Near-null subaperture layout design is similar to the null case where the subaperture departure is not considered. What we need to do is arrange the subapertures according to the overlapping ratio and selection of TF or TS incorporated with near-null optics. But, especially for the near-null subaperture test, we should further determine the counter-rotating angle of the CGH pair in order to compensate as much aberration as possible. Therefore, given a test asphere, it is critical to calculate coefficients P4; and P6i of Zernike terms Z4 and Z6, respectively, for singlepass wavefront aberrations of different subapertures. Then we can solve Eq. (19) to obtain the counter-rotating angle a_{i} for each ring of subapertures. Note that the phase function of two CGHs is already determined.

The subaperture aberration coefficients P41 and P® can be estimated by Eq. (7) for conic surfaces. For general surfaces, we can also make use of ray tracing with lens design software, e.g., Zemax. The two CGHs are modeled as a Zernike standard phase or a Zernike fringe phase. We first set the diffraction order to be zero and then check the Zernike fringe coefficients. As expected, the coefficients of Zernike terms Z4 and Z6 are dominant and can be used to calculate the counterrotating angle a according to Eq. (19). We then set this angle as an initial guess and change the diffraction order to be +1. The default merit function of the root-mean-square (RMS) wavefront centroid is used to finally determine the optimal counter-rotating angle and the axial distance of the test asphere from the CGHs. With the lens design software, the wavefront error can also be checked to be within the dynamic range of measurement.

Figure 16 Subaperture stitching is like playing with jigsaw puzzle pieces in 3-D space.