I am currently working on an optical arrangement consisting of a QPD that measures the fluctuations of an incoming HeNe laser beam that is reflected by a mirror. The goal is to add a second QPD to the optical arrangement to form a linear combination that effectively cancels out the (angular) fluctuations from the laser beam itself so that we can only focus on the fluctuations produced by the mirror.
In order to solve this problem, I have written a program for calculating the different contributions of the fluctuations of the HeNe laser and fluctuations from the mirror, for each QPD (program script attached). The goal of the program is to find the optimal combination of L0, L1, L2, and f2 that cancels the fluctuations from the laser beam (while retaining solely the fluctuations from the mirror) when adding the fluctuations of QPD 1 and QPD 2 together.
By running this program for different combinations of distances and focal lengths, I have found that the following values should work to cancel out the effects of the oscillations from the HeNe laser beam (assuming a focal length of 0.2 m for the lens in front of the original QPD):
L0 = 1.0000 m (distance from laser tube to mirror)
L1 = 0.8510 m (distance from mirror to lens in front of QPD 1)
L2 = 0.9319 m (distance from beamsplitter to lens in front of QPD 2)
f2 = 0.3011 m (focal length of lens in front of QPD 2)
Based on these calculations, I propose to try the following lens for QPD 2:
1’’ UV Fused Silica Plano-Convex Lens, AR-Coated: 350 - 700 nm (focal length 0.3011 m). https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6508