Double slits experiment: how does the which-way entropy vary with the distance between slits and screen?

When the screen is just behind the slits we have perfect which way information. The entropy is log 2. It decreases if I place the screen in the Fresnel region (not to far). It decreases much more in the Fraunhofer region (great fresnel number) and information tends to zero when the distance L tends to infinity. I would like to know the forumula giving the which way entropy h(L,a,b,lambda)
where a is the width of the slit, b their distance, lambda the wave length of the particles (all are fixed parameters) and L the distance that varies in the different devices.
Is it correct to say that when in the device the screen is far from the slits, the particle is in a pure state and near them we have a mixture?
Thanks