Astronomical Instrumentation G. H. Rieke for Astronomy 518 Fall, 2010

Transcription

1 Astronomical Instrumentation G. H. Rieke for Astronomy 518 Fall, Introduction, radiometry, basic optics August The telescope August Detectors September Imagers, astrometry September 16, Photometry, polarimetry September Spectroscopy October Adaptive optics, coronagraphy October Submillimeter and radio October 28, November 2 9. Interferometry, aperture synthesis November X-ray instrumentation November 4

2 Chapter 1: Introduction 1.1. Why Is This Material Important? Role of New Technology Progress in astronomy is fueled by new technical Opportunities (Figures from Cosmic Discovery, Martin Harwit, 1984). For a long time, steady and overall spectacular advances were made in telescopes and, more recently, in detectors for the optical. In the last 60 years, continued progress has been fueled by opening Figure 1.2. Pace of major discoveries a very personal view from Martin. Figure 1.1. Growth in sensitivity for astronomical observations, from Harwit new spectral windows: radio, X-ray, infrared, gamma ray. We haven't run out of possibilities: submillimeter, hard X- ray/gamma ray, cold IR telescopes, multi-conjugate adaptive optics (MCAO), gravitational waves are some of the remaining frontiers. To stay at the forefront requires that you be knowledgeable about new technical possibilities. We also need to "work smarter": much future progress will come from combining insights in different spectral regions. Astronomy has become panchromatic. This is behind much of the push for Virtual Observatories. To make optimum use of a VO requires you to understand the capabilities and limitations of a broad range of instruments so you know the strengths and

3 limitations of the data you are working with. Figure 1.3 is a nice summary of the impact of new technology on new discoveries. Before ~ 1950, discoveries were driven by other factors as much as by technology, but since then technology has had a discovery shelf life of only about 5 years! Most of the physics we use is more than 50 years old, and a lot of it is more than 100 years old. You can do good astronomy without being totally current in physics (but you need to know physics very well). The relevant technology, in comparison, changes rapidly. Figure 1.3. Time the necessary technology was available prior to making a major discovery with it Basics of radiometry Basic Terms in Radiometry Virtually all we are going to discuss in this book is measuring photons. Therefore, we lead off with a short description of how their production is treated in radiation physics. To compute the emission of an object, consider a projected area of a surface element of it, da, onto a plane perpendicular to the Figure 1.4. Emission geometry from a radiation source. direction of observation (Figure 1.4). This area is da cos θ, where θ is the angle between the direction of observation and the outward normal to da. The spectral radiance per frequency interval, L ν, is the power (Watts) leaving a unit projected area of the surface of the source (in m 2 ) into a unit solid angle (in ster) and unit frequency interval (in Hz), and the subscript lets us know this is a frequency-based quantity. It therefore has units of W m -2 Hz -1 ster -1. Similarly, we can define a spectral radiance per wavelength interval, L λ, where indicates a wavelength-based quantity. The radiance, L, is the spectral radiance integrated over all frequencies or wavelengths, and the radiant exitance, M, is the integral of the radiance over solid angle. It is a measure of the total power emitted per unit surface area in units of W m -2. For a black body,

4 where is the Stefan-Boltzmann constant and T is the temperature in Kelvin. The irradiance, E, is the power received at a unit surface element some distance from the source. It also has units of W m -2, but it is easy to distinguish it from radiant exitance if we think of a source so distant that it is entirely within the field of view of the detection system. In this case, we might find it impossible to determine M, but E still has a straightforward meaning. These terms are all from physics. For astronomers, the most commonly used quantity is the spectral irradiance, the irradiance per frequency or wavelength interval, E or E ; we call this quantity the flux density, with units of W m -2 Hz -1 (frequency units), or W m -3 (wavelength units). In fact, astronomers have their own unit, the Jansky (Jy), which is W m -2 Hz -1. Also, the integral of the radiant exitance over the source gives the total output, that is, the luminosity of the source. The energy of a photon is where c is the speed of light and h is Planck s constant. Conversion to photons/second can be achieved by dividing the various measures of power output just shown in eqn.(1. 2). To make calculations simple, we generally deal only with Lambertian sources. For them, the radiance is constant regardless of the direction from which the source is viewed. In the astronomical context, a Lambertian source has no limb darkening (or brightening). In fact, we usually deal only with the special case of a Lambertian source, a black or grey body (a grey body has the same spectrum as a black body but with an emission efficiency, or emissivity ε, less than 1). We then have where k is the Boltzmann constant, T is the temperature in Kelvin (K), and we have assumed the radiation is into a medium with a refractive index of 1 (e.g., a vacuum). We also have where r is the distance to the source and A is its surface area. By the way, it is convenient to convert from frequency to wavelength units by Figure 1.5. Terms describing the propagation of a photon, or a light ray. Time has been frozen, but you should imagine that the photon is moving at the speed of light in the direction of the arrow. We will often draw the photon as lines marking the surfaces of constant phase, called wavefronts. They are separated by the wavelength. The amplitude of the electric field, its wavelength and phase, and the direction it is moving characterize the photon. From George Barbastathis, MIT open course, 2004.

5 means of which can be derived by differentiating to derive the relation between d and d Image formation and the wave nature of light OK, some source has launched a stream of photons in our direction. How are we going to catch it and unlock its secrets? A photon is described in terms that are illustrated in Figure 1.5. The behavior of the electric field can be expressed as where A is the amplitude, is the angular frequency, and is the phase. Another formalism we will encounter later is to express the phase in complex notation: where j is the imaginary square root of -1. In this case, the quantity is envisioned as a vector on a two dimensional diagram with the real component along the usual x-axis and the imaginary one along the usual y-axis. The angle of this vector represents the phase. We will discuss this formulation further in later chapters. Figure 1.6. wave fronts at the focal plane. For efficient detection of this light, we use optics to squeeze it into the smallest possible space. The definition of the smallest possible space is a bit complex. We want to map the range of directions toward the target onto a physical surface where we put an instrument or a detector. This goal implies that we form an image, and since light is a wave, images are formed as a product of interference. The collector must bend the rays of light from a distant object and bring them to a focus at the image plane (see Figure 1.6). There, they must interfere constructively, requiring that they arrive at the image having traversed paths of identical length from the object. This requirement is expressed in Fermat s Principle, which is expressed in a number of ways including: The optical path from a point on the object through the optical system to the corresponding point on the image must be the same length for all neighboring rays. The optical path is defined as the integral of the physical path times the index of refraction of the material that path traverses.

6 What tolerance is there on the optical path length? Figure 1.6 shows how this tolerance can be determined. If the light waves impinge on the focal plane over too wide a range of angle, then the range of path lengths across the area where we detect the light can be large enough to result in a significant level of destructive interference. From the figure, this condition can be expressed as Here, l is some characteristic distance over which we collect the light say the minimum size of a detector at the focus of a telescope. Equation (1.10) seems to imply that the size of this detector enters into the fundamental performance of a telescope. However, there is another requirement on the optical system. The beam of light entering the telescope is characterized by an area at its base, A, normally the area of the telescope primary mirror, and a solid angle, πθ 2 where θ is the half-angle of the convergence of the beam onto the telescope (i.e., the angular diameter of the beam is 2 θ). The product of A and can never be reduced as a beam passes through an optical system, by the laws of thermodynamics. This product (for a refractive index of 1) is called the etendue (French for extent or space). Assuming a round telescope and detector and a circular beam (for convenience with more mathematics we could express the result generally), we find that an incoming beam with Figure 1.7. Refraction and Snell s Law. The ray passes from the medium with refractive index n into the one with index n. (where is in radians, is the wavelength of the light, and D is the diameter of the telescope aperture) is just at the limit expressed in equation (1.11) regardless of detector size. Equation (1.12) should be familiar as the diffraction limit of the telescope. This latter interpretation arises because the destructive interference in Figure 1.6 is the fundamental image-forming mechanism. The smaller the telescope the broader the range of angles on the sky before destructive interference at the focal plane starts to reduce the signal, corresponding to the limit of the resolution element of the telescope. Figure 1.8. The law of reflection.

7 1.3. Optical Systems We use optical elements arranged into a system to control light so we can analyze its information content. These elements work on two different principles, the law of refraction (Figure 1.7) and the law of reflection (Figure 1. 8). Refraction is described by Snell s Law (refer to Figure 1.7 for symbol definitions): The law of reflection simply states that the angle of incidence and angle of reflection are equal, or in Figure 1.8, =. A simple lens (Figure 1.9) is made of a transparent material with an index of refraction greater than that of air. The surfaces are shaped so the rays of light emanating from the point to the left are brought back to a point on the right. This process is imperfect, in part because the index of refraction is a function of wavelength, so different colors are brought to different points, a flaw called chromatic aberration. A number of other flaws are also apparent if one tries to bring a number of points to images with lens, that is if one is working with a significant field of view. These issues will be discussed in Chapter 2. Although real lenses have thickness as shown in Figure 1.9, we can analyze many optical systems ignoring this characteristic using the thin lens formula. Figure 1.9. Operation of a simple lens.

8 Figure Image formation by lenses. The object to the left is at the focal point of the left lens, defined as the position (at the focal length from the lens) where its rays are converted to a parallel ray bundle by the lens. The lens to the right takes this parallel bundle and converts it to converging rays that come to a point at its focal point. Figure Any ray that passes through the focal point of a lens is converted by the lens into a ray parallel to the lens optical axis (ray 1). Similarly, any ray that passes through the center of the lens is not deflected (ray 2). Figure 1.10 shows a simple optical system that collimates the light from a source, and then focuses it to a point. A more general characteristic is shown in Figure 11. The principles illustrated in Figure 1.11 let us determine the imaging properties of the lens. We can abstract the lens to a simple plane that acts on the rays as shown in Figure 1.12.

9 Figure Quantities used in the thin lens formula. From this figure, it is readily derived that: and These equations are described as the thin lens formula and are amazingly useful for a first-order understanding of an optical system containing a number of lenses (and/or mirrors). If our lenses really are thin, then we can compute their focal lengths as where n is the index of refraction of the lens material (we assume it is immersed in a medium with n = 1) and R1 and R2 are the radii of curvature of its surfaces, assigned positive signs if the curvature is directed Figure The Lagrange Invariant. to the right. For a spherical mirror, f = R/2 where R is the radius of curvature. These concepts lead to another formulation of the principle of preservation of entendue, called the Lagrange Invariant. The quantities are illustrated in Figure 1.13.

10 A concave mirror can also form images, just like a lens (Figure 1.14). Although a little more awkward to demonstrate with simple pictures, its image-forming properties can also be described by the thin lens formula (eqn (1.14))and its image size by eqn. (1.15). Compared with a lens, a mirror reflects all colors the same and so is free of chromatic aberration. In general, reflection works better for a broad range of wavelengths because we do not have to find a suitable transparent material. Multiple mirrors and/or lenses are combined into optical systems. The convention is that these systems are drawn with the light coming in from the left, as in the figures above. The elements (individual mirrors or lenses) of a system can take light from one point to another, forming real images (as in the cases illustrated above), or they can make the light from a point diverge (e.g., for a lens with concave surfaces, or a convex mirror). In the first case, there is a real image, while in the latter case, the image is virtual. All of this behavior is described by the thin lens formula, if one pays attention to the sign conventions (for lenses, the image distances d 1 and d 2 are both positive for a real image, but a virtual image Figure A concave mirror can have imaging properties similar to those of a simple lens. Figure A lens with concave surfaces forms a virtual image it looks like the light is coming from a point but it is not. appears to be to the left of the lens and d 2 is therefore negative see Figure 1.15). The combination of optical elements can correct for the image flaws associated with having a large field of view and can be used to divide the light in ways that let us analyze its information content, such as in a spectrograph. A series of lenses can also be designed to compensate for the chromatic aberration of each element. 1.4 Power received by an optical system Basic geometry An optical system will receive a portion of the source power that is determined by a number of geometric factors (plus efficiencies). If you refer to this diagram and follow it carefully, you will

11 never get confused on how to do radiometry calculations in astronomy (guaranteed, but not money-back). As the Figure 1.16 shows, the system accepts radiation only from a limited range of directions, called its field of view (FOV). The area of the source that is effective in producing a signal is determined by the FOV and the distance between the optical system and the source (or by the size of the source if it all lies within the FOV). This area emits with some angular dependence (e.g., for a Lambertian source, the dependence just compensates for the foreshortening and off-axis emission direction), and the range of emission directions that are intercepted by the system is determined by the solid angle, Ω, that its entrance aperture of the system subtends as viewed from the source:, Figure Geometry for detected signals. where a is the area of the entrance aperture of the system and r is the distance from it to the source (we assume the entrance aperture is perpendicular to the line from its center to the center of the source). If the aperture is circular, where is the half-angle of the circular cone with its vertex on a point on the surface of the source and its base at the entrance aperture of the detector system. If none of the emitted power is lost (by absorption or scattering) on the way to the optical system, then the power it receives is the radiance of the source emitted in its direction multiplied by (1) the source area within the system FOV times (2) the solid angle subtended by the optical system as viewed from the source. We often get to make this even simpler, because for us many sources fall entirely within the FOV of the system. In this case, the spectral irradiance is a convenient unit of measure, that is the flux density (equations (1.4) and (1.5)) How much gets to the detector?

12 Once the signal reaches the optical system, a number of things happen to it. Obviously, part of it is lost due to diffraction, optical aberrations, absorption, and scattering within the instrument. Only a portion of the signal incident on the detector is absorbed in a way that can produce a signal: this fraction is called the quantum efficiency. All of these efficiencies (i.e., transmittances < 1) should be multiplied together to get the net efficiency of conversion into an output electrical signal. If any of the terms vary substantially over the accepted spectral band, the final signal must be determined by integration over the band. In fact, we usually restrict the spectral band with optical elements (e.g., filters). Figure Atmospheric absorption and scattering. From

13 Figure Atmospheric transmissionfor Dome C in the Antarctic, from For groundbased telescopes, there is another important component to the transmission term, the absorption by the atmosphere of the earth. The overall absorption is shown in Figure 1.17 the windows through which astronomers can peer are obtained by turning the figure at the top upside down. The atmosphere is opaque at all wavelengths shorter than 0.2 microns. Figure 1.18 shows the transmission under exceptionally dry conditions in the submillimeter and millimeter-wave, and for wavelengths longer than 1 cm it is transparent until about 100m, where absorption by the layer of free electrons in the ionosphere becomes strong. Over a considerable portion of the region of good transparency, man-made transmissions can interfere with sensitive measurements (with the proliferation of nifty radio-transmission devices like cell phones, this problem is worsening). A specific set of frequency ranges have been set aside for radio astronomy; trying to observe at other frequencies is definitely at your risk. Many of the long-lived atmospheric constituents are well-mixed, that is the composition of the air is not a strong function of altitude. However, water is in equilibrium with processes on the ground and has an exponential distribution with a scale height (the distance over which the concentration is reduced by a factor of 1/e) of about 2 km. In addition, the amount of water in the air is reduced rapidly with decreasing temperature. Therefore, there is a premium in placing telescopes for water-vapor-sensitive wavelengths on high mountains, and even in the Antarctic. The atmosphere can also contribute unwanted foreground emission that raises the detection limit for faint astronomical objects. There are many components (Leinert 1998), but most of them play a relatively minor role. However, the airglow lines that start in the micron range (Figure 1.19) and become totally dominant in the near infrared bands (Figure 1.20) are a basic limitation to the achievable sensitivity from the ground.

14 Figure Sky brightness in the visible and near infrared, from Wikipedia article on sky brightness Another major source of interference occurs in the mid-infrared, beyond 2 microns. Here, the thermal emission of the atmosphere and telescope dominates all other sources of foreground. In the clearest regions of atmospheric transmission, telescopes can be built with effective Figure Airglow spectrum in the 1.6 micron atmospheric window, from Ramsay et al emissivities of about 5%, that is the foreground is about 5% of that expected from a blackbody

15 cavity at the temperature of the telescope. Nonetheless, this emission dominates over the zodiacal and galactic radiation at these wavelengths (which is the fundamental foreground for our vicinity in space) by a factor of more than a million Detectors: basic principles Gathering light on the scale demanded by astronomers is difficult and expensive. Consequently, they demand that it be converted as efficiently as possible into electronic signals they can analyze. However, efficiency is not enough. The detectors have to be very well behaved and characterized; artifacts in the data due to detector behavior can easily mask interesting but subtle scientific results, or create spurious ones. Three basic types of detector meet the goals of astronomers, in different applications: In photon detectors, the light interacts with the detector material to produce free charge carriers photon-by-photon. The resulting miniscule electrical currents are amplified to yield a usable electronic signal. The detector material is typically some form of semiconductor, in which energies around an electron volt suffice to free charge carriers; this energy threshold can be adjusted from ~ 0.01 ev to 10eV by appropriate choice of the detector material. Photon detectors are widely used from the X-ray through the mid-infrared. In general, except in the X-ray, a single mobile charge carrier is produced per absorbed photon. In a simple sense, the performance of the detector is then characterized by its quantum efficiency, the proportion of incoming photons that are absorbed to produce charge carriers. The performance of photon detectors in the far ultraviolet and particularly in the X-ray has another dimension. The energy of the individual photons substantially exceeds that required to produce a single free charge carrier. The absorption of a photon therefore can yield multiple charge carriers, whose average number is termed the quantum yield. In the X-ray, the number of charge carriers produced by an absorbed photon is a useful indicator of its energy, allowing low-resolution spectroscopy. In thermal detectors, the light is absorbed in the detector material to produce a minute increase in its temperature. Exquisitely sensitive electronic thermometers react to this change to produce the electronic signal. Thermal detectors are in principle sensitive to photons of any energy, so long as they can be absorbed in a way that the resulting heat can be sensed by their thermometers. However, in the ultraviolet through mid-infrared, photon detectors are more convenient to use and are easier to build into large-format arrays. Thermal detectors are important for the X-ray and the far-infrared through mm-wave regimes. The ultimate limit to the performance of a thermal detector is determined by two parameters: 1.) its absorption efficiency; and 2.) thermal noise. The role of absorption efficiency is straightforward, although optimizing this parameter is a demanding goal in detector design and fabrication. Thermal noise arises from the basic physics of the devices. They must be connected to a low-temperature heat sink by a low-conductivity thermal link so the absorbed photon energy can raise the temperature of the detector element. Thermal noise is generated due to thermodynamic fluctuations across this thermal link. Minimizing it requires that these detectors be operated at very low temperatures. Since photon detectors work very well in the optical and

16 infrared, and do not require such low temperature operation, they are strongly preferred for these spectral regions. We will return to thermal detectors in the chapter on submillimeter instrumentation. In coherent detectors, the electrical field of the photon interacts with a signal generated by a local oscillator (LO) at nearly the same frequency. The interference between the electrical field of the photon and that from the LO produces a signal with an amplitude that increases and decreases at the difference frequency, termed the intermediate frequency (IF). If this signal is passed through an appropriately nonlinear circuit element, this amplitude variation can be converted to a real signal at the IF (rather than just the amplitude variation in a higherfrequency signal). The IF signal is put into a frequency range that is compatible with further processing and amplification using conventional electronics. This signal encodes the frequency of the input photon and its phase. The phase of the photon is equivalent to a timing constraint, so the detectors are limited by the Heisenberg Uncertainty Principle; it is not possible to determine the phase and energy of the photon with unlimited accuracy. This limit is termed the quantum limit. Coherent detectors must also be illuminated in a way that preserves the electrical wave nature of the photons, which translates into a requirement that the photons must strike the detector sufficiently normal to its sensitive area that there is insignificant change of the phase across that the wavelength of the photon and D is the telescope aperture diameter. In general, for similar reasons, coherent detectors are only sensitive to a single polarization. The restrictions in field of view and polarization together are called the antenna theorem. In addition, coherent detectors have relatively narrow spectral response (if measured in frequency units, which are appropriate given their principle of operation) and have limited sensitivity to continuum emission at high frequency (due to the quantum limit). We will return to them in the chapter on submillimeter astronomy, where these issues are no longer serious because of the relatively low frequency of operation. 1.5 Noise Photons obey Bose-Einstein statistics, so they do not arrive strictly independently of each other, as a result of quantum mechanical effects. Consequently, the noise is increased from the usual dependence on the square root of the number of photons received (appropriate only for independent events) to: where <N 2 > is the mean square noise, n is the average number of photons detected, ε is the emissivity of the source of photons, τ is the transmittance of the optical system, and η is the detector quantum efficiency. Inspection of eqn. (1.21) shows that the correction is only potentially significant on the Rayleigh Jeans regime of the emitting black body, that is at wavelengths much longer than the peak of the blackbody emission. Because of the efficiency term, ετη, in fact the correction is rarely large enough to worry about. Therefore, we can take the noise to just be proportional to the square root of the number of photons detected. We have now justified the normal assumption, that the signal photons follow Poisson statistics - so in the case of modestly large signals, the uncertainty is just the square root of the number of

17 photons detected (for a simple detector without gain, this uncertainty is the square root of the number of signal electrons that are produced). This number can be determined from the power detected using eqn.(1.2). In fact, a rigorous definition of quantum efficiency makes use of this assumption. The detective quantum efficiency (DQE) is where (S/N) out is the observed ratio of signal to noise and (S/N) in is the potential ratio of signal to noise for the incoming photon stream as determined by ideal counting statistics alone. DQE is a way to quantify the loss of information content in the photon stream as a result of our detecting it with a less-than-perfect technology. References Leinert, Ch. et al. 1998, A&AS, 127, 1: night sky emission Ramsay, S. K., Mountain, C. M., & Geballe, T. R. 1992, MNRAS, 259, 751 Recommended Reading Barbastathis, George 2004, Optics, MIT open course, good course on optics in general, and its free! Harwit, Martin 1984, Cosmic Discovery, The MIT Press Rieke, Detection of Light, 2 nd edition, The standard on astronomical detectors, emphasizes physical principles of operation, also gives basics of radiometry