Stitching error calculation method for the slope data on a square subaperture

The data on subaperture in this paper is collected by a Hartmann test device or a Hartmann–Shack wavefront sensor. The slope data on each subaperture of the test optical component is obtained via the linear least squares fitting routine in this paper. Importantly, the error transfer formulas are deduced when the measurement data are polluted by the random noise, which will affect the uncertainty of stitching parameters, such as tilt or defocus. In particular, the accuracy formulas for stitching evaluation, which can be used to calculate the stitching error of each point on each subaperture for both the parallel mode and the serial mode, are derived mathematically. Therefore, this paper provides these formulas to estimate exactly the stitching error in each subaperture if the variance of random noise has been estimated and if the overlapping area is also given in advance. The results of simulation experiments show that the stitching accuracy formulas proposed are verified and they can be used to evaluate stitching accuracy. The reason why the error of the parallel stitching mode is less than that of the serial stitching mode is presented theoretically.