We explore the use of first and second order same-time atomic spatial corre
lation functions as a diagnostic for probing the small scale spatial struct
ure of atomic samples trapped in optical lattices. Assuming an ensemble of
equivalent atoms, properties of the local wave function at a given lattice
site can be measured using same-position first-order correlations. Statisti
cs of atomic distributions over the lattice can be measured via two-point c
orrelations, generally requiring the averaging of multiple realizations of
statistically similar but distinct realizations in order to obtain sufficie
nt signal to noise. Whereas two-point first order correlations are fragile
due to phase fluctuations from shot-to-shot in the ensemble, second order c
orrelations are robust. We perform numerical simulations to demonstrate the
se diagnostic tools. (C) 1999 Optical Society of America.