  Coherent diffractive imaging (CDI) is widely used to characterize structured
samples from measurements of diffracting intensity patterns. We introduce a
numerical framework to quantify the precision that can be achieved when
estimating any given set of parameters characterizing the sample from measured
data. The approach, based on the calculation of the Fisher information matrix,
provides a clear benchmark to assess the performance of CDI methods. Moreover,
by optimizing the Fisher information metric using deep learning optimization
libraries, we demonstrate how to identify the optimal illumination scheme that
minimizes the estimation error under specified experimental constrains. This
work paves the way for an efficient characterization of structured samples at
the sub-wavelength scale.
