It is often desirable to measure an optical component whose aperture exceeds the capacity of the measurement device. However, stitching of sub-aperture measurement data into a single measurement of an optical component is a challenging problem since mechanical motions of the test component relative to the reference surface of an interferometer can not be made with interferometric accuracy. Even more challenging than the need to compensate for rigid body motion between the sub-aperture measurements is the need to account for imperfections in the reference surface itself. In this paper we show, both in simulation and experimentally, how the use of a time-delayed source (TDS) simplifies the stitching of transmitted wavefront measurements from domes and windows. This is accomplished by making it possible to obtain phase-shifted interferometric measurements using only the light reflected by two surfaces from a dome or window without the use of a reference surface.