# Achromatic doublet lens

I am trying to build an achromatic doublet lens with a focal length of 40mm and a diameter of 40mm. I cannot seem to find this commercially available anywhere and I do not want to order a custom lens since I just need one for my school microscopy project.

Can anyone please help me to identify the lenses needed so I can maybe buy two lenses and cement together to form an achromat.

Any help would be really appreciated. Thanks

• Is it the diameter a constraint? I mean, will the lens will inside a tube or will be in a lens holder in an optical bench? – José Antonio Díaz Navas Mar 8 '18 at 11:36
• It will be difficult to get an achromatic doublet working at F/1. Think that systems having that F-number will not be doublets. Further, it is difficult also to get a commercial system satisfying all our needs. In particular, your doublet as far I know it is not commercially available. At this time, what I can suggest is to combine a commercial doublet with a singlet, finding the best separation on axis to get an EFL of 40mm, and minimising the longitudinal chromatic aberration. As a school project, I assume that the optical quality required will not be so good. – José Antonio Díaz Navas Mar 11 '18 at 15:20

This question might not meet some of the criteria of this website and might be soon closed.

Anyway.

It is quite hard to cement two lenses together while maintaining a high optical performance, such as that usually provided by achromats.
This is why this is usually done industrially by specialised companies.

You want a focal length of $40$ mm, but you should also specify the wavelengths that you are planning on using.

Achromats are usually used for two reasons:

• Either you want to focus two different wavelengths to the same point, for which you want to have a look at the focal shift plots provided by companies that sell achromats

• Or you don't care about the wavelength and just want to use the fact that a plano-convedx + plano-concave lens cancel each other's aberrations, resulting in a "better" kept beam.

• Or both

Which one is it in your case?

Why are you specifying the diameter you want? Is it as simple as wanting to fit in a mount, or does it depend on the numerical aperture $NA = D/f$ of your microscope lens?

In the US and in the UK (where are you from?), one of the companies that sells optical components is Thorlabs. You can see here an example of cemented achromatic doublet. They do not have $40$ mm diameter, 'cause it's kinda of weird dimension, but they have $30$ and $50$.
You should look at the Anti-Reflection (AR) coating plots and are the focal shift plots for your wavelengths, .

• But if you reallly want to do it yourself, I can give you the formulae you need to work out the lenses you need. – SuperCiocia Feb 25 '18 at 16:51

I would suggest that you reconsider your specification of a $40\, \rm mm$ focal length and a 40 mm diameter which even for a simple lens is not so easy.

If it was a simple thin lens with both surfaces having a radius of curvature $R$ then you could use the lens maker's formula $\frac 1 f = (n-1)\left (\frac 1R + \frac 1R \right )$, where $n$ id the refractive index of the glass and $f$ the focal length of the lens to evaluate the necessary radius of surfaces to produce a lens with focal length $40\, \rm mm$.
If $n=1.5$ the this gives $R= 40\, \rm mm$ giving a maximum aperture, which the lens a sphere, of $80\, \rm mm$.

Given that the simplest achromatic doublet is a converging lens followed by a diverging lens you are not going to get the aperture that you desire with a focal length of $40\,\rm mm$.

I have simplified matters in that you can get lens made of materials with higher refractive indices but the point I am making is that you need to change the aperture and/or the focal length to more realistic values.

Telescope makers design achromatic lenses and here is an example of what is involved although the examples that are given are for lenses with a focal length greater than your specification. Good microscope objectives have a number of lens as can be seen in this diagram

which is taken from this website which gives a good overview of what is required.

I would imagine that as a start (and end) for a school project you should start with a simple combination of two commercially available lens, one a biconvex lens and the other as a plano-concave lens a shown below?

which is taken from the Wikipedia article achromatic lens.

If you want the component lens to look like a single lens then you must make sure that the radii of curvature of adjacent sides are as close to one another as possible and given that there will be imperfections you should consider using a suitable oil between the lenses to reduce the effect of such imperfections.