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Study optical aberrations, angular resolution, CCD detectors, telescope mounts, and more in observational astrophysics.
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Observational Astrophysics in the visible light Shai Kaspi Technion - April 2019
Optical Aberrations • Departure of the performance of an optical system from the predictions of geometrical optics. • Occurs when light from one point of an object after transmission through the system does not converge into a single point. • Aberration leads to blurring of the image produced by an image-forming optical system.
Monochromatic aberration • Are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. • Spherical aberration – due to spherical surface of the system. • Coma aberration – point sources are distorted to have tail due to their off axis position.
Chromatic aberrations • Are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. refractive index High low
Catadioptric TelescopeSchmidt camera Schmidt–Cassegrain telescope
Angular Resolution The minimum distance between distinguishable objects in an image. Caused by Airy diffraction. Airy radius: Ra= 1.22 λ f/ D θ is the angular resolution in radians. λ is the wavelength of light. D is the aperture diameter. f is the focal length.
Image Scale • The number of millimeters at the focal plane of an object with an angular size of 1 radian. • Plate Scale = 1/fo (fo is the effective focal length of the telescope in millimeters) • Translating the radian to arcseconds one gets: • Plate Scale = 206264.8/fo in arcsec/mm • The number of arcseconds per pixels of a specific detector. • A telescope with focal length of 7 meter will have an image scale of 29.5 arcsec/mm, and with ccd pixel of 24 micron each pixel will be 0.7 arcsec/pix.
Field of View • Angular area of sky that is visible through an eyepiece or can be recorded on a detector, expressed in angular diameter. • Determined by the diameter of the eyepiece aperture or the detector - D. • θ = D/fo in radians • f o– effective focal length.
f- number • D is the aperture diameter • f - focal lebgth of the optical system • f-number is N or F = f/D • Smaller f-number (f/3) is called “faster” optics while larger f-number (f/7) is called “slower” optics. Fast optics slow
Angular Magnification • The ratio of the angle of the object seen through the telescope divided by the angle of the object without the aid of the telescope • M = fo /fe • fo = effective focal length of the telescope • fe = the focal length of the eye piece.
Telescope Mounts • Alt-azimuth mount - allow telescopes to be moved in altitude, up and down, or azimuth, side to side, as separate motions • Equatorial mount - has north-south "polar axis" tilted to be parallel to Earth's polar axis that allows the telescope to swing in an east-west arc, with a second axis perpendicular to that to allow the telescope to swing in a north-south arc
Guiding the Telescope • Equatorial mounts have a motor in the RA axis that is tracking the moving skies. • To make fine tracking we use a guiding star and move the telescope accordingly
Seeing • The blurring of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index. • One of the biggest problems for Earth-based astronomy. • Measured as Full Width Half Maximum (FWHM) of a point source. Df
Air mass • The optical path length through Earth’s atmosphere for light from a celestial source. • Light is attenuated by scattering and absorption in the atmosphere. • Airmass X ~ 1/cos(zenith-distance) • m(X) = m0 + k*X Passband k ----------------- U 0.6 B 0.4 V 0.2 R 0.1 I 0.08
Detectors • Human eye was the first detector when looking at the skies. • But, the eye respond to the rate of photons from the source and weak sources cannot be detected, as well as not able to record the signal. • Using integrating detectors one can use long exposure time to see the weak sources as well as to record the signal.
Photographic Plates • First integrating detectors were photographic plates with black and white emulsion. • Emulsion is not linear in respond to light. • Emulsion has relatively low sensitivity to light (about 2-3 % efficiency, with up to 10% with special treatment). • Photoelectric detectors like Photomultipliers and photodiodes were used for some time.
Charge Coupled Device (CCD) • Two dimensional highly light sensitive solid-state detector consist of an array of picture elements – pixels. • Of order of a few thousands pixels square, with each pixel at a size of 10 to 20 microns, the CCD is a few centimeters square. • Has high efficiency of detecting 50% to 95% of the photons that fall on it.
Operation mode • The charge accumulated in each pixel is read out as a tiny electric current. • The current is amplified and converted (using an analog-to-digital convertor) into Analog Data Unit – ADU or “count”. • Each “count” represent a number of photoelectrons – this number is the GAIN. • The counts in each pixel are stored in binary mode to a certain numerical precision. • If a pixel value can be a 16-bit binary number then the value is ranging from 0 to 65535 (= 216 – 1) • A number above that gives saturation.
Front illuminated CCD • CCD is a matrix of a layered semiconductors. • Each pixel is constructed with a light sensitive layer at the front, conductive layer in the middle, and the registering layer at the back. • The active matrix on its front surface and simplifies manufacturing. • The matrix and its wiring, however, reflect some of the light, and thus the registering layer can only receive the remainder of the incoming light; the reflection reduces the signal that is available to be captured.
Back illuminated CCD • A back-illuminated sensor contains the same layers, but orients the conductive layer behind the registering layer by flipping the silicon wafer during manufacturing and then thinning its reverse side so that light can strike the registering layer without passing through the conductive layer. • This improve the chance of an input photon being captured from about 60% to over 90%. • Placing the wiring behind the light sensors can lead to a host of problems, such as cross-talk, which causes noise and dark current. Thinning also makes the silicon wafer more fragile.
Frame Transfer CCD • have a parallel register that is divided into two separate and identical areas, termed the Image and Storage arrays.
Matching imager to a telescope • Choosing a detector with pixel size of about a third of the FWHM of a point source
