The requirements, and hence degree of difficulty, for undertaking a survey are closely connected to the scientific goals. This topic is rarely discussed, and perhaps it is for this reason that we have been unable to invent labels for the three types of survey described below more imaginative than A, B and C. Notwithstanding the uninspiring terminology, the differences among survey types are important.
4.1 Survey Type A: Find a Quasar
The least demanding surveys might be termed the ``find an object to
study'' category. The identification of bright quasars at redshifts z
> 1.7 to investigate the
properties of the Lyman-
forest or other absorption lines
arising from intervening systems is a familiar example. One is simply
interested in quasars that are bright enough and in an accessible
portion of the sky that they may be observed successfully at high
spectral resolution and signal-to-noise ratio. It is of little
interest how the objects are found, whether the selection is uniform as
a function of position on the sky, or
even if the selection is efficient in the sense of identifying a large
fraction of the such quasars brighter than some specified flux limit. A
more demanding type of survey is required if a statistical study of the
incidence of absorbers is attempted and the probability of identifying a
quasar is not independent of the presence/absence of an
absorber.
Another example is the ``proof of existence'' survey for which the identification of one or a few objects achieves the goal. Detection of a quasar with a redshift of z > 6 or of a radio-quiet BL Lac could fall in this category. However, following success in such a search, the scientific goals usually evolve into establishing a quantitative estimate of the surface density of such objects and a survey of the most demanding type (Section 4.3) is required. Even in the event of failure to identify an example of the class sought (the more usual outcome), a quantitative survey is a prerequisite for obtaining any information about the confidence with which one can rule out its existence.
4.2 Survey Type B: Find Quasars Consistently
More demanding are surveys which satisfy the requirement of homogeneity, in the sense that the fraction of quasars identified is constant as a function of position on the sky and the procedures used to select the candidates. A well-defined flux limit must usually be established and the method utilized for selection must be equally effective, irrespective of where on the sky the quasar lies. A generalization of this approach is a sample reaching different flux, or selection, limits as a function of position on the sky, but where the area covered to a specified limit is known.
In the optical, implementation of such surveys was difficult prior to
when the combination of CCD detectors and automated plate scanning machines
became capable of providing reliable flux calibration for relatively
faint objects over areas of many square degrees. The subsequent
selection from photographic material was also fraught with
problems. Photographic plates can exhibit significant changes in
sensitivity from plate to plate and several optical selection
techniques depend critically on the atmospheric seeing. These
impediments have largely been overcome and homogeneous samples have
provided significant constraints on the form of quasar clustering
(Shanks et
al. 1987,
Boyle 1991,
Andreani and
Cristiani 1992).
Exploiting the very prominent Lyman- and C IV emission lines
visible on low-resolution slitless spectroscopic plates to identify
samples at redshifts z ~ 2 is a very efficient method
for generating such a sample (e.g.,
Clowes and Campusano
1991,
Osmer and Hewett
1991). An assumption underlying such an approach is that the
spatial clustering of quasars is not related to the properties
of the emission lines.
The exact efficiency of homogeneous surveys is not critical. While the ability to select a larger fraction of the quasar population can only help the experiment, homogeneity is the key. A sample comprising, say, 60% of the quasar population in 100 deg2 will normally provide a superior catalog compared to one where additional effort has resulted in 70% of the population being identified but at the expense of covering only half as much area. This view is not held universally; for example, the practice of increasing the surface density by ~ 10% through scanning two objective-prism plates of the same area of sky with orthogonal dispersion directions, rather than doubling the size of the sample using two plates of adjoining fields, occurs frequently. Our comment may not apply if the aim is to detect quasar pairs with separations less than the angular extent of the prism spectra, but this is not usually the case.
One of the most elegant implementations of a survey in this category
was Osmer's
(1982) demonstration that, subject to the assumption
that emission line properties were not a strong function
of redshift, the space density of quasars at redshifts above z ~
3.5 must undergo a significant decline. Osmer achieved this result by
applying a selection technique based on the detection of emission
lines. He then used the statistics of the number of objects detected at
low-redshift, through the presence of their C IV 
1549 emission,
compared to the number of objects seen at high redshifts, where
Lyman- was visible, to
achieve his goal. At no stage did
Osmer quantify (in an absolute sense) the effectiveness of the
technique, nor was it necessary to do so.
4.3 Survey Type C: Find Quasars Consistently and Predict What Won't Be Found
The third and most demanding type of survey is one for which the
probability of detecting a quasar of a given redshift, flux, and SED
can be specified. An absolute magnitude or luminosity can be calculated
from the redshift, observed flux and SED, so it is equivalent to specify the
intrinsic quantities, absolute magnitude, redshift and SED. The
requirement is thus to determine the
probability of detection as a function of these quantities,
P (M, z, SED), which is often termed the survey selection
function. At other wavelengths the terminology is different but the
requirements are identical; at radio wavelengths a radio-power replaces
the absolute magnitude and a power-law exponent, , may replace
SED when the spectra are well approximated by a power-law in
frequency. The relative ease with which
accurate radio fluxes could be obtained and the much simpler form of
quasar SEDs in the radio regime meant that surveys of this type have been
possible for more than a decade, allowing Gull, Peacock, Wall and
others to derive quantitative constraints on the form and evolution of
the luminosity function (Dunlop and Peacock (1990) and references
therein). However, the distribution of radio-power for the population
is such that radio surveys are not able to detect the
majority of quasars because of their weak radio powers, p, i.e.,
P(p, z, ) ~ 0 for
most quasars at
significant redshifts. Thus, radio surveys have enabled a quantitative
analysis of the evolution of only a subset of the quasar population.
In the optical regime, several factors conspire to make
determining P (M, z, SED) more difficult. First, most selection
techniques
focus on a particular aspect of quasar SEDs to detect the
objects: an ultraviolet excess, or presence of strong broad emission
lines for example. Second, selection techniques are applied to very
narrow wavelength windows; even broadband magnitudes employ
observed-frame passbands of only ~ 800 Å. Third, quasar SEDs
in the rest-frame optical and ultraviolet exhibit large changes in
form over narrow wavelength regions, such as the discontinuities in
continuum level at ~ 1216 Å and at or below 912 Å due to
intervening absorption, and the occurrence of high equivalent
width emission lines of Lyman- and C IV. As a consequence the
observed-frame properties of quasars vary significantly, and at
times very rapidly, as a function of redshift. The sudden change in
the effectiveness of the ultraviolet excess technique at redshift
z ~ 2.2 when the Lyman- emission line moves from the U
band into the B
band corresponds to a rapid change in P (M, z, SED)
to ~ 0 above redshift z ~ 2.2 for most quasar SEDs. Given
that quasars exhibit a broad range of SEDs, and that
detection is itself dependent on the SEDs, quantitative
results require the determination of the selection function.
Work on selection functions for emission line objects located using slitless spectroscopy was undertaken by Clowes (1981), but application to a sample of significant size was not possible at that time. Gratton and Osmer (1987) applied a similar approach to reconciling the apparent differences in inferred space densities of emission line objects arising from surveys using wide-field Schmidt telescope objective-prism data and the much deeper 4-metre grism plate material. Schade (1991) develops a procedure that addresses the problem of calculating a luminosity function from a sample in which the selection is made according to quasar's emission line properties. The completion of surveys that include the determination of the selection function has had to await investigations at the redshifts, z > 3, where the number of objects is small, and historically there has been a sequence of claims for ``redshift cutoffs'', each of which has proven illusory following the application of an alternative selection technique. Schmidt, Schneider and Gunn (1986a, b) published the first detailed description of how to quantify a major quasar survey, a CCD-based, slitless spectroscopic type. In retrospect, their strategy, probing relatively faint magnitudes over a small area, was not optimal, and subsequently, application of the same technique to a much larger area has produced an impressive number of high-redshift quasars (Schmidt, Schneider and Gunn 1991). Schmidt et al. (1994 in preparation) are in the final stages of producing their quantitative analysis. Taking a different approach based on broadband colors, Warren et al. (1991a, b) also developed a quantitative procedure to determine the efficiency of their selection and results are in press (Warren, Hewett and Osmer 1994). Completion of two undertakings of this type demonstrates that quantitative results are now feasible.