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by Roger N. Clark
Introduction
Some photography, including birds, general wildlife photography, sports and other photography of action at a distance, as well as astrophotography requires resolving small details while having enough signal-to-noise to produce a quality image. This becomes difficult when the action is fast requiring short exposure times (e.g. wildlife action, especially near sunrise or sunset), or when the signal is extremely faint, as in astrophotography.
Many photographers, especially beginning wildlife photographers seem most concerned with focal length. But aperture is equally important. The lens collects the light, the focal length spreads out the light, and the pixel chops up the light into small details to make up the image. The larger the diameter the lens, to more light it collects. The longer the focal length, the more the light is spread out over the pixels, and different sized pixels will collect different amounts of light from a given lens. Adding a teleconverter (TC) increases the focal length, so spreads the light out more, potentially resolving more detail, but the light gathered by the lens is not increased, so signal per pixel decreases, along with signal-to-noise ratio. It is the drop in signal-to-noise ratio that people perceive as increased noise in an image. Similarly, if the pixel size is decreased, the light per pixel is decreased while resolution is potentially increased. But again the total light collected by the lens has not changed, to signal-to-noise ratio decreases. In fact there is little difference between adding a TC and decreasing pixel size.
The above properties are well known in scientific remote sensing applications (e.g. aircraft and spacecraft sensors) and well described by basic physics. These properties also apply to wildlife, sports, and other photography requiring lenses (or telescopes) where exposure time is limited (e.g. a short exposure time is needed to prevent blur due to subject movement). These principles include wildlife action photography with telephoto lenses, and even astrophotography with a telephoto or wide angle lens, or with a telescope.
Executive Summary
A significant conclusion is that for telephoto reach, smaller pixels are better than a camera with larger pixels with the use of TCs, all else being equal. Telephoto reach is more than simply focal length; it is lens diameter, and focal length coupled with pixel size.
The A Omega Product (Etendue)
The Etendue of a system determines fundamental performance of the lens plus camera, so bear with me while I try and describe it. There are also several non-intuitive results (at least for most photographers) that come out this concept which should help photographers choose and understand the performance of different lenses and cameras. This knowledge should lead to better choices. For example, should one choose a used Canon 1D Mark III camera or a newer 7D camera to give the best performance for bird photography? (We define best performance as giving the most pixels on the subject with actual resolved detail and highest signal-to-noise ratio.)
Another example, I have a 300 mm f/4 lens, but I want more telephoto reach. I can't afford a 500 mm f/4 lens, but will a 300 mm f/2.8 really be much better than my 300 f/4? After all, both lenses have the same focal length. We shall see, however, that the increase in aperture makes a big performance increase, so yes, the move up to the larger lens will be a significant improvement assuming quality lenses.
The basic formula for Etendue can take several forms (see references), but comes down to the diameter of the lens (or telescope) collecting the light, and how finely that light is separated in the focal plane to form the pixels in an image. It matters little if the light in the focal plane is sampled by many tiny pixels by a short focal lens, or larger pixels fed by a longer focal length lens. What matters is the size of the detail on the subject that is projected into the focal plane, sampled by the pixels, and how much light is delivered to each pixel. The basic physics says to use the largest diameter lens to obtain the highest signal-to-noise ratio, and the combination of focal length and pixel size to resolve the desired detail.
For example, let's say we have a lens that collects 1,000,000 photons on a subject and we have 10,000 pixels. That leaves us with 1,000,000/10,000 = 100 photons per pixel. If we want finer detail, we can make the pixels smaller, for example, by cramming 20,000 pixels into the same sensor area, but then we have less light per pixel: 50 photons per pixel in this example. It is like feeding people pieces of pie. Our pie is only so big, so to feed more people, each must get a smaller piece of pie. The alternative is to buy a larger pie. Some may think the larger (photographic) pie in this situation is a larger sensor, but a larger sensor dose not collect more light over a given amount of detail. Only a larger lens can collect and deliver more light. So in photography, the more pie analogy is a larger diameter lens. This is the basic reason why an f/2.8 lens of a given focal length will deliver more light to the sensor than an f/4 lens of the same focal length over a given time interval (exposure time).
In telephoto photography, another factor, besides lens quality is diffraction. Diffraction limits detail in an image. One can boost focal length (e.g. add a teleconverter, TC, or buy a longer focal length lens of the same aperture diameter) but ultimately, detail is limited by diffraction. With today's digital cameras, diffraction plays a significant role at f/ratios of f/8 and even smaller with small sized pixels. Diffraction effects were covered in part 1 and are included in the calculations here (see: Telephoto Reach and Digital Cameras, Part 1. An example: one has a 300 mm f/4, would imaging results be much better with 400 mm f/5.6 assuming both are top quality lenses? The answer is no. The 300 mm f/4 has an aperture of 300/4 = 75 mm and the 400 f/5.6 has an aperture of 71.4 mm. If both lenses were diffraction limited, the 400 f/5.6 lens would have slightly worse performance.
The two factors that are the fundamental metrics in system performance are the lens collecting area (A), and the angular size of a pixel (omega). The collecting area is simply proportional to the square of the diameter of the lens (technically, the lens entrance pupil). The signal-to-noise ratio is proportional to the square root of the collecting area, so is proportional to the lens diameter. These concepts are illustrated in Figure 1.
The angular size of a pixel (omega) is proportional to the focal length of the lens and the pixel size. The longer the focal length, the smaller the angular size of a pixel. Similarly, for a given focal length a smaller pixel will see a smaller angular size. The angular pixel size also determines the number of pixels on the subject, and thus the fundamental limit to the detail that can be recorded. The amount of light collected by the pixel is proportional to the pixel area, so omega squared. For this study I use square arc-seconds. The actual detail resolved is dependent on diffraction and other lens aberrations. The A*omega factor (proportional to lens area times linear pixel size squared divided by focal length) gives the relative signal delivered to each pixel and the signal-to-noise ratio is proportional to the square root of the A*Omega product.
The angular size of a pixel also determines the pixels or detail we can get on a given subject. We define this detail as the lens + camera acuity. The acuity is defined as the inverse of the angular linear pixel size, and pixel size in arc-seconds is used here. There are 3600 arc-seconds in one degree; the Moon appears about 1800 arc-seconds across. The human eye resolves detail down to about 30 arc-seconds in bright light. As we shall see, it is difficult to resolve detail smaller than about 1 arc-second with today's DSLRs and available telephoto lenses (that 1 arc-second metric can be surpassed with large amateur telescopes).
In the following discussions, the lenses are assumed to be perfect, limited only by diffraction. All lenses are assumed to have the same transmittance. The latest super telephoto lenses come close to diffraction limited performance.
Figure 1 illustrates these properties. The lens in panel a of Figure 1 delivers A1 light to each pixel with resolution omega1. In panel b the pixel size is half that in panel a so the light per pixel drops by 4. Thus, the image in panel b has twice the pixels on a subject (assuming the subject is small in the frame, and we measure linearly) but the image is noisier. In panel c, the camera has the same pixel size as that in panel a, but the lens focal length is double. Thus the detail is the same as in panel b with the same noise per pixel. Panel d has the same focal length lens and the same pixel size as in panel b so the images have the same pixels on subject. But the lens in panel d is half the diameter so the light delivered to each pixel is 4 times less in a given exposure. Therefore the system in panel d has a signal-to-noise ratio half that in panel b. Focal length, lens diameter and pixel size all play significant roles in system performance and image quality. Next we will explore performance of common lenses and pixels found in today's photography market.
Figure 2 shows basic trends for 7 lenses and pixel sizes representative of the cameras available today and the last few years. The trend lines (see the figure caption) indicate that if one trades pixel size or adds TCs, one can gain acuity, but lose signal-to-noise ratio in a given exposure time. Note, changing ISO does not change a camera's sensitivity. Changing ISO tells the camera's metering system to change exposure time, and make a corresponding change in signal gain after the signal is read from the sensor. So as one increases ISO, the computer reduces exposure time and increases gain, essentially telling the camera to digitize a smaller signal range.
Figure 2 shows a lot of complexity so let's limit the parameters to 3 cameras and 3 lenses (Figure 3). Again, we assume all three cameras have pixels with the same efficiency. Given the choice of buying an expensive pro-level camera (camera A) versus a consumer level camera (camera C), which would give better performance. The prevailing view on the net is that cameras with smaller pixels produce noisier images. But that is not the whole story. To get the same detail on a subject with camera A as with the smaller pixels of camera C, one would need to add a 2X TC to camera A. But when one does that the signal-to-noise ratio drops to that of camera C. Both cameras produce similar images with almost the same detail on subject with nearly the same apparent noise (signal-to-noise ratio).
But there are more implications to the above example. Camera C is producing the detail on subject with the same signal-to-noise ratio as camera A, but camera C is doing it without teleconverters. Teleconverters slow down the autofocus (AF) system, so camera C would have better fast action AF performance (assuming the AF systems were similar in both cameras). It is also likely that the TCs are not perfect and there is additional degradation of the image quality beyond diffraction. A significant conclusion is that for telephoto reach, smaller pixels are better than a camera with larger pixels with the use of TCs.
Now let's consider pixel efficiency. Pixel efficiency has been derived for some cameras (see: Digital Sensor Performance Summary, Figure __). We examine 3 cameras and include their relative pixel efficiency: a Canon 1D Mark III (7.2 micron pixels), and newer generation 1D Mark IV (5.7 micron pixels) and 7D (4.3 micron pixels). The results for these three cameras and for 3 lenses are shown in Figure 4. Now we see that even though the 1DIII has larger pixels, the pixels have lower collection efficiency so plot lower in terms of relative signal-to-noise ratio. The results show that the 1DIV with a 1.4x TC produces slightly more detail (higher acuity) than a 7D camera with no TC when using the same lens. The 1D Mark III needs a 2x TC to beat the acuity of the 7D or 1DIV+1.4x TC but has much lower signal-to-noise ratio. The 2X TC would also significantly slow down AF performance.
Next let's compare lenses on the same camera (Figure 5). How does performance improve going from a 300 f/4 to 300 f/2.8 to 500 f/4 to 600 f/4 lenses? If we start with a 300 f/4, like many beginning wildlife photographers do, the acuity is limited and many photographers want more reach. The 300 f/2.8 can give wonderful shallow depth-of-field, but when TCs are added, focal length is substantial and a large boost in acuity. The 300 f/4 with a 2x TC is f/8 (so will not autofocus on consumer cameras but will on the pro series) and the about 0.4 with a relative S/N of about 13 in Figure 5. However, the 300 f/2.8 with a 2x TC is at f/5.6 (so will autofocus on consumer cameras), the acuity is higher at about 0.45, while delivering better S/N (18 in figure 5). Further, the autofocus performance is fast at f/5.6 than at f/8, giving another edge to the 300 f/2.8 lens. Thus, if one cannot afford a 500 or 600 mm lens, the 300 f/2.8 is still a significant leap in performance over the 300 f/4.
Diffraction affects acuity of smaller aperture lenses. For example, compare the 300 f/2.8 + 2x TC point (follow the 300 f/2.8 trend down two points to the f/5.6 line) with the 600 mm f/4 bare. The 600 mm f/4 lens has an acuity of about 0.5, whereas the 300 + 2x TC = 600 mm f/5.6 has an acuity of about 0.45. The loss in acuity is due to diffraction from the smaller aperture. Aperture plays a key limiting role in the ability of a lens to resolve fine detail. Not only does the larger diameter lens deliver more light, but diffraction effects are less, improving resolution of fine detail and improved contrast in fine details. This of course assumes equally high quality among the various lenses.
So far we've discussed the trends assuming a constant wide open aperture. What happens if one closes down the aperture diaphragm is shown for two cameras in Figure 6. For cameras with larger pixels, stopping down has minimal effects up to about f/8, but diffraction effects become larger at smaller apertures (larger f/ratio numbers). Cameras with smaller pixels show the diffraction effects at larger apertures.
Often photographers are faced with low light and needing to boost ISO to maintain a fast enough exposure time to prevent blur due to action in the scene or camera shake. The effects of ISO are illustrated in Figure 7. Digital camera sensors have only one sensitivity. Changing ISO only tells the camera to expose for a shorter period and boost the signal more than at lower ISOs. Thus, as one boosts ISO to shorten exposure, S/N drops with the square root of the relative increase in ISO. Acuity is not affects unless noise becomes very low then noise can mask fine detail. Thus, it is better to keep ISO low if exposure times are fast enough to prevent blur (unless of course one is trying to make artistically blurred images).
Here is a demonstration of the effects described in the above post on Etendue. Three cameras, with pixels sizes ranging by almost a factor of 2, same lens, same exposure time, same ISO (1600), same lens aperture diameter. Can you tell what the cameras are? I'll give the answers, but a hint: they are mentioned above. Another hint. The signal-to-noise ratios on a 16x16 pixel block on the gray patch below the 1 in "1px" are (in no particular order): 8.4, 10.5, 11,8, again in the order I would predict. Which camera has the highest S/N, and which has the lowest? The images are from the raw data, converted with the same settings in ACR, then a very small white balance correction (less than 1%) applied in photoshop. Statistics on 16-bit data, Adobe RGB. Presented here, of course is 8-bit sRGB jpeg.
Here are the detail on the comparison. Left: 7D + 500 mm lens at f/4. Center: 1D4 + 500 mm + 1.4x TC at f/5.6, Right: 1D2 + 500 mm + 2x TC at f/8. So the 7D image has the highest S/N, the 1D4 next and the 1D2 is the lowest. But there is a slight bias. The 7D pixels are 4.3 microns, and 1D4 are 5.7 microns, for a ratio of 1.33. As we only have 1.4x TCs, the 1D4 image size (pixels on subject) is 5.2% more magnification so 5.2% more pixels on subject. But that also means the signal is lower by 1.052 squared, so the S/N on the 7D would be 5.2% higher. I measured the S/N of the 7D (on the gray patch noted above) to be 11.8, the 1D4 S/N = 10.5 and the 1D2 S/N = 8.4. Thus, the 7D came out 12% higher. But the measured efficiency of the 7D is about 6% higher than the 1D4 (see Figure 10 at: Digital Camera Sensor Performance Summary). Thus with 5% and 6% more efficiency we should have seen a ratio of 7d to 1D4 S/N's of 11% amd we measured 12%, which is impressively close!
Now the 1D4 to 1D2 pixel ratios is 8.2/5.7 = 1.44, so the jump from 1.4x on the 500 with the 1D4 to the 2x on the 1d2 is virtually a perfect match. If the 1D2 were the same pixel efficiency as the 1D4, the images would be identical (assuming no loss from the 2x TC). But the 1D2 pixel are less efficient by over a factor of 2 (see Figure 10 referenced above), so the S/N on the 1D4 should be higher by about 1.45x but it measured as 10.5/8.4 = 1.25, so the 1D2 came out 16% better than expected, which is still very close. My 1D2, deing quite old with a lot of shutter actuations shows a little variation from exposure to exposure so the difference is likely due to variation in shutter speed. Note this is only 0.2 stop.
So the results of the test are very close to predicted and well explained by Etendue. Equalizing the cameras, especially 1D4 and 7D produces nearly identical images. But wait, the 1D4 image looks a little better than the 7D image. That is because the focal length is slightly greater so slightly better resolves the detail. It someone has a 1.3x TC, we could make the images look even closer.
The bottom line for photographers is the 7D is not a noisy camera compared to other cameras. it is all in how it is used. 1D series cameras have many advantages but not in lower noise when one equalizes pixels on subject and exposure time with the same lens. If I couldn't afford a 1D series in the canon line, I would choose the 7D for bird photography. The same principles apply to all other cameras, especially those made in the same generation. Smaller pixels give more pixels on subject with a shorter focal length lens, and larger pixels do not have an advantage concerning noise.
Another factor: f/8 AF is slower. If one needs 2X TCs and f/8 a lot, it would probably be better to get a camera with smaller pixels and work at f/5.6 for the faster AF.
An up and coming myth is the very misunderstood big pixels are less noisy idea.
A larger pixel enables the collection of more light, not that they collect more light. Consider this analogy: You have two buckets, one that holds 2 gallons of water and one that holds 1 gallon of water. You put the 2-gallon bucket under the faucet and turn on the water for 1 second. Now you put the 1 gallon bucket under the faucet and turn on the water at the same intensity for one second. Assume the amount of water was not enough to overfill either bucket. Which bucket has more water? (If you answer I hate story problems you fail the class.) If your answer is both buckets have the same amount of water, you are correct. Now what controls how much water is in the bucket? It is not the size of the bucket; it is the force and duration of the water controlled by the faucet.
In digital photography, the bucket is the pixel, the faucet is the lens and the time the faucet is on is the exposure time. There is one thing missing in the analogy, and that is focal length which spreads out the light so if the faucet has a spray nozzle on the end the spray would expand a further distance from the faucet. Now for the larger bucket, if it has a larger diameter, it would collect more water because it sees a larger area. But if the smaller bucket were moved closer to the sprayer, so it collected the same angular area, it would also collect the same amount of water. People talk about the same sensor field of view, but there is also the same pixel field of view. When the pixel field of view is the same, regardless of pixel size, the two pixels collect the same amount of light in the same amount of time and produce the same signal-to-noise ratio.
So in the case of digital cameras, the amount of light collected is controlled by the lens, its focal length and the exposure time. The larger pixels only ENABLE the collection of more light when the exposure time is long enough. With digital cameras, that only happens at the lowest ISO. At higher ISO, the buckets (pixels) never get filled.
So to manage noise in digital camera images, one must manage the lens aperture, the focal length, and the exposure time. The focal length manages the pixel field of view. So it is not the pixel that controls the observed noise in an image.
Conclusions
Both aperture and focal length are important in producing fine detail on a subject with good signal-to-noise ratios. Adding TCs reduces light to each pixel by spreading the light out, and the reduction of light to each pixel is the same as reducing pixel size. For comparisons of different camera + lenses, in terms of noise, there is no difference between adding TCs or reducing pixel size. Smaller pixels do not inherently produce noisier images because there is a continuum trade between acuity and signal-to-noise ratio, whether by increasing focal length or decreasing pixel size.
One can trade high signal-to-noise ratio for detail on a subject. For example. in low light situations, use a shorter focal length lens (e.g. 300 f/2.8 instead of 300 f/2.8 + 1.4x TC).
To collect more photons in a single pixel, at least one of these conditions must hold: 1) larger diameter lens, 2) shorter focal length for the same diameter lens, and/or 3) larger pixel. For example, a larger bucket in a rain storm is needed to collect more water. But while the pixel collects the light, it is the lens that delivers the light, and the larger the diameter of the lens, the more light you pump to the pixel. The larger pixel simply enables more light to be collected without overflowing.
Cameras with larger pixels are NOT inherently less noisy. The larger pixels only enable more light to be collected to produce higher signal-to-noise ratio images. But it is the lens and exposure time that deliver the light to the pixels.
Larger pixels = less detail. It is a continuum trade between detail and light per pixel. There is no free lunch. If you want the same detail on a subject as a camera with smaller pixels, and you increase focal length to get that detail, you won't have higher signal-to-noise ratio images just because your camera has larger pixels. With the same detail and same lens diameter, you'll get the same signal-to-noise ratio per pixel regardless of pixel size for a given exposure time. No free lunch and no magic large pixels.
Lens aperture is equally important to focal length in overall system performance. Buy the largest aperture lens you can afford and that you have the ability to carry.
Additional Reading
Telephoto Reach and Digital Cameras, Part 1
Pixel Size, ISO and Noise in Digital Cameras
http://www.newport.com/Tutorial-Light-Collection-and-Systems-Throughput/381845/1033/content.aspx
http://en.wikipedia.org/wiki/Etendue
Crop Factor and Digital Cameras
Digital Cameras: Does Pixel Size Matter? Factors in Choosing a Digital Camera (Does Sensor Size Matter?) Good digital cameras are photon noise limited. This sets basic properties of sensor performance.
The f/ratio Myth and Digital Cameras.
Etendue, or Optical Throughput.
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http://www.clarkvision.com/articles/telephoto.system.performance
First Published March 23, 2012
Last updated May 23, 2017.