Over the last couple of months I was tuning the backfocus distace of the focal reducer-C 0.72x for the Takahashi FS-60C/CB. I used ASTAP to build through focus graphs of stars’ HFR (hyperbolic fit) at different backfocus, as described here. At the right backfocus distance, lowest HFR for stars at the corners and at the center is found at the same focus position. The process also provided valuable info on sensor tilt, which I was able to correct placing some layers of adhesive tape between the camera and the filterwheel at the right places 😅.
I’m now certain that my backfocus distance is right and my sensor is perpendicular to the optical axis.
Unfortunately, even though this is a dedicated reducer for the FS-60C, at the right backfocus stars at the corners are as small as possible but they are visibly distorted. Their aberrated shape is also color dependent. In H-Alpha, corner stars display an inward-pointing comatic shape. You can see an example here. No processing on that image other than stretching and a bit of unsharp masking.
I know that one can use BXT or other AI tools to correct that but I’m still not on board with those tools so here is an alternative approach based on techniques used to create mosaics.
Considering that the distortion is dependent on « focal plane region » (center, sides, corners), star shapes in the final image can be improved by averaging frames captured at large position offsets so that throughout the final image, data is the average of different focal plane regions.
In cases where distortion depends on distance from focal plane center, offsets should ideally be large enough to average opposed regions of the focal plane.
This is the result of my first test. The image shown is a crop of a larger mosaic of 25 panes. The panes’ overlap was about 3/4 of image width and 2/3 of image height (I intended 2/3 on each direction but I made a mistake in my python script 🙄). Again, no processing on that image other than stretching (no deconvolution, no unsharp mask, nada).
You can see that within the area covered by a sigle image from the sensor (marked in yellow in the image) stars are round throughout. Because only a simple average without rejection was used to stack the panes, starts are slightly bigger than in the original image. I think a tighter shape can be obtained with strong rejection on stacking (as distortion direction varies but the star center remains).
Of course this has a big drawback : because of the large offsets, the final image has less integration time compared to capturing all frames at the same position. One could wonder if it would not be better to just use the dedicated f/6.2 flattener (that produces quite decent star shapes on the corners) instead of this f/4.2 reducer… The flattener requires 2.16 times more exposure time to achieve the same SNR.
Dividing the focal plane in thirds (9 regions) a mosaic of 25 panes at 2/3 overlap would be required to cover each portion of the central image with data from all 9 regions of the focal plane. This means that the central part of the mosaic gets only 9/25 of total integration time (36%, as shown in the following figure). Not good…
📷 image.png
The red rectangle shows the area covered by a single pane.
On the other hand, you do get a mosaic, and if one continues to add panes (to get a larger distortion-free area), more of the integration time lands on the area of interest : in the previous example, adding 5 panes (20% more integration) increases the distortion-free area by 33.3%.
A better option might be using more overlap. The following figure shows percentage of total integration in a mosaic of 16 panes at 3/4 overlap. The central portion of the image benefits from all panes. Almost 60% of total integration time lands in the central area equivalent to a single image (black rectangle on the figure).
📷 image.png
I’m quite happy with the results so far and will keep making some experiments in this direction.
Let me know what you think.
Clear skies !
Ricardo
You can see the stars looking like small comets.
You can see that the stars are quite round and smaller than I expected from the averaging of different areas of the focal plane. Continuing with the “small comet” analogy, my explanation is that the “tails” from different areas point in different directions and are thus diluted in the result, whereas the “nucleus” is reinforced. 