Detecting gradual dust build up using an optical emitter and detector?

I have a machine that has a slide-in screen meant to collect dust, but I do not have visible access to that screen unless I pull it out.

I am looking to develop a small embedded system that can detect and notify the user when the screen is starting to be covered, or completely blocked with the dust.

I was thinking about using an optical emitter and detector combination which detected the amount of light that would be transmitted through the screen. And upon a certain threshold of light not meeting the detector, then I would like some notification (could just be an LED) to light up.

Can anyone recommend a method for this type of threshold detection, where it isn't just a binary output of proximity or not; but rather, some more continuous value which, once a threshold is hit, notifies me when the screen is completely covered?

You don't say how big a screen, or how homogeneous the dust layer is-could dust gather more in one area than another? Another thing to consider: your sensor/emitter will ALSO collect dust. Do they collect dust faster than the screen, or perhaps more sensitive?

Regardless, there are certainly analog output sensors available, from something cheap like a photo-transistor, to expensive (hundreds of dollars) modules. You need to figure out how sensitive and accurate this needs to be; what your environment is, etc.