Etendue is related to the Lagrange invariant and to the more general optical invariant of the optical system. It is a quantity that is conserved through an optical system and it can be used to show how radiance is conserved. Wikipedia defines all this stuff pretty well so if you want to go into the gory details check it out here: https://en.wikipedia.org/wiki/Etendue. Computing Etendue is fine, but Etendue doesn't include sensor effects and signal strength is what you really want to know. To do that, I personally find it more useful to simply compare the ratio of sensor signal strengths for two systems to see how they compare. Here's how to compute signal ratios:
S1/S2 = (F2/F1)2 (T1/T2) (1-CO12)/(1-CO22) (R1/R2) (P1/P2)2
Sn = Signal strength
Fn = Focal ratio
Tn = Optical transmission (due to surface coatings taking into account the number of surfaces)
COn = Central obscuration ratio (= Dsecondary/Dprimary)
Rn = Sensor responsivity (QE)
Pn = Pixel dimension
Here's an example:
System 1: 14" aperture, F = 10.8, CO = 0.32, Transmission = 0.85 (8 surfaces @ 0.98), R = 0.65, P = 9.0 um (C14 w/16803)
System 2: 11" aperture, F = 10.0, CO = 0.31, Transmission = 0.85 (8 surfaces @ 0.98), R = 0.75, P = 3.8 um (C11 w/ASI-1600MM-C)
Plugging in the numbers:
S1/S2 = 4.1, which says that the 14" system will produce 4.1 times as much signal as the 11" system.
Finally, if you want to compare a 127 mm scope to the 14" both with a 16803 (as proposed by the OP:)
System 3: 127 mm aperture, F = 5.4, CO = 0, Tranmission = 0.85 (8 surfaces @ 0.98), R = 0.65, P = 9.0 um (NP127 w/16803)
S1/S3 = 0.224, which means that the refractor will have a signal almost 4.5x larger than the C14. If you use F/11 for the C14, you'll get a number that is pretty close to the ratio given by the OP's numbers. It is important to understand that in this particular case, the reason that the results are so close is because the cameras are the same. Therefore, all that counts is the irradiance in the focal plane, which is closely related to Etendue (and which doesn't take into account all the other stuff that contributes to the final irradiance at focus.) Just remember that what you gain in irradiance with the smaller refractor, you lose in image scale (along with sampling in object space.) To increase both signal strength and image scale, you need a larger aperture. So, unfortunately, there is no free lunch. Larger aperture is always a benefit and that's why professional telescopes are so large.
Edited by jhayes_tucson, 08 May 2019 - 10:38 PM.