Math Is Fun Forum

sulley

Member

Registered: 2012-11-26

Posts: 6

Interesting Optics Problem

Good Afternoon Everyone,

I have a problem that I was hoping you clever people may be able to help me with.

So, I am working on a camera focusing rig for a small camera module. The camera has a 42° FOV and the nominal focal distance required is 83mm. This is the distance along the centre line between the camera and a focus calibration image. This image is located on an inclined plane to provide 50mm of depth of field across the FOV. I am wanting to find the relationship between the focal distance and the length of the inclined plane and the angle required to maintain a DOF of 50mm

I have attached an image which will hopefully makes this easier to understand. This image has been knocked together in Visio, and I have used it to produce rough values for Theta and H, but it's very iterative and nasty, so I am trying to establish the formulae required to calculate angle theta and length H when I vary the focal distance. Regardless of how many triangles I draw on this image, I'm unable to progress.

Any help would be appreciated, any questions do let me know.

Regards,

Rob

Last edited by sulley (2014-11-24 02:15:57)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Interesting Optics Problem

hi Rob,

Welcome to the forum.

First I made my own diagram using Sketchpad and took some measurements:

Then I looked for a trigonometrical solution.  Couldn't spot an easy one, but there may be one lurking in there somewhere.  Meanwhile, here's the one I found that managed to calculate EH.  Once you have that, all the other lengths and angles are relatively ( ) easy to find.

Let angle BEH be alpha.

substitute this in (2)

and adding (1)

This re-arranges to

One solution is negative.  The other is EH ≈ 44.125 which agrees nicely with the Sketchpad answer.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sulley

Member

Registered: 2012-11-26

Posts: 6

Re: Interesting Optics Problem

Thank you Bob for your assistance! All sorted now!

Could you tell me where I can find more info on this SketchPad application please?

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,895

Re: Interesting Optics Problem

Hi,

I did this in Geogebra, which is a great freeware package for geometry (and more) and is available at http://www.geogebra.org/:

For a different FD, move point B along the horizontal AB axis. To change the DOF, move point E along the AE line.

The next image is the result of moving point B to reduce the FD (AB) to 70mm, followed by moving point E up-and-right along the AE line to restore the DOF (FE) to 50mm:

Here is a little movie demonstrating the changes that occur to other measurements and the shape of the drawing when changing the values of B and E.

For the movie I had the 'Axes' display switched off, otherwise I could have snap-located B at exactly 70mm from A. I don't know how to position E precisely (maybe by formula or some other trick? - but F's position is governed by E's, which makes that an interesting hurdle...).

Last edited by phrontister (2017-02-25 22:27:30)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Interesting Optics Problem

Could you tell me where I can find more info on this SketchPad application please?

Geometer's Sketchpad: http://www.dynamicgeometry.com/

GeoGebra: www.geogebra.org/

Last edited by ShivamS (2014-11-27 12:49:07)