Terry D. Oswalt
Editor-in-Chief
Howard E. Bond
Volume Editor

Planets, Stars and
Stellar Systems
volume 2

Astronomical Techniques,
Software, and Data


Planets, Stars and Stellar Systems
Astronomical Techniques, Software, and Data



Terry D. Oswalt (Editor-in-Chief )
Howard E. Bond (Volume Editor)

Planets, Stars and
Stellar Systems
Volume 2:
Astronomical Techniques,
Software, and Data
With 121 Figures and 32 Tables


Editor-in-Chief
Terry D. Oswalt

Department of Physics & Space Sciences
Florida Institute of Technology
University Boulevard
Melbourne, FL, USA
Volume Editor
Howard E. Bond
Labrador Lane
Cockeysville, MD, USA

ISBN 978-94-007-5617-5
ISBN 978-94-007-5618-2 (eBook)
ISBN 978-94-007-5619-9 (print and electronic bundle)
DOI 10.1007/978-94-007-5618-2
This title is part of a set with
Set ISBN 978-90-481-8817-8
Set ISBN 978-90-481-8818-5 (eBook)
Set ISBN 978-90-481-8852-9 (print and electronic bundle)
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Series Preface
It is my great pleasure to introduce “Planets, Stars, and Stellar Systems” (PSSS). As a “Springer
Reference”, PSSS is intended for graduate students to professionals in astronomy, astrophysics
and planetary science, but it will also be useful to scientists in other fields whose research interests overlap with astronomy. Our aim is to capture the spirit of 21st century astronomy – an
empirical physical science whose almost explosive progress is enabled by new instrumentation,
observational discoveries, guided by theory and simulation.
Each volume, edited by internationally recognized expert(s), introduces the reader to a
well-defined area within astronomy and can be used as a text or recommended reading for
an advanced undergraduate or postgraduate course. Volume 1, edited by Ian McLean, is an
essential primer on the tools of an astronomer, i.e., the telescopes, instrumentation and detectors used to query the entire electromagnetic spectrum. Volume 2, edited by Howard Bond, is a
compendium of the techniques and analysis methods that enable the interpretation of data collected with these tools. Volume 3, co-edited by Linda French and Paul Kalas, provides a crash
course in the rapidly converging fields of stellar, solar system and extrasolar planetary science.
Volume 4, edited by Martin Barstow, is one of the most complete references on stellar structure
and evolution available today. Volume 5, edited by Gerard Gilmore, bridges the gap between
our understanding of stellar systems and populations seen in great detail within the Galaxy
and those seen in distant galaxies. Volume 6, edited by Bill Keel, nicely captures our current
understanding of the origin and evolution of local galaxies to the large scale structure of the
universe.
The chapters have been written by practicing professionals within the appropriate subdisciplines. Available in both traditional paper and electronic form, they include extensive

bibliographic and hyperlink references to the current literature that will help readers to acquire a
solid historical and technical foundation in that area. Each can also serve as a valuable reference
for a course or refresher for practicing professional astronomers. Those familiar with the “Stars
and Stellar Systems” series from several decades ago will recognize some of the inspiration for
the approach we have taken.
Very many people have contributed to this project. I would like to thank Harry Blom and
Sonja Guerts (Sonja Japenga at the time) of Springer, who originally encouraged me to pursue this project several years ago. Special thanks to our outstanding Springer editors Ramon
Khanna (Astronomy) and Lydia Mueller (Major Reference Works) and their hard-working editorial team Jennifer Carlson, Elizabeth Ferrell, Jutta Jaeger-Hamers, Julia Koerting, and Tamara
Schineller. Their continuous enthusiasm, friendly prodding and unwavering support made this
series possible. Needless to say (but I’m saying it anyway), it was not an easy task shepherding
a project this big through to completion!
Most of all, it has been a privilege to work with each of the volume Editors listed above and
over 100 contributing authors on this project. I’ve learned a lot of astronomy from them, and I
hope you will, too!

January 2013

Terry D. Oswalt
General Editor



Preface to Volume 2
Volume 2 of Planets, Stars, and Stellar Systems is entitled “Astronomical Techniques, Software,
and Data.” When I began my astronomical career in the 1960s, astronomical techniques, at
least for optical observers, consisted mostly of exposing and developing photographic plates,
or obtaining single-channel photometry with a photomultiplier tube. Software, if used at all,
was run using punched cards that you took over to the computer center and came back 24
hours later to pick up the output (which often consisted of pointing out the typographical errors
in your FORTRAN code). Computations were done with a slide rule or a mechanical Friden

calculator (the most advanced model could actually calculate a square root, although it took
about 15 seconds to do so!). Data consisted of photographic plates or strip-chart recordings of
your photometry or hand-written columns of numbers or plots prepared with a Leroy lettering
set. If you needed data from a collaborator, the plates had to be shipped to you in a sturdy
wooden box or you had to travel to your colleague’s institution or the tables of numbers had to
be mailed to you.
The advances in astronomical methods in recent decades have come in steady steps, but
as I look back from our contemporary viewpoint to 40 or 50 years ago, they are all but inconceivable. I hold in my hand a computing device orders of magnitude more powerful than the
room-sized computer of 1965 (and it can even make telephone calls!). What’s that bright thing
next to the moon? Just start up the app, aim the phone at the sky, and it will tell you. In the
old days you made a finding chart by laboriously pulling out a Palomar Sky Survey print and
photographing it with a Polaroid camera; now, in a few seconds, and from any mountaintop
observatory in the world, I can display a Digitized Sky Survey image of any point in the sky, and
read off the coordinates just by moving the cursor. Do you want the spectral-energy distribution of your source from the far-UV, through the optical, to the near- and mid-IR? You can find
all of that in a few moments now.
The venerable Chicago Stars and Stellar Systems had two volumes dedicated to “Astronomical Techniques” and “Basic Astronomical Data.” The new volume captures the basic spirit of
those SSS volumes, in terms of introducing the reader to some of the basic observing and dataanalysis techniques, but of course many of the actual topics are vastly different from, or didn’t
exist at all, five decades ago.
Volume 2 starts with two articles (Stetson, and Massey & Hanson) describing modern
techniques of astronomical photometry and spectroscopy, primarily at optical wavelengths.
The next two articles (Tokunaga, Vacca, & Young, and Snik & Leller) move to the realms of
techniques of infrared astronomy and polarimetry of astrophysical sources. As I have already
mentioned, the availability of multi-wavelength sky surveys has transformed modern observational astronomy, and the amazing breadth of survey data available now (or in the near future)
is comprehensively reviewed by Djorgovski, Mahabal, Drake, Graham, & Donalek.
Moving to still longer wavelengths, Wilson reviews the techniques of radio astronomy, and
then Monnier & Allen reveal the methods of interferometry at both radio and optical frequencies. To understand your data, you usually have to calibrate them to absolute physical units, and
these techniques are explained by Deustua, Kent, & Smith.


viii


Preface to Volume 2

The new science of astroinformatics is reviewed by Borne. Statistical methods of particular
utility in astronomy are discussed by Feigelson & Babu, and the volume closes with a review of
modern numerical techniques in astronomy by Wood.
This volume would not have been possible without the contributions of the authors, the
guiding influence of the other volume editors and the editor-in-chief, and the staff at Springer.
I thank all of them, and I hope that the new PSSS volumes will have as much influence on
contemporary astronomy as the old and still cherished Chicago SSS volumes did.
Howard E. Bond
Cockeysville, MD
USA


Editor-in-Chief
Dr. Terry D. Oswalt
Department Physics & Space Sciences
Florida Institute of Technology
150 W. University Boulevard
Melbourne, Florida 32901
USA
E-mail:

Dr. Oswalt has been a member of the Florida Tech faculty since 1982 and was the first professional astronomer in the Department of Physics and Space Sciences. He serves on a number of
professional society and advisory committees each year. From 1998 to 2000, Dr. Oswalt served
as Program Director for Stellar Astronomy and Astrophysics at the National Science Foundation. After returning to Florida Tech in 2000, he served as Associate Dean for Research for the
College of Science (2000–2005) and interim Vice Provost for Research (2005–2006). He is now
Head of the Department of Physics & Space Sciences. Dr. Oswalt has written over 200 scientific
articles and has edited three astronomy books, in addition to serving as Editor-in-Chief for the

six-volume Planets, Stars, and Stellar Systems series.
Dr. Oswalt is the founding chairman of the Southeast Association for Research in Astronomy (SARA), a consortium of ten southeastern universities that operates automated 1-meter
class telescopes at Kitt Peak National Observatory in Arizona and Cerro Tololo Interamerican
Observatory in Chile (see the website www.saraobservatory.org for details). These facilities,
which are remotely accessible on the Internet, are used for a variety of research projects by
faculty and students. They also support the SARA Research Experiences for Undergraduates
(REU) program, which brings students from all over the U.S. each summer to participate oneon-one with SARA faculty mentors in astronomical research projects. In addition, Dr. Oswalt
secured funding for the 0.8-meter Ortega telescope on the Florida Tech campus. It is the largest
research telescope in the State of Florida.
Dr. Oswalt’s primary research focuses on spectroscopic and photometric investigations of
very wide binaries that contain known or suspected white dwarf stars. These pairs of stars, whose
separations are so large that orbital motion is undetectable, provide a unique opportunity to
explore the low luminosity ends of both the white dwarf cooling track and the main sequence;
to test competing models of white dwarf spectral evolution; to determine the space motions,
masses, and luminosities for the largest single sample of white dwarfs known; and to set a lower
limit to the age and dark matter content of the Galactic disk.



Volume Editor
Howard E. Bond
9615 Labrador Lane
Cockeysville, MD 21030
USA
E-mail:

Dr. Bond received his Ph.D. in astronomy from the University of Michigan in 1969.
From 1970 to 1984, he was a faculty member in the Department of Physics and Astronomy at Louisiana State University. In 1984, he moved to the Space Telescope Science Institute
in Baltimore, Maryland, which manages the scientific programs of the Hubble Space Telescope.
At STScI, Dr. Bond helped develop the peer review procedures for Hubble observers. He managed the Hubble Postdoctoral Fellowship Program from 1994 to 2002. He was a cofounder of

the Hubble Heritage Project, which makes the most spectacular HST images available to the
public, and has received both the Klumpke-Roberts Award of the Astronomical Society of the
Pacific and the Education Prize of the American Astronomical Society. Dr. Bond was involved
in the development of the Wide-Field Camera 3 for the Hubble telescope, serving on the WFC3
Scientific Oversight Committee from 1998 to the present.
Dr. Bond’s research interests are in observational stellar astronomy. He has published
over 500 scientific papers, concentrating particularly on planetary nebulae and their central
stars, white dwarfs, stellar chemical compositions, binary stars, and transient astrophysical
phenomena. He is an active user of the Hubble Space Telescope, having received observing time
on the telescope in all 20 peer-review cycles.
Bond served as Councilor of the American Astronomical Society from 1987 to 1989, and
was Managing Editor of Publications of the Astronomical Society of the Pacific from 1991 to
1997. In 2008, he became Astronomer Emeritus at the Space Telescope Science Institute, and is
currently continuing his research programs as an independent contractor and consultant.



Table of Contents
Series Preface..........................................................................................
Preface to Volume 2..................................................................................
Editor-in-Chief.........................................................................................
Volume Editor .........................................................................................
List of Contributors ..................................................................................

v
vii
ix
xi
xv


Volume 2
1 Astronomical Photometry...............................................................

1

Peter B. Stetson

2 Astronomical Spectroscopy.............................................................

35

Philip Massey ⋅ Margaret M. Hanson

3 Infrared Astronomy Fundamentals ...................................................

99

Alan T. Tokunaga ⋅ William D. Vacca ⋅ Erick T. Young

4 Astronomical Polarimetry: Polarized Views of Stars and Planets............ 175
Frans Snik ⋅ Christoph U. Keller

5 Sky Surveys .................................................................................. 223
S. George Djorgovski ⋅ Ashish Mahabal ⋅ Andrew Drake ⋅ Matthew Graham ⋅
Ciro Donalek

6 Techniques of Radio Astronomy....................................................... 283
T. L. Wilson

7 Radio and Optical Interferometry: Basic Observing Techniques

and Data Analysis .......................................................................... 325
John D. Monnier ⋅ Ronald J. Allen

8 Absolute Calibration of Astronomical Flux Standards .......................... 375
Susana Deustua ⋅ Stephen Kent ⋅ J. Allyn Smith

9 Virtual Observatories, Data Mining, and Astroinformatics .................... 403
Kirk Borne


xiv

Table of Contents

10 Statistical Methods for Astronomy.................................................... 445
Eric D. Feigelson ⋅ G. Jogesh Babu

11 Numerical Techniques in Astrophysics............................................... 481
Matt Wood

Index................................................................................................ 503


List of Contributors
Ronald J. Allen
Science Mission Office
Space Telescope Science Institute
Baltimore, MD
USA
G. Jogesh Babu

Department of Statistics
The Pennsylvania State University
University Park, PA
USA
and
Center for Astrostatistics
The Pennsylvania State University
University Park, PA
USA
Kirk Borne
George Mason University
Fairfax, VA
USA
Susana Deustua
Instruments Division
Space Telescope Science Institute
Baltimore, MD
USA

Andrew Drake
California Institute of Technology
Pasadena, CA
USA
Eric D. Feigelson
Department of Astronomy & Astrophysics
The Pennsylvania State University
University Park, PA
USA
and
Center for Astrostatistics

The Pennsylvania State University
University Park, PA
USA
Matthew Graham
California Institute of Technology
Pasadena, CA
USA
Margaret M. Hanson
Department of Physics
University of Cincinnati
Cincinnati, OH
USA

S. George Djorgovski
California Institute of Technology
Pasadena, CA
USA

Christoph U. Keller
Sterrewacht Leiden
Universiteit Leiden
Leiden
The Netherlands

Ciro Donalek
California Institute of Technology
Pasadena, CA
USA

Stephen Kent

Fermi National Accelerator Laboratory
Batavia, IL
USA


xvi

List of Contributors

Ashish Mahabal
California Institute of Technology
Pasadena, CA
USA

Philip Massey
Lowell Observatory
Flagstaff, AZ
USA

John D. Monnier
Astronomy Department
Experimental Astrophysics
University of Michigan
Ann Arbor, MI
USA

J. Allyn Smith
Austin Peay State University
Clarksville, TN
USA


Frans Snik
Sterrewacht Leiden
Universiteit Leiden
Leiden
The Netherlands

Peter B. Stetson
Dominion Astrophysical Observatory
Herzberg Institute of Astrophysics
National Research Council Canada
Victoria, BC
Canada

Alan T. Tokunaga
Institute for Astronomy
University of Hawaii
Honolulu, HI
USA

William D. Vacca
SOFIA
NASA Ames Research Center
Moffett Field, CA
USA

T. L. Wilson
Naval Research Laboratory
Washington, DC
USA


Matt Wood
Department of Physics and Space Sciences
Florida Institute of Technology
Melbourne, FL
USA

Erick T. Young
SOFIA
NASA Ames Research Center
Moffett Field, CA
USA


1

Astronomical Photometry
Peter B. Stetson
Dominion Astrophysical Observatory, Herzberg Institute of
Astrophysics, National Research Council Canada, Victoria, BC,
Canada

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2
2.1

2.2
2.3

General Properties of Photometric Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photographic Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
4
5
6

3
3.1
3.2
3.3
3.4
3.5
3.6
3.7

The General Photometric Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Atmospheric Extinction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bandpass Mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zero Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Higher-Order Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Differential Photometry; Time-Domain Photometry . . . . . . . . . . . . . . . . . . . . . . . .


9
11
12
16
16
19
21
22

4
4.1
4.2
4.3
4.4

Measuring the Instrumental Magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photoelectric Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aperture Photometry with CCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concentric-Aperture Photometry with CCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Profile-Fitting Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23
23
24
27
30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33


T.D. Oswalt, H.E. Bond (eds.), Planets, Stars and Stellar Systems. Volume 2: Astronomical Techniques, Software,
and Data, DOI 10.1007/978-94-007-5618-2_1, © Springer Science+Business Media Dordrecht 2013


2

1

Astronomical Photometry

1 Introduction
Astronomers use the term “photometry” to refer to the precise measurement of the apparent
brightness of astronomical objects in particular specified ranges of electromagnetic wavelength
in and near the optically visible band. Historically, this task has been most commonly carried out
with the human eye, photographic plates, photomultiplier tubes, and – most recently as of this
writing – charge-coupled devices. At wavelengths significantly shorter or longer than the optical
region, different detector technologies must be used, and some other term than “photometry”
is often used to name the process.
The basic unit of astronomical photometry is the magnitude. The modern magnitude scale
is logarithmic, with a flux ratio of 100 defined to be precisely five magnitudes;
a photometric
√
difference of one magnitude, therefore, corresponds to a flux ratio of   ≈ .. Magnitudes
increase numerically as the objects become apparently fainter. The conversions between flux
F and magnitude m are m = constant − . log F and F ∝ .(constant−m) . For quick mental
calculations, it is useful to remember that a factor of two in flux is about three-quarters of a
magnitude, and differences of one, two, three, and four magnitudes correspond to flux ratios of
about two and a half, six and a quarter, sixteen, and forty. Also, . log . ≈ . = .%,
and most photometrists tend to use the terms “about one one-hundredth of a magnitude” and
“about one percent” interchangeably.

This magnitude system – a legacy from the ancient days of subjective, naked-eye brightness
estimates – often causes bewilderment or scorn among some of our colleagues in the physics
community, who feel that more fundamental units, such as erg cm− s− nm− , would be of more
practical use and greater scientific rigor. For example, at wavelengths much longer than we
are concerned with here, the “jansky” (defined as − W m− Hz− ) is the most commonly
used basic unit of astronomical flux. For our purposes, however, the traditional magnitude system still provides some valuable advantanges, most notably in helping to compartmentalize the
observational error budget.
This is because the most widely used methods of astronomical photometry are fundamentally differential in nature: the measuring instrument, properly used, observes the brightness
ratio between two astronomical objects. As we have seen, this ratio can be expressed as a magnitude difference, and under ideal experimental conditions it can in principle be measured with
a precision ultimately limited only by the Poisson statistics of the detected photons. Throughout
history, the precision of possible flux-ratio measurements has exceeded the accuracy of the available magnitude-to-flux conversions (the “constant” in the above equations, which is actually a
function of wavelength) by several orders of magnitude. This means that photometric measurements expressed as magnitude differences (= flux ratios) relative to some specified reference
network of standard stars can retain their quantitative meaning and scientific validity for many
decades or centuries, while subsequent generations of more fundamental experiments progressively refine the estimated magnitude-to-absolute-flux conversion. Most astronomical problems
relying on photometry for their solution can benefit from the one percent, or millimagnitude,
or micromagnitude precision possible from a well-designed photometric experiment without
being adversely affected by the typically few percent uncertainty in the estimated magnitudeto-flux conversion factor at any given wavelength (e.g., Massey et al. 1988; Hamuy et al. 1992).
When photometric measurements are published on a well-defined magnitude scale, future
investigators will be able to apply their own contemporary notion of the magnitude-to-flux
conversion to historical results, without having to remember and correct for the conversion
that was considered to be valid at the time when each different set of observations was made.


Astronomical Photometry

1

Astronomical photometry is a measuring process, and the observations themselves contain both random and systematic measurement errors that are usually at least as large as the
uncertainties we ultimately want in our derived results. Accordingly, it is hardly ever sufficient
to imagine the most obvious way of performing a particular measurement. At each step of the

way it is essential to consider all possible sources of random and systematic error, and much of
the experimental design is aimed at finding clever ways to reduce the random uncertainties, to
induce systematic errors to cancel themselves out, and to obtain reliable quantitative estimates
of those unavoidable uncertainties that remain. Numerous examples of these basic principles
will appear below.
Bessell (2005) has provided an up-to-date, comprehensive survey of modern photometric
systems in both historical and contemporary astrophysical context. I will not attempt to duplicate his information (or his reference list) here. Instead, the purpose of this chapter is to provide
an overview of the basic principles and techniques of astronomical photometry. The discussion
will relate to the optical range of wavelengths, and as far into the near infrared and the near
ultraviolet as the same techniques may be said to be appropriate. That is to say, the discussion
will stop at that point in the infrared where the thermal emission of the equipment, and the
relatively poor stability of both the terrestrial atmosphere and the currently available generation of detectors become (for now, at least) the dominant impediment to photometric precision.
The relevance of the present discussion will also cease at that point in the near ultraviolet where
the opacity of the atmosphere prevents useful observations from our planet’s surface. I shall also
concern myself primarily with photometry of stars. Photometry of extended objects like galaxies
adds an entirely different class of problem, such as defining the spatial extent of individual entitities of various morphologies in some meaningful and homogeneous way, and disentangling
the contributions of overlapping objects. These problems have no clear and obvious solution,
and should be treated separately.
I am much better at remembering the past than predicting the future. The subject matter of
this chapter will therefore be dominated by collective lessons learned by astronomers during,
roughly speaking, the six decades from about 1950 to 2010. This interval is neatly bisected by
the date 1980, which is approximately when the charge-coupled device, or CCD, began to have a
serious impact on astronomical observations (e.g., Leach et al. 1980). In the future, innovations
like queue-scheduled observing and dedicated telescopes for large-scale surveys will increasingly and profoundly change the way in which astronomical photometry is done. It can only be
anticipated that the consumers of astronomical photometry will become ever more decoupled
from those who produce it. I hope that the present chapter will be interesting and educational
for the former, and a useful introduction to the field for those hoping to become the latter.

2 General Properties of Photometric Detectors
Before the discussion proceeds further, we should understand that the blanket term stellar photometry embraces a number of recognizable subtopics. First, there is what I will call “absolute”

or “all-sky” photometry, where the purpose is to measure the magnitude differences (or flux
ratios) among objects widely separated on the sky. This may be contrasted with “relative” photometry, which seeks to measure the magnitude differences among objects that can be observed
simultaneously, and “time-domain” photometry, which wants to track changes of brightness in
the same object observed at different times. Second, we should recognize that there are some

3


4

1

Astronomical Photometry

practical differences between measuring magnitudes (e.g., for estimating a distance, or defining
a variable-star light curve) and colors (= magnitude differences or flux ratios between different
wavelength bands for a given object in order to estimate, e.g., temperature, reddening, or other
crude properties of its spectral-energy distribution). Third, different types of measuring equipment produce data requiring different types of treatment to provide useful photometric results.
Among these, the photographic plate, the photomultiplier tube, and the CCD may be taken as
prototypes representing three very different classes of photometric detector.

2.1 Photographic Plates
Historically, the first of these detectors to see astronomical use was the photographic plate. This
is an area detector, capable of recording an image of a significant area of sky and acquiring
positional and photometric information for hundreds or thousands of targets simultaneously.
The quantum efficiency of plates is low, typically of order 1% (e.g., Latham 1976; Kaye 1977),
but for some applications (for instance, color-magnitude diagrams of star clusters) the multiplex
advantage of recording many targets at once more than makes up for this shortcoming. The plate
itself requires careful chemical processing to develop the latent astronomical image and render
it permanent, but once this has been done the plate can be analyzed in detail later, and it serves

as its own durable data record.
The principal shortcoming of the photographic plate is that it is a non-linear photometric detector: there is no simple or universally applicable relationship between a star’s apparent
brightness on the sky and the properties of its recorded image on the plate. The photographic
image of a faint star is a faint, gray, fuzzy patch whose size is set by the astronomical seeing, telescope aberrations, and the scattering of photons within the photographic emulsion. The images
of slightly brighter stars are not much larger than those of fainter stars, but become progressively
blacker for stars that are brighter and brighter. For stars that are brighter yet, the photographic
image saturates, meaning the central blackness remains roughly constant, while the apparent
diameter of the star image on the plate grows with increasing stellar brightness. At extremely
high flux levels, the photographic emulsion can “solarize”: it actually de-exposes itself and the
centers of bright star images turn from black back into gray.
The index of photometric brightness that one extracts from a photographic plate, therefore, is a conflation of the blackness and diameter of the star image. This relationship is not
necessarily constant even for plates from the same emulsion batch that have been exposed and
developed on the same night. Therefore, to obtain the best possible photometry from a photographic plate, it is important to have independently determined magnitudes for a sequence
of stars on that plate, spanning the full brightness range of the target stars. These can be used
to calibrate an empirical relationship between some photographic magnitude index, however
defined, and stellar magnitude on a true photometric scale.
The light-sensitive component of the photographic emulsion consists of grains of silverhalide crystal, of diverse sizes, suspended in a jelly-like substrate. In general, the more sensitive
the emulsion the coarser the grain size, but grain dimensions of order 0.1 μm to a few μm are
typical. Statistical variations in the distribution of these grains within the emulsion substrate
typically limit the precision achievable with a single photometric measurement to not better
than 2–5% (e.g., Stetson 1979).


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2.2 Photomultipliers
The photomultiplier tube is a technology of World War II vintage. The light of a star, collected by
the telescope, is projected through a filter and onto a photocathode where some fraction (typically ∼10%; e.g., Giannì et al. 1975) of the photons will cause the ejection of photoelectrons.

These are accelerated through a static electric field until they hit a dynode, where the augmented
energy of each individual photoelectron causes the ejection of a number of low-energy secondary electrons. These are in turn accelerated through the electric field until they hit another
dynode, producing a still larger cloud of low-energy electrons. This process continues through
several more stages, resulting in a final amplification factor that can be as great as 100 million,
and producing a final burst of electrons large enough to be detected by macroscopic laboratory
equipment. In the earlier years of photoelectric photometry, the amount of DC current emerging from the photomultiplier, as displayed in analog form on a dial or on a paper-chart recorder,
was the measure of the target star’s brightness. Later, pulse-counting circuitry was developed
which can detect the output current spike produced by each initial photoelectron. The number
of such spikes counted in a fixed amount of time (of order, for instance, 10 s) is a reliable, digital
measure of the flux from the target star.
Inside the photoelectric photometer, an aperture – usually a simple hole in a piece of metal –
is positioned in the focal plane of the telescope. The astronomer centers the image of the target
of interest in this aperture, and the light passing through the hole is optically relayed through
the filter and a “Fabry,” or “field” lens to the photomultiplier (e.g., Johnson 1962). The purpose
of the field lens is to produce an image of the entrance pupil (the telescope’s primary mirror or
lens) on the photocathode of the photomultiplier. Presuming that the primary mirror or lens
and the photometer and its individual parts are rigidly attached to the telescope itself, the image
of the pupil is fixed in location on the photocathode, and does not move either as the telescope
is pointed to different places on the sky or as the star image wanders in the entrance aperture
due to imperfect tracking. Furthermore, the image of the pupil occupies a finite area that can be
matched in size to the photocathode. Therefore, any positional variations in the sensitivity of the
photocathode itself are both averaged out and invariant during the observations. As a result, the
photomultiplier can be an almost perfect linear photometric detector, subject only to Poisson
statistical variance in the production of photoelectrons, as long as the photon arrival rate is low
enough that multiple pulses in the output are not often blended together and counted as one.
A simple and reliable correction formula can be applied when the number of coincident pulses
is a small fraction of the total (perhaps a correction of a few percent at a count rate of 1 MHz,
e.g., Giannì et al. 1975), thus somewhat increasing the useful dynamic range of the instrument.
There are no other important instrumental noise sources.
The major practical shortcoming of a photomultiplier is that it is only one “pixel” and therefore can measure only one object at a time. The “pixel” – that is to say, the fixed entrance

aperture – must be large not only to contain the wings of the stellar profile; it must also allow for
the star image to wander due to seeing and imperfect telescope tracking while the observation is
being made. Typically aperture diameters of order ten or tens of arcseconds are used. This large
an aperture also lets in a significant quantity of diffuse sky light – terrestrial skyglow, scattered
moonlight, zodiacal light, and unrecognized astronomical objects – whose contribution can
be estimated from separate offset observations of “blank” sky regions. This both increases the
necessary observing time and limits the faintness of objects that can be practically observed:
at a good, dark site on a moonless night, the sky brightness is typically apparent magnitude

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20 or 21 per square arcsecond at blue and green wavelengths, and still brighter in the red and
near infrared. With a measuring aperture of order ten arcseconds in diameter (∼100 square
arcseconds in area), then, the apparent sky brightness would contribute comparably with a target star of apparent magnitude 15 or 16, while a target star of apparent magnitude 20 or 21
would represent a mere 1% perturbation on top of the sky contamination.

2.3 CCDs
The charge-coupled device, or CCD, combines many of the best properties of the photographic
plate and the photomultiplier, and then some. First, it is an area detector, capable of simultaneously recording many science targets in its field of view. Second, when properly adjusted, it is
a fairly linear detector: the output signal is very nearly proportional to the flux received. Third,
it has high quantum efficiency: modern chips record nearly 100% of the incident photons at
visible wavelengths (e.g., Leach et al. 1980; Suntzeff and Walker 1996; Burke et al. 2005).
CCDs are physically small compared to photographic plates. Plates with dimensions up to

0.35 m and even 0.5 m square have been used for astronomical imaging while, in contrast, individual CCDs have dimensions of at most a few centimeters. Some modern mosaic cameras
containing arrays of CCDs with overall dimensions as large as ∼25 cm are in routine operation
(e.g., Baade et al. 1999), and still larger arrays are being developed. The financial cost of such
cameras, as well as the computing facilities required to handle the large volumes of digital data,
can be considerable.
Unlike photomultipliers, early generations of CCDs were plagued by high “readout” noise,
a constant uncertainty in the conversion of detected analog signal to digital output data caused
by intrinsic amplifier noise. This could be much larger than the Poisson statistics of photon
arrivals and a significant limiting factor in low-flux-level applications. Early CCDs also tended
to have fabrication defects that could corrupt the data from small patches, or columns, or rows
of pixels, sometimes amounting to as much as a few percent of the total detector area. Modern
design and fabrication techniques have largely eliminated readout noise and detector blemishes
as major causes for concern. Finally, CCDs are highly effective at detecting charged particles as
well as photons. In a photon-counting photomultiplier, the arrival of a charged particle (which
might be a cosmic ray or a radioactive decay product from the environment near the detector)
produces a single pulse in the output: it has the same effect as just one more photon in the
diffuse sky light. In a CCD, an energetic particle impact can liberate thousands of electrons
and invalidate the signal from one, or a few, or many pixels. Long-term exposure to energetic
charged particles eventually leads to deterioration of the detector.
In comparison to photomultiplier data, CCD images require appreciable computer processing to remove instrumental signatures. Unlike the case with the photoelectric photometer with
its field lens and its single photocathode, different scientific targets impinge on different parts
of the detector. In principle, each of the thousands or millions of pixels that constitute a CCD
can have its own individual zero point and scale for flux measurements.
Since the digital image produced by a CCD camera contains some irreducible noise level
originating in the readout and amplification electronics, the device is tuned to provide some
non-zero output signal in the presence of zero input signal, so that the noise fluctuations cannot ever produce an apparently negative output when an amplified low-level input signal is
presented to the analog-to-digital converter. This produces some positive, roughly constant,
zero-point offset in the relationship between input flux and output digital signal. The mean



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1

value of this offset can be determined by programing the electronics to read out more pixels
than are physically present in the device; these phantom pixels contain only the bias offset in
the flux scale (plus noise). It can also happen that the reaction of the device to being read out
can impose some constant pattern in the zero-signal bias across the face of the device. For a
well-behaved detector, the effective flux-measurement zero point of each pixel can be relatively
easily accounted for by subtraction of a suitable “bias” frame. This is constructed by averaging
together many (to reduce the net effects of readout noise) individual digital images obtained
with zero exposure time.
Normalization of the digital image to a common flux scale for each pixel requires division
by a suitable “flat-field” image. This usually turns out to be the most delicate of the basic calibration steps, and is often a dominant source of inaccuracy in the final scientific photometry.
Separate flat-field images are required for the different filters employed by the observer, because
the throughput of each filter and the spectral sensitivity of the detector itself may both vary as
functions of position in the focal plane. A flat-field image is produced by averaging a large number of exposures to a uniform source of illumination. Usually this is either a white target placed
in front of the top end of the telescope tube (or the inside surface of the dome itself) and illuminated by electric lamps (“dome flats”), or the twilight sky observed after sunset or before sunrise,
when it is not dark enough to observe astronomical targets ("sky flats").
Dome flats have the advantage that they can be obtained in the daytime when astronomical
observations are impossible, so a large number of individual exposures in each of the different
filters can be taken and averaged to reduce the Poisson and readout noise to insignificant levels.
In contrast, for sky flats, only a limited amount of time is available between when the sky is
dark enough not to saturate the detector in the shortest practical exposure time, and when it
is no longer bright enough to overwhelm any background astronomical objects. This makes it
difficult to obtain high-quality sky flats for a large number of filters on any one occasion.
On the other hand, a dome flat is relatively vulnerable to scattered light, because the inside
of the dome is illuminated. Particularly with an open telescope tube (such as a Serrurier truss
design), light entering the side of the tube can be scattered off of the inside of the tube components, the telescope’s top end, and the inside of the primary mirror hole, and reach the CCD
without having passed through the normal optical chain. This can produce a pattern of additional diffuse illumination across the detector which has nothing to do with the throughput of

the actual optical system. This compromises the use of the flat field as a measure of the spatial sensitivity variations of the camera. (Grundahl and Sørensen (1996) present a simple and
clever way to diagnose scattered-light problems with CCD cameras.) In the case of sky flats,
with the dome shutter and wind screen maximally restricting the light illuminating the inside
of the dome, the diffuse illumination reaching the camera can be dominated by light following
the canonical optical path, and scattered-light problems can be minimized.
Sky flats have the additional advantage that the overall spectral-energy distribution of scattered sunlight is likely to more closely resemble that of other astronomical objects than the light
emitted by incandescent light bulbs. Even when photographic color-balance filters are employed
to make the incandescent light bluer in the optical regime, these can still pass light in the nearinfrared range (∼700–1,000 nm), which can be a serious problem with a short-wavelength filter
that has a significant red leak of its own. Red leaks are a common problem with near-ultraviolet
U filters (e.g., Argue 1963; Shao and Young 1965). Designed to transmit primarily light
at ∼350 nm, they are often insufficiently opaque in the near-IR – which was not a problem with
photocathodes that were themselves insensitive at the longer wavelengths, but is a serious concern with CCDs that are often quite sensitive at those same wavelengths. Available incandescent

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lamps produce many orders of magnitude more photons at ∼800 nm than at ∼350 nm, so even
with a red leak that seems small in percentage terms, short-wavelength dome flats can be dominated by photons of completely inappropriate wavelength (see, e.g., Stetson 1989a, > Sect. 1,
for an example). This is less of a problem with sky flats, where short-wavelength photons are
abundant compared with long-wavelength ones.
Optimum flat-fielding is clearly contingent on the specifics of the dome, the telescope, the
camera, the filters, the detector, and the scientific goals, so it is impractical to provide a universal
set of best practices. On a personal level, I have had generally good results by combining dome
flats and sky flats in the following way. The mean sky flat in a given filter is divided by the mean

dome flat in the same filter. The resulting ratio image is then smoothed using a kernel of a few
pixels and, finally, the mean dome flat is multiplied by the smoothed ratio image:
Flat = Dome × ⟨

Sky
.
⟩
Dome smoothed

The dome flat, which is the average of a very large number of individual well-exposed, diffusely
illuminated images, contains the best information on the relative quantum efficiencies of individual pixels. The sky flat is typically based on a smaller number of images, and since the sky
brightness is varying rapidly with time during twilight, it is difficult to obtain the optimum
exposure level in each individual image; therefore, individual pixels in the sky flats can be subject to Poisson statistics. However, the sky flat contains the purest information on the global
sensitivity variations across the face of the filter/detector combination. Multiplying the dome
flat by the smoothed ratio of Sky:Dome retains the excellent pixel-to-pixel Poisson statistics of
the dome flats, but restores the large-scale illumination pattern of the sky flats.
If the scientific goal of the observation is to measure the surface brightness of an extended
astronomical object, it may also be desirable to subtract a “dark” frame to account for the fact
that over time the CCD can accumulate thermal signal from within the detector itself. This dark
signal is not necessarily uniform over the detector, especially when – as sometimes happens –
some components within the CCD itself act as light-emitting diodes (e.g., Suntzeff and Walker
1996). Typically, a dark frame is constructed by averaging a number of exposures obtained
under ordinary observing conditions, but with the camera completely sealed off from any incident astronomical or environmental light by a dark slide. The dark frames may be obtained with
the same integration time as the science frames, or – if the detector system is well behaved so
the dark signal accumulates linearly over time – they may be proportionately scaled to different
integration times. For most purposes of stellar photometry, the dark current can be considered
merely another component of the incident diffuse sky light, and dark frames can be omitted.
Finally, it can happen that the actual time that the camera shutter is open can differ from
the time intended by the observer. A finite amount of time, typically of order 100 ms can pass
between when the control computer instructs the mechanical shutter to open and when it is in

fact completely open. Similarly, some amount of time passes between the instruction to close
and when the shutter is actually closed. These two time delays need not be numerically the same.
Furthermore, if the shutter itself is placed closer to the focal plane than to a pupil, vignetting
by the shutter aperture as it is opening and closing can cause different parts of the imaged field
to receive different total exposure times. If the shutter timing error is of order 100 ms, then in
a 10-s exposure this can cause a systematic, possibly position dependent, 1% error in the fluxes
inferred for the science targets. Obviously, the systematic error becomes worse for shorter exposures, and may be negligible for much longer exposures. However, shutter-timing corrections,
whether constant timing offsets or two-dimensional correction maps, can readily be estimated