基于湍流中调制传递函数的数学模型,从理论上研究了大气相干长度和系统光瞳直径对积分分辨率和像斑半径的影响.采用内插值法,分别给出长曝光和短曝光条件下分辨率和像斑半径的近似代数解.结果表明,在系统光瞳直径小于大气相干长度时,分辨率主要受光瞳直径限制,增大光瞳直径可提高分辨率,然而随着其值的继续增大,对分辨率的改善不再明显,因为当光瞳直径大于大气相干长度时成像性能逐渐由湍流限制.光瞳直径与大气相干长度的比值趋于无穷大时,分辨率和像斑半径受大气相干长度的限制有一个极限值.短曝光条件下,去除了大尺度漩涡所产生的倾斜效应,系统的积分分辨率和像斑半径性能要好于长曝光条件.对于短曝光近场,与长曝光相比,其积分分辨率的最大值提高了3.5倍,像斑半径最小值减小了1/2.

Based on the mathematical model of modulation transfer function in atmospheric turbulence,the combined effect of atmospheric coherence length and optical pupil diameter on integral resolution and spot radius were investigated.Approximate algebraic solutions of resolutions and spot radii are derived for long-term exposure and short-term exposure by use of interpolation method.The result shows that the resolution is mainly limited by the pupil diameter while the pupil diameter is smaller than atmospheric coherence length,and can be enhanced by increasing the value of the pupil diameter.However,the resolution will not be significantly improved with further increase of the pupil diameter,since the imaging performance is gradually limited by turbulence while the pupil diameter is larger than atmospheric coherence length.There are limiting values for the resolution and spot radius restricted by atmospheric coherence length while the ratio of the diameter to atmospheric coherence length tends to infinite.For short-term exposure,since the tilt effect due to large-scale eddies is eliminated,the integral resolution and the spot radius are better than that of long-term exposure.Especially,for the near field of short-term exposure,the maximum value of integral resolution is approximately increased by a factor of 3.5 and the minimum value of spot radius is approximately decreased by a factor of 1/2,as compared with the case of long-term exposure.