Tilting mirror in Fourier plane

[KikiFleck]

Hello everyone,

I am working on a 4f optical system and would like to ask you a question. I have positioned a tilting mirror that allows movement in the X and Y directions in the Fourier plane of my microscope. Then, I form my image on the image plane, where it is captured by a camera. I would like to understand the physical justification and demonstration of why a translation in the Fourier plane also results in a translation in the image plane. I observe that my image shifts accordingly on the camera, I would like to justify it well.

Thanks

 

[Andy Resnick]

Hello everyone,

I am working on a 4f optical system and would like to ask you a question. I have positioned a tilting mirror that allows movement in the X and Y directions in the Fourier plane of my microscope. Then, I form my image on the image plane, where it is captured by a camera. I would like to understand the physical justification and demonstration of why a translation in the Fourier plane also results in a translation in the image plane. I observe that my image shifts accordingly on the camera, I would like to justify it well.

Thanks

This is a little confusing, because a shift in the Fourier plane equates to a phase in the image plane (or vice-versa). If I understand your setup, your mirror is not in any conjugate plane- not conjugate to any image plane or Fourier plane?

 

[KikiFleck]

My mirror is positioned in the Fourier plane, while my camera is in the image plane. I don't have the mathematical or physical justification showing that tilting the mirror by an angle causes a physical shift on my camera, resulting in the imaged object moving in the camera's field of view. Thanks for your answer

 

[Gleb1964]

I don't see a reason to have a mirror at the Fourier plane. The mirror surface is "invisible." Probably, it should be an object or source placed at the Fourier plane through the mirror reflection. Right?

 

[Andy Resnick]

My mirror is positioned in the Fourier plane, while my camera is in the image plane. I don't have the mathematical or physical justification showing that tilting the mirror by an angle causes a physical shift on my camera, resulting in the imaged object moving in the camera's field of view. Thanks for your answer

If a tilt mirror is really placed at the Fourier plane, then your OP sentence " I have positioned a tilting mirror that allows movement in the X and Y directions in the Fourier plane of my microscope" doesn't make sense. Tilting the mirror should not produce any shift at the Fourier plane- could there be an alignment issue?

 

[DaveE]

Isn't this just from geometrical optics? Changing the angle from the focal plane (Fourier plane) creates an offset in the image plane. Like tilting a simple lens a little bit. Maybe I'm not understanding your question though. A sketch would be helpful.

https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/08/3-image-motion.pdf

 

[KikiFleck]

Thanks for your answer. Here is the draw of my setup to help, because i'm not clear maybe.

 

[DaveE]

https://phydemo.app/ray-optics/simulator/

 

[Andy Resnick]

Thanks for your answer. Here is the draw of my setup to help, because i'm not clear maybe.

First question: What is "MLA"? Second question- How did you align the tilt mirror?

 

[Gleb1964]

"MLA"- Micro Lens Array I suppose.