Hiding behind some vague words when asked to provide explanations won't do.

Let me help you explain; a

conveniently found article will assist us:

Quote: The CCD signal-to-noise ratio calculation in the tutorial uses the following equation:

**SNR = PQet / [ PQet + Dt + Nr2 ]1/2**

where P is the incident photon flux (photons/pixel/second), Q(e) represents the CCD quantum efficiency, t is the integration time (seconds), D is the dark current value (electrons/pixel/second), and N(r) represents read noise (electrons rms/pixel).

Examination indicates that the equation above is simply structured as a ratio of total signal generated during the exposure time divided by the combined noise attributable to the three noise components described previously. The three noise sources are not correlated, and the denominator incorporates appropriate values for each noise component: the square-root of the signal accounts for the photon noise, dark noise is equivalent to the square-root of the product of dark current and integration time, and the square-root of N(r)-squared corresponds to the read noise component.

We can simplify the formula by renaming

**PQet **as

**S**(ignal).

Which means:

**SNR = S / [ S + Dt + Nr2 ]1/2**
or:

**N = [ S + Dt + Nr2 ]1/2**
"Same technology" have to be interpreted as "same pixels", and not some kind of magic which allows two imaginary sensors to nicely match "equivalence"; so we're only allowed to vary

**P** (or

**S**, in the simpler form). (Note: "equivalence" works with a constant

**t** and varies the photon flux

**P** instead - by changing the f-stop)

Let's consider the case with two sensors with the "same technology" i.e. "same pixels";

**f** is the crop factor between the two. Reminder: that's per-pixel SNR.

On the other sensor, let's get the same "total light" over the entire sensor area:

**SNRcrop = (S * f^2) / [ (S * f^2) + Dt + Nr2 ]1/2**
The pixel count will necessarily be:

Pixels_crop = Pixels / f^2

So far, I'm pretty confident with what I wrote

Now, could you (or anyone else) explain how "non-cropped sensor's" total SNR might be equal to "crop factor sensor's" total SNR, in conditions where Dt and Nr are significant?

I'm genuinely curious. Really. Enough not to care who's right and who's wrong. And because of this, please show me the courtesy of responding

**only** if you have a proper explanation.