Phase contrast microscopy works by exploiting the phase difference between two paths of light which pass through a probe point of a specimen:
One path, the "background" path, is the path the light through the slide would take without a specimen being present.
The second one, the diffracted light path, is scattered into a much wider cone because it encounters the sample and is subject to a small dephasing due to the higher refractive index of the probe point of the sample.
In order for the small phase difference between the two paths to interfere as destructively as possible, the background-path light is channeled through a piece of glass that phase shifts it by -90°, and also dims it so that it doesn't outshine the diffracted light. The diffracted light is scattered so wide that it doesn't pass through this phase shifting device.
The two light paths are then brought together again through refocussing in the image plane, as in classical microsopy. There they interfere destructively, giving a nice black on white image of the specimen.
My question is the following:
Why isn't the background light subject to exactly the same small phase shift due to the specimen as the diffracted light, given that both light paths impact the sample on the exact same spot?
It seems like there is a superposition between "light interacts with specimen" and "light does not interact with specimen", giving rise to the two light paths. However, the specimen point is sized around a micrometer, much too large for this quantum stuff to be relevant.
What am I missing?