In the typical analysis of aero-optical wave-front data, the three lowest-order spatial modes (namely, unsteady piston as well as and tilts) are removed from the experimentally measured wave fronts. These modes are commonly corrupted by mechanical disturbances. In this work, an algorithm called the stitching method was developed that takes advantage of the advective nature of the optical aberrations caused by turbulent structures to recover the unsteady global X-tilt and piston modes from experimental time-resolved wave fronts. One-dimensional modeling and related uncertainty analysis showed that for the wave fronts collected with sufficient sampling frequency, the algorithm is able to correctly recover the aero-optical component of the unsteady X tilt. In this manner, the time series of true wave fronts can be recovered. To further validate the stitching method, spatiotemporal wave-front measurements were conducted on a Mach 0.6/0.1 forced shear layer. The predicted results for the rms of the aero-optical X tilt from the stitching method agree well with the modeled results. Since the stitching method recovers the time series of the aero-optical global X tilt, the global tilt spectra were also computed and presented. This information can be used by system designers to specify the requirements for adaptive-optics system components, such as fast steering mirrors in airborne directed energy systems.