One of the most frequent areas where I think people might get confused using a smart telescope is how long might they enhance or record. Better put, how long should they keep stacking images? All the smart telescopes do their thing by taking relatively short time exposures (4 to 15 seconds) and then averaging them into a stack of previous exposures. The telescope software is careful to align the images as they are acquired before adding. Gradually, the final image you see in your phone or tablet gets better as more and more images are acquired. In principle, these scopes can go on indefinitely until the object is no longer in a good part of the sky, or it goes behind a tree, or the wind shakes the telescope, or the battery runs down. But does that mean 20 minutes on an object is twice as good as 10 minutes?
The answer is no. Images improve as the square root of the time. What do I mean by improve? Images get better when the signal to noise ratio gets larger. The signal in our case is a star, a galaxy or a nebula. The noise is the background sky, which since we are on the Earth, includes light pollution glare from the atmosphere. Without going into the math, trust me, the image signal to noise will only improve as the square root of the time.
So, suppose you kind of like your image, but would really prefer to make it twice as good -- double the signal to noise. Well, to double the signal to noise, you have to go the square of the time you did originally. If you liked the image at 10 minutes and want to double the signal to noise, then you need to keep stacking for 90 minutes longer until you get to 100 minutes.
For me that leads to practical decisions as to whether it will be worth it and even whether I can track that long before the object heads into the trees. Or worse, the chance a skunk will want to become my night assistant will increase.
Since the light pollution is the main culprit with all this, I tell people that going to a darker site is really the best way to get good images faster. Think about it. If you wanted to really improve your 30 minute image decisively (a factor of two), then you'd have to stack for about 30x30 or 900 minutes. That comes to 15 hours! For that kind of timing you could drive somewhere and camp out for a night and be done more quickly.
Of course there are ways of combining images from separate nights. And the smart scope vendors often combine the efforts of many of their users. (There will be a Markarian Chain observing event by Vaonis soon. I know I helped image a comet for Unistellar too.) But I'm way too lazy to combine my own and it seems to go against the rapid gratification of the smart telescopes. My advice is, If you like what you're seeing and can't go a square times the time again, then it's often better to cut to store it and chase down another object.
Great post, Jim. Here is small correction. It is true that S/N ratio increases by the square root of the time but the calculation to square the time (in seconds or minutes) is not correct. Imagine a 10 minute exposure. By this calculation you would need 100 minutes to double the S/N ratio. However if we were to measure in seconds, 10 min = 600 seconds. Squaring gives 36000 seconds, which is 10 hours, rather than 100 minutes!
The correct calculation is that doubling the S/N ratio requires 4 times as long an exposure (so, 40 minutes in this example). To triple the S/N ratio requires 9 times as long an exposure, and so on.
Thanks, Jim for the professional explanation. Another law of diminishing returns. Using a Stellina in a frustrating high-Bortle area near San Diego has, in a practical manner, demonstrated precisely your conclusion. Vaonis has posted on its App the recommended default viewing time for each of its cataloged objects, but also suggested that doubling the time may improve resolution. I have found that to be true only when seeing is at its best….and here that is a function primarily of Pacific air humidity. Query—how might exposure time help in resolution…my guess has been, at least of dim deep sky objects, that one needs—at least on a Stellina—fairly long exposure for each stacked image. However, is it correct that exposure time may…
Great information! I am not far from your location (Rockford, IL), and I have wondered how long to keep imaging with my Vespera in our light polluted sky. It seems like you don’t gain a lot by going much longer than the software recommends.
Great explanation!