  For segmented telescopes, achieving fine co-focus adjustment is essential for
realizing co-phase adjustment and maintenance, which involves adjusting the
millimeter-scale piston between segments to fall within the capture range of
the co-phase detection system. CGST proposes using a SHWFS for piston detection
during the co-focus adjustment stage. However, the residual piston after
adjustment exceeds the capture range of the broadband PSF phasing
algorithm$(\pm 30 \mu m) $, and the multi-wavelength PSF algorithm requires
even higher precision in co-focus adjustment. To improve the co-focus
adjustment accuracy of CGST, a fine co-focus adjustment based on
cross-calibration is proposed. This method utilizes a high-precision detector
to calibrate and fit the measurements from the SHWFS, thereby reducing the
impact of atmospheric turbulence and systematic errors on piston measurement
accuracy during co-focus adjustment. Simulation results using CGST demonstrate
that the proposed method significantly enhances adjustment accuracy compared to
the SHWFS detection method. Additionally, the residual piston after fine
co-focus adjustment using this method falls within the capture range of the
multi-wavelength PSF algorithm. To verify the feasibility of this method,
experiments were conducted on an 800mm ring segmented mirror system,
successfully achieving fine co-focus adjustment where the remaining piston of
all segments fell within $\pm 15 \mu m$.
