Astronomical Instrumentation G. H. Rieke Contents: 0. Preface 1. Introduction, radiometry, basic optics 2. The telescope 3. Detectors 4. Imagers, astrometry 5. Photometry, polarimetry 6. Spectroscopy 7. Adaptive optics, coronagraphy 8. Submillimeter and radio 9. Interferometry, aperture synthesis 10. X-ray instrumentation Introduction Preface Progress in astronomy is fueled by new technical opportunities (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 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, neutrinos, and gravitational waves are some of the remaining frontiers. To stay at the forefront requires that you be knowledgeable about new technical possibilities. You will also need to maintain a broad perspective, an increasingly difficult challenge with the ongoing explosion of information. Much of the future progress in astronomy will come from combining insights in different spectral regions. Astronomy has become panchromatic. This is behind much of the push for Virtual Observatories and the development of data archives of many kinds. To make optimum use of all this information requires you to understand the capabilities and limitations of a broad range of instruments so you know the strengths and limitations of the data you are working with. As Harwit (1984) shows, 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 and you absolutely must be up to date on it, or you will rapidly fall behind. 2 Introduction Chapter 1: Introduction 1. Basics of radiometry 1.1 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 Figure 1.1. Emission geometry from a radiation source. surface element of it, dA, onto a plane perpendicular to the direction of observation (Figure 1.1). This area is dA cos θ, where θ is the angle between the direction of observation and the outward normal to dA. The specific intensity, Lν, is the power (Watts) leaving a unit projected area of the surface of the source (in m2) 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. In physics, the same quantity is usually called the spectral radiance (in frequency units); we will use the common astronomical terminology here and refer the reader to Rieke (2003) for a table of terminology conversions. Similarly, we can define a specific intensity per wavelength interval, Lλ, where indicates a wavelength-based quantity. The intensity, L, is the specific intensity 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, where is the Stefan-Boltzmann constant and T is the temperature in Kelvin. The integral of the radiant exitance over the source gives the total output, that is, the luminosity of the source. 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. The most commonly used quantity is the flux density, the irradiance per frequency or wavelength interval, E or E; it has 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 10-26 W m-2 Hz-1 . 3 Introduction 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 by equation (1.2). To make calculations simple, we generally deal only with Lambertian sources. For them, the intensity 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 for the specific intensities in frequency and wavelength units: where k is the Boltzmann constant, T is the temperature in Kelvin (K), and n is the refractive index (virtually always n = 1 for astronomical sources). We also have Figure 1.2. Terms describing the propagation of a photon, or a light ray. Time has been frozen, but you should imagine that where r is the the photon is moving at the speed of light in the direction of distance to the the arrow. We will often draw the photon as lines marking the source and A is its surfaces of constant phase, called wavefronts. They are surface area. It is separated by the wavelength. The amplitude of the electric also convenient to field, its wavelength and phase, and the direction it is moving convert from characterize the photon. From George Barbastathis, MIT open frequency to course, 2004. wavelength units by means of 4 Introduction which can be derived by differentiating to derive the relation between d and d. An easy way to remember the conversion is that multiplying the flux density in W m-2 Hz-1 by c/2 with c = 2.998 X 1010 cm/s and in m gives the flux density in W cm-2 m-1. 1.2 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 1.2. 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 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 1.3. wave fronts at the focal For efficient detection of this light, we use plane. 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 1.3). 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.” 5 Introduction The optical path is defined as the integral of the physical path times the index of refraction of the material that path traverses. What tolerance is there on the optical path length? Figure 1.3 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, ≈ πθ2 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).