice. However, since most objects we will look at are not resolved (e.g. tey are point sources), te magnification is irrelevant. Te most important criteria for most applications is te telescopes ligt gatering power, or ow many potons it collects. Tis is proportional to te area of te primary. 2.3 Resolution Because of te wave nature of ligt, any time tere is an obstacle tat it interacts wit (suc as an aperture, mirror, lens etc.) if te pat lengts of ligt from different regions is different, te waves can interfere wit eac oter and will be be eiter out of pase (in wic case tey cancel and no ligt is visible) or in pase (causing a concentration of ligt). Tus, altoug stars are so far away tat tey appear effectively as point sources, te image made at te telescope will ave a finite size because of tis penomenon of diffraction. Te resolution is te smallest angular separation between 2 stars tat can be resolved by te instrument. For a telescope of diameter / meters, at wavelengt 0 [m], te resolution in arcsec is given by ;:=<> 0 / (5) te image (makes it wider). you can see tis effect on te bottom of a swimming pool on a sunny day; you never see images of te sun, just brigt lines dancing over te bottom of te pool. Tis is an amplified example of seeing but troug a very tick atmospere indeed. (See Fig. 6 for te effect on an image). 2.4 Types of Telescopes Tere are many different telescope optical configurations, and tey all ave different advantages. Most telescopes ave a primary mirror, wic is te main ligt collector, and some ave a secondary mirror wic redirects te ligt to a desired focus. Some of tese different configurations are sown in Fig. 7. We rarely acieve te diffraction limit of a telescope in te optical, but it is possible in te infrared at times from te ground. One of te reasons we don t acieve te diffraction limit is because of te effect of seeing. Seeing is te blurring of an image caused by turbulence in art s atmospere. ir of different densities as different indices of refraction,?, and tis causes te ligt to be refracted sligtly differently. In oter words, te atmospere acts as if it is full of small lenses wic re-directs te ligt sligtly and tis blurs Figure 3: xamples of a 4 telescope types, sowing te ligt pats for (a) a refractor; (b) prime focus reflector; (c) cassegrain focus reflector; (d) newtonian focus reflector. 2.5 Image problems and coma Off axis ligt gets distorted into a cometlike appearance. Te correction is to eiter put a tin lens, or corrector plate in front of te system, or to make te primary mirror a little yperbolic. 2

$cromatic aberration Because ligt of different wavelengts refracts differently (by different amounts) in glass, te focus of a lens will be different for different$ $Figure 6: Ideal image from a point source, te effect of te wave nature of ligt (diffraction), te effect of te art s atmospere seeing.$ $Multiple lens components can correct for tis in refractors, and a corrector plate can correct for tis in a reflector.$ Te solution is to create an asperical or parabolic mirror - but tis is more expensive. (wic are called dynodes) and are collected at an annode.

Te solution is to create an asperical or parabolic mirror - but tis is more expensive. (wic are called dynodes) and are collected at an annode.

in of about 10C, e.g. for every incident poton tere will be 1 million electrons detected out te back. Tese require very stable power supplies.

Typical optical tubes ave low response D toward te IR Q peaks near 30% at 4000 xcellent response time limited around 50 ps (due to electron travel time in tube).

3 cromatic aberration Because ligt of different wavelengts refracts differently (by different amounts) in glass, te focus of a lens will be different for different colors. series of lenses can correct for tis. Not present on reflectors. Figure 6: Ideal image from a point source, te effect of te wave nature of ligt (diffraction), te effect of te art s atmospere seeing. Figure 4: Cromatic aberration and its solution. astigmatism Off axis rays in te orizontal and vertical plans focus at different points. Multiple lens components can correct for tis in refractors, and a corrector plate can correct for tis in a reflector. sperical abberation Parallel ligt striking te sperical mirror near te center will come to a focus farter from te mirror tan does ligt striking te mirror off axis. Te solution is to create an asperical or parabolic mirror - but tis is more expensive. (wic are called dynodes) and are collected at an annode. ac time te electrons strike a dynode, tey produce a secondary sower of electrons. Typically te potomultiplier tube will experience a gain of about 10C, e.g. for every incident poton tere will be 1 million electrons detected out te back. Tese require very stable power supplies. Figure 7: Layout of a potomultiplier tube. Limitations and caracteristics Figure 5: Sperical aberration, and te image from a parabolic mirror. Typical optical tubes ave low response D toward te IR Q peaks near 30% at 4000 xcellent response time limited around 50 ps (due to electron travel time in tube). In oterwords, excellent instrument for very ig time resolution applications. Higly linear in very low ligt level conditions. 3 Potoelectric Potometer Te potomultiplier is a ligt sensitive electrode wic emits eb wen potons strike it as a result of te potoelectric effect. Te eb are accelerated by electrodes 4 Potograpy Te potograpic process is a cemical reaction wic occurs wen ligt strikes film. ll potograpic processes rely on oxidation-reduction reactions. 3

4 [ R H mulsion contains crystals of silver alide (gbr, gcl, gi or a combition) suspended in a gelatin. Ligt striking te emulsion creates a latent image 1. Quantum of ligt frees an ef 2. ef is captured by gg ion 3. gg ions migrate to neutralize carge 4. Lattice alows migrated gg ions to form a speck of g grain 5. Tis is called te latent image wic is proportional to te number of potons Te image is made visible wit a developer, wic reacts wit te silver alides and creates metallic silver. Te greater te intensity of ligt, te greater te density of silver. By adding ef to te silver alide, we liberate te g, and tis binds to te latent image specks. fter developing, a stopbat is used to render te developer inactive. Ten a fixer is applied to break up te non-exposed silver salts, so tat tese areas become transparent on te film. If H is te ratio of te transmitted to incident intensity of ligt, ten IKJL5MONQP HSRUTWVYX (6) were is te mass of silver. If T [ is te density or VZX mass of metallic g per unit area, ten [\ IKJL MON P \^] I_JL MONa` Hcb (7) Hurter and Driffield Curve describes te linearity of te potograpic process. Te dynamic range over wic film beaves in a linear manner is only about 2.5. Figure 8: HD curve for potograpic exposure. Te speed of film is a measure of [ for a given d. slow speed film as small grains and tus ig resolution, and a ig speed film as large grains and a low resolution, so tere is always a trade-off. noter factor in selecting te film is te contrast (g ). Low contrast films ave small canges in optical density wit large canges in exposure, and te films are fast. Hig contrast films give very large canges in density wit small canges in exposure, and tey are slow (typically te film is black and wite). 5 Carge Coupled Devices Te carge coupled device was conceived at Bell Labs in 1970 (Boyle & Smit, 1970), and te first one was produced by Faircild lectronics wit a format of 100 e 100 pixels in Te first astronomical use was at Kitt Peak National Observatory in CCD is a Si-based semiconductor arranged as a 2-D arrange of elements. Te operation of a CCD depends on te potoelectric effect in semiconductors (suc as Si). Incoming potons of ligt greater tan te energy gap can excite electrons, wic are ten free to move about te material. Limitations: low exposure optical density not dependent on xposure, d, were d is te intensity of ligt e te exposure time. medium exposure Linear (useful) region were IKJL MONa` dfb ig exposure Saturation - were all grains are developed to g low potons will pass troug wit no effect Not very sensitive to UV and blue altoug we overcome tis by coating te detectors wit organic dyes. Hig energy cosmic rays can trigger events Te carge generated is collected in a series of electrodes, or pixels. Te electrons are kept from moving between te pixels by external voltages. 4

time varying voltage can cange te electric potentials to move te carge across te CCD and down to be read out and digitally encoded. Tis carge transfer process is nearly noise free and 100% efficient.

5 time varying voltage can cange te electric potentials to move te carge across te CCD and down to be read out and digitally encoded. Tis carge transfer process is nearly noise free and 100% efficient. Figure 9: Readout pattern of a carge-coupled-device. CCD detectors must be operated at temperatures near 150K, so are mounted at te end of a LNi dewar. mateur CCD cameras are cooled electrically. t room temperatures, tere is a lot of signal coming from te CCDs wen tere is no ligt. Tis is called dark current. 6 Spectroscopy 6.1 Dispersion te Grating quation Diffraction gratings function by te principle of interference. s ligt is reflected off of a grooved surface, te ligt will ave taken different pat lengts. Parallel ligt of wavelengt l m coming in at incident angle n to te grating normal, comes in to two adjacent grooves, separated by o. Geometry sows tat te pat difference, p S is given by prqsltoyuwvxzy {~}v xzyn (8) Ligt from adjacent grooves will be in pase and interfere consstructively if p S is equal to integral multiples (ƒ ) of te wavelengt m : were ƒ ƒ m lto uwv xoy {~} vxzyn (9) is te spectral order. Figure 10: Scematic view of te CCD gates wic control te voltages and carge transfer. Figure 11: Interference of ligt from a spectroscopic grating. 6.2 Te Spectrometer Device Q DR Linear Precision rea CCD 90% 10j yes med-ig small PMT 30% 10k yes vig vsmall Poto low 2.5 no med large Note: DR = Dynamic range Basic elements of a spectrometer: slit focal point of te telescope brougt to slit. collimator parallelizes te ligt diffraction grating disperses te ligt eac m of ligt comes off te grating at a different angle lens focuses te dispersed beam of ligt on te detector (typically a CCD) 5

6 Figure 12: Optical layout of te Kitt Peak RC Spectrograp, sowing te major elements. ŵ Boyle, W. and G. Smit (1970), Carge Coupled Semiconductor Devices, Bell Systems Tecnical Journal 49,

IMAGE ILLUMINATION (4F 2 OR 4F 2 +1?)

IMAGE ILLUMINATION (4F 2 OR 4F 2 +1?) IMAGE ILLUMINATION ( OR +?) BACKGROUND Publications abound wit two differing expressions for calculating image illumination, te amount of radiation tat transfers from an object troug an optical system