Introduction

The Earth's atmosphere imposes several limitations on our ability to perform astrometric measurements from the ground in both the optical and radio regions of the spectrum. First, we are limited to wavelengths where the absorption is not too great, i.e. the broad optical region from the ultraviolet to the near-infrared, scattered regions in the infrared and broad regions at radio wavelengths. The fundamental limitations imposed by the atmosphere are different in the optical and radio and in this chapter we will deal with those important for the optical; the radio part is largely dealt with in Chapter 12 on radio interferometry, except for a summary given here on the precision limitations imposed by the atmosphere. The second problem created by observing through the atmosphere is refraction of the light waves as they pass through different levels of the atmosphere. If it were only refraction through a stable medium, the problem would be very simple; however, the atmosphere is a turbulent medium that causes variations in the amount of refraction both spatially and temporally and it therefore limits the precision and accuracy of our observations. In this chapter we will deal with both effects using the developments in Schroeder (1987, 2000) as the basic reference.

Refraction through a plane-parallel atmosphere

When we are dealing with relative positions in fields of view less than several degrees, it is sufficient to adopt a plane-parallel atmosphere for the model. In cases where we need to consider the total displacement, such as with meridian circles, it is necessary to adopt atmospheric models that are substantially more complicated, such as those developed by Garfinkel (1967) and Auer and Standish (2000). For the purposes of this chapter we can safely use the plane-parallel atmosphere.

Why do we need another text on astrometry?

Astrometry entered a new era with the advent of microarcsecond positions, parallaxes, and proper motions. Cutting-edge topics in science are now being addressed that were far beyond our grasp only a few years ago. It will soon be possible to determine definitive distances to Cepheid variables, the center of our Galaxy, the Magellanic Clouds and other Local Group members. We will measure the orbital parameters of dwarf galaxies and stellar streams that are merging with the Milky Way, define the kinematics, dynamics, and structure of our Galaxy and search for evidence of the dark matter that constitutes most of the Universe's mass. Stellar masses will be determined routinely to 1% accuracy and we will be able to make full orbit solutions and mass determinations for extrasolar planetary systems. If we are to take advantage of microarcsecond astrometry, we need to reformulate our study of reference frames, systems, and the equations of motion in the context of special and general relativity. Methods need to be developed to statistically analyze our data and calibrate our instruments to levels beyond current standards. As a consequence, our curricula must be drastically revised to meet the needs of students in the twenty-first century.

In October 2007, IAU Symposium 248 “A Giant Step: From Milli- to Micro-arcsecond Astrometry” was held in Shanghai, China. Approximately 200 astronomers attended and presented an array of outstanding talks. I was asked to present a talk on the educational needs of students who might wish to study astrometry in the era of microarcsecond astrometry and to organize a round-table discussion on the topic. In the process of preparing my talk and organizing the session, I realized that I had a unique opportunity to bring together the experts on virtually all topics that might be covered in an introductory text on astrometry. This book is the result of the advice from many individuals in the worldwide astrometric community, most of whom were present at that Shanghai meeting and in particular the 28 authors who wrote the 28 chapters.

Introduction

The goal of this book is to present an introduction to the techniques of astrometry and to highlight several applications of those techniques to the solution of current problems of astrophysical interest. In some cases we require the absolute positions of objects to establish reference frames and systems, while in others we need the change in position with time to obtain the distances and tangential velocities of the objects. The astrometric procedures necessary to solve those problems have been laid out in considerable detail by Konig (1933, 1962), Smart (1931), and others, so we will summarize the methods used to transform raw coordinate measurements of celestial objects on photographic plates and CCDs to their corresponding coordinates on the celestial sphere. We recommend that the reader consult the above references where clarification is needed. Once we have the desired celestial coordinates and their changes with time that yield parallaxes and proper motions, we can then create catalogs of those quantities and apply them to the solution of problems in galactic structure, the masses of stars, membership in star clusters, dynamical studies of objects in the Solar System, and extrasolar planets, and to help to set limits to some cosmological models.

Telescope and detector alignment

We normally assume that our telescope and detector have been carefully aligned so that the image quality will be optimum over the field of view (FOV). However, even if the apparent image quality is good over the FOV, it may be that residual misalignments remain that complicate the transformation from detector to sky. Quite often, high-order polynomials are used to absorb the effects of those misalignments. Unfortunately, that procedure obscures the interpretation of the transformation terms and can lead to spurious and/or lower-accuracy results.