With the objective of designing a telescope system for the Gig-E, a system of two lenses is implemented. A rough schematic of the telescope system is attached. Variables in the system include the focal lengths of the two spherical lenses(f1, f2), distance between the lenses(t), distance between the test mass and the lens combination(u), distance between the other lens and the sensor(v). Also the size of the object to be desired ranges from 3’’ which is the size of the test mass to 1’’ which is approximately focusing on the beam spot implying that the required magnification ranges from 0.06089 to 0.1826 (since the sensor image circle size if ¼”)
The lenses are selected to be 2” in diameter so as to ensure sufficient collected power.

Going through the focal lengths available, namely 50, 100, 150, 200, 250 mm, and noting that the object distance would be within the ranges of 1500 to 2500 mm, plots of various accessible u and v for different values of t were obtained. This optimization was done to ensure the proper selection of the lenses. Additionally, a sensitivity analysis was performed and plots depicting the dependence of magnification on the precision limiting measurements of u (1 mm) and t (5 mm) were obtained. (These were scatter plots quantifying the deviation from the desired magnification ranges). The plots depict the error term induced on the magnification if there was an error in measuring the distance between the lenses as 5mm and if the precision in measuring the object to lens distance by 1mm.

The telescope design might be limited by spherical aberrations and coma, which might be resolved by either using aspherical lenses or by increasing the f-number (typically with an f number around 5 or 6). The use of aspherical lenses particularly parabolic lenses was considered, however this was found to be quite an expensive route. 

Analyzing the plots and taking into consideration the restrictions of the slotted lens tubes, the precision in measurement of the distances, a 150 mm- 250mm focal length solution is proposed. With a diameter of 2”, the f number is computed to be 2.95 and 4.92. With this combination and the object distances lying between 1500 to 2500 mm, the image distance to the sensor varies between 51 to 100mm. So a slotted lens tube controlling the distance between the lenses would be required.

I also considered a combination of focal lengths 250mm and 250mm, as then both of the lenses would at least have an f number of 4.92. The results for this combination are also attached. The image distance from the lens combination is about a 100 to a 140 mm. However, this would require much longer slotted length tubes thereby adding to the cost of the system. The number of accessible u-v points is the same as that for the 150-250 combination. 

I am still trying to search for a much more concrete way of quantifying aberrations.