It is a bit disappointing to be unable to show a clear gravitational signal, even with all of the successful exposures that were taken, but I recognized the difficulty of this measurement early on. In addition to the variables I anticipated, there are some additional uncertainties that I now recognize.
Here is my updated list of confounding variables:
- Lens distortion. This seems to be the largest one, measuring many arcseconds by the time one reaches the edge of the frame. There are two ways to combat it: take the before and during images with the exact same center and orientation on the sky (which I found impractical with my equipment), or calibrate the lens. I did the latter, but found that this too was sensitive to overall gain/magnification assumptions.
- The variation in positions due to the stars twinkling is about 2 arcseconds. I attempted to mitigate this by multiple exposures, but more were needed than I obtained.
- Centering and orientation. I did the best I could to position and orient the reference stars to the coordinate of the sun’s center during mid-eclipse, but the rigid transform technique requires an adequate collection of uniformly distributed stars. With only five or six, there may have been biases in this calibration of the order of arcseconds.
- Temperature variation. My reference images were taken during Minnesota spring and summer evenings, usually light-jacket weather. The eclipse pictures were taken at midday in Idaho. Although we noticed a cool-down during the eclipse, only a few of us felt the need to put on our fleece. Silicon has a thermal sensitivity of 2.5 ppm per degree K, which could account for some of the error. Overall however, this is small compared to the uncertainties displayed, since even a 10-degree K difference would show an error of 0.02 arcseconds per thousand radial distance. There may be other artifacts of temperature change however, see the following regarding focus.
- Focus variations. As one focuses the image on the detector, there is a geometric gain involved. I measured the travel on my telescope focuser for one turn of the fine-focus knob. I also noted that best focus could be determined to within 1/8 turn of that knob. This worked out to be 0.3mm, which, at the focal plane of a 480mm lens is about 0.6 arcseconds per thousand, a significant amount!
- Algorithm sensitivities. The before images were taken at night, sometimes with a partial moon providing background illumination of the sky. The during images were taken in the presence of the corona, a strong offset of the background level, and one which has a directional gradient as well. It is possible that the first stage of processing, starPos.m, could have been influenced by this difference. I do not have any estimates of its sensitivity.
- Published star positions. I used reference star locations from Stellarium, which uses the latest publicly available database of star locations. I used J2000 epoch numbers out of habit, but perhaps I should have used current date coordinates. This would only affect the errors comparing my observed positions with the published ones, not the errors between observed “before” and “during” star positions.
While I am not surprised at the failure to find the gravitational deflection signal, I am disappointed I did not get a bit closer. Regardless, it has been a wonderful project to undertake. I learned much and re-learned more. I hope the descriptions of the process have been enlightening. If you have read this far, perhaps you have found the narration worthwhile or even enjoyable. Best wishes and clear skies to all future solar eclipse observers!