The general term “astrometry” is used to describe methods by which the positions of stars may be determined. We noted briefly in Chapter 1 that meridian telescopes were used to determine the right ascensions and declinations of stars, and we wish to repeat here that this work has been of fundamental importance to all astronomers. However, meridian telescopes have now been made obsolete by space-based observations and ground-based telescopes equipped with CCDs. Meridian telescopes were never an effective way to determine the coordinates of faint stars, galaxies, comets, and asteroids.

Today, most astrometric measurements are made with area detectors. The positions of stars on an image formed by a telescope are directly related to their actual positions in the sky, so it might seem that the analysis should be simple and straightforward. This is not really the case. The geometry in Figure 11.1 shows the basic relationships. The center of the lens of a telescope is at C and the focal plane is at FF′. A well-made lens should produce an image of plane GG′ in the plane FF′. The plane GG′ may be thought of as being tangent to the celestial sphere at point A. The sky appears as a spherical dome on which the stars appear as points. Thus, in a photograph a star at S is projected to T on the tangent plane, and an image of T is formed at T′.

Although the optical telescope is the most venerated instrument in astronomy, it developed relatively little between the time of Galileo and Newton and the beginning of the twentieth century. In contrast to the microscope, which enjoyed considerable conceptual development during the same period from the application of physical optics, telescopes suffered from atmospheric disturbances, and therefore physical optics was considered irrelevant to their design. The realization that wave interference could be employed to overcome the atmospheric resolution limit was first recorded by Fizeau and put into practice by Michelson around 1900, but his experience then lay dormant until the 1950s. Since then, first in radio astronomy and later in optical and infrared astronomy, interferometric methods have improved in leaps and bounds. Today, many optical interferometric observatories around the world are adding daily to our knowledge about the cosmos.

The aim of this book is to build on a basic knowledge of physical optics to describe the ideas behind the various interferometric techniques, the way in which they are being put into practice in the visible and the infrared regions of the spectrum, and how they can be projected into the future. Some techniques consist of optical additions to existing large telescopes; others require complete observatories which have been built specially for interferometry. Today all these are being used to make accurate measurements of stellar angular positions, to discern features on stellar surfaces and to study the structure of clusters and galaxies.

Observational astronomers have taken advantage of each new development in detector technology. We compared visual observations, photographic plates, photoelectric photometers, and CCD cameras in Chapter 8. Our purpose in this chapter is to discuss how astronomers employ modern optical light detectors to measure astronomical sources in a scientifically useful way. We will focus our discussions on photoelectric and especially CCD photometry.

Fundamentally, there are two approaches to astronomical photometry. The simplest, differential photometry, compares sources sufficiently close together on the sky so that differential first-order extinction can be neglected. More complex is all-sky photometry, which takes full account of the extinction terms for stars observed far apart on the sky over the course of a night. In addition, photometry is done differently with photoelectric photometers compared to CCD cameras. We will begin with a short overview of photoelectric photometry and spend most of the chapter on CCD photometry.

Photoeletric photometry

As we noted in Chapter 8, a photoelectric photometer is of a fundamentally different design than a CCD camera. A single-channel photometer can be trained on only one star at a time. It is important that the star be carefully centered in its aperture. Often a range of aperture sizes is available; the smaller apertures are used in crowded fields and also when the seeing is very good. In between measurements of a star it is necessary to take measurements of the sky.

Many astronomy instructors adopted the first edition of Observational Astronomy as their primary text in advanced undergraduate courses. One of us (GG) used it as the primary text for an advanced undergraduate course in astronomy beginning in 1997. Unfortunately, the first edition went out of print in the late 1990s. By that time it had also become apparent that it was in need of revision. In particular, the charge coupled device (CCD) had already displaced nearly all other detectors in astronomy, but the first edition included only a short appendix on CCDs. Several chapters, instead, focused on photographic techniques. These included photometry, astrometry and spectroscopy. We have replaced all discussions of photographic techniques with CCD techniques in the present edition. We eliminated the chapters on classification of stellar spectra and radio astronomy and added chapters on light and detectors. In addition, we have reordered the material in several chapters in a way we hope is more pedagogically useful.

Most of the discussions about classical astronomical instruments, such as plate measuring engines and filar micrometers, have also been reduced or eliminated. The first edition remains a useful resource on these topics, and we encourage the interested reader to check with their local university library for copies.

The present edition of Observational Astronomy was the Master's thesis project of David Oesper at Iowa State University.

The intersection of three great circles on the surface of a sphere forms a three-sided figure. Such a figure is referred to as a spherical triangle, and it has some interesting properties. For example, the sum of the angles in a spherical triangle will usually be greater than 180°, whereas in a plane triangle this sum is exactly 180°. Consider the spherical triangle formed by the celestial equator and the hour circles of the vernal equinox and a star as in Figure 4.1. (An hour circle is a great circle that passes through a specified point on the celestial sphere as well as the north and south celestial poles.) The intersections of the three great circles have been labeled A, B, and C. Circles through the poles cross the equator at angles of 90°, so ∠B and ∠C are each equal to 90°, and the sum of the three angles will necessarily be greater than 180°.

The intersection of two planes cutting through a sphere forms an angle in a spherical triangle on the surface of the sphere. Each plane must pass through the center of the sphere. Thus, ∠A in Figure 4.1 is the angle between the hour circle planes through the vernal equinox and through the star. Note that ∠A is also equal to ∠BOC.

It is customary, just as in plane trigonometry, to label the sides of a triangle with lower case letters a, b, and c indicating the sides opposite the angles A, B, and C. Note that the length of a side is expressed in terms of an angle measured from the center of the sphere, as shown in Figure 4.2.

Today, astronomical databases once available only at the largest university libraries are but a mouse click away on the Internet. Except for a few very large catalogs described in Chapter 3, virtually any astronomical data can be downloaded from public-access websites. In addition, astronomical software has become more advanced and easier to use. Although it is not possible to give a complete listing of important astronomy software and Internet sites in this appendix, we have been careful to select those that should be most useful. While we cannot guarantee that all the websites listed below will remain active while this textbook remains in print, we have checked that they were active as of August 2005.

As stated earlier, the CCD has become the detector of choice in most astronomical applications. Its many advantages were listed at the end of the previous chapter, and some of its practical applications will be described in Chapters 10, 11 and 13. In this chapter we shall describe the necessary steps involved in eliminating noise and other sources of error so that CCD images can be used for accurate analysis.

Noise in the data

A raw CCD image contains information about your science targets. It also contains noise. Noise is usually categorized as random or systematic. Random noise causes a measured quantity to deviate from the “true” or “expected” value according to simple statistical relations, such as the normal distribution (see Appendix 1). Random noise cannot be eliminated; it can only be measured (characterized) so that its contribution to the signals from the science objects can be understood. A major advantage of a CCD over some other types of detectors is that its noise can be characterized accurately.

Systematic noise is caused by one or more processes that are not characterized by statistical distributions describing random events. Systematic noise can result from known sources or unknown ones. Known sources can be corrected; this is part of the calibration process. We will discuss below several types of known systematic noise in CCD data and how to correct for them. The presence of unknown systematic noise is always the greatest fear of the observational astronomer.

Historical introduction

The Earth orbits a star, the Sun, at a distance of 140 million km, and the distance to the next closest star, α-Centauri, is more than 4 · 1013 km. The Sun is one star in our galaxy, the Milky Way. The Milky Way has 1011 stars and the distance from the Sun to its center is 2.5 · 1017 km; it is one galaxy in a large group of galaxies, called the Local Group and the distance to the next nearest group, called the Virgo Cluster, is about 5 · 1020 km. The Universe is made up of a vast number of clusters and superclusters, stretching off into the void for enormous distances. How can we learn anything about what's out there, and how can we understand its nature?

We can't expect to learn anything about distant galaxies, black holes or quasars, or even the nearest stars by traveling to them. We can maybe explore our own solar system but, for the foreseeable future, we will learn about the Universe by using telescopes, on the ground and in space.

The principal methods of astronomy are spectroscopy and imaging. Spectroscopy measures the colors of light detected from distant objects. The strengths and wavelengths of spectral features tell us how an object is moving and what is its composition. Imaging tells us what an object looks like. Because distant stars are so faint, the critical characteristic of a telescope used for spectroscopy is its light-gathering power and this is determined principally by its size, or “collecting area.” For imaging, the critical characteristic is its resolution.

Students at the level of advanced undergraduates or beginning graduate students have often found that much information needed in the everyday practice of astronomy is not easily accessible. The necessary details are not to be expected in most textbooks, and one must often refer to early copies of some journals or to a professor's notes. It is my intention that this book should provide students with a ready reference of a practical nature.

For many years a course in astronomical techniques has been taught at Wellesley College, and the students there have been able to apply all of the methods described here. This book is thus based on the notes which I have developed while teaching this course. Over the years I have encountered a number of excellent books which were either to serve as texts for practical courses or as general handbooks for the use of amateur astronomers. My feeling has been that none of these covered the topics which I felt were most necessary at the level which I felt could be most useful.

It is my hope that this book will fill a real need in the reference material available to astronomers at many levels.

Aperture synthesis Aperture synthesis is the way that the Van Cittert–Zernike theorem (section 3.3) is used in practice to get higher resolution images than a single large aperture will allow. Although Michelson's stellar interferometer was the first implementation of the concept, and occurred before the formalization of coherence theory, its real application began in the late 1940s in radio astronomy, where today it is responsible for almost all high-resolution images. At radio frequencies the problem of getting high angular resolution is very acute because of the long wavelengths involved, and Michelson's stellar interferometer inspired Martin Ryle (1952) to use the same idea in radio astronomy. And so, while optical aperture synthesis languished for 60 years for lack of suitable electronics, the radio astronomical applications of the technique blossomed. There are several excellent texts on the theory and practice of aperture synthesis, mainly directed to the radio regime, such as Thompson (2001), Perley and Schwab (1989) and Rohlfs (1996), which will give the reader insight not only into the principles but also the techniques involved.

The optics of aperture synthesis

Suppose we measure the complex spatial coherence function due to a distant source using two receivers separated by a vector r lying in a plane normal to its direction in inertial space. Following this observation, we can change the vector and make another measurement, and so on, until a sufficiently large bank of data for γ (r) is accumulated.

Time as we use it in our ordinary lives is based on the rotation and revolution of the Earth with respect to the Sun. These combined motions cause the Sun to appear to move continually around the heavens, and we define solar noon as the moment each day when the Sun crosses an observer's meridian. We could easily use the interval from one noon to the next to define the day, but in order to make all of the daylight hours part of the same calendar day, we start and end our days at midnight. The division of the day into twenty-four hours is strictly arbitrary and dates back to ancient Egypt, perhaps even earlier. The Greeks divided the periods of daylight and darkness into twelve equal parts to make twenty-four divisions in each day. The length of the hour defined in this way gradually changes throughout the year as the length of day and night varies with the seasons. The custom of dividing the hour into sixty minutes and the minute into sixty seconds is one of the last vestiges of the sexagesimal system of counting developed by the ancient Babylonians.

Today we keep track of time with a variety of clocks that range in complexity from sundials of the simplest sort to atomic clocks of the greatest precision.

Introduction

The atmosphere behaves like a very thick bad piece of glass in front of your telescope, a piece which is constantly changing. The result of this bad optical element is that the image of a point star is not what the simple physics would lead us to expect, namely the diffraction pattern of the geometrical entrance aperture, but a much more complicated and diffuse image. The image has two general properties: an envelope, which is the image recorded in a long-exposure photograph (longer than, say, one second) and, within it, an internal speckle structure which is continuously and rapidly changing and can only be photographed using a very short exposure (less than about 5 ms, as in figure 5.1). The angular diameter of the envelope, which is called the “seeing,” has a value between 0.5 and 2 arcsec at a good observing site; this is determined by the averaged properties of the atmosphere, which are the subject of this chapter. On the other hand, although the speckle structure is changing continuously, the angular diameter of its smallest distinguishable features correspond to the diffraction limit of the complete telescope aperture. For comparison, figure 5.2 shows the same effect in the laboratory when imaging a point source through the bad optics of a polythene bag.

Michelson (1927), in his book Studies in Optics, refers to the effect of the “seeing” on his 1890 stellar interferometer.

Introduction

This chapter is about the practical side of interferometric astronomy. There are many instruments which have been built to use coherence measurements in order to gather information about stellar and other cosmic structures, all based on the principles which have already been discussed theoretically. The plan of the chapter is to discuss first the building blocks and techniques which are common to many interferometers, with some mention of advantages and disadvantages of different approaches. Then we shall describe the way in which various interferometers use these building blocks, with one or two examples of their results. Most of the material of this chapter is based on published material, and some valuable references which have been used intensively are the chapters in the course notes from the 1999 Michelson Summer School (Lawson 2000) and the Proceedings of the SPIE meetings on Stellar Interferometry up to 2004 (SPIE 1994–2004). The latter are unfortunately not available freely to the public; we have therefore made an effort to cite work published in the open literature as far as possible.

Every interferometer is built from several definable blocks, or subsystems, of which the maximal set is illustrated schematically in figure 8.1. First, the global “aperture” of the interferometer, which defines its angular resolution limit, is the bounding region within which there are several subapertures, separated by the vectors r which will be the arguments of the measured values of the coherence function.

We live on the surface of a planet that permits us to observe the distant Universe through a narrow window of the electromagnetic spectrum. While astronomers have expanded their vision with telescopes in Earth orbit, they still carry out most astronomical observations from the ground. As such, astronomers have to take into account the effects of the atmosphere on their observations. In this chapter we will discuss the five distinct ways the atmosphere affects the light from astronomical sources: extinction, refraction, seeing, scintillation, and dispersion.

Extinction

The Earth's atmosphere blocks most of the electromagnetic radiation arriving from space. Astronomers look through two “windows” in the electromagnetic spectrum to learn about extraterrestrial sources, the optical/near infrared (Figure 7.1) and radio. The optical window covers wavelengths from about 3000 Å to about 9000 Å. Several windows of moderately high transmission continue through the infrared up to about 26 microns. The windows in the radio band begin near 1 mm and end near 20 m. We will focus on the optical to near-IR window in this chapter.

We noted in Chapter 5 that the Johnson U bandpass is partly determined by the atmosphere's ultraviolet cutoff. Other bandpasses in the optical are determined by the filter transmission curves. The infrared JHKLM system (shown in Figure 7.1) is determined by the narrow windows between the deep molecular absorption bands.

Stars

When we wish to study the characteristics of a star, it is crucial that we be able to identify it with absolute certainty. Many resources are available to the astronomer to assist in star identification, and the method of choice depends largely on the brightness of the star. If the star is brighter than about fourth magnitude, the problem is quite simple, for there are not very many stars of comparable brightness. Once we set our telescope to the proper coordinates, there will probably be only one sufficiently bright star in the typical field of view. On the other hand, when we try to locate a star of eighth or ninth magnitude, there may be six or more stars in a field 30 arcmin in diameter. The numbers of progressively fainter stars in a given field increases dramatically. There are so many sources of error involved in setting a telescope that it is not reasonable to expect that the desired star will always be the one nearest the center of the field even if the coordinates are known and the telescope is set with great precision. Therefore, when trying to identify faint stars we must usually rely on maps or charts on which each star has been identified in some reliable manner. The observer can then compare the pattern of stars depicted on the chart with the pattern actually seen in the telescope and make a positive identification.