  We present the transient source detection efficiencies of the Palomar
Transient Factory (PTF), parameterizing the number of transients that PTF
found, versus the number of similar transients that occurred over the same
period in the survey search area but that were missed. PTF was an optical sky
survey carried out with the Palomar 48-inch telescope over 2009-2012, observing
more than 8000 square degrees of sky with cadences of between 1 and 5 days,
locating around 50,000 non-moving transient sources, and spectroscopically
confirming around 1900 supernovae. We assess the effectiveness with which PTF
detected transient sources, by inserting ~7 million artificial point sources
into real PTF data. We then study the efficiency with which the PTF real-time
pipeline recovered these sources as a function of the source magnitude, host
galaxy surface brightness, and various observing conditions (using proxies for
seeing, sky brightness, and transparency). The product of this study is a
multi-dimensional recovery efficiency grid appropriate for the range of
observing conditions that PTF experienced, and that can then be used for
studies of the rates, environments, and luminosity functions of different
transient types using detailed Monte Carlo simulations. We illustrate the
technique using the observationally well-understood class of type Ia
supernovae.
