I went through all the elog entries related to CCD calibration. I was wondering if we can use Spectralon diffuse reflectance standards (https://www.labsphere.com/labsphere-products-solutions/materials-coatings-2/targets-standards/diffuse-reflectance-standards/diffuse-reflectance-standards/) instead of a white paper as they would be a better approximation to a Lambertian scatterer.
On calculating the accessible u-v ranges and the % error in magnification (more precisely, %deviation), I got %deviation of order 10 and in some cases of order 100 (attachments 1 to 4), which matches with Pooja's calculations. But I'm not able reproduce Jigyasa's %error calculations where the %error is of order 10^-1. I couldn't find the code that she had used for these calculations and I even mailed her about the same. We can still image with 150-250 mm combination as proposed by Jigyasa, but I don't think it ensures maximum usage of pixel array. Also for this combination the resulting conjugate ratio will be greater than 5. So, use of plano-convex lenses will reduce spherical aberrations. I also explored other focal length combinations such as 250-500 mm and 500-500mm. In these cases, both the lenses will have f-numbers greater than 5. But the conjugate ratios will be less than 5, so biconvex lenses will be a better choice.
Constraints: available lens tube length (max value of d) = 3" ; object distances range (u) = 70 cm to 150 cm ; available cylindrical enclosures (max value of d+v) are 52cm and 20cm long (https://nodus.ligo.caltech.edu:8081/40m/13000).
I calculated the resultant image distance (v) and the required distance between lenses (d), for fixed magnifications (i.e. m = -0.06089 and m = -0.1826 for imaging test masses and beam spot respectively) and different values of 'u'. This way we can ensure that no pixels are wasted. The focal length combinations - 300-300mm (for imaging beam spot), and 100-125mm (for imaging test masses) - were the only combinations that gave all positive values for 'd' and 'v', for given range of 'u' (attachments 5-6). But here 'd' ranges from 0 to 30cm in first case, which exceeds the available lens tube length. Also, in the second case the f-numbers will be less than 5 for 2" lenses and thus may result in spherical aberration.
All this fuss about f-numbers, conjugate ratios, and plano-convex/biconvex lenses is to reduce spherical aberrations. But how much will spherical aberrations affect our readings?
We have two 2" biconvex lenses of 150mm focal length and one 2" biconvex lens of focal length 250mm in stock. I'll start off with these and once I have a metric to quantify spherical aberrations we can further decide upon lenses to improve the telescopic lens system.