Incoherent light imaging has been widely used in astronomical observation,industrial production,medical treatment and other fields.It is of great value to study the theory and application of incoherent light imaging.However,incoherent light imaging in atmospheric environment is inevitably affected by atmospheric turbulence,which leads to blur and distortion of the image,and degrades the quality of the image obtained.Blur is the high-order aberration caused by turbulence,which makes the light unable to effectively concentrate on one point to smooth the image,while distortion is caused by the nonlinear change of wavefront phase,which makes the image pixels move.The degradation of image in turbulent flow can be expressed as the superposition of the point spread function corresponding to multiple point sources,and the blur and distortion of the point spread function also reflect the degradation degree of the image.The blur and distortion caused by turbulence are important factors limiting the application of incoherent imaging.It is important to study the blur and distortion of point spread function caused by turbulence to alleviate the degradation of turbulent image.In the current methods of turbulence image degradation,many algorithms are based on the condition of isoplanatism,and the anisoplanatism of turbulence can not be ignored.At the same time,there is a lack of research and analysis on the blur and distortion of the point spread function under anisoplanatic conditions.In order to simulate the anisoplanatic effect,a turbulence imaging model is constructed based on the principle of ray propagation and phase screen superposition.The wavefront phase corresponding to the target point source can be calculated,and the point spread function corresponding to the target point source can be obtained by Fourier transform.The model can simulate the light emitted by different point sources through different turbulent paths to obtain the blur and distortion under anisoplanatic conditions.Since the scenario of horizontal imaging is relatively common,this scenario is chosen as the verification scenario,and the simulation model is verified by the modulation transfer function area and isoplanatic angle.The results show that the simulated value of the area of the modulation transfer function is consistent with the theoretical value,and the difference is small.If the number of statistics is increased,the error can be further reduced.The simulated value of the isoplanatic angle is consistent with the theoretical value,and the simulated value is slightly larger than the theoretical value.This is because the theoretical value is obtained based on the assumption that the pupil tends to infinity,and the pupil diameter is limited during simulation,so the simulated value is slightly larger than the simulated value.This means that the model can simulate the blur and distortion in anisoplanatic conditions well.In addition,we use the relationship between the average correlation coefficient and the isoplanatic angle to define the approximate invariant region of the image and give the trend of the region of the image approximate invariance with r0.The approximate invariant region of the image square is convenient to understand the variation degree of the point spread function and can provide a reference for setting hyperparameters in image restoration algorithms.The distribution of turbulence can also affect the blur and distortion of the point diffusion function.From the process of light propagation in turbulence,we speculate that the blur effect is mainly caused by the turbulence on the lens side,while the distortion effect is mainly caused by the turbulence on the object side.To verify this hypothesis,we designed two extreme turbulence scenarios:one in which turbulence is concentrated on the camera side,and the other in which turbulence is concentrated on the object side.The simulation results show that under the same conditions,when turbulence is concentrated on the lens side,the area of the modulation transfer function is smaller and the approximate invariant region of the image space is larger,while when turbulence is concentrated on the object side,the situation is opposite.This means that for the same turbulence strength,turbulence closer to the lens can produce more blur effects,and turbulence closer to the object can produce more distorting effects.Moreover,even if the weak turbulence is concentrated on the lens side,the blur effect on the image is much greater than that of the strong turbulence concentrated on the object side,while the distortion effect is the opposite.This proves that the blur of image degradation is mainly contributed by turbulence near the lens side,and the distortion of image degradation is mainly contributed by turbulence near the object side.Since the light is propagated from the object to the lens,this can explain the reason why the operation of tilt before blur is more reasonable than that of blur before tilt in the turbulent image degradation model.In ground-to-air imaging,turbulence is concentrated on the lens side,which means that the blurring effect is much more than the distortion effect,and the image restoration algorithm based on spatial invariance is very effective.However,in air-to-ground imaging,turbulence is concentrated on the object side,which means that blur has less impact on imaging,while distortion has more impact on imaging.In this case,the image restoration algorithm should consider how to reduce the impact of distortion.It also shows that in turbulent image restoration,a suitable restoration algorithm should be selected according to the degraded scene of the image to achieve better restoration effect.
Turbulence image degradationImage blurImage distortionModulation transfer function areaAverage correlation coefficient
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