Differential tilts between square apertures

An expression is derived and studied that relates optical turbulence strength to the variance of the tilt difference between square apertures. This expression additionally depends upon the separation between the apertures and the direction in which tilts are measured. When a sensor, such as a Hartmann sensor, uses a lenslet array with square subapertures, the expression derived here is appropriate for computing the turbulence strength from the measured tilts. The expression derived here and the published expression for the equivalent circular aperture case are compared. Approximate expressions for this differential tilt variance are also derived.