The above file was set up to observe the raw wavefront resulting from the Zernike Fringe Phase surface (Afocal Mode, Reference OPD as 'Absolute 2' -- see the Help File page at 'The Setup Tab > System Group (the Setup Tab) > System Explorer > Advanced Options (System Explorer) > Reference OPD' for more discussion on this setting).

The thing to keep in mind is that the Zernike Fringe/Standard Coefficient analysis is a fit performed on the resulting wavefront error. So, in this setup, the analysis is fitting our designated range of Zernike coefficients to the raw wavefront created by this surface. In addition, this fit is not necessarily a 'closed-form' solution. In reality, Z1, being a piston term, could be any number of values, and it wouldn't affect the overall shape of the raw wavefront.

Since it simply offsets the base phase by the piston term, the resulting fit is unchanged. Rather, you can associate the generated piston term with the constant term in the Z4 (Defocus) equation. We defined three waves of Z4, meaning the Z4 computation for any radial point on the surface is:

          Z4 = 3 waves * (2*ρ^2 - 1)

When ρ is zero, we are left with -3, which is what Z1 reports. Again, since this tool is performing a best fit on some data, it cannot know if there was some constant phase defined on the surface itself -- it only generates Zernike terms based on the system's wavefront error.

Still, you can always monitor your system with tools like the Surface Phase analysis to see what the surface itself is imparting (in this case, with a Z1 term of zero, we can again see that the resulting phase shift at the center of the surface will be -3 waves due to the construction of the Z4 expression):

You can also use operands like OPTH to monitor the accumulated optical path length of specific rays traveling through your system.