That's what's been done so far [0], both on the ground and in space. As I understand it, the further your disk is from your telescope, the better. But your stick needs to be rigid enough to keep the disk exactly in its place. And a rigid stick has weight.
For Proba-3 the goal is to have the two satellites more than 100m apart. If you want to do that with a stick, your stick has to be longer than the ISS. That should tell you a thing or two about the complexity and cost of building and launching that stick.
I do have to admit I'm not exactly sure what the advantages are of having the disk further away from the telescope. I suspect it's to do with the interaction between the light and the edge of the disk, but I'm not sure.
The even more extreme version of this JPL has been working on with their Starshade program. Not specifically a cornograph, but same concept of blocking light from a star to look for something more dim, in this case its looking for exoplanets. But it is a much larger scale. A 25 m deployable shade in formation 100 km away with the same level of mm precision.
Edit: Just to be clear on status of this, Starshade is still in early technology demonstration phase that they can actually build the shade and do the formation maintenance. This is not in full build or slated to launch any time soon.
Huh, very interesting- and counterintuitive that distance matters. If anyone here knows why I’d love to learn more!!
EDIT: maybe not so counterintuitive after all: if you scale everything up, you get a higher fidelity sensor and more signal to noise. Same reason telescopes want to be big: to collect more light especially from dim signals. Distance of the occulter then reduces perspective distortion that would eclipse the inner parts of the sensor more than the outer ones. Just my speculation though.
I'm speculating past my understanding here, but wouldn't some sort of diffractive effect around the edge of the disk explain it? Like the further you are into the far field of that diffraction the better or such?
For Proba-3 the goal is to have the two satellites more than 100m apart. If you want to do that with a stick, your stick has to be longer than the ISS. That should tell you a thing or two about the complexity and cost of building and launching that stick.
I do have to admit I'm not exactly sure what the advantages are of having the disk further away from the telescope. I suspect it's to do with the interaction between the light and the edge of the disk, but I'm not sure.
[0] https://en.wikipedia.org/wiki/Coronagraph