  Recent confocal experiments on colloidal solids motivate a fuller study of
the projection of three-dimensional fluctuations onto a two-dimensional
confocal slice. We show that the effective theory of a projected crystal
displays several exceptional features, such as non-standard exponents in the
dispersion relations. We provide analytic expressions for the effective
two-dimensional elastic properties which allow one to work back from sliced
experimental observations to three-dimensional elastic constants.
