Comparing Sensor SNR

We’ve seen how SNR curves can help us analyze digital camera IQ:

SNR-Photon-Transfer-Model-D610-4

In this post we will use them to help us compare digital cameras, independently of format size.

The graph above shows the noise performance in terms of SNR of the Nikon D610 at base ISO.  Raising the ISO does not change the Exposure (the Signal) but because it may raise the gain amplifying the signal in e^- before it is converted to ADUs it can result in effectively lower read noise figures (if you are interested see Emil Martinec’s pages for why).  The Exposure at which saturation (or clipping) occurs generally drops about one stop for every stop increase in ISO, except sometimes near base ISO where manufacturers try to eek out all they can from a sensor’s dynamic range.

Here is an estimate of how average channel read noise and saturation  vary with changing ISO in the D610, derived from DxOMark.com data:

D610 Sensor Data

And here is how they change in the Olympus E-M1

EM1 Sensor Data

When we plot the relative SNR curves against absolute Exposure in lx-s this is what we get:

Landscapers Comparative Noise IQ Chart

The solid lines (red and blue) represent the cameras’ noise (SNR) performance at base ISO.  The E-M1’s is identical to DxO’s average Full SNR curve while the D610’s has been normalized to match the smaller format’s 16MP sensor resolution.

The dashed lines show how SNR varies with increasing ISO as a result of these changes: as amplification of the signal S in e^- is increased the output starts clipping at a lower Exposure – but at the same time input-referred read noise may be reduced, ameliorating performance in the deep shadows, thus Dynamic Range, as evidenced by the dashed lines in the picture.  I haven’t shown ISOs higher than 400 for the D610’s because the change in read noise is minimal after that, as is apparent from the earlier chart.

The red colored band represents the noise performance advantage of the larger frame sensor versus the smaller format’s at base ISO, from highlights to shadows .  The dashed lines show that in this case the larger format bests the smaller one throughout the ISO range as well, sporting better SNR and DR at all tonal levels at every ISO.

This graph is especially useful in situations where photographers are able to maximize image IQ by exposing the brightest desirable highlights in the scene just short of clipping (sometimes referred to as exposing to the right or ETTR) while remaining within their artistic constraints, which are typically dictated by DOF (controlled by the f-number) and motion blur (controlled by shutter speed).   Together f-number and shutter speed are the main determinants of Exposure for a given scene.  This is often the case in daylight captures and generally true of landscapes off a tripod because exposure time can  then be chosen almost arbitrarily (hence the chart’s name).

If on the other hand, due to artistic constraints (say the need for longer DOF and/or shorter exposure time), the brightest desirable highlights result in an exposure a couple of stops short of clipping at base ISO, the top end of the SNR curve would not contain any useful image information and be wasted.   In this case the image SNR envelope starting point would effectively be a couple of stops down the curve, as shown for the FF camera in the figure below.  However, that would also mean that there are two stops of worthless highlight ‘headroom’ which could be used to the photographer’s advantage by raising ISO – if doing so resulted in effectively lower read noise.  We know that for every stop we raise ISO we lose about a stop of  (in this case unneeded) DR in the highlights – but we may also gain increased SNR in the deep shadows, hence better noise performance and extended DR. This combined effect is shown in the figure below: the sensor saturates at an Exposure two stops lower than before but by raising the ISO two stops from base, noise performance in the shadows has been improved.

Landscapers Comparative Noise IQ - 2 stops

As a result of the lower Exposure (say due to two stops less aperture with the same shutter speed) and the correspondingly higher ISO, top SNR for the FF camera has dropped to a value of 150 from 249 and eDR to 12.7 stops from 13.8.

The fact that Exposure is now two stops short of the ideal for IQ (ETTR)  does not mean that the camera is limited to it.  All  photographers need to do is relax one of their constraints related to f-number and/or shutter speed and select the appropriate ISO to get back to ETTR and max IQ – artistic requirements permitting.

Incidentally the situation depicted above is classic Equivalence, where shutter speed is held firm assuming it provided just enough motion freezing at base ISO – and the f-number dialed into the full frame camera is doubled (say from f/4 to f/8)  in order to provide the desired depth of field, equivalent to f/4 on a format with sensor diameter half its size like mFT.   In this case you can see that the larger format still comes out on top both in terms of SNR and DR throughout the tonal range.   In fact in practice (relative to Photographic Dynamic Range) it would still hold its own if  constraints forced it to have 2 stops less maximum Exposure than the shown mFT camera at base ISO.

This is one of the reasons why  a larger format will typically provide better IQ in landscape captures than a smaller one – and not just noise IQ, as we will see in future posts.

4 thoughts on “Comparing Sensor SNR”

  1. You’ve an interesting site. I definitely need to spend more time s-l-o-w-l-y reading through your posts, but would like to ask a question if I may.

    I’ve heard that full frame sensors provide ‘cleaner’ images than crop sensors IRRESPECTIVE of photoreceptor size. Is this true?

    This seems completely counter-intuitive to me as it is my understanding that, at least for an idealised sensor, image noise is equivalent to ‘shot’ or ‘poisson’ noise; so I would expect (all else being equal) larger photoreceptors to produce a better SNR and therefore cleaner image at low light levels.

    Could you possibly shed some light on this for me?

    Cheers, and sorry for asking such a newb question.

    1. I’ve heard that full frame sensors provide ‘cleaner’ images than crop sensors IRRESPECTIVE of photoreceptor size. Is this true?

      Hi Andrew, this question is only hard to answer depending on what one means by all else equal. For instance if we assume that both formats are under the same exposure it’s easy to show that the number of photons per unit area incident on both sensors will be the same if the rest of the equipment is the same. That means that the larger area of the FF frame sensor will see about 2.25 more photons than the crop’s. Assuming no read noise it does not really matter how you count those photons: i.e. 100k in one million Pixels, 10k photons in each of 10 MP, 1 in 100 MP or… In the end it’s always the same 100G photons collected and processed to produce your, say, 2MP final image. And as you say the more photons you have the better the SNR of the final image of the same subject displayed at the same size and resolution, so FF wins irrespective of pixel pitch, aotbe.

      1. Hi Jack. Thanks for the quick response! I don’t mean to try your patience, but I’m still a bit confused.

        By “all else being equal”, I mean quite literally just that – pixel size and design, manufacturing quality control, SNR firmware, exposure – the only variable being the overall dimensions of the sensor itself.

        I get that a FF sensor will see more photons in total – it does after all have a larger surface area. But assuming that both the FF and crop sensor have identical pixel pitch, then every individual photoreceptor on both sensors will receive (on average) the same number of photons, and should therefore each produce the same SNR, no? I fail to see how photons falling on the area of a FF sensor that extends beyond that of a crop sensor can contribute to better SNR for pixels in the center of the FF where coverage of the two sensors is identical.

        Perhaps the biggest source of my misunderstanding lies here: you say that it doesn’t matter how the photons are counted. Why this should be eludes me. With regards to producing a clean image, aren’t we most interested in variance between pixels? So for a given sensor area, wouldn’t 100M photons divided over 10MP (an average of 10 photons per pixel) generate a SNR of 3, but if divided over just 1 MP (an average of 100 photons per pixel) generate an SNR of 10, suggesting that pixel size is the dominant factor in providing a clean image?

        Or put another way, assuming the same 6 micron sized pixels are used on a FF sensor (24.0MP) and on an aps-c crop sensor (10.7MP), an exposure that results in 100M photons falling over the FF sensor would generate an average SNR of 2.04 at each pixel, while the same exposure would result in 44M photons falling over the crop sensor generating a near identical SNR of 2.03. While the FF sensor in this instance would offer better resolution, wouldn’t these two sensors produce similar noise in the final image? Or does image scaling mean that the FF sensor wins?

        I’m wondering then if the reasoning that FF produces less noise irrespective of pixel size is something like this:
        If FF pixel size > crop pixel size, FF wins due to better SNR.
        If FF pixel size ≤ crop pixel size, FF wins due to scaling.
        So FF always wins, aotbe.

        Again, thank you for your time, and I sincerely appreciate any clarification you may be able to provide. Cheers.

  2. Hi again Andrew,

    Yes, I think you got it. Assume perfect photon-counting pixels of the same size in the two formats’ sensors as suggested, both exposed to the same angle of view and Exposure. Say that 10k photons are incident on the average pixel under that uniform Exposure. What’s the SNR of the captured image in the raw data? Then you display the final image from both cameras at 2MP at the same size (say 1920×1080). Assuming a perfect video chain, what’s the SNR of the displayed image?

    What counts is the SNR of the final image, displayed at the same size independently of format. How many incident photons correspond to one pixel of the final image in both cases?

    Things are only a little more complex when introducing non idealities and other things being equal (like DOF for instance).

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