I love to analyze. Actually, I sometimes suffer from analysis-paralysis (ask my wife!) My favourite tool is MathCAD which allows you to work in algebraic notation and is wonderful at keeping track of dimensions. All of the calculations in this project were done in it using SI units except where noted.
So I got started with what I knew.
The first value is the size of the KAF8300’s pixel and the second is the Nyquist sampling number. Given these values I can calculate the following: (Note: the pixel size is in metres and the pixel scale is in radians to calculate focal length)
So the ideal focal length for my site and camera is about one third of my current telescope’s focal length.
But what about the aperture? Two factors govern the choice of aperture diameter: one is diffraction limit and the other is the focal ratio. I will tackle diffraction first. For that I need one more piece of information to do the calculation.
This is the wavelength of green light, typically used in calculations: So the diffraction limited aperture is then:
That’s a pretty small aperture and a very slow focal ratio, not really what I want. But the good news is, since this aperture is much smaller than anything I am likely to choose, I can stop worrying about being diffraction limited.
I would like a much lower focal ratio than I have now. My field of view would be wider and my exposure times would be shorter. So what’s a reasonable choice for focal ratio? Perhaps a better question is what’s a reasonable aperture? The questions are obviously linked. If the focal ratio is very low then the aperture will be big and expensive. But if I could cut the focal ratio in half, I will cut my exposure times by a factor of four, all other factors being equal. That’s a pretty good incentive to reduce the focal ratio.
Aperture, aperture oh how I love thee! At one point in the past I even designed a 500mm (20in) Harmer-Wynne astrograph. Fortunately, cost dissuaded me from building it. Now I have been a reflector guy since I built my first 250mm (10in) Newtonian back in the early eighties. (I still have it!) But once I went through the above analysis, I realized a big light bucket would need a big pixel size to match. And I wasn’t about to buy a new camera. As the focal length needed for my existing camera was short and a low focal ratio was desirable, the new aperture was going to be much smaller than I currently had. So much for aperturitis!
One advantage of smaller aperture is that it is more reasonable to consider an unobstructed design like a refractor. A radical thought for an old reflector hand, but this old dog still likes to learn new tricks. The typical obstructed reflector robs contrast from the image which, while it can be dealt with in post-processing, would be nice to get away from. So I decided to look at a refractor.
Being retired (translation: broke), but having plenty of free time (so I’m told by my family), this would have to be a DIY project. Since the plan is to build rather than buy the new scope and grinding lenses is one thing I did not want to get into, I had to at least source a ready-made objective. As I looked around the web it became clear that there was a big price jump above 140mm (5.5in) in diameter. So 140mm seemed about the best bang for the buck. Using it, here’s what the calculations say:
So with a 140mm lens with a focal ratio of 5.3, I need half the exposure time as compared to my current setup. (It’s a bit more complicated than that because of the differences in aperture and sampling but let’s leave it there for now) In addition, my field has widened considerably. Given the number of pixels across the width of the sensor and the pixel scale I get the following:
One image with this setup is therefore roughly equivalent to a mosaic of 8 images using the old scope. When you consider that a typical imaging session for me is 3 or 4 hours, with this new setup will yield the equivalent of 24 to 32 hours of exposure in my usual time. And at the same effective resolution due to improved sampling. And since my sampling is improved I also get a significant increase in SNR.
What’s the catch? (You know there has to be one) Well, there is no getting around the fact that this aperture is smaller and therefore the light grasp is less, probably by a few magnitudes. But I have been able to image objects with surface brightness as low as 21 magnitudes currently with reasonable success so losing a magnitude or two does not bother me too much.. As the field of view is so much larger, I expect to use the setup mostly on large, reasonable bright extended objects that I have avoided, until now, due to the extensive mosaic work involved.
Sign me up, I’m convinced.