Lens Assembly Structural Analysis
Data Recording
In our lab experiments, we must measure and record a colimnated light beam. This is done by shining the beam into a camera (the Casio Exilim EX-F1) and photographing the results. In order to properly interpret the information, it is necessary to understand the effects of the lenses on the image. This is incredibly difficult because of a number of factors. Most importantly, we have no way to directly measure the camera and acquire most of the information that we need. The lens assembly on the Exilim EX-F1 cannot be removed, so we cannot replace it with a custom- built lens assembly of known dimensions. All we can measure are a limited number of lengths, and we know the ranges of F-numbers and focal lengths. In order to solve this problem, a number of significant approximations and generalizations must be made. While the actual lens assembly contains twelve disparate lenses, our approximation has only four, and unlike the actual assembly, our approximation contains only perfect, idealized spherical lenses. These approximations would certainly affect our final results, but most likely not enough to severely skew our results.
Inside the Lens Assembly
This leads to a significant problem: How can we analyze the structure of something we cannot access? We contacted Casio, but the company was unwilling to divulge any detailed information about the lens assembly. Actually dismantling the lens assembly is out of the question unless a second camera could be acquired, and acquiring a second camera to dismantle would be prohibitively expensive. Instead, we chose to geometrically approximate the light paths through the lens apparatus and compare these results with data we were able to acquire. This would prove difficult, but it would also prove to be a generally successful approximation.
A Sliding Scale
By representing the lens assembly numerically, we would be able to calculate the effects of the lens experimentally. This would be done by taking photographs of the light beam and comparing the magnification of the final image with the size of the initial object. These values could be plugged into an Excel spreadsheet, and various values for the spacing of the lenses and their focal lengths could be entered appropriately. In addition, the few known and measurable values could be added as well.
First Iteration
With this known, we were able to create a basic spreadsheet. While many details of this sheet would later be proven wrong or simply be abandoned, the concepts are valid, and it is a sufficient starting point. To make the math easier, the lens asembly would be broken down into the four lenses. For each lens, an image would be generated from the object, and that image would then be treated as the object for the next lens. This means, for instance, that the light rays traveling from the object would pass through the first lens and generate an image at some distance within the lens assembly. This image would then be treated as the object for the second lens, which would generate an image used as the object for the fourth lens, and so on. This was fairly simply done.
