  The Nancy Grace Roman Space Telescope will use its wide-field instrument to
carry out a suite of sky surveys in the near infrared. Several of the science
objectives of these surveys, such as the measurement of the growth of cosmic
structure using weak gravitational lensing, require exquisite control of
instrument-related distortions of the images of astronomical objects. Roman
will fly 4kx4k Teledyne H4RG-10 infrared detector arrays. This paper
investigates whether the pixel centroids are located on a regular grid by
projecting laser speckle patterns through a double slit aperture onto a
non-flight detector array. We develop a method to reconstruct the pixel
centroid offsets from the stochastic speckle pattern. Due to the orientation of
the test setup, only x-offsets are measured here. We test the method both on
simulations, and by injecting artificial offsets into the real images. We use
cross-correlations of the reconstructions from different speckle realizations
to determine how much of the variance in the pixel offset maps is signal (fixed
to the detector) and how much is noise. After performing this reconstruction on
64x64 pixel patches, and fitting out the best-fit linear mapping from pixel
index to position, we find that there are residual centroid offsets in the x
(column) direction from a regular grid of 0.0107 pixels RMS (excluding shifts
of an entire row relative to another, which our speckle patterns cannot
constrain). This decreases to 0.0097 pix RMS if we consider residuals from a
quadratic rather than linear mapping. These RMS offsets include both the
physical pixel offsets, as well as any apparent offsets due to cross-talk and
remaining systematic errors in the reconstruction. We comment on the advantages
and disadvantages of speckle scene measurements as a tool for characterizing
the pixel-level behavior in astronomical detectors.
