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

Abstract

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.