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Theory of bokeh image structure in camera lenses with an aspheric surface

机译：非球面相机镜头的散景图像结构理论

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摘要

We present theoretical, numerical, and experimental analysis of the cause of internal structure in out-of-focus images of point light sources seen in shots taken with camera lenses that incorporate aspheric surfaces. This "bokeh" structure is found to be due to diffraction on the phase grating at the lens exit pupil induced by small-scale undulations (ripples) of aspheric surfaces. We develop a phase-to-intensity transfer function approach which leads to a simple formula for estimating the intensity modulation ratio in the resulting bokeh based on the out-of-focus distance, amplitude, and frequency of surface undulations. Numerical simulations of bokeh image formation are carried out for a parabolic mirror imager and a double Gauss objective. We find that modulation depth in the bokeh structure calculated by light propagation based simulation agrees with theory when the modulation depth is ＜30%. Bokeh images are shown to be more sensitive to manufacturing artifacts of an aspheric surface than corresponding degradation in the lens modulation transfer function for a sharp focused image. We apply the transfer function approach to the calculation of the bokeh produced by a measured aspheric surface in a built camera lens and find reasonable agreement between the calculated and measured bokeh structure.
机译：我们提供了对点光源散焦图像中内部结构起因的理论，数值和实验分析，这些点光源是在包含非球面表面的相机镜头拍摄的照片中看到的。发现这种“散景”结构是由于非球面表面的小尺寸起伏（波纹）在透镜出射光瞳处的相位光栅上引起的衍射所致。我们开发了一种相位到强度的传递函数方法，该方法可得出一个简单的公式，用于基于离焦距离，幅度和表面起伏频率估算最终散景中的强度调制比。对抛物线反射镜成像器和双高斯物镜进行了散景图像形成的数值模拟。我们发现，当调制深度＜30％时，通过基于光传播的模拟计算出的散景结构中的调制深度与理论吻合。散景图像对于非球面表面的制造伪影显示得比对清晰聚焦图像的镜头调制传递函数的相应退化更敏感。我们将传递函数方法应用于由内置摄像机镜头中的非球面测量产生的散景的计算，并在计算和测量的散景结构之间找到合理的一致性。

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