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Lens Assembly Structural Analysis (view source)
Revision as of 17:56, 17 December 2009
, 17:56, 17 December 2009no edit summary
== Third Iteration ==
== Third Iteration ==
(Large illustration pending)
Still assuming that the collimnated light will enter the lens at a zero angle, any given light path will pass through the focal point of the first lens and will then pass through a particular point in the focal plane of the other lenses. This point can be calculated by tracing the trajectory of a theoretical beam of light passing through the center of the first lens at the same angle that the actual beams traced before entering the lens.
<math> \tan\theta = \frac{m}{f _1}</math>
From this and simple geometry, we find that
<math> \tan\theta = \frac{c}{f _2}</math>
and therefore
<math> \frac{m}{f _1} = \frac{c}{f _2}</math>
and therefore
<math> c = \frac{f _2}{f _1} m</math>
where c is the horizontal displacement from the focal point on the focal plane.
From this, we can use a bit of linear regression to chart the size of the image.
<math> y = \frac{l f _2 - s _1 c _1 + s _1 l + c x - l x}{f _2}</math>
By inputting
<math> x = s _2 </math>
we can calculate the magnification of the image.
This approximation is correct, accurate, and valid. It works perfectly, except that it is only correct, accurate, and valid when the collimnated light enters the lens at a zero angle.
== Fourth Iteration? ==
== Fourth Iteration? ==
A fourth iteration would be simple, in theory. The light would have to enter the lens assembly at some angle <math>\theta</math> which could be input by the user. Since
<math> \tan{\theta} = \frac{c}{f _2}</math>
the equation would be very simple to appropriately modify to take this into account.
== Aperture ==
Math for the aperture has been tried. For the third iteration, an aperture can be calculated by finding the magnification of an image at the location of the aperture, and if it is larger than the aperture allows, the amount of image remaining can be calculated by simple ratio.
An aperture would be more difficult to add for the fourth iteration, but it should be possible.
== Future Improvements ==
* Add diagrams to this page
* Solve the fourth iteration