# Infinity-corrected Objective Lens Microscope Design

I am totally new to optics design. I am currently trying to play around with infinity-corrected objective lens and trying to image a slide with a Basler camera. I was able to get my system working with a $$160$$ mm tube length, $$20\times$$ finite objective lens and the camera. I was able to get decent magnified slide images with the setup. As a next step, I am trying to reduce the overall height of the optical assembly. I was reading up on infinity objective lenses and tube lenses to help me in this aspect ([1],[2],[3],[4],[5]).

Here is where I am stuck at and hoping people with some experience in optical design can help out.

Assume that I have selected this particular unit as my $$20\times$$ objective lens. The technical specs say the focal length is 10mm and working distance is 13mm. Since its an infinity-corrected objective lens, a tube lens is needed to focus the image the camera sensor. So based on the equations mentioned  in[4],

Magnification = Tube Length / Objective Focal Length


So for an effective magnification to be $$20\times$$ (on the camera sensor), I should use a tube lens with a focal length of $$200$$ mm. ($$200$$ mm/$$10$$ mm = Magnification of $$20$$). But this is currently making my unit taller than the 160mm tube length design earlier.

Now my query is

1. If an objective is already selected (any off the shelf objective lens) can I reduce the overall height of the system, keeping the same magnification mentioned in the objective just by editing the tube lens focal length? (I am assuming it's not possible)

2. For an objective lens, can the objective focal length be changed from the one that is mentioned the manufacturer's spec sheet? (Again I am assuming it's not possible) I have this doubt because I am confused by what the focal length of the infinity objective lens means. Is it a property of the lens or is it the distance between the sample and first lens in the objective?

3. In infinity lenses, why is Working distance mentioned as higher than the focal length of the lens [6]? Shouldn't focal length (as the lens is inside) be higher than Working distance (which is the distance between the tip of the casing and the sample surface)? I read [7] but it wasn't able to clear this doubt.

4. Is there any way to reduce the height of my overall optical assembly?

PS: I have a Basler camera with a $$1/1.2$$" sensor (If that information is relevant).

Hoping someone can help out. Thanking you in advance.

1. Have you considered that microscopes operate in a 4-f configuration. This means that there's an infinity space between the tube, and objective lens. This space can be changed, without modifying the magnification substantially at the expense of telecentricity, and vignetting if you increase it. If you put your tube lens right after your objective lens, you should still get an image with the correct magnification in the back focal plane of the tube lens. The magnification is always given by the ratios of the two focal lengths, but you have some degrees of freedom if you start playing with the working distance using a telephoto configuration for example (more details in 3)
2. You can possibly change the focal length of a commercial objective lens, but you'd need to have its optical design (from a patent for example). The focal length of the objective lens doesn't tell you anything about the distance to the first lens of the objective lens, this is called the working distance (more details in 3)
3. The focal length is the distance from the principal plane at which parallel ray bundles focus to a point. For any lens, not exclusively infinity-corrected objective lenses, it is possible to have a different working distance, and focal length. Take the telephoto lens below. A collimated ray bundle diverges after hitting a first negative lens. The diverging ray bundle is then focused by a second positive lens. The focal length is the distance from where the input rays appear to bend (principal plane) to where they all meet (focal plane). The focal distance is shorter than the distance between the focal plane, and the second lens, which is the working distance. The disadvantage of this design is that it uses a negative lens, which is harder to manufacture. This generally means that this lens will either suffer loose tolerances, or a high cost.

4. Yes, there are many ways to do this. However, its a whole field called optical design, and it would be out of topic to try and cover it here. I recommend you try to start with the specifications of your system. You have a length limit I understood, but what about the performances of your system in those limits? What kind of resolution, or wavefront aberration do you require? Also, think about how you are going to realize this optics. Are you going to buy spherical lenses, or do you want custom optics with aspherical surfaces?