  Intensity mapping has emerged as a promising tool to probe the
three-dimensional structure of the universe. The traditional approach of galaxy
redshift surveys is based on individual galaxy detection, typically performed
by thresholding and digitizing large-scale intensity maps. By contrast,
intensity mapping uses the integrated emission from all sources in a 3D pixel
(or voxel) as an analog tracer of large-scale structure. In this work, we
develop a formalism to quantify the performance of both approaches when
measuring large-scale structures. We compute the Fisher information of an
arbitrary observable, derive the optimal estimator, and study its performance
as a function of source luminosity function, survey resolution, instrument
sensitivity, and other survey parameters. We identify regimes where each
approach is advantageous and discuss optimal strategies for different
scenarios. To determine the best strategy for any given survey, we develop a
metric that is easy to compute from the source luminosity function and the
survey sensitivity, and we demonstrate the application with several planned
intensity mapping surveys.
