To recap, we demonstrated that chip size determines overall field of view (FOV) whereas pixel size determines resolution, in arc-seconds per pixel (as/p). We then showed how they are derived for various telescope/camera combinations.
Clarification
Following the meeting, I found I needed to make a distinction between the source signal resolution and the image capture resolution.
For example, my Sky-Watcher Esprit 120, with an aperture of 4.73 inches, produces, according to Dawes' limit, a maximum resolution of 4.56/4.73 = 0.96 arc-seconds per pixel (as/p).
What that 0.96 as/p represents is the maximum resolution produced by the optical system (again, according to Dawes) and hence becomes the maximum resolution that is available to the recording system (i.e., the chip) and projected onto the image sensor.
Now, shown below is the calculated image scale for the Nikon D5300 when coupled to the Sky-Watcher Esprit 120.
(Screen above produced from Ron Wodaski's CCD Calculator
http://www.newastro.com/book_new/camera_app.html .)
Now, you may notice that the calculated image scale is 0.94 as/p. Note also that Ron Wodaski's CCD Calculator, excellent as it may be, does not show Dawes' limit for the proposed telescope - just the final calculated image scale telescope/camera combination in question.
And, here is a sample photo taken with this configuration using the Nikon D5300 (IR filter removed).
In this photo, the image scale of 0.94 as/p is very close to the 0.96 as/p Dawes' limit for the telescope, the Esprit 120. In fact, when I upgraded from the Nikon D5300 to the D7500, I was pleased that the image scale (1.03 as/p due to slightly larger pixels) still matched so nicely. And, with our typical seeing of around 2 arc-seconds (on a good night), I should be happy.
But, here's the rub ....
Complication
While driving to the post office after the meeting, it occurred to me that another, important consideration needs to be taken into account when determining the components for your target image scale - the Nyquist sampling theorem, or simply the Nyquist theorem. Basically, the theorem states that to adequately convert an analog signal to digital (sampling), you need to sample at a frequency of at least twice the frequency of the source signal.
This is more commonly understood in the context of audio recordings but applies to other forms of signal as well.
So, either the 0.94 as/p for the D5300 (or the 1.03 as/p for the D7500, which we will see) should be sufficient to capture images when the seeing is, say, 2 arc-seconds, which is infrequent and why those scales work under most circumstances.
But, my aim has been to record at roughly 0.5 arc-seconds/pixel in order to take advantage of those rare times when the seeing is close 1.0 arc-seconds. Ok, probably won't happen but we may very occasionally experience 1.5 arc-second seeing.
And, by imaging at the tighter scale of 0.5 as/p, I would in effect be sampling at 4x the source signal, when we have 2 arc-second seeing.
Now, that 4x may amount to what's called oversampling and I have seen a recommendation of 3x in various astrophotography forums.
Enter the 8 inch
Now, lately I've been testing the Celestron NexStar 8SE, which yields a 0.43 as/p image scale (with my current camera, the D7500).
And that more than satisfies the Nyquist sampling requirement for 2 arc-second seeing. The trick is to autoguide the combination without having to resort an in-line off-axis-guider (OAG) and instead use a separate guide scope mounted piggy-back on the OTA.
I'm still working out the wrinkles in that configuration and am strongly considering the EdgeHD version with a 0.7x focal reducer which yields a more comfortable 0.61 as/p, as shown below, which would meet the Nyquist requirement at 1/3x 1.8 arc-second seeing. Close enough.
(Screen above produced from Ron Wodaski's CCD Calculator
Now, I've also been considering the Celestron 9.25inch EdgeHD, along with 0.7x focal reducer. Coupled with the Nikon D7500's 4.22um pixel size, that combination would yield an image scale of 0.53 as/p. And Parijat would be so pleased. But, I'm also considering a future camera having smaller pixels and so will probably end up with the much less expensive 8 inch EdgeHD (and less expensive focal reducer).
For you own experimentation, here is a link to Ron Wodaski's CCD Calculator.
Stay tuned for a prequel on how to calculate image scale at the pixel or chip level.
Stay tuned for a prequel on how to calculate image scale at the pixel or chip level.
William Shaheen
Superstition Mountain Astronomical League®
Gold Canyon, Arizona
Gold Canyon, Arizona
June, 2018
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