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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-alpha 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-alpha 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 lambda1549 emission, compared to the number of objects seen at high redshifts, where Lyman-alpha 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, alpha, 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, alpha) ~ 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-alpha 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-alpha 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.

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