Changes

where <math> M _1 </math> is the size of the object and <math> M _2 </math> is the size of the image.

where <math> M _1 </math> is the size of the object and <math> M _2 </math> is the size of the image.

By repeating these calculations for all lenses in the lens assembly, a final image magnification could be calculated.

By repeating these calculations for all lenses in the lens assembly, a final image magnification could be calculated.

Unfortunately, there were problems with this approximation, namely that it uses the wrong type of light. This approximation assumes that the object is a physical thing, which would allow light rays to leave it from any angle, allowing the required light rays shown in the illustration to pass through the lens. However, the light used is collimnated laser light, meaning that all the light rays are parallel when they enter the lens assembly. Therefore, this approximation is invalid.

Unfortunately, there were problems with this approximation, namely that it uses the wrong type of light. This approximation assumes that the object is a physical thing, which would allow light rays to leave it from any angle, allowing the required light rays shown in the illustration to pass through the lens. However, the light used is collimated laser light, meaning that all the light rays are parallel when they enter the lens assembly. Therefore, this approximation is invalid.

== Second Iteration ==

== Second Iteration ==

[[Image:Thin_Lenses_005_(Single_Ray).png|thumb|Two light paths, from an object off the left side of the frame. The vertical lines are the lenses. Notice how the light rays cross through the focal point and continue through to the next lens.]]

[[Image:Thin_Lenses_005_(Single_Ray).png|thumb|Two light paths, from an object off the left side of the frame. The vertical lines are the lenses. Notice how the light rays cross through the focal point and continue through to the next lens.]]

If the light entering the lens assembly is colimnated and enters the , then the top and bottom beams (the only two beams needed to locate the image) will travel through the first lens parallel, and both will cross through the focal point. The size of the image will then be

If the light entering the lens assembly is collimated and enters the , then the top and bottom beams (the only two beams needed to locate the image) will travel through the first lens parallel, and both will cross through the focal point. The size of the image will then be

<math> \frac{M _1}{f} = \frac{M _2}{L-F}</math>

<math> \frac{M _1}{f} = \frac{M _2}{L-F}</math>

where <math>\theta</math> is the entry angle at a given lens, <math>O</math> is the directional offset at the given lens, F is the focal length of the given lens, S is the spacing between the given lens and the next lens, and <math>R_p</math> is the value of any value R at the previous lens.

where <math>\theta</math> is the entry angle at a given lens, <math>O</math> is the directional offset at the given lens, F is the focal length of the given lens, S is the spacing between the given lens and the next lens, and <math>R_p</math> is the value of any value R at the previous lens.

Given these equations, we can further calculate the magnification of the image by recalculating the position of its edges. Assuming the image is symmetrical on some X and Y axis, we can find its size by tracing the position of its edges, defined as the offset plus or minus half the size of the object. Given these, we can calculate the image's size and location on each of the lenses, as well as the sensor.

Given these equations, we can further calculate the magnification of the image by recalculating the position of its edges. Assuming the image is symmetrical on some X and Y axis, we can find its size by tracing the position of its edges, defined as the offset plus or minus half the size of the object. Given these, we can calculate the image's size and location on each of the lenses, as well as the sensor.

== Aperture ==

== 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.

[[Image:Lens_side_trim.png|thumb|A side view of the lens assembly. Notice that because of the entry angle, one of the illustrated beams is cut off before reaching the second lens. The final image will be only the remaining half of the original.]]

An aperture would be more difficult to add for the fourth iteration, but it should be possible.

 

The above equations can generate images magnified or offset beyond what the camera can resolve, as the camera lens assembly has a radius of 3.75 cm. To compensate for this and prevent resolution of an image larger than the camera can allow, we need to superimpose over our final offset and magnified image the effects of the lens assembly. At any given lens, the image will be at either its maximum or minimum magnification counting from the previous lens. These lenses can be generated by the equation

 

 

where O is the O-coordinate for the given lens, <math>O_c</math> is the O-coordinate for the center of the image circle at this lens, and M is the magnification of the image at the given lens.

An aperture for the fourth iteration is being calculated and will be posted alongside the fourth iteration.

These coordinates are used to set the center of the lens superpositions. With this known, and with the image magnifications known, we can draw the lens superpositions and observe what of the image is cut off by the lenses.

== Future Improvements ==

== Future Improvements ==

* Add diagrams to this page

* Unknown