  By a novel reciprocal space analysis of the measurement, we report a
calibrated in situ observation of the bunching effect in a 3D ultracold gas.
The calibrated measurement with no free parameters confirms the role of the
exchange symmetry and the Hanbury Brown-Twiss effect in the bunching. Also, the
enhanced fluctuations of the bunching effect give a quantitative measure of the
increased isothermal compressibility. We use 2D images to probe the 3D gas,
using the same principle by which computerized tomography reconstructs a 3D
image of a body. The powerful reciprocal space technique presented is
applicable to systems with one, two, or three dimensions.
