Here is a brief and preliminary summary of rms of centroid displacements calculated at a number of different exposure time values. To get the results I did the following for each value of exposure time:
1. Take a set of images. I took 2000 images for shorter exposure times, 1000 images with exposure times greater than 1 second, and 200 images with exposure time 4.4 second. I tried to keep the maximum pixel count to be roughly the same (about 2430 plus/minus 40).
2. Obtain the centroids for each image frames in a set. I saved centroids as an array of n by m by 2, where n is the number of image frames that I took, m is the number of centroids in each frame, and 2 for x and y coordinates.
Then I iterated through the centroid sets to calculate total rms, using various N_av values. If N_av = 100; then reference centroids were obtained by averaging the centroids of first 50 and the last 50 frames, and remaining 100 frames are averaged to get the other (or non-reference) centroids. I think this method gives a better view of the centroid reproducibility than fixing the number of reference centroids to be, say, first 1000 and last 1000 frames and varying the number of frames to be averaged for non-reference centroid.
Datasets of centroids are labelled as spcdet_I_t, where spcdet stands for "same (maximum) pixel count (with) differen exposure times", I the value of the current that drives the light source, and t the exposure time that I used.
Here are the plots:
It can be seen from these plots that the benefit of averaging multiple frames quickly diminish once we go over 1 second. I am investigating if there is any way to improve the reproducibility while using the same sets of images.
Issues that need further investigation:
1. Effect of pixels with unusually high pixel count. Dark images that we took show that, with longer exposure times, not only overall dark noise increase (and become less uniform) but also several pixels show unusually high pixel count (even higher than 2000), without a light source on. More investigation is needed to determine how much this affects the centroids calculation and to devise an way to deal with it.
2. Extra/Duplicate centroids. As exposure time increased, I observed that duplicate centroids start to appear, i.e., HS_Centroids##centroids had duplicate entries. The number of duplicate entries increased as exposure time increased. I believe this is due to the images getting noisier as exposure time increases. So After taking initial reference centroids, I removed duplicate centroid entries before calculating rms. I am thinking about adding a method to do this in HS_Centroids class.
In addition, there were one 'false' centroid when the exposure time was 4.4 seconds. For now I chose to manually remove it myself before calculating rms.