Infinity Corrected Microscope - Building from Scratch

Question

I took an optics course a few years back, and am trying to figure out how to build an infinity-corrected microscope from discrete optical components which are listed in references [2] (lenses) and [3] (mounting equipment).

I have gone through a number of books trying to figure out how to actually assemble this with some simple lenses, tubes, and lens mounts. The problem is that all of them have an example like that above, but don't spell out what I need to do to determine:

1. Total magnification (I'm assuming it is the ratio of the focal length of the eyepiece lens over the focal length of the objective lens).
2. How close the lenses should be (I think the objective and tube lenses should be close, just not closer than the focal length of either, and I don't know what the focal length should be for the tube lens either). What about the distance between the tube lens and eyepiece lens? I thought the gap between the tube lens and eyepiece lense could be arbitrary in length, but the diagrams I find seem to indicate otherwise.
3. What kind of lenses to actually use (Do all of them have to be convex lenses? Some examples should the use of a "plano convex" lens instead of a "convex convex" lens for the eyepiece).

If anyone could point out how I would design this or steer me towards some resources that can provide a definitive answer on how to design an infinity corrected microscope, eyepiece and all included, it would be greatly appreciated.

Thanks!

References

1. Microscope Optical Components Introduction, Accessed 2014-03-04, <http://www.olympusmicro.com/primer/anatomy/components.html>
2. Experimental Grade Optics, Accessed 2014-03-04, <http://www.anchoroptics.com/pages/category/Experimental%20Grade%20Optics.cfm>
3. Modular Mounting Components, Accessed 2014-03-04, <http://www.edmundoptics.com/optomechanics/modular-mounting-components/>

Answer 1

The Magnification is a combination of all of the focal lengths of the picture you have shown above. A real image is created by the objective and tube lens. This creates an image of what you have at the object plane that is magnified by:

$M = \frac {f_{tube lens}}{f_{objective}}$

So, if you were to measure the size of the image, it would be M times larger than the object that is placed to the left of the objective lens.

One common confusion is that many microscope objectives actually create an image all by themselves without a tube lens. There are several standards including objectives that create images 160 mm and 170 mm away from the microscope objective. In your diagram, it implies an infinity corrected objective lens. This means that the image created by the microscope objective is infinitely far from the objective lens. This might lead you to believe that since the light is collimated from the microscope objective, you can place the tube lens anywhere you want. That is not technically correct because of two factors: vignetting and the optical design of the tube lens.

Vignetting means that the light escapes the size of the lens. In your diagram, this would happen if the tube lens is too small. Many infinity corrected objectives are designed for tube lenses that are 180 mm from the objective lens. If the tube lens is not placed at a distance close to 180 mm, you can have vignetting or performance from optical aberrations may cause the image to degrade.

Now, take the final step to the eye of the observer. This is the eyepiece. Your eye prefers (is relaxed) when looking at infinity. Therefore, the eyepiece is typically designed to project the image created by the objective-tube lens pair to infinity. Your diagram actually shows the image at 25 cm instead of at infinity. For this case, the eyepiece is placed at nearly one focal length away from real image (image plane 3 in your diagram).

The final magnification is $ M_{total} = M \times \frac{25 cm}{f_{eyepiece}} $

There are additional considerations including:

1. Working distance of the objective (distance between objective and object)
2. Eye relief (distance between eyepiece and observer's eye)
3. Pupil or eyebox (sometimes you look inside a microscope and it is black until you line up your eye with the microscope)
4. Illumination (most objects require some external light source to illuminate them so you can see them!)

One last consideration. If you just want to put the image onto a camera. In which case, you don't need the eyepiece!