# Eigenmode Wavefront Decoupling Algorithm for LC-DM Adaptive Optics Systems
## 4 Results
### Experimental Setup  
The setup of the LC-DM cascade AO system was constructed in the laboratory for a 2 m telescope (Figure 6). The system mainly constitutes two parts, namely AO and imaging parts. The AO part mainly includes the TTM, DM, LC, and the WFS. The DM is a 145-unit continuous surface DM produced by ALPAO, with an aperture and a stroke of 30 mm and approximately 3 \(\upmu\)m, respectively. The LC is manufactured by Meadowlark optics Company, with the fast LC materials synthesized by us. The number of pixels is 256 \(\times\) 256, the response time is 0.65 ms, and the effective aperture is 6.14 mm. The WFS is an SH wavefront sensor manufactured by FIRST-LIGHT company. The camera frame rate is approximately 1.67 kHz, the pixel size is 24 \(\upmu\)m, and the number of microlenses is 20 \(\times\) 20. The receiving aperture is approximately 5.8 mm. The imaging part includes visible and infrared cameras. The visible camera is an iXon ultra 897 model camera produced by ANDOR, with a pixel size of 16 \(\upmu\)m, a number of pixels of 512 \(\times\) 512, and a spectral response range of 400-900 nm. The infrared camera is a Cheetah-640 CL short-wave infrared camera produced by the Xenics company, with a pixel size of 20 \(\upmu\)m, a number of pixels of 320 \(\times\) 256, and a spectral response range of 900-1700 nm.  
For AO correction in a wide band range, in the system, a xenon lamp with a wavelength of 400-1700 nm is selected as the light source. After collimating through lens L1, the beam becomes parallel with a clear aperture of 20 mm. Producing chromatic aberration during collimation is easy. Hence, the KF51 + TF3 + KF51 triplet is used to achieve the purpose of an achromat. After the light beam is reflected through the DM and TTM, it is split using a 950 nm high-pass dichroic. The light with the 950-1700 nm waveband passes through the dichroic and is focused using the focusing lens L2 onto the infrared camera for imaging. For the reflected 400-950 nm waveband, L3 and L4 are contracted, and then, the beam is split using a 700 nm high-pass dichroic. The light of 700-950 nm passes through the dichroic, and the 400-700 nm beam is reflected. The beam is expanded using a 4f system composed of L5 and L6.  
Subsequently, the beam is reflected through another 700 nm high-pass dichroic plate and enters the WFS for aberration measurements. The light with the 700-950 nm waveband that passes through the 700 nm high-pass dichroic plate is incident on the LC after being expanded through lenses L7 and L8, and the corrected beam passes through the 4f system composed of L8 and L9. After two reflections, this light is focused with focusing lens L10  
Figure 6: Optical layout of the LC–DM AO system.  
onto the visible camera for imaging. Table 1 presents the parameters of each lens of the system.  
In the system, the DM, LC, and WFS are all in the conjugate position. After the correction of the low-order aberrations of the whole band by using the DM, the infrared 950-1700 nm band can provide ideal imaging. Then, the residual error remaining after DM correction is passed to the LC for the secondary correction. At this time, low-order components in the residual error are eliminated, leaving only high-order aberrations in the 700-950 nm waveband. After the secondary correction through the LC, the AO correction and imaging of the 700-1700 nm wide band are realized.