Chapter 1 reviews the image restoration/reconstruction problem in its general setting. We first discuss linear methods for solving the problem of image deconvolution, i.e. the case in which the data is a convolution of a point-spread function and an underlying unblurred image. Next, non-linear methods are introduced in the context of Bayesian estimation, including Maximum-Likelihood and Maximum Entropy methods. Finally, the successes and failures of these methods are discussed along with some of the roots of these problems and the suggestion that these difficulties might be overcome by new (e.g. pixon-based) image reconstruction methods.

Chapter 2 discusses the role of language and information theory concepts for data compression and solving the inverse problem. The concept of Algorithmic Information Content (AIC) is introduced and shown to be crucial to achieving optimal data compression and optimized Bayesian priors for image reconstruction. The dependence of the AIC on the selection of language then suggests how efficient coordinate systems for the inverse problem may be selected. This motivates the selection of a multiresolution language for the reconstruction of generic images.

Chapter 3 introduces pixon-based image restoration/reconstruction methods. The relationship between image Algorithmic Information Content and the Bayesian incarnation of Occam's Razor are discussed as well as the relationship of multiresolution pixon languages and image fractal dimension. Also discussed is the relationship of pixons to the role played by the Heisenberg uncertainty principle in statistical physics and how pixon-based image reconstruction provides a natural extension to the Akaike information criterion for Maximum Likelihood estimation.

This paper reviews near infrared instrumentation for large telescopes. Modern instrumentation for near infrared astronomy is dominated by systems which employ state-of-the-art infrared array detectors. Following a general introduction to the near infrared wavebands and transmission features of the atmosphere, a description of the latest detector technology is given. Matching of these detectors to large telescopes is then discussed in the context of imaging and spectroscopic instruments. Both the seeing-limited and diffraction-limited cases are considered. Practical considerations (e.g. the impact of operation in a vacuum cryogenic environment) that enter into the design of infrared cameras and spectrographs are explored in more detail and specific examples are described. One of these is a 2-channel IR camera and the other is a NIR echelle spectrograph, both of which are designed for the f/15 focus of the 10-m W. M. Keck Telescope.

The Near Infrared Waveband

In the last ten years there has been tremendous growth in the field of Infrared Astronomy. This growth has been stimulated in large part by the development of very sensitive imaging devices called infrared arrays. These detectors are similar, but not identical, to the better-known silicon charge-coupled device or CCD, which is limited to wavelengths shorter than 1.1 µm. In particular, near infrared array detectors are now sufficiently sensitive that images of comparable depth to those obtained with visible-light CCDs can be achieved from 1.0 µm to 2.4 µm and high resolution IR spectrographs are now feasible.

This lecture introduces the opportunities presented by ground-based telescopes for new discoveries in the thermal infrared, and discusses techniques used to make sensitive observations in an environment with high background flux levels from atmospheric emission and from the telescope structure and mirrors.

Mid-IR astronomy—opportunities and problems

The capability now exists to observe mid-IR astronomical objects with spatial resolution of a third of an arcsecond and sensitivities reaching well below a mJy. Both imaging and spectroscopy with new array instruments on optimized large telescopes are producing new data on sources from comets, to active galactic nuclei. With sensitivity to emission from cool dust, diagnostic lines from ionized gas and molecular species, and the capability to look through clouds opaque in the visible, many new results are appearing, and many more can be anticipated. In particular, our understanding of the star formation process should improve significantly in the next decade. Yet all of this is achieved operating through the earth's atmosphere which absorbs and distorts the signals, and which, together with the telescope structure itself, radiates into the beam up to a million times the power detected from the source. The problems encountered, and the techniques used to make ground based mid-IR observations will be discussed here.

IRAS (Infrared Astronomical Satellite) revealed how fascinating and complex the IR sky is at wavelengths of 12, 25, 60 and 100 µm. The IRAS mission lasted for 300 days in 1983 completing an all sky survey with a 57-cm diameter cooled telescope.

In this chapter, instrumental principles will be discussed, with emphasis on system behaviour and without any preconceptions about the wavelength at which one observes. Practical illustrations will inevitably relate to a particular wavelength region (optical and radio, which is where the experience resides). It may therefore be necessary to scan chapter 6 before attempting to understand the present chapter in detail.

Telescopes

The first optical element of an astronomical observing system is always a telescope (disregarding the atmosphere for the present discussion). It is important to realize that, in general, a telescope will modify the polarization of the radiation before the polarimeter measures it. It is equally important to have some general feeling for the conditions under which such modification is likely to be appreciable and how it can be minimized.

The guiding principle is symmetry; any departures from full symmetry will modify the polarization. The considerations below illustrate this, but full understanding will require mathematical treatment by Mueller or Jones calculus, with optical constants applicable to the wavelength of interest.

Oblique incidence on a mirror produces both diattenuation (polarizing action) and retardation (wave plate action). These effects are minimal at near-normal and, somewhat surprisingly, at grazing incidence; the largest effects occur at intermediate angles of incidence, the details depending on the values of the real and imaginary parts of the refractive index (which in their turn depend on the wavelength).

In this final chapter, several original papers from the literature are introduced, primarily as illustrations of modern instrumentation. The focus of this book being the measurement of polarization, the astronomy involved was a secondary consideration in selecting these particular papers from the wide range available. Readers are urged to test their grasp of polarimetric fundamentals by selecting a dozen or so further papers from those listed in the subject index of the more recent volumes of Astronomy and Astrophysics Abstracts under ‘polarimeters’, ‘polarimetry’ or ‘polarization’.

Multi-channel optical polarimetry using photomultipliers

A suitable example of optical polarimetry by the ‘classical’ technique of 100 Hz modulation and photomultiplier detectors is given in Können and Tinbergen (1991) and Können et al. (1993). It concerns an attempt to detect ice crystals in the upper parts of the Venus atmosphere by using the polarization peak at the 22° halo angle as a diagnostic. A large body of earlier Venus polarimetry exists, and scientific results derived from it are reviewed in Van de Hulst (1980, section 18.1.5 and references therein).

The terrestrial 22° halo and related phenomena owe their polarization to birefringence of the ice crystals that produce the halo. These crystals operate as 60° prisms, deviating the light from the Sun by an amount depending on the refractive index of the ice, hence by an amount which depends on the polarization of the light.

Almost every issue of the leading astronomical journals includes some polarimetry, either directly or indirectly. Polarimetry as a working tool has clearly come of age. Optical and radio techniques are most advanced, but infrared, sub-millimetre and ultraviolet are following on rapidly, while X-ray techniques are being developed also. There is no technical reason why astronomers should not use polarimetry when it suits their astronomical purposes; polarimetry often yields information that other methods of observation cannot give, and this is the main reason why all astronomers, and today's students in particular, should understand the basic ideas behind polarimetry.

Within the astronomical context, the degree of polarization is often low; a few per cent is typical, though both higher and (much) lower values occur. A polarimetric measurement is basically that of the ratio of the small difference between two signals to their sum. Difference and ratio methods have been devised to measure this small difference without systematic bias or drift errors, but photometric noise (detector noise or photon noise of the signal itself) is always present. To reduce this noise to the low level required for sufficiently accurate polarimetry, considerable observing time on a large telescope is generally needed. Polarimetry should therefore not be used indiscriminately, but only when it provides insight which other methods cannot give. Such judgment also requires a grasp of polarimetric basics.

This book aims to create an awareness of what polarimetry can do and at what price (in observing time, in complexity of equipment and of procedures).

In het land der blinden is Eénoog koning. This saying in my mother tongue contains a sufficient number of Germanic roots for English speakers to guess that the situation depicted is only marginally better than ‘the blind leading the blind’. It aptly describes the current situation in astronomical polarimetry and provides the justification for my attempt to write a primer for students and other polarimetric novices. If we can take today's students straight from polarimetric fundamentals to what is best in modern research practice, then five years from now we shall have a polarization community with both eyes wide open and firmly fixed beyond present-day horizons. That is what this book is about.

Polarimetry, performed mainly by optical or radio specialists, has already made a considerable impact on astronomy, and it deserves to be a standard observational technique, to be used whenever it is best for the job in hand. Accordingly, all astronomers should acquire polarimetric basics. My aim is to allow the reader, starting at first principles, to make use of the very latest literature. To preserve readibility, I have omitted most of the historical development. The References section at the end of the book reflects this attitude; interested readers can always trace the history backwards from modern papers.

I have tried to resist any tendency to write a comprehensive monograph.

In this chapter, the main concepts of polarized radiation will be introduced and discussed. These concepts apply at all wavelengths. Electromagnetic radiation will be treated as a continuous travelling-wave phenomenon. Quantum considerations can be postponed until the moment the radiation strikes a detector and is converted into an electrical signal. Ideal detectors are not sensitive to polarization, and, to the extent that a real-life detector can be seen as an ideal one preceded by polarization optics, quantum and polarization considerations can live side by side without the one influencing the arguments concerning the other. Of the electromagnetic wave, only the electric vector will be considered; the corresponding magnetic vector follows from Maxwell's equations.

Astronomical signals are noise-like. These noise-like variations of electric field strength (of the electromagnetic wave) may be passed through a narrow-band filter, so that a ‘quasi-monochromatic’ wave remains. Such a wave contains a very narrow band of frequencies and may be seen as a sinusoidal carrier wave at signal frequency, modulated both in amplitude and phase by noise-like variations. The highest frequencies (the fastest variations) in the modulating noise determine the width of the sidebands around the carrier wave in the frequency spectrum. Any wide-band (‘polychromatic’) signal may be seen as the sum of many quasi-monochromatic signals, all with different carrier frequencies and generally each with its own amplitude and phase modulation.

In this chapter I shall discuss the scientific reasons for measuring the polarization of astronomical signals. The central question is: ‘What does nature express as polarization rather than as some other property of the signal?’. This, of course, is the scientific point of departure for all astronomical polarimetry, but the basic concepts of polarization and (un)polarized radiation needed clarification before scientific necessity could be discussed properly. This chapter will be only a brief overview of the relevant astronomy; a number of recent reviews are available to help the reader become familiar with the astronomical applications. The subject of this book is polarimetry, the desirability of measuring the polarization will be taken for granted.

The light of most stars is itself unpolarized. In fact, whenever one needs an optical ‘zero-polarization’ reference source, one is generally pushed to use stars rather than lamps. The reason for the low polarization is the great distance (point source) and the spherical symmetry of most stars: any linear polarization there might be is averaged out over the star's visible disc. In the radio domain, antenna properties are highly polarization-dependent, and without specialized techniques large spurious apparent polarization is generated within the instrument. Thus, circumstances conspired to make astronomical polarimetry a late arrival. Even in the spectral regions of greatest instrumental sophistication, polarimetry remained a specialist technique; solar physics has been the notable exception. As a corollary of this lack of attention to polarimetry, awareness of polarization-induced photometric errors within telescopes and instruments has been minimal.