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Contents
In today's Digital Camera market there is a bewildering array of models
to choose from. I recently faced such a decision when I wanted to buy
a small point and shoot digital camera. I wanted a small size, high megapixel
count, fast response time (low shutter lag), and low noise camera.
I did not get what I wanted because it did not exist at the time of my
purchase. After a little research, I find I never will get what I
wanted, unless someone comes up with a way to break the laws of physics.
I hope to show you what I mean in this article.
The sensor in today's digital cameras uses a charge-coupled device, CMOS sensor or other similar device that is an array of pixels. Each pixel, is a semiconductor material that absorbs photons and generates electrons. The electrons are gathered and held in what is called a potential well, or voltage well that prevents the electron from drifting away. The analogy is a bucket of water holding rain drops, and the photons are the rain drops falling on the buckets. This analogy is shown in Figure 1.
When the image is ready to be read out, the analogy is a bucket brigade where the water from the first bucket is emptied into the analog-to-digital (A to D) converter, then the water from the next bucket is poured into the first bucket, which then gets poured into the A to D converter, and so on. The walls of the bucket must be thick enough so the water does not leak out and get into the adjacent bucket. This sets minimum sizes for the walls and sizes of the hole the water can fall into, and in the electronic world, how big the electron well walls must be, how far apart they must be, and restricts the size of the active area where photons are absorbed to generate electrons. Even if some advances are made in these areas, there is one fundamental limit: photon counting statistics.
Figure 1. Photon rain: the analogy of photons falling into
buckets which collect the rain drops. A larger bucket collects more
drops. Given two sensors with equal numbers of pixels, and each
with lenses of the same f/ratio, the larger sensor collects more
photons yet has the same spatial resolution. (The lens for the
larger sensor would have a longer focal length in order to cover the
same field of view is the system with the smaller sensor.)
In the analogy of the photon rain filling buckets, as shown in Figure 1, the, larger the bucket, the more drops that can be collected in a given amount of time. This is important for a very fundamental reason: the accuracy of the signal measured is directly proportional to the size of the signal. In the physics of photon counting, the noise in the signal is equal to the square root of the number of photons. For example:
Table 1
Photons Noise signal-to-noise 9 3 3 100 10 10 900 30 30 10000 100 100 40000 200 200
The Light that is absorbed in the silicon sensor does so over a very limited range. Back to the bucket in the rain analogy. Making a deeper bucket does not help with electronic sensors because the light will not penetrate any deeper. So to collect more light, only area matters, and this is why in Figure 1, the bucket depth is the same for small and large pixels.
Why is this important? It turns out that the noise in good modern digital cameras is dominated by photon counting statistics, not other sources. This is explained in detail at: The Signal-to-Noise of Digital Camera images and Comparison to Film. Some of the data from articles on the clarkvivion.com site are shown here for several cameras: a top end professional DSLR: the Canon 1D Mark II, a prosumer DSLR: the Canon 10D, and Point and Shoot cameras, "P&S": the Canon S60 and S70. Figure 2 and 3 show that the the top pro model as well as the consumer point and shoot camera discussed here are photon noise limited. In fact, all modern digital cameras tested in the last few years have been shown to be photon noise limited 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#part_4 Digital Camera Sensor Performance.
Figure 2. The Canon 1D Mark II is photon noise limited at all ISO settings.
Only photon noise shows the square-root dependence on signal seen here.
Figure 3a. The noise from the Canon S70 point and shoot consumer camera is photon noise limited
for all levels above about 10 photons. Blue points are measured values, and the red
line is a model with: maximum signal = 8,200 photons (electrons), read noise = 4.1 electrons.
Only photon noise shows the square-root dependence on signal seen here.
Figure 3b. The signal-to-noise from the small sensor, 2.3 micron pixel
pitch, Canon S70 point and shoot consumer camera is compared to that from
a large sensor, 8.2 micron pixel pitch, Canon 1D Mark II DSLR camera.
The signal-to-noise ratio of an 18% gray card is at 0-stops, with
brighter parts of the image are to the right, and darker parts to the
left, following each curve. For example, the Canon 1D mark II at
ISO 100 would record a signal-to-noise ratio of about 100 on the
18% gray card but only about 10 in shadows at -5.5 stops (follow
the magenta line).
The 1D Mark II has about 13 times the sensitivity of the small S70 camera.
The lower slopes of the lines above a signal-to-noise ratio of about 8
indicates the noise in the images are photon noise dominated, while at
lower ratios, the signal becomes increasingly read noise dominated.
An example of large versus small pixels and the effects on image quality is illustrated in Figures 4 and 5. Figure 4a and 4b shows the full scene recorded by two cameras set at the same ISO (ISO 400), same f/stop (f/4.5), and same exposure time (1 second). The pixel pitch (the distance from one pixel to the next; the actual pixel area sensitive to light is slightly smaller) is 8.2 microns for the large pixel camera (Canon 1D mark II) versus the small pixel camera (Canon S70). Both cameras have almost identical read noise at ISO 400: 5.6 electrons for the 1D Mark II and 4.3 electrons for the S70, thus the S70 has a slight advantage! But despite the read noise advantage, the larger pixels of the big camera collects so much more light per pixel that the image quality is much better than the small pixel camera (Figure 5).
Figure 4a. The Canon 1D Mark II DSLR full test scene: books in a bookshelf.
ISO 400, f/4.5 1, second exposure.
Figure 4b. The Canon S70 Point and Shoot camera full test scene: books
in a bookshelf. ISO 400, f/4.5, 1 second exposure.
Figure 5. Full image crops from Figures 4a and 4b. The crops are from
raw converted 16-bit TIF images converted by Canon Zoombrowser software
with the same (default) settings for both cameras. Both cameras recorded
the same exposure at the same ISO, and same f/ratio: ISO 400, f/4.5, 1
second exposure. The large pixels of the 1D Mark II produce higher
signal-to-noise images than the small pixels of the S70. Both cameras
are photon noise limited, as are these images. The signal-to-noise
ratio is abut 3.6 times higher for the 1D Mark II image, equal to the
ratio of the pixel pitch from each camera.
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, the analogy shown in Figure 1. 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 on over twenty years of sensor development. The setting of ISO implies that cameras with different size pixel collect the same amount of light per unit time for a given f/ratio. That is incorrect (see the section on f/ratio myth below). 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 6 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. Long exposures will include an additional noise source: dark current. Dark current will be discussed in future additions to this article.
A large dynamic range is important in photography for many situations. The pixel size in digital cameras also affects dynamic range. Dynamic range is defined here to be the maximum signal divided by the noise floor at each ISO. The noise floor is a combination of the sensor read noise, analog-to-digital conversion limitations, and amplifier noise. These three parameters can not be separated when evaluating digital cameras, and is generally called the read noise. The measured read noise near unity gain is essentially equal to sensor manufacturer's published specifications for read noise, so the zero signal case is read noise limited. As you might have surmised by now, with the larger pixels collecting more photons, those larger pixels also have a higher dynamic range. Figure 7 shows the measured dynamic range from 3 cameras with significantly different pixel sizes as a function of ISO. The full sensor analyses for these 3 cameras (as well as other cameras) can be found at: http://www.clarkvision.com/articles/index.html#part_4. Large pixel cameras are currently limited by noise in downstream electronics, such as from the analog-to-digital converters. If such noise could be eliminated, the dynamic range could increase in cameras with large pixels by about 2 or more stops when operating at low ISOs. The current smallest pixel cameras do not collect enough photons to benefit from higher bit converters.
Figure 7. The dynamic range for 3 different cameras is shown, along
with models that show what performance would be if electronics noise
after the sensor was zero.
Large pixel cameras have a larger dynamic range. The small pixel camera
has a very good dynamic range at low ISO, but that range rapidly deteriorates with
increasing ISO. The larger pixels have greater dynamic range at all ISOs,
beating smaller pixel cameras. Further, the large pixel cameras have high dynamic
range over a larger range of ISO.
The measured dynamic range (symbols) is shown with models of
the expected dynamic range (dashed lines). The dynamic range is often limited
by the A/D converter and other electronics in the system,
illustrated by the measured data falling below the model at lower ISOs.
The dynamic range for more cameras can be found at
Digital Camera Sensor Performance Summary
http://www.clarkvision.com/articles/digital.sensor.performance.summary.
Sensor sizes in smaller cameras are specified by a strange parameter, like 1/1.8" which dates from TV camera tubes from the 1950s. In my opinion, this is simply to confuse consumers as to the true nature of the small sensors. See Sensor Sizes http://www.dpreview.com/learn/?/Glossary/Camera_System/Sensor_Sizes_01.htm for more details. Here are some simple translation numbers
Table 5
Sensor Size (mm)
Type Width Height
1/6 2.40 1.80
1/4 3.60 2.70
1/3.6" 4.00 3.00
1/3.2" 4.54 3.42
1/3" 4.80 3.60
1/2.7" 5.37 4.03
1/2.5" 5.76 4.29
1/2.3" 6.16 4.62
1/2" 6.40 4.80
1/1.8" 7.18 5.32
1/1.7" 7.60 5.70
1/1.6" 8.08 6.01
2/3" 8.80 6.60
1" 12.80 9.60
4/3" 18.00 13.50
APS C 23.70 15.70 (1.6x crop; also called 1.8")
APS-H 28.7 19.1 (1.3x crop)
35 mm film 36.00 24.00
Diffraction also limits the detail in an image. The diffraction spot diameter in the focal plane of an optical system is proportional to the f/ratio according to the formula: Diffraction spot diameter = 2 * 1.22 w * f / D = 2.44 * w * f_ratio, where w = wavelength, f = focal length, D = aperture diameter, and f_ratio is the f/ratio of the optical system. The diffraction spot size is given in the table below:
Table 6
================================================
red= Green= Blue=
0.6 0.53 0.47
micron micron micron
================================================
f/ratio diffraction spot diameter in microns
================================================
2 2.9 2.6 2.3
2.8 4.1 3.6 3.2
4 5.9 5.2 4.6
5.6 8.2 7.2 6.4
8 11.7 10.3 9.2
11 16.1 14.2 12.6
16 23.4 20.7 18.3
19 27.8 24.6 21.8
22 32.2 28.5 25.2
32 46.8 41.4 36.7
45 65.9 58.2 51.6
64 93.7 82.8 73.4
================================================
The wavelengths are the approximate centers of the red, green and blue filters in digital cameras. Note the diffraction size is larger for redder colors.
Compare the diffraction diameters with pixel sizes in digital cameras. The Canon 1D Mark II discussed above has 8.2 micron pixel spacing, and with the blur filter which is used on most Bayer-sensor cameras, the resolution is perhaps 30% worse, so about 11 microns. At about f/8 the camera pixels + blur filter matches the blur due to diffraction. But the same trade point in the small sensors in the Canon S60, with 2.7 micron pixel spacing, occurs at f/2.8. This diffraction spot size versus pixel size trade point occurs at a 20% degradation in high frequency contrast (80% MTF). The contrast reduction is shown in more detail in Figure 8. Diffraction at this point is beginning to limit resolution but not seriously so. But using apertures smaller than this trade point means the image resolution is becoming more limited by diffraction, not the sensor. Unless you work with very fast lenses all the time, you need larger pixels in order to maintain image detail. Thus, cameras with a larger sensor containing more pixels have the advantage against being limited by diffraction.
Figure 8. Diffraction affects image detail by reducing contrast.
The technical term for the contrast reduction is called the
Modulation Transfer Function (MTF) and describes the contrast
the camera delivers as a function of the spacing of lines (called the
spatial frequency).
Here the spatial frequency is expressed in terms of pixel spacing.
As the f/stop increases, the diffraction spot becomes larger, and
fine detail in the image becomes reduced in contrast.
The red, green and blue lines show the diffraction effects for red,
green and blue wavelengths of light for f/ratios 1, 2, 4, and 8.
In order to make a given print size, the image must be enlarged from the small image in the focal plane of the camera. For example, say you want to make 8 x 10 inch (203 x 254 mm) prints. If your sensor is like the S60 at 7.18 x 5.32 mm, one would need about a 36 times enlargement. Such extreme enlargement would magnify any lens imperfections, and vibration during the exposure. The larger sensor of the 1D Mark II, with its 28.7 x 19.1 mm sensor, needs only a 10.6 times enlargement (making an 8 x 12 inch print), or 3 times less enlargement of lens imperfections and vibration than the S60.
Traditionally in photography, larger formats
have produced better images on the final print. A major factor in image
quality is the enlargement factor. Large formats (like 8x10 or 4x5 film
and now large format digital scanning backs) produce spectacular large
prints that can't be matched by smaller (e.g. 35mm and smaller) formats.
Those factors scale to even smaller formats of present point and shoot
small sensor digital cameras.
There is a common idea in photography that exposure doesn't change between different size cameras when working at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). The myth is that every camera will provide the same signal-to-noise images as long as the same exposure time and f/ratio lens is used, from the camera with the smallest sensor, to the camera with a large sensor.
The concept of constant exposure for a given f/ratio leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is the spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject.
The rate of arrival of photons in the focal plane of a lens
per unit area per unit time is proportional to the square of
the f-ratio. Corollary: if you keep f/ratio constant, and change
focal length then the photons per unit area in the focal plane is
constant but spatial resolution changes.
So how does this apply to making smaller cameras?
The problem is that if you scale a camera down, say 2x in linear size, the aperture drops by 2x in diameter, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x (linearly or 4x the area), and the pixel size drops by 2x (linearly or 4x the area, to give the same spatial resolution on the subject). The aperture has collected only 1/4 the number of photons. If we kept the same sensor, then each pixel would collect the same number of photons because each pixel now sees a larger angular area (4x larger). But we want the same resolution, so the pixels are 2 times smaller (4x smaller area). The smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant.
Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Thus, photons delivered to a pixel for a given resolution on the subject goes as the square of the aperture (and camera size)! Decreasing your camera by 2x means 4x less photons per pixel if you want to maintain field of view and megapixel count!
This is just what we observe with small cameras: their smaller sensors have smaller full well capacities, that get filled for a given exposure time with a smaller number of photons. That in turn means higher noise because there are fewer photons.
A good example is the Canon 20D with 6.4 micron pixels and a maximum signal at ISO 100 of 50,000 electrons, compared to the Canon S60 with 2.8 micron pixels with a maximum signal of about 11,000 electrons at ISO 100. The pixel size is (6.42 *6.42) / (2.82 * 2.82) = 5.2x scaling, similar to the 50000/11000 = 4.5 scaling of maximum recorded signal.
Then, for photon noise limited systems, signal-to-noise ratio achievable in an image is the square root of the number of photons collected, so signal-to-noise ratio scales linearly with the camera pixel size. That concept is illustrated in Figure 5, above: the small sensor camera produced a noisier image than the larger sensor camera even though the f/ratio, exposure and ISO are the same for the two cameras.
If you tried to make a smaller camera that collects the same number of photons as a larger camera, you must keep the aperture constant. Given a camera, for example, with a 50 mm f/1.4 lens then to shrink the camera 2x in size (linear dimensions), you would need a 25 mm f/0.7 lens that had double the resolution if you wanted to keep the same detail in the image. That means the smaller camera would not be much smaller, due to the lens, and might be more expensive due to the lens specifications.
See also: The f/ratio Myth and Digital Cameras http://www.clarkvision.com/articles/f-ratio_myth
Check out this web page for more info on this subject:
http://www.stanmooreastro.com/f_ratio_myth.htm
After understanding the concepts in the f/ratio myth, there
is another major implication of scaling sensors.
Given the identical photon noise, exposure time, enlargement size,
and number of pixels giving the same spatial resolution (i.e. the
same total image quality), digital cameras with different sized
sensors will produce images with identical depths-of-field. (This
assumes similar relative performance in the camera's electronics,
blur filters, and lenses.) The larger format camera will use a
higher f/ratio and an ISO equal to the ratio of the sensor sizes to
achieve that equality. If the scene is static enough that a longer
exposure time can be used, then the larger format camera will
produce the same depth-of-field images as the smaller format camera,
but will collect more photons and produce higher signal-to-noise
images. Another way to look at the problem, is the larger format
camera could use an even smaller aperture and a longer exposure to
achieve a similar signal-to-noise ratio image with greater depth of
field than a smaller format camera. Thus, the larger format camera
has the advantage for producing equal or better images with equal or
better depth-of-field as smaller format cameras.
The details of these concepts are discussed here:
The Depth-of-Field Myth and Digital Cameras
http://www.clarkvision.com/articles/dof_myth
Different Sized Pixels in the Same Sized Sensor
We have considered cameras with the same number of pixels and different sized sensors and shown that cameras with larger sensors and larger pixels collect more light, thus have better low light and high ISO performance. But now we also have choices of different cameras having the same sized sensors but with pixels varying in size and number. What are the implications of this situation?
There are apparently heated debates on the net regarding this issue with passionate arguments for smaller and for larger pixels in the same sized sensor. Many have used data in this article and my Digital Camera Sensor Performance Summary article to argue both sides. Like many positions on extremes, some of these arguments ignore key factors.
The argument for smaller pixels goes like this. Smaller pixels in the same sized sensor record finer details. You can always average pixels to get back to effectively larger pixels. In high signal parts of an image this argument is correct except for one factor: smaller pixels have lower dynamic range (see Figure 7, above). If your smaller pixel blow the highlights, you have lost all the image detail. But if you don't blow the highlights, smaller pixels are better when you have plenty of light. The noise in the image will be dominated by photon noise (the best one can do) and you can in software trade noise for resolution. And by averaging pixels, one can improve the dynamic range. So higher megapixel cameras have merit.
In a perfect camera, the only noise you would record would be that from photons (the ultimate physical limit). But cameras have other sources of noise (see Digital Camera Sensor Performance Summary), including read noise, electronics noise, and noise from dark current (thermal noise). This changes the equation on pixels, low light performance, and high ISO photography.
As light levels fall, whether in the shadows of a daytime scene, indoor photography with low light, to night photography, cameras must make do with less light for the image. This means that the electronics noise in the camera becomes a greater portion of the total noise we perceive in images. And it is this fact that limits the idea of making smaller and smaller pixels. This electronics noise is also a factor in the reduced dynamic range of smaller pixels. So with the increased apparent noise, lower dynamic range, and the fact that lenses can not deliver finer and finer detail because they become diffraction limited, the image quality can't increase forever as pixel size decreases. Another factor in small pixels is the absorption length of photons in the silicon sensor: it ranges from about 1 micron for blue light to over 7 microns for red light (see Table 1B at Digital Camera Sensor Performance Summary). The absorption length will also limit the image detail, especially toward red colors. So the are detrimental effects of pixels that are too small.
Now lets consider large pixels. The ultimate in high signal-to-noise ratio, high dynamic range, and high ISO performance would be one large pixel. Obviously a camera with one large pixel does not form a very good image. Clearly some pixels are necessary to provide an image, and recent full frame cameras with 20+ megapixels deliver outstanding image detail. Too few pixels are bad for image quality and too many pixels are bad for image quality. So there must be an optimum.
My Apparent Image Quality (AIQ) model, discussed in more detail in Digital Camera Sensor Performance Summary shows an optimum pixel size (Figure 9). For cameras with diffraction limited lenses operating at f/8, the model predicts a maximum AIQ around pixels of 5 microns. Many APS-C cameras are operating near that level, but as of this writing, full frame 35 mm digital cameras have a way to go (peaking near 33 megapixels).
Figure 9. Apparent Image Quality, from
Digital Camera Sensor Performance Summary.
The models closely predict
performance for all modern cameras (within about 10% for
large pixels, and 20% for small pixels). Older cameras and sensors fall below the
model, e.g. typically due to low fill factors. Higher quantum
efficiency (QE) sensors than the model (45%) would plot above the model (by a
factor of square root 2, 1.41x higher AIQ for a ~100% QE sensor).
Solid colored lines indicate constant sensor size in megapixels. Dashed
colored lines indicate constant format sized sensors. The "Full-Frame"
sensor is the same size as 35-mm film. As one moves to the left along a
constant format line, AIQ first increases until diffraction begins to
take effect, then AIQ decreases. Diffraction at f/8 is used for the Full
Frame, 1.3x-crop, and 1.6x-crop sensors, and f/7 for the 4/3 sensor
(long dashed lines), f/4 for the Full Frame and 2/3" small-format sensors,
and f/2.8 for the smallest sensor shown, 1/1.8" (short dashed lines). The
smaller f/ratios are needed as sensor size decreases in order to
make the model fit observed data. This indicates smaller format cameras
must have very high quality lenses in order to deliver performance at
high megapixels. Diffraction limits the effective megapixels. When pixels
become very small, they hold so few electrons that dynamic range
suffers, and this causes the turn down in AIQ at pixel sizes below 2 microns
pixel pitch. See the discussion of diffraction, below, which will
further limit AIQ. For example, the AIQ for the Canon 7D plots above
the model line for its 1.6x crop sensor. But that AIQ will only be
realized of the lens used with the camera is diffraction limited below f/8.
To prove image quality degrades as light levels decrease, and that the concept of adding pixels together also has limits, consider the images in Figures 10 and 11. These images are from Figures 8 and 13 in the article Night and Low Light Photography with Digital Cameras. Figure 10 shows an image with a single 1 second exposure at ISO 1600 of a low light scene (a night scene illuminated by light from the Moon near first quarter) . The image in Figure 11 is 64 images obtained at 1/20 second, ISO 1600. The image in Figure 11 has a total exposure time of 3.2 seconds so in a camera with no electronics noise the image would appear better than the image in Figure 10. The Figure 11 image is clearly lower in quality than that in Figure 10. Read noise from the sensor is the main reason for the degradation.
The images in Figures 10 and 11 illustrate that combining pixels does not equal a single image. The concept of a camera with many small pixels that are averaged to simulate a camera with larger pixels with the same sensor size simply does not work for low light/high ISO conditions. Again this points to sensors with larger pixels to deliver better image quality in high ISO and low light situations.
Figure 10.
The moonlit test scene: a 1 second exposure at ISO 1600, 50mm, f/1.8, no dark
subtraction. The number of photons recorded in Patch B, mid-level gray, was
only 38.2 per pixel. Note: this is the image quality one would expect if the ISO of
the camera were set at 16,000! Even though the camera has no such setting, one can
achieve it by digital post processing.
Figure 11.
The moonlit test scene: 64 frames, each 0.05 second exposure at ISO 1600, 50mm, f/1.8,
with dark subtraction were combined with using sigma clipped median
combine. The total exposure time was 3.2 seconds. Compare to the 1 second
exposure time image in Figure 10.
The final image was stretched to give a similar histogram distribution as the
1-second exposure in Figure 10. This images proves that when multiple images are combined, less
than one photon per pixel per frame can be accumulated to show significant image
detail, but it is no match for a single exposure, even a shorter one.
Now let's look at some noise levels in cameras with different sized pixels. Examine the data in Table 2 for cameras spanning a large range of pixel size.
Table 2
full well Gain Read Pixel
Camera (electrons) Electrons/ Noise Spacing Sensor size
ISO 100 DN ISO100 electrons (microns) pixels mm
Canon 1DMII 52,300* 13.02 16.6 8.2 3504 x 2336 28.7 x 19.1
Canon 10D 44,200 11.4 16 7.4 3072 x 2048 22.7 x 15.1
Canon S60 11,000* 2.7 14 2.8 2592 x 1944 7.18 x 5.32
Canon S70 4,300* 1.03 4.1 2.3 3072 x 2304 7.18 x 5.32
*The Canon 1D Mark II has a true full well of 79,900 electrons at ISO 50.The data in Table 2 shows some small differences in some columns in other columns. The fundamental thing driving the parameters is the pixel size, which is proportional to the pixel spacing column (manufacturers tend to not publish the actual sensor size). One can see that read noise is fairly constant between very different detectors, indicating similar and mature electronics from the lower cost P&S camera to the most expensive. But the pixel size drives two parameters, and both multiply together against signal-to-noise with lower pixel size: the full well capacity and the Gain.
It works out that for the same "camera speed," like ISO 100, for a given scene brightness and lens with the same f/ratio, the wells on each camera will fill to their capacity. This is approximately true between cameras because the basic design, including "wall" thickness of the electronic walls are similar.
The noise from the sensor in electrons is, to a good approximation:
N = (#electrons2 + read_noise2)1/2
But we are concerned with noise in our images, so the 16-bit integer scaled noise is:
N16b = {([(DN*fw/65535)1/2] * 65535/fw)2 + (read_noise * 16/gain)2}1/2
where N16b is the 16-bit noise in image data numbers (DN), fw is the pixel full well capacity in electrons, read_noise is the read noise (e.g. from Table 2) in electrons, and the gain is the gain in electrons/DN (e.g. from Table 2).
The effect of the noise in a photon noise limited camera is illustrated by comparing the cameras discussed on this page:
Table 3
ISO 100 Maximum Signal ISO 100 darkest shadow
----------------------- ------------------------
Camera Noise in 16-bit DN Noise in 16-bit DN
----------------------- ------------------------
Total Photon Read Total Photon Read
Canon 1D Mark II 281 281 20.4 20.4 0 20.4
Canon 10D 295 295 22.5 22.5 0 22.5
Canon S60 627 622 83 83 0 83
Canon S70 1021 1019 64 64 0 64
Photon = noise due to photon counting statistics.The realization from Table 3 is even though the read noise is similar in terms of electrons, the effect on the image is huge because of the gain factor. Thus shadow detail on a small sensor is severely compromised as the gain factor drops.
Now let's look at data for ISO 400. The gains in electrons/DN from Table 2 are 4 times smaller as is the number of electrons (photons). While the actual full of the sensor has not changed, the number of electrons converted to DN is 1/4 that of the full well in Table 2.
Table 4
ISO 400 Maximum Signal ISO 400 darkest shadow
----------------------- ------------------------
Camera Noise in 16-bit DN Noise in 16-bit DN
----------------------- ------------------------
Total Photon Read Total Photon Read
Canon 1D Mark II 575 574 41 41 0 41
Canon 10D 620 614 90 90 0 90
Canon S60 1293 1250 332 332 0 332
Canon S70 2054 2037 267 267 267
The data in Table 4, when compared to Table 3, shows that the DSLRs
have lower noise at ISO 400 than the point and shoot S60 at ISO 100.
The poor relative performance of the small sensor S60 is mainly a property
of photon counting statistics, and can not be improved unless the laws of
physics get changed. At the low end, the read noise of devices could
be improved, but that will likely to apply to all sensors, large and small.
Thus the large sensor will always have an advantage due to the difference
in gain factor between the larger full well pixel and the smaller full well.
Current good quality sensors in digital cameras are photon noise limited. This means there is no possible improvement in performance for the high signal region (bright things in an image) except to increase quantum efficiency of the devices and/or the fractional active area for which the sensor converts photons to electrons (called the fill factor). As both of these properties are reasonably high already, there is limited room for improvement. And even if these properties were improved, there would still be a big difference between large and small pixels. Larger pixels have higher signal-to-noise ratio at all levels, but especially at low signal levels. The obvious improvement still possible would be to reduce the read noise, but that would likely improve large sensors also, thus large sensors with large pixels will always have an advantage. Whether the difference in noise 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.
When choosing between cameras with the same sized sensor but differing pixel counts, the one with larger pixels (and fewer total pixels) will have better high ISO and low light performance, while the one with more pixels can deliver images with finer detail in good light. You will need to decide where that trade point is. My models show the optimum in DSLR-sized sensors have pixels around 5 microns. You will need to determine what your prime imaging will be. For low light work, I might bias the pixels to a little larger than 5 microns; if low light/high ISO work is not as important, I might bias my choice to slightly smaller than 5 microns. For P&S cameras with small sensors, I prefer cameras with pixels larger than 2 microns.
Because good digital cameras are photon noise limited, the larger pixels will always have higher signal-to-noise ratios unless someone finds a way around the laws of physics, which is highly unlikely.
Image detail can be blurred by diffraction. Diffraction is more of an issue with smaller pixels, so again cameras with larger pixels will perform better, giving sharper images with higher contrast in the fine details.
See also:
Film Versus Digital Executive
Summary.
Also, see the article Dynamic Range of an Image
which shows that real scenes can have over 10 photographic stops of
dynamic range (a factor of over 1000).
Then explore the article on
The Signal-to-Noise of Digital Camera
images and Comparison to Film.
This page shows images and noise graphs of some point and shoot digital cameras compared to a DSLR. The results are similar to the research presented on this page. http://www.dpreview.com/reviews/sonydscf828/page14.asp
DN is "Data Number." That is the number in the file for each pixel. I'm quoting the luminance level (although red, green and blue are almost the same in the cases I cited).
16-bit signed integer: -32768 to +32767
16-bit unsigned integer: 0 to 65535
Photoshop uses signed integers, but the 16-bit tiff is unsigned integer (correctly read by ImagesPlus).
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 max 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
The Two Classes of Digital Cameras http://www.kenrockwell.com/tech/2dig.htm
More on the f/ratio Myth: http://home.earthlink.net/~stanleymm/f_ratio_myth.htm
Home Page: ClarkVision.com
Back to: Digital Imaging Information index on this site: http://www.clarkvision.com/articles
First Published February, 2005.
Last updated January 3, 2010.