# Sixty-Nine-Element Voice Coil Deformable Mirror for Visible Light Communication
###### Abstract  
To overcome the atmospheric turbulence aberration, and improve the quality of light beam in visible light communication (VLC), a compact 69-element deformable mirror (DM) using micro voice coil actuators was designed based on systematic theoretical analysis. The structural parameters of the micro voice coil actuator were optimized by electromagnetic theory and the finite element method. The DM was optimized from the aspects of thermal deformation, response time, coupling coefficient, and other parameters. Finally, wavefront fitting and residual calculation were completed according to the influence function. The optimized voice coil deformable mirror (VCDM) has a large phase stroke, good thermal stability, a short response time of less than 0.7 ms, and a large first resonance of 2045 Hz. The fitting residuals of the VCDM for the first 10 Zernike modes with a PV value of 8 \(\upmu\)m are all below 10 nm (RMS). Compared with a similar DM, the obtained results from our compact VCDM indicate that it has a higher wavefront fitting precision. VCDM corrected complex random aberrations in the VLC scenario and improved the coupling efficiency of the signal beam, proving that the compact VCDM with high performance and low cost has a good application prospect in VLC systems. visible light communication; phase modulation; deformable mirror; voice coil actuator +
Footnote †: journal: _photonics_  
0000-0002-0001-5000-0002-0000][PERSON]  
0000-0002-0002-0002-0002-0002-0002-0002-000 piezoelectric (PZT) DM. For a compact VCDM, a relatively small coupling coefficient is valuable to obtain a high wavefront correction precision. In addition, it should be noted that it is expensive using custom-developed VCDM with complex structures for astronomical observations. In applications, such as retinal imaging, biological microscope, and optical communication, a compact and relatively inexpensive DM with high electro-optical performance is necessary. Different kinds of DMs have been investigated, such as PZT DM [7], magnetic fluid DM [8], electrostatic DM [9], micro-electro-mechanical system (MEMS) DM [10; 11], and voice coil DM (VCDM) [12; 13]. Furthermore, several DMs specially used for laser communication have been investigated. [PERSON] proposed a CVD SiC DM with monolithic cooling channels. The faceplate is 200 mm in diameter and 3 mm in thickness, and it is actuated by 137 stack-type PZT transducers arranged in a square grid [14]. [PERSON] developed a Water-cooled stacked-actuator flexible mirror for high-power laser beam correction. The deformable mirror has a diameter of 120 mm and 121 piezo actuators in a hexagonal arrangement [15]. Compared to PZT DMs, VCDMs have the merits of low driving voltage and linear response. However, standard VCDMs have two obvious drawbacks: (1) large coil diameter with a high cost that cannot be used in a compact VCDM, (2) high coupling coefficient that is difficult to correct high-order aberrations. In the paper, an alternative compact VCDM is presented by deriving theoretical equations that could guide a reasonable design. The designed micro voice coil actuator (VCA) has a small diameter of about 2 mm, only about a tenth of a standard one, which allows a compact VCDM with a high density of actuators. To decrease its coupling coefficient and power dissipation and improve its electro-optical performances, the VCDM's structure is simplified and optimized based on analyzing factors that affect its electro-optical performances, such as resonant frequency, power dissipation, coupling coefficient, response time, and so on. In fact, these parameters are influenced by the interactions among multi-physical fields, such as electromagnetic, thermal, stress, and strain fields. For example, increasing the current in a voice coil can produce a large electromagnetic force and increase its phase stroke. However, it can also lead to a large thermal dissipation, and even distort VCDM's thin mirror.