http://www.clarkvision.com/articles/does.pixel.size.matter2
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The noise in good modern digital
cameras is dominated by photon counting statistics, not other sources.
Why this is important is that because of this fundamental limit,
performance properties of digital cameras can be predicted and
the results modeled with simple equations. This performance level
is called photon noise limited and is the best that can be achieved.
This is explained in detail at:
The Signal-to-Noise of Digital Camera images and Comparison to Film.
So far, all modern digital cameras tested in
the last few years have noise that is dominated by photon noise at signal
levels above a few tens of photons. For example, see sensor analyses
and further references at:
http://www.clarkvision.com/articles/index.html#sensor_analysis.
This web page shows example images that illustrate differences in performance between a camera with large pixels and one with small pixels. Ignore the color balance differences, and examine the noise. A small pixel can not collect as much light as a large pixel, much like different sized buckets in a rain storm: the large bucket collects more water. But how much? For the range of cameras tested so far, that range amounts to a factor of about 16. The effect of this ability is the small pixel camera operating at a low ISO of 100 is like operating a large pixel camera at ISO 1600. The example images of a night scene showing Waikiki Beach and the city of Honolulu illustrate these effects.
Full Scenes
Figures 1 through 4 show two different exposures with two different cameras of the Honolulu night scene. The large pixel camera, a Canon 1D Mark II DSLR has pixel spacing of 8.2 microns, so the pixel active area is a little smaller than 64 square microns. The Canon S70 camera has a pixel spacing of 2.3 microns, and an active area less than 5 square microns (probably less than 4). The focal lengths for the two cameras were selected to give approximately the same field of view considering the different aspect ratios of the two cameras, and the limited ability to finely zoom the S70. The full scenes look reasonable in image quality, but one can not tell the details of the noise. For that we need full size examples. In comparing images, ignore the color balance differences between cameras. All images on this page were taken at the same f/ratio.
Figure 1. Honolulu night scene with a large pixel camera, 4 seconds
and iso 400. Image from camera defaults with no post processing
modifications.
Figure 2. Honolulu night scene with a small pixel camera, 4 seconds
and iso 400. Image from camera defaults with no post processing
modifications.
Figure 3. Honolulu night scene with a large pixel camera, 15 seconds and iso
100. Image from camera defaults with no post processing
modifications.
Figure 4. Honolulu night scene with a small pixel camera, 15 seconds and iso
100. Image from camera defaults with no post processing
modifications.
Full Scale Image Crop Comparisons
The above images are really too small to see the full image quality, so let's compare side-by side image crops at full scale (Figures 5 through 9). Figure 4 shows the image quality at ISO 400 with the exposure and f/stop the same on the two cameras. Note the noise in the small pixel (S70) camera compared to that in the large pixel camera.
The higher signal-to-noise ratio of the image data from the large pixel camera allows the image to be enhanced do bring out subtle details (Figure 6). If the same enhancement was done to the small pixel camera image, the result is poor (Figure 7).
Figure 5. Full scale crop comparisons of the night scene taken with
the same exposure, f/stop and ISO for both cameras.
Image from camera defaults with no post processing
modifications.
Figure 6. Full scale crop comparisons of the night scene taken with
the same exposure, f/stop and ISO for both cameras, from Figure 5.
Image from camera defaults with no post processing
modifications on the small camera, but adjusted to show more details
in shadows and highlights in the large camera image. Processing
included: photoshop CS2 shadow/highlight (50% shadow, 30%
highlight), small curves adjustment and unsharp mask.
Figure 7. Full scale crop comparisons of the night scene taken with
the same exposure, f/stop and ISO for both cameras.
Both images were adjusted in the same way to show more details
in shadows and highlights in the large camera image. Processing
included: photoshop CS2 shadow/highlight (50% shadow, 30%
highlight), small curves adjustment and unsharp mask. The small
pixel camera has so much noise that the adjustments are detrimental
to the small camera image but not the large camera image.
The large pixel camera enables one to take higher ISO images and still maintain higher image quality over the small pixel camera (Figure 8). In fact, for the cameras used in this test one needs to go to extreme differences in ISO between the small and large pixel cameras (Figure 9) where ISO 100 images from the small pixel camera show similar image quality to ISO 1600 images from the large pixel camera. This large difference is accurately described by the "Unity Gain ISO" discussed below.
Figure 8. Large and small pixel cameras compared with the same
f/stop but the large pixel camera was boosted 4x to ISO 1600 and the
exposure reduced 4x to 1 second. The large pixel camera still
shows lower noise.
Image from camera defaults with no post processing
modifications.
Figure 9. Large and small pixel cameras compared where the ISO
and exposure times were adjusted to give similar image quality.
The large pixel camera was boosted to ISO 1600 and the
exposure reduced to 1 second. The small pixel camera ISO was
reduced to 100 and the exposure time increased to 15 seconds.
The images from the two cameras have similar noise.
Image from camera defaults with no post processing
modifications.
The reason why the large pixel camera does so well compared to the small pixel camera is basic physics of how the cameras collect light. The small pixels collect less light similar to the way a small bucket collects less rain water than a large bucked in a rain storm.
Camera manufacturers set ISO based on some fraction of the maximum signal that can be recorded. The maximum signal is is called the full well capacity, which is the maximum number of electrons (converted photons) that a pixel can hold. Larger pixels in general hold more electrons. For current technology of CCD and CMOS sensors, the full well capacities run about 800 to 1600 electrons per square micron. These values haven't changed much in over twenty years of sensor development. The setting of ISO implies that cameras with different size pixels collect the same amount of light per unit time for a given f/ratio. That is incorrect (see f/ratio Myth. The ISO definition relates to the fraction of light relative to the full well capacity, not the total light collected. For a given f/ratio and exposure time, a camera with larger pixels collects more photons. The camera designers change the gain of each camera based on the full well capacity. A property called the Unity Gain shows the true sensitivity of a sensor. Figure 10 shows some measured unity gains for different cameras. The much higher ISOs at unity gain of large pixel cameras shows that they have much better low light performance. This analysis does not include thermal noise, which becomes significant after minutes of exposure time. More on this topic can be found at: Digital Camera Sensor Performance Summary Digital Camera Sensor Performance Summary and Digital Cameras: Does Pixel Size Matter? Factors in Choosing a Digital Camera.
Camera manufacturers define the number of photons collected for each camera differently so we see the same numbers in our image files. For example, in the small pixel size camera, a smaller number of photons gives maximum signal (e.g. number 255 in an 8-bit image) than a larger pixel size camera. A specific example using the cameras used for the images on this web page: a Canon S70 with 2.3 micron pixel pitch produces images where 255 in an 8-bit image corresponds to about 4,300 electrons, but in a 1D Mark II with 8.2 micron pixel pitch gets about 53,000 electrons at number 255 in the 8-bit image, when both cameras are set to ISO 100. This happens when using the same f/ratio and same f/stop on both cameras. That means the large pixel camera collects 12 times the light even when working at the same f/ratio and exposure time (53,000 photons/4,300 photons ~ 12). A factor of about 12 to 16 is common for the Unity Gain ISO difference between small and large pixel cameras currently on the market. You can compute the approximate ISO factor change between two cameras by squaring the ratio of the pixel pitches, e.g. for the S70 and 1D Mark II that would be: (8.2/2.3)2 = 12.7.
Current good quality sensors in digital cameras are photon noise limited and that is the best one can do (improving electronics will not improve the noise). This means that the basic performance can be modeled and predicted. The number of photons a digital camera collects in each pixel is directly related to the size (area that converts photons into electrons) of the pixel. The more photons collected, the better the signal-to-noise ratio in the image, thus the larger pixel sizes do better in this regard. Larger pixel cameras have better signal-to-noise ratios at all levels, but this becomes more obvious especially at low signal levels. In the extremes of current digital cameras with small cameras having pixel sizes near 2-microns, and large pixel cameras (currently found in DSLRs), there is a factor of about 12 to 16 in photons collected. That means the large pixel camera performs at ISO 1200 to 1600 with similar noise and dynamic range performance of a small pixel camera operating at ISO 100. If you are a DSLR owner, do you take all your pictures at ISO 1600? If you are a small pixel point and shoot cammera user, do you use ISO 400 often? If so, that is like using ISO 6400 on a large pixel DSLR in terms of noise and dynamic range performance! (Such effective ISO's can be achieved with DSLRs by setting the ISO to 3200 and the meter compensation to -1 stop.) It is this fundamental difference of pixel size as to why large pixel DSLRs have such great noise performance, which leads to low light and fast action performance. Whether the difference in noise performance is great enough for you to choose a larger sensor, and thus likely a larger and heavier camera, is a decision you must make for yourself.
The fundamental error in measuring a photon signal is the square root of the number of photons counted, Poisson Statistics. The maximum number of photons one can count with a sensor is the maximum number of electrons in that can be held in the well. There is one electron per photon. If one fills the pixel well with 40,000 electrons, then the noise in the signal is square root 40,000. So whatever the signal is, the error (noise) is square root of the number of electrons (photons). The more photons counted, the higher the signal-to-noise. The signal-to-noise = # photons/square root(# photons) = square root(# photons) In the shadows in an image, one may get only a few hundred photons, so the noise is square root of those few hundred.
The Poisson Distribution http://mathworld.wolfram.com/PoissonDistribution.html
Signal-to-Noise Ratio in digital imaging: http://www.photomet.com/library_enc_signal.shtml
Photon noise: http://www.roperscientific.de/tnoisesrc.html
Digital Camera Sensor Performance Summary.
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First Published December 22, 2006.
Last updated November 2, 2008.