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Just interested in choosing the right smartphone for lowlight photography I have following contenders.
Option 1 has 16 MP, Aperture f/1.8, OIS, with sensor size 1/2.6" and 1.12 μm pixel size
Option 2 has 12 MP, Aperture f/2.0, OIS, with sensor size 1/2.3" and 1.55 μm pixel size
Pixel count and pixel size are largely irrelevant since you can often trade noise for detail via noise reduction and downscaling. This may not apply if the gaps between the pixels are relatively large compared to the pixels themselves. I do not think that it makes much of a difference in your case since the pixel sizes are quite similar.
What's most important is the total amount of light hitting the sensor, which is proportional to A / f², where A is the sensor area and f is the aperture. In your case, this works out to:
Option 1: 18.20 / 1.8² = 5.62
Option 2: 23.25 / 2.0² = 5.81
So option 2 captures about 3.4% more light than option 1, which is negligible. Sensor design will have a much larger impact on noise performance in low light than the theoretical light capturing abilities of these two camera assemblies.
For two phones listed above, the answer is indeterminate. Even though option 1 captures less light per pixel and thus has higher per-pixel noise, you can apply more noise reduction before the picture becomes too fuzzy to tolerate, which means you may still end up with a less noisy picture overall. And given that we're talking about only a 3.4% difference (see Jules's answer), I think it's pretty likely that the higher-resolution camera will yield better pictures.
With that said, I'd be remiss if I didn't point out that choosing the best smartphone for low-light photography is like choosing the best Ford Fiesta for moving a concert grand piano.
Even APS-C isn't great in low light. And the best cell phones aren't even what I would call good. As others have mentioned, the amount of light hitting a sensor is proportional to the surface area divided by the square of the aperture. So assume (for example) a 33 mm^2 cell phone sensor at f/1.8, you get:
33 / (1.8 * 1.8) = 10.2
Now if we fill in an APS (full frame) sensor:
864 / (x^2) = 10.2
we get x = 9.2. So for a given megapixel count, assuming all else is roughly equal, the full-frame camera gets more than 4.5 stops more light per pixel.
To put it another way, if you compared such a cell phone to a DSLR with an f/1.8 lens (apples to apples here), if the DSLR were shooting at ISO 100, the cell phone would have to use a longer shutter speed even at ISO 1600 (typically, a cell phone's max ISO).
Alternatively, if you keep the same ISO level (and thus, in theory, comparable noise levels), a full-frame sensor would take shots ~23x as fast. If the shot takes 1/100th of a second on a DSLR, then, you'd expect it to take a quarter second on the cell phone.
And this would likely remain true even if camera manufacturers stopped improving their large sensors right now, because there just isn't that much room for improvement in terms of how much light a sensor gathers at this point. No matter how much image stabilization you do, no matter how many times you try to take the shot and pick the best one, that's only going to get you a couple of stops, realistically. The other 2.75-ish stops make the difference between a high keeper rate and an appallingly bad keeper rate.
Plus with 30-ish megapixels on a modern FF camera instead of 12 or 16, you can apply much heavier noise reduction before the picture becomes too soft. :-)
The major thing while choosing a mobile camera you have to keep in mind is, when it comes to mobile imaging the quality depends on much more factors than just pixel count, Aperture, stabilization, sensor size and pixel size. This is because heavy post processing is involved in mobile images as the raw output is unpalatable due to noise(very tiny sensor). Most mobile image processing pipelines include Noise filtering, edge enhancement, contrast enhancement, pixel correction and most of all extra added processing for low light shots such as multi frame processing. Multi frame processing works on multiple number of frames ranging between 3 to 9 generally and fuse them to reduce noise and enhance features like edges and colors. Every smart phone makers have their own algorithm with specific advantages.
So the best way to judge the quality of a smartphone's low light performance is to put it to use or go by the reviews of the same.
According to my math (which should be verified, because I'm no math scholar) ...
Option 1's aperture allows 11% more light to reach the sensor than Option 2's aperture.
Option 2's pixels capture 38% more light than Option 1's pixels (since they are 38% larger).
Stands to reason then that Option 2 will capture more light in any lighting conditions. That doesn't mean its pictures will have better results. Its pictures will be 4 megapixels smaller, and may be noisier than Option 1's pictures.
The crop factor between the two sensor sizes is:
(1/2.3)/(1/2.6) = 1.13
So the f/1.8 aperture of the smaller sensor is equivalent to f/2.03 on the bigger sensor (1.8*1.13). So the smaller sensor also has a slightly smaller aperture.
