I've just started using an IDAS LPS-V1 filter to help with my high LP (Light Pollution). I image with a Canon T3 and was wondering if the new OPT Triad filter or the Cyclops Duo-Band filter would provide any significant improvements. This started me down the road to calculating the various noise sources in my images to see what effect either of these filters would have on the noise in the collected images.
After having reviewed some of the "noise analysis" articles it became clear that there are three main sources of noise in AP images:
- Read Noise
- Dark Current Noise
- Sky Glow Noise
If anyone is interested I can describe the procedure for calculating these noise sources (using PI) based on 2 Bias images, 2 Dark Frame images, and, 2 Light images (Light images must be registered to one another).
The result of the analysis is the following equation:
S/N(t) = SQRT[T/{(RN^2)/t + DCcps + SGcps}]
where
- T = total exposure time (sec)
- RN = Read Noise (counts)
- t = subframe exposure time, i.e., exposure time for each image (sec)
- DCcps = Dark Current (counts/sec)
- SGcps = Sky Glow (counts/sec)
This equation calculates the relative Signal-to-Noise of the integrated image (all images stacked) for a total exposure time of T (sec) when a sub exposure time of t (sec) is used. In other words, if T = 12000 sec (200 min) and t = 600 sec, then the equation will calculate the S/N for the summation of 12000/600 = 60 images.
For my Camera/Filter/Telescope/LP combination the result is (for an arbitrary total exposure time of 200 min) for the Red channel:
S/N(t) = SQRT[12000/{(15.77^2)/t + 1.13 + 34.8}]
A plot of the above equation is shown in the first image below.
One of the benefits of this graph is that it helps determine the proper Sub-Frame exposure time. This graph shows that Sub-Frame exposures of 120 sec or greater will produce the same final stacked result. Thus any exposure of 120 sec or greater would be acceptable for optimum S/N. This is the best technique I know for determining your best subframe exposure time.
With the above equation I can now determine whether one of the "dual band" filters would provide any improvement in stacked image S/N. The OPT filter will reduce the bandpass for the Ha signal from 18 nm for the LPS-V4 filter to 3 nm. This is a reduction of a factor of 6. This would reduce SGcps by a factor of 6. This changes the above equation to
S/N(t) = SQRT[12000/{(15.77^2)/t + 1.13 + 34.8/6}]
A plot of this equation is shown in the second image below.
Two points are clear:
1) The sub frame time needs to be increased to at least 420 sec to achieve optimum S/N, and,
2) The optimal stacked S/N has increased by about a factor of 2.2! Good news. Looks like the filter will definitely help.
The same analysis for the Green and Blue channels isn't as spectacular because their spectral passband is only reduced by about a factor of 3. However, the improvement still looks encouraging.
This has been a fun little trip into noise analysis. It has convinced me that either of the new dual-band filters would significantly increase my stacked image S/N.
Also, because the Sky Glow dominates my noise (even with one of the dual-band filters), a cooled camera would not provide any significant reduction in noise because the Dark Current noise is insignificant compared to the Sky Glow noise.
All in all this has been an enlightening adventure.
Comments welcomed.
Thanks for looking.
Steve
