Angular magnification of an out-of-focus eyepiece

1. Jun 5, 2013

chromatic

I'm trying to simulate light rays going through an eyepiece to characterize its magnification in function of the distance from the optical axis (image distortion). Attached is a figure showing the simulation console.

Some lenses in the eyepiece are movable to correct for myopia/hypermetropia.

When the object is exactly at the focal point (rays from a single point all exit parallel), magnification is easily calculated from the angle of exiting rays.

HOWEVER, when the lens correct for myopia, the rays exiting from the eyepiece are not parallel, how can I calculate magnification in function of the distance from the optical axis (image distortion) in that case?

Thanks a lot!

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2. Jun 5, 2013

sophiecentaur

I'm just wondering whether you need to worry about this. If your eye/eyepiece are treated as a compound then will the actual image size on the retina be very different from when the eyepiece is used for 'normal vision?

3. Jun 5, 2013

chromatic

Probably the distortion will only change by couple of percents, but for big fields of view (~90 degree), the distortion is big and need to be compensated by an algorithm, it would be optimal to have quantitative values for out-of-focus distortion so the algorithm can take that in consideration.

4. Jun 6, 2013

Andy Resnick

Let me make sure I understand the question- you want to calculate the distortion as a function of defocus?

5. Jun 6, 2013

chromatic

Yes, distortion as a function of defocus, wich is the same as magnification as a function of defocus and image height.

6. Jun 10, 2013

Andy Resnick

I don't think there's a clean analytic expression. There are the 'stop-shift formulas' (for example http://books.google.com/books?id=kS...ge&q="stop shift formulas" distortion&f=false), but I haven't ever used those, and unless you know how much the stop moves to accommodate your defocus requirement, I don't see how it can be easily used.

I wonder if you simply have to grind through the ray-trace code; have it tell you what the distortion is for a variety of defocus layouts and hope you can fit a curve.....

Upon re-reading what you originally asked, tho, I wonder if there is a simpler approach. My guess is that you are simply altering the optical power of the eyepiece to account for myopia, so you may be able to create a (reasonably) simple thin lens approximation instead of the detailed lens layout.

7. Jun 11, 2013

chromatic

Thank you for your replies, I finally got it to work. I ran the simulations with rays coming from infinity instead of rays
exiting from the object (right to left instead of left to right on figure) and I computed the density of intersection points with the object using Gaussian kernel density estimation. I chose to points with maximum density to calculate magnification. To simulate accommodation, I simply use thin lens formulas to find appropriate initial conditions (angle versus position on the pupil).
Cheers
Sim

Last edited: Jun 11, 2013