Astronomical Instruments

Contents

Optical Telescopes

• Optical Telescopes -- The purpose of a telescope is to collect light and then to have the image magnified. The larger the telescope's main light-collecting element, whether lens or mirror, the more light is collected. It is the total amount of light collected that ultimately determines the level of detail. All optical telescopes fall into one of three classes (see Figure 01). In the refracting telescope, light is collected by a 2-element objective lens and brought to a focal plane. By contrast the reflecting telescope uses a concave mirror for this purpose. The mirror-lens, or catadioptric, telescope employes a combination of both mirrors and lenses, resulting in a shorter, more portable optical tube assembly. All telescopes use an eyepiece (located behind the focal plane) to magnify the image formed by the primary optical system. Other instruments can be placed in the focal plane for various purposes, e.g., a photo-electric cell to measure the luminosity, the slit of a spectrograph to analyse the light, or a thermo-couple to measure temperature. The advantage of reflecting telescope is that it has no chromatic aberration. Moreover, mirrors can be manufactured to much larger dimensions than lenses. Reflectors can also be made from a great variety of materials, because all that matters is the reflecting surface, whereas lenses have to be made from special types of glass. However, it has the problem of "spherical

		aberration" - light from different parts of the spherical surface do not focus at the same point. The problem persisted until 1721 when technique developed to grind non-spherical mirror. Refractor has it own problem of chromatic aberration causing color fringes around the image. The problem was resolved with doublet lens in 1729, and triplet objective in 1765. Large lens has other problems with imperfections, such as bubbles and streaks, it also sage in the middle and distort the received image - creating a limit on the maximum size of about 5 meters for the refractor.
Figure 01 Telescope, Types [view large image]	Figure 02a Mauna Kea [view large image]	Figure 02a is the aerial view of Mauna Kea in Hawaii. It shows the domes that house many of the world's largest telescopes.

The magnification of a telescope is given by the formula:

M = OF / f, -------------------- (1)
where OF is the focal length of the objective, and f that of the eyepiece.

The resolution (limit) of a telescope is given by the formula:

R (in sec of arc) = 2.3 x 10⁵ x (/A), ------------------- (2)
where is the wavelength and A is the diameter of the aperture. For example, if A = 100 cm and = 4000x10^-8 (yellow light) then R = 0.092^".

Interferometer is used to measure the size of astronomical objects. By careful analysis of the resulting interference pattern, the position of a point source, or fine detail in an extended one, can be resolved. The same formula for the resolution above is applicable except the aperture A is replaced by the baseline between the two receivers. This technique has been used extensively with radio telescopes; it is now also applied to the optical telescopes as well.

The table below lists 19 optical telescopes more than 5 meters across (around the world in 2012) and other interesting sites :



Observatory	Location	Aperture (m)	Characteristics
Gran	Canarias	10.4	Largest single-aperture optical telescope
Keck	Mauna Kea, Hawaii	10.0	36 segment mirror
Keck II	Mauna Kea, Hawaii	10.0	Interferometry optical
Hobby-Eberly	Mt. Fowlkes, Texas	9.2	Inexpensive, mainly for spectroscopy
Southern African	Sutherland, S.A.	9.2	Similar to Hobby-Eberly (redesigned)
Large Binocular	Mt Graham, Arizona	2 x 8.4	Two telescopes in one mount
Subaru	Mauna Kea, Hawaii	8.3	Observational performance optimized
VLT (Very Large Telescope)	Cerro Paranal, Chile	8.2	4 units combined as an interferometer
Gemini North	Mauna Kea, Hawaii	8.1	Twin of Gemini South
Gemini South	Cerro Pachon, Chile	8.1	All sky coverage with Gemini North
MULTIPLE MIRROR	Mt Hopkins, Arizona	6.5	Combination of six 1.8 m telescopes
Twin Magellan	Las Campanas, Chile	6.5	Two telescopes located 60 meters apart
James Webb Space Telescope (JWST), 2022	Solar orbit at L2 Lagrange point ~ 1.5x106 km from Earth	6.5	Observations from long-wavelength visible (red) through mid-infrared (0.6–28.3 µm)
Large Zenith (defunct in 2016)	Maple Ridge, B.C., Canada	6.0	Rotating liquid-metal mirror
Bolshoi (Large) Azimuthal	Caucasus Mountains	6.0	Max. size for 1 piece solid mirror
Hale	Mt. Palomar, Ca.	5.0	Previous generation (1950-1990) limit
Hooker	Mt. Wilson, Ca.	2.5	Discovery of cosmic expansion (1917)
Hubble Space Telescope	Low Earth orbit	2.4	Observations outside the atmosphere
Yerkes	Williams Bay, Wisconsin	1.0	World's largest refractor (1897)
Kepler Spacecraft (retired in 2018)	Avoid the Milky Way Center	0.95	2662 Exo-planets found

Table 01 Optical Telescopes


By 2010 there are about 50 telescopes on Earth with at least 2.5 meters in aperture diameter. Figure 02b below shows the locations for these giant telescopes (from "Astronomy", Vol. 38, Issue 11, November 2010).



Figure 02b Large Telescopes of the World [view large image]	Size [view large image]

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Radio Telescopes

Radio Telescopes -- It is an instrument for collecting radio waves from celestial objects. The radiation is reflected from a parabolic dish to an aerial (dipole), situated at the focal point, from which the signals are led to a radio receiver. Because the wavelength of radio waves is very large (from 0.3 mm to 30 cm), a radio telescope with an aperture comparable to the optical telescope would have a very poor resolution according to Eq. (2). A considerable increase in resolution can be obtained by using the technique known as interferometry (or VLBI for the very large scale by using hundreds of radio dishes and/or intercontinental links). The method involves linking the antennas together resulting in an effective diameter equal to the largest separation (baseline) between the individual antennas. Such method also effectively increases the collecting area of the receiving antenna thus increasing the sensitivity. Figure 03 shows a two dishes implementation which records the signals with magnetic tapes (or hard disks or via

Figure 03 Interferometer [view large image]

optical fiber). The arrival time of the signals (and hence the time difference) are kept in another tape on the same device. Then they are brought together to a processing center to produce an image (in false colors).

In another application of the VLBI, a known celestial object (usually a quasar) is used as a fixed reference, the variation in arrival time of the signals is interpreted as the motion of the Earth's tectonic plates, the Earth's dynamic motion in space, etc.

The table below lists some of the large radio telescopes and arraies in the world:



Observatory	Location	Resolution (arcsec)	Characteristics
EHT	Hawaii, ...	~ 20x10-6	Black Hole imagings of M87 and MW
VLBA	USA	< 0.001	VLBI implementation in USA
ALMA	Atacama Desert, Chile	> 0.005	Large submillimeter array
SKA	South Africa, Australia	0.03(SA) - 3.3(Aus)	Show Milky Way center from 500 - 50 pc
VLA	Socorro, NM	> 0.04	Largest (dish) synthesis array
(now defunct) Arecibo	Puerto Rico	> 0.2	Largest fixed dish (until 2016)
Effelsberg	Effelsberg, Germany	> 0.6	Largest single dish
Parkes	NSW, Australia	> 0.9	Largest in southern hemisphere
Green Bank	Green Bank, WV	> 2.0	Birthplace of NRAO in 1956
FAST	China, Guizhou	~ 2.9 arcmin	Completed in 2016, Largest fixed dish now

Table 02 Radio Telescopes

The Arecibo Telescope had suffered damages in August and November 2020 to its dish and cable. The cable finally snapped on December 1, 2020 sending debris onto the dish (see Figure 03a, and "Arecibo Observatory Telescope Collapses, Ending Era Of World-Class Research"). Completion of the FAST telescope (Five-hundred-meter Aperture Spherical Telescope) in China, 2016 is a good replacement (see Table 02). However, it seems to have poor resolution as shown in the table. The best estimate at its high frequency limit of 3 GHz is 0.7 arcmin.

Figure 03a Arecibo Telescope, End of [view video]

October 2022 news reports that NSF would not fund the telescope’s reconstruction. It is soliciting proposals from universities or other groups that could establish a new center for STEM (science, technology, engineering and mathematics) education and outreach at Arecibo with an annual budget of $1 million per year for five years.

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Infrared Telescopes

• Infrared Telescopes -- Infrared radiation (wavelength between 1 and 1000 mm) from space is mostly absorbed by the atmosphere (see Figure 04): so the largest infrared telescopes are built on the tops of high mountains, installed on special high flying aircraft or balloons, or better yet on satellites orbiting the earth. However, atmospheric absorption is not the only obstacle to analyse this type of radiation on earth: the main problem, which also occurs in space, is to distinguish the signal

		collected from the "background noise", i.e., from the enormous infrared emissions of the Earth or of the instruments themselves, since object which is not at absolute zero, emits infrared radiation. So everything around the instruments (including the telescope) produces "backround noise". Therefore, special photographic film is used to produce
Figure 04 Atomspheric Absorption [view large image]	Figure 05 Infrared Telescope [view large image]	a "thermograph" of a celestial body, and the instruments must be cooled continuously by immersion in liquid nitrogen or helium (Figure 05).

The table below lists some of the infrared telescopes in the world :



Observatory	Location	Stweardship	Aperture (m)	Date / Duration
NASA IRTF	Mauna Kea, Hawaii	UH	3.0	Since 1979
UKIRT	Mauna Kea, Hawaii	UH	3.8	Since 1978
SOFIA	Airborne	NASA/DLR	2.7	Started operation in 2010, lifetime ~ 20 years
Spitzer	Heliocentric orbit	NASA/JPL	0.85	Launched 2003, in-flight date to 2015
Herschel	Orbiting at Lagrangian point 2	ESA	3.5	Launched 2009, in-flight date to 2013
WISE	Geocentric orbit	NASA/JPL	0.4	From December 2009 to early 2011
ISO	Geocentric orbit	ESA	0.6	From 1995 to 1998
IRAS	Geocentric orbit	NASA/IPAC	0.6	Operated for ten months in 1983

Table 03 Infrared Telescopes

Acronym:  IRTF - Infrared Telescope Facility.
                UKIRT - United Kingdom Infrared Telescope.
                SOFIA - Stratosphere Observatory for Infrared Astronomy.
                SPITZER - Space Infrared Telescope Facility; named to Spitzer Space Telescope in honor of the late
                              astrophysicist Lyman Spitzer Jr., who first conceived of a large telescope in orbit.
                HERSCHEL - Far Infrared Space Telescope, named to Herschel in honor of the English astronomer.
                WISE - Wide-field Infrared Survey Explorer.
                ISO - Infrared Space Observatory.
                IRAS - Infrared Astronomical Satellite.


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High Frequency Observations

		Observations of High Frequency Radiation -- As shown in Figure 04, radiation with wavelength shorter than 310 nm are absorbed in the Earth's stratosphere, high above any terrestrial observatory. These short wavelength radiations can be studied only by instruments carried on very-high--altitude balloons, rockets, satellites, and spacecraft.
Figure 06 Grazing Telescope [view large image]	Figure 07 Scintillator [view large image]

Although attempts to study the sun's UV spectrum from balloons were made during the 1920s, it was not until 1946 that rocket-borne instruments made this possible. Only limited additional progress was made until 1962, when the first Orbiting Solar Observatory (OSO) satellite was launched by the National Aeronautics and Space Administration (NASA). It returned thousands of UV spectra, including the first extreme-ultraviolet (wavelengths below 91 nm) observations of the solar corona. The International Ultraviolet Explorer (IUE) was in orbit between 1978 and 1996. Its large telescope (0.45 m aperture) made possible the first UV observations of objects beyond the Milky Way. The Extreme Ultraviolet Explorer (EUVE, 1990-1999) was the first orbiting observatory to focus on that part of the spectrum. Ultraviolet spectroscopy has been particularly valuable because many of the most abundant atoms and ions in the universe have their strongest lines in that region of the spectrum. Right now there are no dedicated ultraviolet observatories in orbit. The Hubble Space Telescope can perform a great deal of observing at ultraviolet wavelengths, but it has a very fairly small field of view.

X-rays are typically emitted by gaseous bodies with temperatures ranging from 10⁶ to 10^{8 o}K. Conventional telescopes cannot be used at x-ray (or EUV) wavelengths because mirrors abosrb x-rays rather than reflect them, unless the x-rays graze the surface at a very shallow angle. Satellites such as ROSAT (in orbit between 1990-1999), and the Chandra X-ray observatory (since July, 1999) utilize "grazing incidence" telescopes (GRITs), which bring x-rays to a focus by reflecting them at shallow angles from the surfaces of nested sets of tapering, tubelike reflectors as shown in Figure 06. X-ray observations have discovered a variety of objects, ranging from hot patches and cool "holes" in the Sun's outer atmosphere to swirling discs of hot gas surrounding collapsed stars and black holes to hot clouds of gas in intergalactic space.

Gamma rays are the most energetic form of electromagnetic radiation. Because their wavelengths are far smaller than the sizes of the atoms in a mirror, gamma rays cannot be focued by reflection, and the early gamma-ray satellites were unable to form images of sources or even determine their positions with confidence. Modern gamma-ray imaging systems and spectrometers, such as those carried on board the Compton Gamma Ray Observatory (CGRO, 1991-2000), make use of scintillators (see Figure 07), which are devices that convert gamma rays into visible photons that are more easily detected and analyzed. Among known gamma-ray sources are the Milky Way, some pulsars, and some quasars. Most puzzling of all are the 2600 gamma-ray bursts detected by CGRO. The next generation gamma-ray observatory is GLAST (Gamma-ray Large Area Space Telescope) scheduled to be launched in 2005. It is designed for making observations of celestial gamma-ray

sources in the energy band extending from 20 MeV to more than 300 GeV. Figure 08a is a gamma-ray sky animation - constructed from simulating the first 55 days of GLAST observations of cosmic gamma-ray sources. It shows the plane of our Milky Way Galaxy as a broad U-shape, with the center of the galaxy toward the right. Besides the diffuse Milky Way glow, the simulated objects include flaring active galaxies, pulsars, gamma-ray bursts, the flaring Sun, and the gamma-ray Moon. The GLAST (now renamed to FERMI) was finally launched on June 11, 2008 many years behind schedule. It will study

Figure 08a Gamma-ray Sky [view animation]

gamma-rays from extreme environments in our own Milky Way galaxy, as well as supermassive black holes at the centers of distant active galaxies, and the sources of powerful gamma-ray bursts.

Figure 08b is another GLAST gamma-ray sky map taken in the period from August 4 to October 30, 2008. The map highlights the "top ten" list of five sources within, and beyond the Milky Way. Within our galaxy: the Sun traces a faint arc across the sky during the observation dates, LSI +61 303 is an X-ray binary star, PSR J1836+5925 is a type of pulsar that is only seen to pulse at gamma-ray energies, and 47 Tuc is a globular star cluster. A fifth galactic source (unidentified), just above the center of the galactic plane, is a variable source and has no clear counterpart at other wavelengths. Beyond our galaxy: NGC 1275 is a large galaxy at the heart of the Perseus galaxy cluster, while 3C 454.3,

Figure 08b Gamma-ray Sky 2 [view large image]

PKS 1502+106, and PKS 0727-115 are active galaxies billions of light-years away. Another unidentified source, seen below the galactic plane, is likely beyond the boundaries of the Milky Way. Its nature remains a mystery.


Table 04 lists the three types of gamma-ray sources in the Milky Way (MW). It is thought that they may be associated with the unknown dark matter particle (dmp). The m_p denotes the mass of proton (nucleon).



Instrument	Gamma-ray Energy	Process	Source	Distribution
INTEGRAL	511 kev	Annihilation of e-e+	~ 0.003 mp light dmp	Around the center of MW
EGRET	~ 1 Gev	Annihilation of dmp	~ 60 mp neutralino	Faint galactic background
HESS	~ 100 Gev	Annihilation of dmp	~ 20000 mp heavy dmp	Point source at MW center

Table 04 Gamma-ray Sources in Milky Way

Acronym: INTEGRAL - INTErnational Gamma-Ray Astrophysics Laboratory (a space instrument combining fine                 spectroscopy and imaging of gamma-ray emissions in the energy range of 15 keV to 10 MeV ).
                EGRET - Energetic Gamma Ray Experiment Telescope (space telescope for detecting 30 MeV - 30 GeV                 gamma-rays).
                HESS - High Energy Stereoscopic System (a system of ground based Cherenkov Telescopes for the                 investigation of cosmic gamma rays in the 100 GeV energy range).

Meanwhile the Swift satellite (Figure 09) was launched into a low-Earth orbit on November 20, 2004 already. Its mission is to solve the mystery of Gamma-ray bursts (GRBs). They are the most powerful explosions in the Universe since the Big Bang. They occur approximately once per day and are brief, but intense, flashes of gamma radiation. They come from all different directions of the sky and last from a few milliseconds to a few hundred seconds. So far scientists do not know what

causes them. Do they signal the birth of a black hole in a massive stellar explosion? Are they the product of the collision of two neutron stars? Or is it some other exotic phenomenon that causes these bursts? Swift is designed to look for faint bursts coming from the edge of the universe. On September 2005, astronomers announce that they have detected a cosmic explosion (GRB) at the very edge of the visible universe. The explosion occurred soon after the first stars and galaxies formed, perhaps 500 million to 1 billion years after the Big Bang. It was probably caused by the death of a massive star. It is believed that this observation opens the door to the use of GRBs as unique and powerful probes of the early universe.

Figure 09 Swift [view large image]

The key to unravel the nature of GRB comes in part from the discovery that they are narrowly focused beams. This realization allowed astronomers to estimate energies for individual bursts and hypothesize the number of total bursts occurring over a given time interval. The usual assumption of spherical emission would over estimate the released energy and under estimate the number of GRB. By 2007, astronomers can link the most common type of GRB, those lasting 20 seconds or longer, with the collapse of massive stars about 30 or more times larger than the Sun. While the short GRB (lasting just a few milliseconds) came from a neutron star crashing into a black hole or another neutron star.

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Attenuation of Astronomical Measurements

One of the astronomical measurements is the distance to various celestial objects. Figure 01 shows 9 different methods to measure the distance. Four of those methods (Cepheid/TRGB, PNLE, Tully-Fisher, Type-1a supernovae) employ the relationship between distance D (in cm), absolute, apparent magnitudes M and m ( luminosity of the ElectroMagnetic wave, see "Star Magnitudes") :


5xlog10(D) = m - M + 97.5 ---------- (1) Thus, this method involves the knowledge of the intrinsic magnitude M of certain celestial object (the standard candle). The apparent magnitude m is the measurement on Earth for such object. The quality of the measurement is subjected to the scattering and absorption of the EM wave on its journey to the detector. The effect is called attenuation (or extinction), which includes gas and dust around the source, and in the Earth's atmosphere.

Figure 10 Standard Candles [view large image]

There are many ways to express the effect of attenuation. Different method is used for particular environmet. The following is an attempt to summarize 4 cases with example(s) :


1. Attenuation - Mathematically, it is expressed by the attenuation coefficient :
   

   Figure 11 Attenuation [view large image]

   
   
   Figure 11,a shows the attenuation coefficients of absorption bands for some molecules and scattering by water droplets (i.e., rains), depending on the wave length or frequency of the EM waves. There are 2 windows of minimum attenuation at Visible and Microwave frequencies, the transmission is blocked by the Far-IR in the middle. The combined effect is additive, i.e,
   _total = _absorption + _scattering ---------- (5).


2. Transmission - This effect is opposite to attenuation as shown by Figure 11,d, in which the curves are up side down and even the wave length scale is reversed. Mathematically, the Transmission T is expressed by :
   


3. Mean Free Path - It is defined as the traveling distance of a particle such a photon before it is scattered off the original path by collision with another particle such as the proton (on the average). Mathematically, it can be expressed as :
   

   		att = 1/nA ---------- (7), where n is the number density of the scatterers (the protons), and "A" its scattering cross section (see Figure 12). If L is longer than the distance from the source to the detector, then we can be sure that there is no attenuation of the photons or EM wave during its journey from wherever to Earth. Such consideration is applicable for photon traveling through cosmic distance to Earth.
   Figure 12 MFP [view large image]	Figure 13 Cosmic History [view large image]	The mean free path att can be considered as the inverse of the attenuation coefficient, i.e., att = 1/ for one photon.

   Here's three examples :
   
   • Galaxy started to form at cosmic density ~ 10^-26 g/cm³ (see Figure 13). For proton mass m_p = 1.6x10^-24 g,
     n ~ 10^-2 cm^-3. Since the photon-electron scattering cross section is A ~ 10^-26 cm^-2, _att ~ 10²⁸ cm ~ 10⁴ Mpc which is about the distance to the proto-galaxies. Thus, EM waves should not suffer any extinction from there to here.
   • The cosmic density at the event generating CMBR is about 10^-20 g/cm³ (see Figure 13) giving n ~ 10⁴ cm^-3 and
     _att ~ 10²² cm ~ 10 kpc (see Figure 11,b). This is a rather short mean-free-path (cosmically speaking), that's why the mathematics of CMBR has to include the effect of photon-electron scattering (see "Cosmological Parameters").
     
     <skip detail>
     Figure 11,b is taken from a research paper on "Cosmic physics: the high energy frontier", which plots the mean free path for ultra high energy gamma-ray attenuation vs. energy. The curves include electron-positron pair production off the Cosmic Background Radiation (CBR). There are also two estimates for pair production off the extragalactic radio background and a curve for double pair production. The physics of pair production by single photons in magnetic fields eliminates all photons above ~ 10¹⁵ Gev and produces a terrestrial anisotropy in the distribution of photon arrival directions above ~ 10¹⁰ Gev.
   
   
   • At the time of hadronization when quarks combined to form hadrons about 10^-5 sec after Big-Bang, the cosmic density is about 10¹⁷ g/cm³ (see Figure 13) giving n ~ 10⁴¹ cm^-3 and _att ~ 10^-15 cm which is shorter than the size of nucleon. The collisions are so frequent that the whole system becomes viscous plasma with very little leaking of EM waves.
   
   

   Reddening Correction - It is now recognized that there is a lot dust/grain of various size in the disk of the Milky Way (MW). The density of various forms of matter in the Sun's vicinity is estimated to compose of 42.3% InterStellar Matter (ISM ~ 3.5x10-26 g/cm3), 44.3% baryonic matter, and 13.4% dark matter, i.e., the ISM comprises nearly 1/2 of the total mass (near the Sun). Depending on the viewing direction, the EM waves would become reddened to various degrees affecting the original characteristics of the stars such as surface temperature and the distance from Earth. The following is a brief summary for the procedure to correct such reddening effect.

   Figure 14 Color Index [view large image]

   See "Interstellar Extinction" for more details.

   • The apparent magnitude is measured by one of the bandpass filters - U. V, B, R, I (see Figure 14,a). Usually, the filter V for visible light is often adopted to calculate the distance and designated as m_v (abbreviated to "V").
   • The color or surface temperature of a star is defined by subtracting the magnitudes between two adjacent filters, e.g., B-V. As shown in Figure 14,c, if B > V in the stellar spectrum, then B-V > 0 (since V is more negative - meaning brighter, and colored red); the reverse is for B-V < 0 (colored blue, also see Figure 14,b).
   • An object's color excess is defined by :
     E_B-V = (B-V)_observed - (B-V)_intrinsic ---------- (8),
     where "intrinsic" denotes "normal" such as from a similar star known to be clear of obstruction by ISM. In the solar neighborhood, the rate of interstellar extinction E_B-V ~ 1.0 mag/kpc (averaged at a wavelength of 5400x10^-8 cm).
   • Figure 11,c shows the extinction curve of the Milky Way from visible to far UV, where A_V is the extinction at Visible bandpass, while R_V = A_V/E_B-V is a constant depending on the characteristics of the ISM. It shows that extinction is roughly proportional to 1/ with a bump at 2175x10^-8 cm, the origin of which is unknown (see "2175 Feature"). Note that the curves level off (flattened) as E_B-V 0, R_V .




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Footnotes:

^aIn adaptive optics, light from the primary mirror is directed onto a smaller flexible mirror behind which a large number of actuators are located. The actuators distort the shape of the mirror to cancel out distortions in the incoming wavefronts of light that have been caused by the atmosphere. Wavefront distortions are sensed by monitoring a suitable bright star, or an artificial "star" generatged by shining a powerful laser beam into the upper atmosphere. All these operations are computerized. Computers have so revolutionized astronomy, in fact, that researchers rarely look through the telescope or work in the dome during observations. Instead, they operate the instrument in comfort from a control room.


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References:

1. A complete listing of the World's Largest Optical Telescopes -- http://www.seds.org/billa/bigeyes.html