# Optics: Determining focal length for collimated beam

1. Apr 8, 2012

### pierce023

Hello all.
I am in the process of designing a mechanism for collimating laser diodes for a personal project.
I don't have training in optics so I am stuck with this problem:

I need to determine the focal length of a lens that can be used to collimate a laser beam with divergence 45 degrees (full angle).
I also need to determine what the distance is between the laser diode emitter and the lens surface.
The goal is to get a beam roughly 10mm diameter with a minimal divergence angle.

Attached is a diagram I drew which should make the problem clear.
I haven't been able to find the information I need on the internet.
If any of you can tell me how I can determine this, please let me know.

Have a great day. :)

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Last edited: Apr 8, 2012
2. Apr 8, 2012

### Andy Resnick

You are not asking the right question (or not thinking of the correct specification)- the focal length of the collimating lens is given by what beam divergence you want.

Laser beams (Gaussian beams) conserve the quantity w*q, where w is the beam waist and q the divergence angle. You have the initial q, the initial w (it's about the size of the beam exiting the diode),and the final w (10 mm, which is also the focal length of the lens)- this means your final q is constrained to be the ratio (w_i/w_f) * q_i. If that q_f does not meet your spec, you need to expand the beam larger- using a longer focal length lens, for example.

3. Apr 8, 2012

### Bob S

A compact laser beam expander/collimator often requires a pair of lenses, one objective (focusing) lens and a defocusing lens as shown in Fig. 7 in

http://farside.ph.utexas.edu/teaching/em/lectures/node92.html

The defocusing lens makes the collimator more compact.

4. Apr 8, 2012

### Drakkith

Staff Emeritus
Work the problem backwards. Take two parallel rays 10 mm apart entering from the upper and lower edges of the lens and find the required lens to make them focus at a 45 degree angle.

If you don't know how to work such a problem then you may need to learn, as it's hard for us to help you since we don't know what shape you want the lens, what material it's constructed from, the setup of your project, the wavelength of the light, etc.