# Transition from Coherent to Incoherent Light / Partially coherent Light for Imaging

I want to know how to model partially coherent/incoherent light for imaging applications. Usually, you find mathematical treatments of imaging just for the extreme cases. For the coherent light, there is a mixing term when two light intensities $$I_1$$ and $$I_2$$ meet (interference):

$$I_{tot} = I_1 + I_2 + \sqrt{I_1I_2} \cos(\theta)$$

with some angle $$\theta$$. In the incoherent case, the mixing term is just missing: $$I_{tot} = I_1 + I_2$$.

However, in reality there is no perfect coherent or incoherent light. How to treat this case? I assume that the mixing term is multiplied with a factor to reduce it dependent on the "degree of coherence".

How to treat imaging theory with partially coherent light? The modulation transfer function (MTF) for incoherent light continuously goes down for larger line pairs/mm, but for incoherent light the MTF (or better amplitude transfer function ATF) stays constant and drops to zero at half the cut-off frequency for incoherent light (see https://www.telescope-optics.net/mtf2.htm)