Considering shot noise alone, the converter and the crop have identical SNR.
Agreed on the shot noise part, but why sould shot noise be the only relevant? in fact it's read noise the DR limiting factor, so in the deep shadows the crop will have a better SNR.
SNR doesn't linearly correlate with the total amount of light collected, it also depends on how many photocaptors gathered that light.
In a 2X Teleconverter each of all photodetectors of the sensor captures 1/4 the amount of light that is captured by each of the photodetectors of the crop.
Since with the teleconverter we have 4 times more photodetectors the total amount collected is the same on both scenarios.
When we dive into the deep shadows (low exposure, read noise), the SNR of the teleconverter photodetectors becomes 4 times worse. Once reescaled down to fit the size of the crop, the image from the teleconverter only improves SNR by a factor of 2 (
explanation). This means that once both images are equal in size, the crop will still have a 1 stop advantage (SNR will be double) than the teleconverter in read noise dominant areas (deep shadows).
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I measured the light attenuation when using the teleconverter vs crop, using the same aperture/shutter. Just for the magnification the loss should be around 2EV, but I realized my teleconverter is closer to a X2.1 than a X2 teleconverter, so light attenuation should be higher (log2(2,1^2)=2,14EV). Comparing RAW values, 2,14EV seems to be exactly the attenuation for the G channel, so it seems light loss in the teleconverter is negligible. The other two channels have slightly higher attenuations which can be the prove of some colouring in the optics:
http://guillermoluijk.com/misc/dupliloss.pngThe distributions are so gaussian like (photon noise) that makes me think any additional vignetting introduced by the teleconverter is negligible. However I checkd for the spatial distribution of the light loss (RAW G channel) and was surprised to find a 'ring' near the borders with
lower light attenuation than in the centre itself:
http://guillermoluijk.com/misc/duplivignetting.pngThe differences are nearly negligible (<0.1EV), but I sill wonder what can be the reason for that. Maybe some form of geometrical distortion that compresses more light per surface unit in that ring than in the center.
The converter can actually provide higher SNR, if you decide to increase the exposure, providing more photons per pixel, without exceeding the pixel well depth. This could be a significant advantage for the converter.
Totally agree. In a situation where achieving exposure is not an issue, we could increase exposure vs the crop in 2EV.
Regards