Zernike polynomials distribution measurement in atmospheric turbulence conditions for adaptive optics efficiency performance: lab and field condition comparison

Measuring the distribution of Zernike polynomials across the atmospheric turbulence spectrum is fundamental to understanding and compensating for optical aberrations introduced by Earth's atmosphere. While raw wavefront slope data from sensors like Shack-Hartmann provides a snapshot of distortion, decomposing this phase map into an orthogonal set of Zernike modes offers deep physical insight into the nature of the turbulence itself. The primary importance lies in modal filtering and system optimization. Atmospheric turbulence follows specific statistical laws, most notably Kolmogorov theory, which dictates how variance distributes among different spatial frequencies. In terms of Zernike modes, this energy is not uniform; low-order terms such as tilt (Z1, Z2), defocus (Z3), and astigmatism (Z4, Z5) typically contain the vast majority of the total wavefront error power. IIn lab experiment a laser diode coupled to an optical fiber was used as a radiation source. A collimating lens diverged the diverging laser beam into a parallel beam with a diameter of 50 mm. The laser beam then struck a flat mirror and was directed to the WFS. A telescope with a magnification of 12x was used to match the laser beam diameter (50 mm) to the WFS entrance pupil (4.8 mm). This reduced the beam size to 4.2 mm and completely fit within the receiving matrix of the wavefront sensor (WFS). Artificial turbulence on the optical stand was created using a fan heater, the flow generated by which corresponded to the atmospheric turbulence of the Kolmogorov spectrum. For field condition experiment the optical trace of 250 m over horizontal path was investigated. . The paper presents the Zernike polynomials spectrum estimation in real optical traces close to urban conditions (refractive index structure constant Cn2 - 10-14 m-2/3). The comparison was performed with lab experiment where fan heater was used as atmospheric turbulence simulator