Page 1 :
Astronomical techniques, L. Bokatial, November 1, 2021, , 1, , Basic optical definitions for astronomy:, , The telescope is the most common instrument used in astronomy. Most people think of a telescope only, in terms of its magnifying power. However, magnification is only one of three powers of a telescope, the, other two being its resolving power and light gathering power. Before we describe various telescopes, we, would like to discuss these concepts as applicable in astronomy., , 1.1, , Magnification:, , The magnifying power of a telescope refers to its ability to make the image appear bigger. If the angle, subtended by a distant object at the objective of a telescope is θi and that subtended by the virtual image at, the eye is θe (Fig.1), then the magnification produced by the telescope is defined as, m=, , θe, θi, , A large value of θe implies that the two objects subtend a larger angle at the eye and hence appear wider, apart. From Fig. 1 we see that, tan θe, fo, =, tan θi, fe, where fo and fe are the focal lengths of the objective and the eye piece, respectively. Typically we are, interested in observing objects at very small angular separations θi . Hence both θe and θi are usually very, small. For small angles we can use tan θ ≈ θ and thus, m≈, , fo, fe, , For example, if a telescope has an objective with a focal length of 60 cm and an eyepiece of focal length, 0.5 cm, its angular magnification is 60/0.5, or 120 times. We say that the magnification is 120 X., , Figure 1:, , 1

Page 2 :
The highest possible magnification of a telescope is limited by its optics which includes the quality of, lenses and mirrors and the thermal insulation of the telescope tube so that the exchange of heat does not, disturb the air inside the tube. The magnification is also limited by the disturbance of light rays suffered in, the Earth’s atmosphere. Also, the higher the magnification, the smaller is the field of view, i.e., the area of, the sky which can be observed by the telescope becomes smaller., , 1.2, , Light gathering power(LGP):, , The light gathering power of a telescope refers to its ability to collect light from an object. Most interesting, celestial objects are faint sources of light and in order to get an image we need to capture as much light as, possible from them.gathering capacity. A telescope’s light-gathering power is directly proportional to the, square of its diameter of its objective. The amount of light a lens or mirror catches depends on its surface, area, and its area with diameter D is ( π4 )D2 . light gathering power is a relative measure, not an absolute, one. It states how two instruments compare with one another, not how much light is gathered. Because the, factor π4 is a constant, we need use only the diameters of the instruments to arrive at a comparative figure., For example, compared with your eye, which has a diameter of about 0.5 cm, a telescope with a 50cm, objective has a light gathering power of, LGP = (, , 50 2, ) = 1002 = 10, 000, 0.5, , The concept that describe the effect of the LGP of telescope is the illumination J, the amount of light, energy per second focused on to a unit area of the resolve image. Since the amount of light collected, from the source is proportional to the area of the aperture, the illumination J ∝ π( D2 )2 . It is also known, that the linear size of the image is proportional to focal length of the lens, therefore, the image area must, be proportional to f 2 , and correspondingly, the illumination must be inversely proportional to f 2 . We, know that linear size of the image is proportional to the focal length of the lens; therefore, the image area, must be proportional to the f 2 , and correspondingly, the illumination must be inversely proportional to f 2 ., Combining these results, the illumination must be proportional to the square of the ration of the aperture, diameter to the focal length. The inverse of this ration is often referred to as the focal ratio,, F =, , f, D, , Thus the illumination is related to the focal ratio by, J∝, , 1, F2, , Since the number of photons per second striking a unit area of photographic plate or some other detector is, described by the illumination, the illumination indicates the amount of time required to collect the photons, needed to form a sufficiently bright image for analysis., We now see that the size of the aperture of a telescope is critical for two reasons: A larger aperture both, improves resolution and increases the illumination. On the other hand, a longer focal length increases the, linear size of the image but decreases the illumination. For a fixed focal ratio, increasing the diameter of, the telescope results in greater spatial resolution, but the illumination remains constant. The proper design, of a telescope must take into account the principal applications that are intended for the instrument., A second important function of a telescope is to produce an image in which objects that are close, together in the sky can be seen as clearly separate. This ability is called resolving power, , 1.3, , Resolving power and diffraction limits:, , We know that the image of a point object through an optical instrument is not a sharp point-like image but, a bright circular disc called the Airy disc. The disc is surrounded by a number of alternate bright and dark, fringes produced due to diffraction. The central bright disc represents the image of the object., 2

Page 3 :
Figure 2: Resolving a pair of two equally bright stars. In a) the stars are easily resolved; in b) the stars are, JUST resolved, and in c) the stars are too close and not resolved., , Now suppose we wish to observe two close stars that appear equally bright. We should be able to see, two Airy discs. However, whether we see them as distinct discs or overlapping each other, depends on the, resolving power of the telescope. Fig. 2 shows three situations where two equally bright stars are closely, placed. The pattern of rings seen at each star image is called the Airy pattern. The two stars are said to, be just resolved when we can just infer their images as two distinct Airy discs (Fig. 2 b). To resolve these, Airy discs, we use the Rayleigh criterion, i.e. ”Two equally bright stars are said to be resolved when the, central maximum of one diffraction pattern coincides with the first minimum of the other”., Resolving power(RP) of telescope is the ability to distinguish two point objects that are close together, in the sky. It is sometimes expressed as the inverse of the minimum angle there must be between two point, objects in order for them to be easily separated:, RP =, , 1, θmin, , The resolving power and the minimum angle depend on the diameter of the objective and also on the, wavelength of the light. For the same wavelength, the resolving power depends directly on the objective’s, diameter. The minimum resolvable angle depends on both the diameter of the telescope’s objective and the, wavelength of light being observed. In general,, θmin =, , λ, D, , where θmin is the minimum resolvable angle, λ is the wavelength, and D is the diameter of the objective in, the same length units. A fundamental limit on the resolution of any instrument, which may be the human, eye or a telescope, arises due to diffraction. The image of a point-like object formed by a telescope becomes, smeared over a certain area due to this effect. Hence it is not possible to distinguish or resolve two objects, if their smeared images overlap. This leads to a lower limit on the angular separation θ between two point, objects that can be resolved by the telescope. The limit at wavelength λ is given by Rayleigh criterion i.e, θ ≥ 1.22, , λ, D, , where D is the diameter of the aperture of the telescope. If the angular separation between two objects, is smaller than this limit, then their images formed by the telescope will overlap. The resolving power, increases with an increase in diameter; hence it is best to have as large a diameter or collection area as, possible. Large aperture is also useful because it allows the instrument to capture a larger amount of the, radiant energy emitted by the star. This is particularly important for detecting faint objects., The diffraction limit of resolution (θ) of a telescope is defined as, θ(radians) = 1.22, 3, , λ, D

Page 4 :
Figure 3: Reflecting telescope used in prime focus mode, , Both λ and D haveto be expressed in the same units. [Note that 1 degree = 60 arc-minutes (60’) = 3600, arc-seconds (3600”)]. R can be expressed in arc-seconds as, θ(arc − sec) = 1.22, , λ, (206265), D, , . Therefore, the resolution of a telescope improves with increasing aperture size and when shorter wavelengths are observed, just as expected for diffraction phenomenon., Based on size alone, the largest telescopes should have large resolving powers. But the resolution of, large telescopes is limited by the passage of light through the Earth’s atmosphere. When we look through, a telescope, we are looking through several kilometres of turbulent air, which blurs the image. At visible, frequencies also, the atmosphere causes considerable distortion that limits the resolution. The intensity as, well as the direction of starlight changes due to the atmosphere. The direction changes due to the refractive, index of the atmosphere. Furthermore, light is scattered and absorbed by the atmosphere. Both of these, effects cause attenuation of light and lead to reduced intensity at the Earth’s surface. The attenuation of light, due to scattering and absorption is called extinction. Moreover, the atmosphere is always changing with, time. The temperature, pressure, and wind velocity at any position show rapid fluctuations. Due to such, fluctuations, the intensity and direction of starlight reaching Earth’s surface also keep changing rapidly with, time. The change in direction and intensity of light is called scintillation. This affects the stars more than, the planets because stars appear as nearly point sources. The Earth’s atmosphere does not allow groundbased telescopes to resolve better than 1-2 arc-seconds in the sky (for even the best astronomical sites). The, major limitation for ground-based astronomy is the Earth’s atmosphere and it can affect the observations in, many ways. Moreover, all wavelengths cannot pass through the atmosphere. This brings us to the concept, of atmospheric windows., , 1.4, , Atmospheric Windows:, , Some of the effects of the Earth’s atmosphere on electromagnetic radiation are: Absorption, scintillation,, scattering and turbulence. Atmospheric molecules such as carbon dioxide and water vapour give rise to, absorption. Thus, only certain bands of frequencies in the electromagnetic spectrum pass through the, atmosphere. These regions of the electromagnetic spectrum are called atmospheric windows. Fig. 3 shows, the absorption properties of the Earth’s atmosphere. On the x-axis is the wavelength in cm and on the y-axis, is the altitude in km at which the intensity of the radiation entering the atmosphere is reduced to half., The atmosphere allows only visible radiation and radio waves to come through to the surface of the, Earth. For observations at other wavelengths we have to fly detecting instruments to altitudes at which these, wavelengths are not completely absorbed. Before the advent of artificial satellites, the instruments were, flown in balloons and rockets. Now-a-days observations are carried at various wavelengths by instruments, on board the space satellites. It is important to remember that astronomers like to observe objects in as, many wavelengths as possible. This helps them to understand astronomical objects better., 4

Page 5 :
Figure 4: Reflecting telescope used in prime focus mode, , 2, , Optical telescope:, , Telescopes have undergone tremendous evolution from Galileo’s times when only refracting telescopes, were used. The most recent telescopes have mirrors that can be actively shaped according to the observer’s, need. The refracting telescopes became outdated very soon because, 1. it was difficult to make good large lenses required for large gathering area,, 2. large lenses were very heavy and balancing the telescope became difficult, and, 3. lenses suffered from optical aberration, Reflecting telescopes with mirrors (parabolic or hyperbolic) have been around for more than a century. In, the last few decades, advanced technologies have been developed which allow the observer to effectively, control the optical system so that it can be adapted to the needs of the observations. Such active and adaptive, optics have completely changed this basic tool of observational astronomy. We now describe various types, of reflecting telescopes. A reflecting telescope is designed by replacing the objective lens with a mirror,, significantly reducing or completely eliminating many of the optical problems. Because the light does not, pass through a mirror, only the one reflecting surface needs to be ground with precision. Also, the weight, of the mirror can be minimized by creating a honeycomb structure behind the reflecting surface, removing, a large amount of unnecessary mass. In fact, because the mirror is supported from behind rather than along, its edges, it is possible to design an active system of pressure pads that can help to eliminate distortions in, the mirror’s shape produced by thermal effects and the changes in the gravitational force on the mirror as, the telescope moves (a process known as active optics). Reflecting telescopes are not completely free of, drawbacks. Since the objective mirror reflects light back along the direction from which it came, the focal, point of the mirror, known as the prime focus, is in the path of the incoming light [see Fig. 4]. An observer, or a detector can be placed at this position, but then some of the incident light is cut off. If the detector is, too large, a substantial amount of light will be lost., Isaac Newton first found a solution to the problem by placing a small, flat mirror in the reflected light’s, path, changing the location of the focal point; this arrangement is depicted in Fig.5. Of course, the presence, of this secondary mirror does block some of the incoming light from the primary, but if the ratio of the, areas of the primary and secondary is sufficiently large, the effect of the lost light can be minimized. A, Newtonian telescope design suffers from the drawback that the eyepiece (or detector) must be placed at a, significant distance from the center of mass of the telescope. If a massive detector were used, it would exert, a significant torque on the telescope., Since the region of the primary mirror located behind the secondary is effectively useless anyway, it is, possible to bore a hole in the primary and use the secondary to reflect the light back through the hole. This, Cassegrain design [Fig. 6] makes it possible to place heavy instrument packages near the center of mass, of the telescope and permits an observer to stay near the bottom of the telescope, rather than near the top,, 5

Page 6 :
Figure 5: Reflecting telescope used in prime focus mode, , as is the case for Newtonians. In this type of design the secondary mirror is usually convex, effectively, increasing the focal length of the system., The classical Cassegrain design uses a parabolic primary mirror. However, an important modification, to the Cassegrain design, known as a Ritchey Chretien design, uses a hyperbolic primary mirror rather than, a parabolic one., , 3, , Telescope Mountings:, , To producing high-resolution, deep-sky images of faint objects we requires that the telescope be pointed at, a fixed region of the sky for an extended period of time. This is necessary so that enough photons will be, collected to ensure that the desired object can be seen. Such time integration requires careful guiding (or, positional control) of the telescope while compensating for the rotation of Earth., Most of the small telescopes (less than 1 metre diameter) use the equatorial mount. In an equatorial, mounting, the pier or the base on which the telescope is mounted is set so that its axis points to the North, Pole. This is done by raising the axis by an angle equal to the latitude of the place. This axis is called the, polar axis. The telescope simply rotate about that axis to to compensate for the changing altitude and azimuth of the object of interest. A rotation about the polar axis is used for adjustment in right ascension. The, telescope is also provided with motion about an axis perpendicular to the polar axis, called the declination, axis, for adjustment in declination. Thus, a combination of these two motions allows the telescope to point, to any object whose equatorial coordinates are known., Since the telescope is fixed on the Earth, it moves with the Earth. In order that the object remains, in the field of the telescope, the mounting is made to rotate in the direction opposite to that of the Earth, , Figure 6: Reflecting telescope used in prime focus mode, , 6

Page 7 :
with the same speed as that of the Earth. Unfortunately, for a massive telescope an equatorial mount can, be extremely expensive and difficult to build. An alternative, more easily constructed mount for large, telescopes, the altitude-azimuth mount, permits motion both parallel and perpendicular to the horizon. All, modern telescopes (larger that 2 m diameter) use Altitude-Azimuth type mount. We know that the altitudes, and azimuths of object change with the location of the observer and with time for the same observer. This, was a major limitation of this type of mounting in earlier times but with advances in the technology using, computers in the past few decades, it is no more an issue., , 4, , Space telescope:, , The main advantages of a telescope over direct observation with the human eye, are magnification, light, collection and resolution. For light collection, one could fabricate telescopes of increasingly large diameters. But these will be limited by the effect of the Earth’s atmosphere. However, if we could put a telescope, in space (high above the Earth’s atmosphere, in a balloon or a satellite), then the Earth’s atmosphere would, not be a limiting factor, and we could achieve diffraction-limited images. In such situations the size of the, telescopes that can be built for such platforms is the only limitation due to the costs involved and limitations, of available technology., The Hubble Telescope of about 2 m diameter is the best example of this type of telescope . Over the, past decade it has made very high quality observations of stars, nebulae, galaxies, supernovae and other, objects. Some of these objects belong to a very early phase of the universe. These observations have led to, improved understanding of these objects., , 5, , Detectors and their use with telescope:, , Detectors are used for measuring the light output from a telescope and play a major role in obtaining, information about the stars, galaxies, etc. The actual light available from an astronomical object is very, small., Detectors are used with telescopes in the following two modes of operation:, • Imaging: This involves taking direct pictures of star fields and extended objects like gas clouds or, galaxies. Since sharp images are required over a wide field which may extend up to several square, degrees, careful optical design is a natural requirement., • Photometry: This involves measuring total brightness, spectrum etc. of single objects. Compared to, imaging mode, poorer images are acceptable in this case but the stellar image has still to be small, enough to enter an aperture or slit of a spectrograph., We now briefly describe various types of detectors., , 5.1, , Types of detectors:, , Detectors used in the imaging mode are mainly 2-dimensional (2D type) since we are trying to form images, of objects in a given area. Examples of such detectors are the photographic emulsion, human eye and the, most modern detector, the chargecoupled device (CCD). Detectors used for photometry of single objects, are 1D type (one dimensional), since they receive photons from one object only. The photometeris a 1D, detector., , Photometer, Before the advent of CCDs, the measurements of light intensity and colour were made using a photometer,, a highly sensitive light meter attached to a telescope. A photometer is still used in the photometry of single, 7

Page 8 :
stars. It is used more commonly for stars whose light output varies with time, called variable stars. The, most important component of a photometer is a photomultiplier tube that is based on the photoelectric, effect. A photon when incident on a photocathode emits an electron. The electric current thus generated is, amplified further and can be measured directly. The calibration of intensity or colour is done by observing, a comparison star. Today, however, most photometric measurements are made on CCD images., , Charge-coupled device, A charge-coupled device (CCD) is a special computer chip of the size of a postage stamp. It contains a large, number (∼ millions) of microscopic light detectors arranged in an array. A CCD can be used like a small, photographic plate, though it is much more sensitive. CCDs detect both bright and faint objects in a single, exposure. The image from a CCD is stored in a digitised form in a computer. Therefore, brightness and, colour can be measured to high precision. Moreover, it is easy to manipulate the image to bring out details., At present, the only major drawback of CCD is that its maximum size is limited (about 70 mm square) as, compared to the most basic 2D detector, i.e., photographic plates which can be as large as 300 mm square., This disadvantage of CCD is also being overcome by combining a large number of CCDs., A basic parameter which defines the efficiency of any detector is its Quantum Efficiency (Q.E.). It is, the ratio of number of photons actually detected (or recorded) by it to the number of photons recorded by, an ideal and perfect detector. Since ideal detector by definition would detect all photons incident on it with, 100% efficiency, this ratio is nothing but the ratio of actually detected photons by the detector versus the, number of photons incident on it. The human eye and photographic emulsion are detectors with the lowest, sensitivity and photomultiplier tubes are only marginally better. The CCD works over a large wavelength, region in the visible band with a Q.E. of the order of 60 − 80%., , 5.2, , Detection Limits with Telescopes:, , Modern detectors like CCDs can detect individual photons, and the limiting magnitude is normally governed, by the background noise. For a typical photographic plate, only about 0.1% of the incident photons are, recorded depending on the type of grains on the film. On such a plate, an image is detectable only after, about 5 × 104 photons have been received. At 200 photons per second, the photographic plate can match, eye’s limit with an exposure of about 4 minutes. Obviously, the plate can detect much fainter objects with, longer duration exposures. The limit to the flux of visible radiation which is detectable is given by, v, Flim, is ∝, , 1, D2 t, , where t is the exposure time and D is the telescope aperture. For a telescope, the magnitude limit in the, visible range, in a very approximate manner without considering any efficiency factors etc., is given by, mlim, ∼ 2 + 5log10 D, v, where D is in mm. Thus using the human eye as the detector along with a telescope we can have the limiting, magnitudes as mv ∼ 12.9 for a 6 inch and mv ∼ 15.3 for an 18 inch telescope., , 8