Step EE-3: Finding the best fit

We now have a way to transform the stars detected in an image into our virtual camera reference frame, but the previous step was just the “rough alignment” based on two bright stars. This is vulnerable to errors in how those two star positions were identified, especially if they were bright enough to saturate the detector, or were influenced by poor atmospheric seeing conditions.

More importantly, we are attempting to measure a tiny change in radial distance from the center of the sun. If we make a small error in where that center point is, by even a fraction of a pixel, it will affect all of our distance measurements to the stars revealed during the eclipse.

This means that it is less important to align the star positions as it is to get their angles with respect to the sun correct. If the angles are correct, then we can measure the radial distance from the image center and be confidant when we compare the “before” distances to the “during” distances that we are measuring from the same center point and are not being fooled by some offset to the actual center. This is particularly important in the before images. In the during image, we can, in principle, locate the center of the sun (though this too has uncertainties since we are seeing the moving moon’s edge, not the sun’s). The collection of observed stars is an unambiguous pointer to the sun’s position at the moment of maximal eclipse.

To this end, the output of step EE-3 is the small additional offset and rotation that places the observed stars in best angular alignment with known angles of the reference stars. This small adjustment will be applied to all of the detected stars to obtain their final position in the reference image plane. Their radial distance from the sun is then easily computed.

Matlab script radialAlign.m was created to do this task. It takes the results from step EE-2, the rough alignment and transform to the reference frame. The output is a set of star positions—the reference star positions in the reference frame, and the slight deviations from those positions as detected in the image.  In an ideal world, the deviations would be zero in the “before” image, and would show some gravitational deflection in the “during” image.

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