We have been investigating how pixel count is related to the centroid displacements by taking several sets of image frames with different camera
exposure time and input current.
It appears that the reason why rms value did not drop as fast as it should (as the number of averaged image frames increases) is that the pixel counts were too high.
As was previously done, we took 5000 images for rms analysis, and the reference set of centroids were generated from averaging 4000 sets of centroids using first 2000 and last 2000 images. Once a set of centroids for each image frame is obtained and saved (it took about 30 minutes to obtain centroids of 5000 image frames), rms analysis could be done in seconds.
(Alternatively, one could average the images first then find centroids, but this is much slower and the rms values do not change much.)
First figure is the log plot of rms versus N_av (number of image frames that are averaged over), where the maximum pixel count was about 2000.
Blue line is the calculated rms values, red line is the linear fit of the rms values, and black line is the line of the ideal slope -0.5. The rms values are in pixel units. The slope of the linear fit is -0.487.
Centroids are obtained from the images taken with the exposure time of 23ms, the value of the current driving light source 28 mA, and the distance between the CCD and the light source was about 50 cm.
Second figure is the plot using images whose max pixel counts were about 2700 (30ms exposure, same current): this gave the fitted slope to be -0.07.
Next two figures are the plots of rms with the same image set (images with max pixel count of 2700), using
1. centroids whose peak pixel counts are below 2048 (45 out of 904 centroids), and
2. centroids whose peak pixel counts are above 2047 (859 out of 904 centroids).
Peak pixel counts were obtained from the first image frame. As pixel counts fluctuate between image frames, it would perhaps be better to use averaged images but the outcome will still be qualitatively the same.
These plots clearly show that centroids with high peak pixel counts are responsible for poor reproducibility of the centroids.
The reason why the value of 2048 was chosen to separate centroids is because the camera will have to use the 12th bit for pixel counts 2048 or above.
I need to do more analysis to determine conclusively if the 12th bit is indeed responsible. What is clear at this point is that, once peak pixel counts go over about 2000, the reproducibility of centroids worsens significantly.
Further investigation revealed that, for the second centroids set (i.e., the centroids obtained from 30ms images) I discussed here, the decrease in centroids reproducibility is due to one spot whose position fluctuated much more wildly than others. That same spot does not cause problems in my first set with lower pixel counts. Here is the 2D plot of rms values of individual centroids fluctuations over image frames. I used griddata command to interpolate values between centroids to get this false color map;
The spot shown on the plot corresponds to the centroid located at the pixel (x,y) = (749,353). Its rms value with N_av = 1000 was 0.055 pixel uniits, which is more than ten times as big as average centroid displacements between two images (which is about 0.003).
Once you remove this centroid from the reference set and redo the analysis, the fitted slope goes back to -0.46.
Since I was wondering if high pixel counts worsens the reproducibility of the centroids, I also generated scatter plot of (1) rms vs peak pixel counts and (2) fitted slope for each centroid vs peak pixel counts (without removing the problematic centroid):
It is evident that one centroid is a huge outlier in rms vs pixel counts plot, but it is not so obvious in the plot of slopes vs pixel counts. Furthermore, there does not appear to be any correlation between pixel counts and the values of the fitted slopes.
And here are the scatter plots after removing the problematic centroid:
which suggests that there is no real correlation between peak pixel counts of centroids and their values of rms or fitted slope. What is still happening, although, is that as we increase pixel counts by either increasing the camera exposure time or the intensity of the light source, the value of the fitted slope increases as well (hence decreases the reproducibility of centroids).
I will continue this discussion in my next post...