2 layers of birefringent crystal, how many rays?

[Lensmonkey]

I am trying to solve a problem my camera exhibits. It has a sensor with 6000x3376 pixels. HD video is 1920x1080. In order to reduce the amount of information to the processor the camera throws away 2 out of 3 pixel lines.

this creates a problem with thin lines tike telephone lines and makes them jagged.

I thought a good idea might be to place behind the lens a plate of Lithium Niobate or some such birefringent crystal to take rays that would normally terminate in the unrecorded pixel lines and displace them vertically to the recorded line. They would combine and blur a little but alleviate the aliasing problem seen here:

It is my understanding that the "ordinary" ray that enters the crystal exits as parallel ordinary and extraordinary rays. One dot becomes two dots. As I understand it each of these rays are linearly polarized orthogonal to each other. If those rays then travel through another crystal, what is the effect on each of these rays?

 

[Lensmonkey]

I understand that a ray of light entering a birefringent crystal becomes polarized into 2 perpendicular linearly polarized light rays that emerge parallel and displaced by a distance. If the 2 rays then pass through a second crystal with the same orientation, say for example the first crystals displace +5 microns vertically and the second +10 microns vertically, how many rays will emerge? Will the ordinary or extraordinary be blocked by the second crystal because of its polarization, if so which one?

 

[mfb]

You can see what the whole setup does for one polarization axis of incoming light and for the other separately.

If the orientation is the same the birefringence of the second crystal does nothing special, it just increases the separation.

Edit: I merged your two threads. I don't think splitting polarizations like that is a good solution. You just blur the image (and the details will depend on the polarization of incoming light), something software can do if necessary.

 

[Lensmonkey]

Thank you for taking the time to answer. I do not follow what you say here:
"You can see what the whole setup does for one polarization axis of incoming light and for the other separately."
could you expand please?
In the question I posit 2 stacked crystals with the same orientation. You have told me that it just increases separation, but please be more specific as far as the number of rays produced. Stated differently (and not very technically!) the image of a dot passes through the crystal and becomes two separate dots displaced by the crystal's properties. Will each of the dots be reproduced and doubled again if they pass through another similarly oriented crystal? Will polarization extinct (hah not a verb?) any of the rays/dots?

As far as methodology for this particular problem, software cannot re-create the missing information that was never recorded by the "dead" pixel lines, only further blur what's left. That's worse, I have tried it, it lead me here! To combat aliasing and moire for still images, pretty much all cameras today use exactly this tactic, called an optical low pass filter or anti aliasing filter. They use a stack of LiNbO3, 1/4 wave, LiNbO3. The LiNbO3 plates are at 90 degrees, with the 1/4 wave in the middle to make the linearly polarized rays from the 1st plate circular so the second LiNbO3 can create 2 more "dots." The end result is 1 dot becomes a square of 4, at a distance (varies by camera and manufacturer) of 1 pixel. What I don't understand yet is if I have to have the 1/4 wave plate if I only want to displace in one direction. I believe one crystal that would displace a ray the distance from the center of the missing two lines would do, but I want to at least try two displacements one from the middle of each missing line only in the vertical direction. And I would like to understand what the effect will be to the stack that is in front of the sensor already (the optical low pass filter). Please educate me if you can!