Stars that look like tiny seagulls or comets in the corners of an otherwise sharp frame almost always mean one thing: the camera sensor is the wrong distance from the field flattener. That distance is called back focus, and getting it right is mostly arithmetic.
What back focus is
A refractor on its own focuses light onto a curved surface. A camera sensor is flat, so the corners fall out of focus. A field flattener or reducer fixes that, but only for one particular distance between its rear thread and the sensor. That distance is its back focus. Most flatteners and reducers for refractors want 55 mm. Schmidt-Cassegrain reducers usually want 105 mm. The exact figure is in the manual for your corrector, and it is worth checking, because not all of them follow the usual numbers.
Get it wrong in either direction and corner stars stretch along lines through the centre of the frame, while the centre itself looks fine. That is why the problem often goes unnoticed until you look at the edges.
Adding up the train
Everything between the flattener and the sensor counts: adapters, a filter wheel or drawer, an off-axis guider, tilt plates, spacers and the camera's own distance from its front thread to the sensor. Each has an optical length, the distance it adds along the light path. Threads that screw into the next part are already accounted for in the published lengths, so you add the numbers as they are.
Many cooled astronomy cameras quote 17.5 mm, but figures from about 6.5 mm to over 20 mm exist, depending on the model and which adapter or tilt plate is fitted. Some quote a figure that only holds with an included extender. The manual says which; it is easy to count it twice or miss it.
Why a filter changes it
A flat piece of glass in a converging beam pushes the focus point back. For the glass used in astronomy filters the shift is close to one third of the glass thickness:
focus shift = t x (n - 1) / n = about t / 3 (n about 1.5)
A 2 mm filter moves the focus back by about 0.67 mm, so the train needs to be that much longer. A 1 mm filter needs about 0.33 mm. It sounds small, but at f/4 or faster the tolerance is only a few tenths of a millimetre, so it can be the difference between round and stretched corners.
A worked example
A refractor with a 55 mm flattener, a 20 mm filter wheel holding 2 mm thick filters, and a camera with 17.5 mm of back focus:
| Flattener wants | 55.00 mm |
| Plus filter glass, 2 mm / 3 | + 0.67 mm |
| Target distance | 55.67 mm |
| Filter wheel | - 20.00 mm |
| Camera | - 17.50 mm |
| Gap to fill | 18.17 mm |
A 15 mm and a 3 mm spacer make 18 mm, 0.17 mm short. Adding a 0.2 mm shim makes 18.2 mm, 0.03 mm long, which is as close as you will get with standard parts. Shims are thin rings that go between threaded parts, and a set covering 0.1 to 0.5 mm costs little and solves exactly this kind of leftover.
How close is close enough
The tolerance depends on focal ratio. The depth of acceptable focus grows with the square of the f-number, so an f/7 system forgives roughly twice the error of an f/5 one. Manufacturers rarely publish a tolerance. As a working figure, about ±0.5 mm is often fine at f/6 and slower, while f/4 and faster, and full-frame sensors, can need ±0.1 to 0.2 mm. The 0.03 mm in the example above is well inside either. The stars are the final test.
Checking it on the sky
Take a short frame of a star field and look at the four corners at 100%. If all four corners show stars stretched along lines through the centre, the spacing is off. Change it by about 1 mm and take another frame: if the corners improve, keep going that way; if they get worse, go the other way. If only one corner or one side is bad, the problem is tilt, not back focus, and spacers will not fix it. Tools such as ASTAP's image inspector measure star shapes across the frame and help tell the two apart.
Common mistakes
- Counting a camera's included extender twice, once in its back focus figure and again as a spacer.
- Forgetting the glass. Each filter in the light path adds about a third of its thickness.
- Using the reducer's number for the flattener, or the other way round, on scopes that offer both.
- Assuming every corrector wants 55 mm. Check the manual.