Turbulence simulation for anisoplanatic imaging based on phase screens with experimental validation of differential tilt variances

Air turbulence can be a major impairment source for long-range imaging applications. There is great interest in the assessment of turbulence mitigation techniques based on machine learning models. In general such models require lots of image data for robust training and validation. Experimental acquisition of image data in field trials is time-consuming and environmental conditions such as daytime and weather cannot be specifically controlled. This image data also depends on specifications of the used devices, i.e. the camera and objective, hence also assessment is limited to these specifications. The latter cons are not present in the case of image-based turbulence simulation. Several methods for turbulence simulation have been proposed in recent years. Many of these are based on phase screens or models turbulent point spread functions (PSFs). Often simple turbulence models such as the Kolmogorov or Von Karman spectrum are used. Therefore these methods cannot provide insight in the influence and relevance of other turbulence parameters such as inner scale and (non-)Kolmogorov power slope. In this work a data fitting procedure for the determination of turbulence model parameters based on experimental data is shown. Hereby the Generalized modified Von Karman spectrum (GMVKS) is used. This spectrum takes into account inner scale and outer scale effects as well as a non-Kolmogorov power slope. Differential tilt variances are calculated from centroid displacements in video sequences of a recorded LED grid. Then the experimental data is fitted to theoretical expressions of DTV by numerical integration over the turbulence model. DTV represents correlation between spatially separated point sources. Image data was acquired in field trials on several days at the same location. Then a beam propagation method using Markov GMVKS phase screens with determined model parameters is used to generate a grid of PSF images which represent degradation for different viewing angles. Anisoplanatic imaging is achieved by spatial shifts of phase screens depending on viewing angle. These grids of PSFs can be overlayed on images of arbitrary input scenes. By interpolation of adjacent PSFs filter kernels can be calculated pixelwise. These kernels can be used for non-uniform filtering to provide anisoplanatically degraded images. For validation, DTVs based on centroid displacements of the simulated PSFs are calculated and compared with the corresponding measured data of LED centroid displacements and theoretical data. Consistency between theory and simulation is demonstrated in terms of PSF shape features such as longexposure MTF, short-exposure MTF and Strehl ratio. Temporal correlation between frames in a stack of PSF grids can be achieved by 2D random walks of phase screens. This procedure preserves the spatial correlation of PSFs, as the spatial statistics of phase screens remain unchanged. Cumulative distribution functions of the model parameters for all recording dates are provided to show the diversity of turbulence conditions. These can be used as prior knowledge for future turbulence simulations to include various model parameters and hence different conditions of image degradation.