## 1 Introduction
The findings revealed that this type of polarization chromatic aberration encompasses out-of-focus aberration and a small amount of spherical aberration, with the out-of-focus aberration potentially reaching up to 1.14 rad [12]. Further contributing to the understanding of wavefront variances, [PERSON] derived a formula for the overall undulation variance in the wavefront for beams of different wavelengths, highlighting differences in wavefront variance under identical transmission conditions [13]. Finally, in 2023, [PERSON] discussed the wavefront distortion differences among beams induced by wavelength disparities in weak turbulence regions [14]. In general, wavefront aberration disparities in beams across weak turbulence, moderate turbulence, and strong turbulence regions are well-documented, albeit with less emphasis on the intricacies of the strong turbulence domain. Moreover, the challenge of effectively addressing aberration differences among beams of varying wavelengths in the strong turbulence region remains largely unresolved. In this article, we meticulously analyze the variances in wavefront phase aberrations within the received cross-section subsequent to the transmission of signal and beacon lights of disparate wavelengths through the strong turbulence region. Additionally, we propose a corrective coefficient method employing wavefront-free correction. This method relies on the relationships of Zernike polynomial coefficients corresponding to beams of different wavelengths. Ultimately, the efficacy of our proposed method is validated through simulation and experimentation. Differential Analysis of Beam Wavefront Aberrations at Different Wavelengths in Regions of Strong Turbulence  
Signal light with wavelength and beacon light with wavelength are Gaussian beams, which, after long-distance transmission through the atmospheric channel, arrive at the surface of the receiving antenna. This process can be approximated as plane wave incidence. In the region of strong turbulence, the phase of the beam is torn into a discontinuous scattering distribution across the receiving cross-section. According to the Markov approximation, the following holds [15]. \[\langle n(R_{1})n(R_{2})\rangle=B_{n}(R_{1}-R_{2})=\delta(z)A(r_{1}-r_{2}) \tag{1}\]  
where \(n(\cdot)\) denotes the refractive index of the air at a point on the cross-section of the transmission path, \(R_{1}\) and \(R_{2}\) represent any position vector on the transmission path cross-section, respectively, and \(B_{n}\) denotes the correlation function between different points. Furthermore, \(A(r_{1}-r_{2})\) denotes the proportionality coefficient, where \(r_{1}\) and \(r_{2}\) represent the position vector on the receiving cross section, and its value in the strong turbulence region is tentatively set to 1 to guarantee uniform homogeneity. \(\delta(z)\) is the shock response function that describes the response function to the effect of the turbulent phase, where z represents the transmission distance along the propagation path. The wavefront phase functions of the signal beam and the beacon beam at the receiving end can be approximated as response functions with phases modulated by turbulence. These can be expressed as follows [15]:  
\[\phi_{\lambda_{1}}=k_{1}\int_{0}^{L}\delta_{n}(\overrightarrow{r},z)dz \tag{2}\]  
\[\phi_{\lambda_{2}}=k_{2}\int_{0}^{L}\delta_{n}(\overrightarrow{r},z)dz \tag{3}\]  
where \(\phi_{\lambda_{1}}\) and \(\phi_{\lambda_{2}}\) denoted the wavefront phase functions for wavelengths \(\lambda_{1}\) and \(\lambda_{2}\), respectively. \(L\) denotes the length of the transmission link, and \(\mathbf{r}\) denotes the position vector in the receiver cross-section. Furthermore, \(\delta_{n}(\overrightarrow{r},z)\) denotes the shock response function; \(k_{1}\) and \(k_{2}\) denote the wave numbers corresponding to wavelengths \(\lambda_{1}\) and \(\lambda_{2}\), respectively.