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I already understand all the theory behind how a bigger sensor leads to better control of depth of field, and lower noise. But I've yet to find a place that can explain why a bigger sensor gives you a bigger dynamic range?

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AFAIK, 5 of the top 10 dynamic range cameras on DxOMark are APS-C sensor cameras and all of them are 35mm form factor and no medium format is there. So, the opening premise of the question isn't really true. –  John Cavan May 14 '13 at 21:51
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@JohnCavan that's true for dynamic range in good light. At ISO100 the APS-C Pentax K5 beats the full frame Canon by over two stops, however at ISO800 and above the full frame Canon is ahead, and in really low light the gap is over a stop, which is about what you'd expect from the sensor area advantage. –  Matt Grum May 15 '13 at 8:16

3 Answers 3

up vote 12 down vote accepted

The size of the sensor does not matter, it is the size of the pixel. Having that said, bigger sensors like in full frame cameras tend to have bigger pixels.

You can estimate the size of the pixel by taking the size of the sensor and divide it by the number of pixels. This calculation is not accurate because most sensors have gaps between the pixels and these gaps differ in size. That is why I'm saying "estimate".

Now, think of a pixel in the sensor as a box and photons as balls. The bigger the box, the more balls it can contain.

Assuming we have box A and B. Box A can contain 256 balls and box B can contain 512 balls. Now lets arrange a box matrix of A type and throw a lot of balls in the air. We want gather some statistics of where the balls fell.

In the middle one of the boxes contains 256 balls and in the edges the boxes contains ~20 balls. We cannot know if in the middle only 256 balls fell or more. Our measure is limited to maximum for 256 balls.

Now lets repeat this experiment but now with boxes of type B. Now we can see that in the middle the box contains 347 balls and on the edges the boxes contains ~20 balls.

Our measure is far more accurate. That's exactly what happens with the photons hitting the sensor. Bigger surface can contain more photons and can measure a larger dynamic range. In our example the dynamic range is twice as big in the bigger box.

If the pixel is full of photons the translation to color will be a fully saturated color but with a larger pixel surface we will get a better result, thus, improved dynamic range.

Here is a picture that can demonstrate my explanation:

Dynamic Range Explanation

For deeper explanation you may want to check this article:

Dynamic_Range

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Nice, I'll now up vote. –  John Cavan May 14 '13 at 22:06
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This answer is a good start, however it is missing a critical factor: Electronic noise. Yes, it is true that you have improved dynamic range (and less photon shot noise) with larger pixels. It should be noted, however, that gains made with larger pixels can be LOST due to electronic noise in the sensor circuit, as well as in the readout and conversion circuitry. Theoretically, the Canon 1D X should have more dynamic range than the Nikon D800, yet the D800 has a full two stops more DR. Why? The D800 has FAR less electronic noise (~3e-) than the 1D X (~36e-). –  jrista May 15 '13 at 0:01
    
Good explanation of the theory but completely ignores the practice! –  Matt Grum May 15 '13 at 8:01
    
The article you linked is really, really great! Compliments –  Revious May 23 at 11:36

There is no reason that a bigger sensor can give a bigger dynamic range or lower noise other than more surface area per pixel, however full frame cameras tend to be higher end units and therefore tend to have better sensors.

Note that there is no reason that a lower resolution, smaller sensor couldn't have better noise and dynamic range performance if made at a similar quality to a full frame sensor. The number of pixels per inch on the sensors surface and the quality of the sensor are the bits that matter.

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Considering ideal sensors where photon noise is the only concern then the larger the sensor the greater the dynamic range. Dynamic range is the difference between the point at which the sensor becomes saturated and the point at which any detail is lost to noise in the shadows.

A larger sensor will either have larger pixels, or more pixels. Larger pixels mean a greater capacity to store charge (all else being equal) and more light being captured per pixel hence less light in the shadows, hence greater dynamic range. More pixels means the similar noise per pixel but more pixels to average over to reduce shadow noise, and hence increase dynamic range.

In reality there are other sources of noise, namely read noise, where the analogue signal produced by the photosites picks up noise prior to being digitized. This can have an effect on dynamic range that is far stronger than differences in sensor size. Low intensity signals from dark areas of the image are particularly sensitive to read noise hence the large impact on DR.

New technology (shortening the path from sensor to ADC, sending the signal twice and comparing the results) can virtually eliminate read noise this enables APS-C sensors such as the Sony Exmor to exceed the dynamic range of Canon's 2.5 times larger full frame sensors by almost an order of magnitude!

It is also necessary to distinguish between dynamic range in good light and dynamic range in poor light. The former is determined mainly by read noise, hence a small sensor can excel provided it has low read noise and a decent enough well depth. The latter is dominated by photon noise (raising the ISO in low light amplifies photon noise but not read noise) hence larger sensors tend to perform better here. Again not every sensor follows the trend.

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The benefit of Sony Exmor is that it is digital readout. The signal is only analog so long as the charge remains in the pixels. Upon read, on-die column-parallel ADC immediately converts the analog charge of each pixel into a digital unit. High frequency components (clock, pll, etc.) are placed elsewhere on the die to eliminate high frequency noise introduction in the ADC circuitry. The image signal is not read twice...a "reset read" is performed when the sensor is reset to accumulate digital CDS as a "negative result", which is then applied to the "image read" upon exposure. –  jrista May 15 '13 at 14:03
    
Per-pixel CDS was eliminated. I don't even think each pixel has an amplifier, as with near-noiseless output, all ISO settings can be achieved with digital amplification. Analog pixel charge is converted immediately to a digital unit, and from that point on error-corrected information transfer of digital information is utilized throughout the rest of the image processing pipeline. That eliminates the chance for contamination of the analog signal by interference of any kind as early as possible. –  jrista May 15 '13 at 14:04
    
Am I correct in saying that, given the same read noise (technology etc) the larger sensor with bigger pixels will have less photon noise and thus better dynamic range because of increase latitude between the lowest charge and saturation point? –  erotsppa May 15 '13 at 16:04

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