  A standard paradigm of localization microscopy involves extension from two to
three dimensions by engineering information into emitter images, and
approximation of errors resulting from the field dependence of optical
aberrations. We invert this standard paradigm, introducing the concept of fully
exploiting the latent information of intrinsic aberrations by comprehensive
calibration of an ordinary microscope, enabling accurate localization of single
emitters in three dimensions throughout an ultrawide and deep field. To
complete the extraction of spatial information from microscale bodies ranging
from imaging substrates to microsystem technologies, we introduce a synergistic
concept of the rigid transformation of the positions of multiple emitters in
three dimensions, improving precision, testing accuracy, and yielding
measurements in six degrees of freedom. Our study illuminates the challenge of
aberration effects in localization microscopy, redefines the challenge as an
opportunity for accurate, precise, and complete localization, and elucidates
the performance and reliability of a complex microelectromechanical system.
