Static Zernike phase-contrast plates have been used extensively in microscopy for half a century and, more recently, in optical telescopes for wavefront sensing. A dynamic Zernike wavefront sensor (WFS) with four phase shifts, for reducing error due to spurious light and eliminating other asynchronous noise, has been proposed for use in adaptive optics. Here, we propose adapting this method for co-phasing the primary mirror of a segmented space telescope. In order to extend the dynamic range of the WFS, which has a maximum range of +/ − λ/2, a phase- contrast plate with multiple steps, both positive and negative, has been developed such that errors as large as +/ − 10λ can be sensed. The manufacturing tolerances have been incorporated into simulations, which demonstrate that performance impacts are minimal. We show that the addition of this small optical plate along with a high precision linear translation stage at the prime focus of a telescope and pupil viewing capability can provide extremely accurate segment phasing with a simple white-light fringe fitting algorithm and a closed-loop controller. The original focal-plane geometry of a centro-symmetric phase shifting element is replaced with a much less constrained shape, such as a slot. Also, a dedicated pupil imager is not strictly required; an existing pupil sampler such as a Shack-Hartmann (SH) WFS can be used just as effectively, allowing simultaneous detection of wavefront errors using both intensity and spot positions on the SH-WFS. This could lead to an efficient synergy between Zernike and SH-WFS, enabling segment phasing in conjunction with high-dynamic range sensing.