The measurement methods of aspheric surface have been developed maturely in the basis of different principles, e.g., geometrical optics, interferometry and profile measurement, which are listed in Table 1. For specular aspheric surface, these methods are quite suitable. Nevertheless, for a rough (i.e., non-specular) surface, the methods of using laser interferometry cannot make function well. One candidate is infrared interferometer [
9]. However, it is 1) expensive due to its precious infrared devices; 2) low sensitivity because of the longer laser wavelength (e.g., 10.6 μm for CO
2 laser); 3) still dependent on null compensators for measuring aspherics. Commercialized coordinate measurement machine (CMM) is also an alternative. Form Talysurf PGI 1240 (Taylor Hobson) is commonly used for measuring surface profile, but its gauge range (~12.5 mm) and traverse range (~200 mm) are not enough for large aspherics (e.g., meter-scale). The multi-probe bar profilometer developed by Itek [
10] utilizes a high precision sphere and multi-linear variable differential transformer (multi-LVDT) sensors for comparison measurement, which has accuracy of 0.15 μm RMS (root mean square). However, it needs a high precision reference sphere, which is costly and complex. Comley et al. [
11] and Gray et al. [
12] reported the profile data of European Extremely Large Telescope (E-ELT) segments (1.4 m size) measured by an off-machine Leitz CMM. Su et al. [
13,
14] investigated a swing arm profilometer for
in situ measurement of aspherics. The machine adopts sphere coordinate and can be calibrated by dual probe, which achieves the sub-micron accuracy. Jing et al. [
15,
16] also reported a swing arm profilometer. They employed a model to raise accuracy to 0.2 μm. Researchers also have developed on-machine measurements for increasing fabrication efficiency [
17].