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Lecture Notes 1/17/2020 Topics in Observational astrophysics Ian Parry, Lent 2020 Lecture 1 • Electromagnetic radiation from the sky. • What is a telescope? What is an instrument? • Effects of the Earth’s atmosphere: transparency, seeing, refraction, dispersion, background light. • Basic definition of magnitudes. • Imperfections in imaging systems. Lecture notes • www.ast.cam.ac.uk/~irp/teaching • Username: topics • Password: dotzenblobs • Email me ([email protected]) so that I can put you on my course email list. 1 1/17/2020 Introduction • Observational astronomy is mostly about measuring electromagnetic radiation HERE (on Earth and nearby) and NOW. Astronomy is an evidence based science. • We measure the intensity, arrival direction, wavelength, arrival time and polarisation state. • Astronomical sources are so far away that the parts of the spherical wavefronts that are ultimately collected by the telescope aperture are essentially flat just before they enter the Earth’s atmosphere. • A telescope is a device that collects pieces of incoming wavefronts and focuses them, i.e. turns them into converging spherical wavefronts. • An instrument is a device that comes after the telescope. It receives the wavefronts and further processes them by either optically manipulating them or converting the energy into measurable signals, or both. Telescope Instrument Primary Optional Optional Detector optics and telescope instrument initial pupil optics optics 2 1/17/2020 Examples • The human eye can be thought of as a telescope (pupil + lens) and an instrument (retina). • Similarly the camera in a phone or a laptop can be thought of as a telescope (pupil + lens) and an instrument (cmos detector). • The lens of an SLR camera is the telescope and the camera body is the instrument. • When a person looks through a telescope their eye is the instrument. • Stonehenge was an instrument (the first working telescopes appeared in 1608). • Precisely where the telescope ends and the instrument begins is subjective. The human eye 3 1/17/2020 Detrimental effects of the Earth’s atmosphere 1) Blocks some or all of the light. Wavelength dependent. Clouds are a major problem. 2) Distorts the plane wavefronts. Blurs images and causes twinkling. 3) Refracts the light causing apparent change in observed wavefront direction. 4) Atmosphere scatters sunlight and it also glows of its own accord adding background light which makes faint objects more difficult to see. The transparency of the Earth’s atmosphere Much of the EM radiation from space does not get to the Earth’s surface – it’s absorbed by atoms and molecules. 4 1/17/2020 5 1/17/2020 Atmospheric absorption of the solar spectrum Air mass = sec (zenith distance) 1.5=sec(48deg) Atmospheric transmission (model) 6 1/17/2020 Turbulence in the Earth’s atmosphere • The plane wavefronts from space are distorted by turbulence in the atmosphere. • Can think of the atmosphere as being made up of lots of cells each with slightly different refractive indices. • The structure of these cells varies with time and there is a range of cell sizes. • Characteristic timescale (cell lifetime), ~0.01 sec • Characteristic length scale, 10‐20cm • Atmospheric “seeing” is a measure of the blurred size of an image for a point source due to atmospheric turbulence. At a good observing site this will usually be in the range 0.4 – 1.5 arcsec with a median seeing of ~0.7 arcsec FWHM. • Adaptive optics is a technique that flattens the wavefronts, i.e. removes the wavefront errors due to atmospheric turbulence and therefore sharpens the images (see later lecture). • Turbulence also causes intensity variations (spatial and Light intensity variations due temporal) across a wavefront (like the light pattern at the bottom of a swimming pool) and so the integrated intensity of a to scintillation are greater for wavefront sampled by the telescope pupil will vary with time. smaller apertures. This is called scintillation and the variations are stronger for smaller apertures. The human eye has a small pupil and scintillation is what causes stars to twinkle. Refraction by the Earth’s atmosphere • The refractive index of the atmosphere is slightly greater than unity so in general, light rays are bent and objects in the sky appear closer to the zenith than they ought to (atmospheric refraction). • Zenith distance is the angle between an object and the zenith. • For 75 a good approximation to the amount of refraction is given by 58".16 tan ζ 0". 067 tan • In general for a spherical atmosphere we have sin ⁄ sin • where is the radius of the layer with refractive index and the subscript 0 denotes the layer of the observer. • R at the horizon is ~34 arcmin. • n is wavelength dependent so point images appear elongated (atmospheric dispersion). 7 1/17/2020 58".16 tan ζ 0". 067 tan Atmospheric refraction 250 200 150 100 Refraction R in arcsec 50 0 0 1020304050607080 Zenith distance in degrees Atmospheric sky background OH airglow Plot is for New Moon. Moonlight makes it much worse especially at shorter wavelengths ‐1 thermal Hz ‐2 W m ‐26 1 Jy = 1 Jansky = 10 L2 is the second Lagrangian point of the Earth‐Sun system Figure from Mountain et al, 2010 8 1/17/2020 Basic definition of apparent magnitudes • In astronomy the “magnitude” system is used to measure how bright celestial objects are • It is based on an ancient system in which the brightest stars (as seen by the unaided eye) were called first magnitude stars and the faintest ones that could be seen were called fifth magnitude stars. • The intermediate second, third and fourth magnitudes were defined subjectively. • Human perception of brightness is essentially logarithmic. • The faintest stars visible to the unaided eye are about 100 times fainter than the brightest ones. Basic definition of apparent magnitudes apparent magnitude 2.5 log 2.5 log where is the intensity (brightness or flux) of an object with 0by definition. (Throughout this course log means base‐ 10 log and ln means base‐e, natural log). Comparing the magnitudes of two objects ∆ 2.5log The intensity is measured in some band pass where is the efficiency and is the flux. 9 1/17/2020 U, B, V, R, I, J, H, K, L, M, N and O refer to apparent magnitudes measured with passband filters. For example, we might say a star has an apparent magnitude of V=14.5 or a galaxy has an apparent magnitude of H=20.3. For λ > 1 μm, the passbands correspond to atmospheric windows (see earlier plot). Central λ FWHM Central FWHM λ(Å) (Å) N 10.6 O 21 Imperfections in imaging systems • Real imaging systems do not produce a perfect point image for a point source. • The best outcome is that the system produces an image which is only limited by diffraction. • In addition there are likely to be optical aberrations. The lowest order optical aberrations are the so‐called Seidel aberrations. • The Seidel aberrations are: 1. Spherical aberration 2. Coma 3. Astigmatism 4. Field curvature 5. Field distortion 10 1/17/2020 θ is the angular radius of 1.22 Diffraction the first dark ring in radians θ ~ FWHM of the PSF Plot shows the light distribution in the Linear scale focal plane. F is the focal length of the imaging system. 1.22 Fθ is the physical size of the 1.22 ring’s radius. This depends only on f‐number N (not D). Diffraction Log scale 11 1/17/2020 Linear scale Diffraction FWHM=0.94μm Log scale Diffraction First dark ring has radius = 1.137μm 12 1/17/2020 Spherical Aberration • This is present on‐axis s for spherical refracting surfaces and spherical reflecting surfaces (hence the name). • The aberrated wavefront is not spherical. • “on axis” means the point source is at the centre of the field of view. Circle of least Spherical confusion Aberration T‐SA is transverse spherical aberration s L‐SA is longitudinal spherical aberration 13 1/17/2020 Spherical aberration Paraxial focus Caustic Circle of least confusion Meridional and sagittal planes for an off‐axis object Sagittal rays have θ=90o Tangential rays have θ=0o The meridional plane is also called the tangential plane and also we refer to tangential rays 14 1/17/2020 The planes here are drawn in the page but they are not actually in the same plane Coma Positive coma is illustrated here (the paraxial image point is nearest to the optical axis). 15 1/17/2020 Astigmatism Field Curvature Σp is the image plane for a flat object plane 16 1/17/2020 Field distortion This is a variation of transverse magnification with field angle. This can be corrected in software so for astronomical instruments it is not important to eliminate it. No distortion Positive or pin‐ Negative or barrel cushion distortion distortion 17.
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