Daniel Browning
Well-known member
Larger sensors are capable of the same DOF and noise as smaller sensors, so they are only worth the extra money if you are going to have more light or thinner DOF.
To make the point easier to illustrate, I've simplified the conditions. Below there is a discussion of the effect of the simplifications, but generally they match reality to within 1/3 to 2/3 stop.
Given any number of cameras all matching the following conditions:
In ample light, the large sensor is capable of:
In low light, the large sensor is capable of:
General conclusions:
So it all comes down to money. If you shoot in low light and can not handle thinner DOF, then the large sensor will be more expensive with no benefit. But at least it will be able to do everything the small one did, including the same DOF. On the other hand, if you shoot in ample light or you can handle thinner DOF, then the large sensor will provide a benefit.
The reason why this is true essentially comes down to aperture. Not the f/number (which is "relative" aperture), but the the physical aperture, absolute opening, or "hole in space". When the per-area performance of the sensor is the same (as in assumptions above and most real life situations), then the DOF, light gathering ability, and noise all depends on only one thing: the aperture of the lens.
The physical aperture of 32mm f/1.2 is 26.6mm. The physical aperture of 50mm f/2.0 is 25mm. They both provide the same FOV on S35 and FF35, respectively, and the DOF is the same because the physical aperture is also the same (~25mm). Light gathering ability and noise, too, are the same: one focuses the light in a smaller space with more intensity, the other spreads it out over a larger space with less intensity. In either case, the total amount of light is the same.
This is true of all formats when given the above assumptions. From 1/3", 2/3", S35, FF35, 645, all the way up to 617. Larger sensors get the same DOF/light/noise by through longer focal lengths, narrower f/numbers, and smaller reproduction ratios. Smaller formats have the same DOF/light/noise through shorter focal lengths, wider f/numbers, and larger reproduction ratios. For example, with a 16.4-foot subject distance, all of the following camera/lens combinations will have the same 40 degree horizontal AOV and 6.7 feet DOF (using h/CoC=1200):
They all have approximately 15mm physical aperture despite the 7-stop difference in f/numbers.
Another way to see it is like this:
For a given capture and display resolution, they all have the same level of diffraction as well, since that, too, depends on physical aperture. Smaller sensors are magnified very much for display, so diffraction is visible at wider f/stops. Larger sensors are not magnified as much, so it takes a much narrower f/stop to get the same effect of diffraction. When the focal length is equalized for field of view, the amount of diffraction is perfectly described by the physical aperture.
The f/number is inversely proportional to the reproduction ratio for any amount of DOF or diffraction for any sensor size.
So as you can see, the physical aperture is a big factor in a lot of things. Many photographers tend to focus on f/number ("relative" aperture), whereas other fields (e.g. astronomy) use the word "aperture" in the correct sense, which is physical aperture.
How what happens when the conditions/assumptions vary?
The same scene should always be given. There are many times when perspective cannot be changed, such as when a cliff prevents forward movement or a wall prevents backward movement. Other times, it is possible to change the perspective, but it is undesirable for artistic reasons (e.g. distortion/compression). In any case, changing perspective is like changing angle of view, scene, or lighting: it's a fundamental element of composition that must be kept constant for any comparison to make sense.
The field of view is just as important in composition as perspective, and can't be compensated other ways for the same reasons. The same maximum f/stop condition is only necessary for larger formats to be capable of thinner DOF. If instead the condition was "same maximum physical aperture (not f/number)", then all formats would be capable of the same DOF. In some comparisons, the smaller format is capable of much thinner DOF (e.g. FF35 vs. MFDB) due to wider physical apertures.
This condition basically states that lenses for larger formats can stop down smaller than lenses of smaller formats, but that's not necessarily the case. For example, if a FF35 lens can activate f/32, and a S35 lens can activate f/20, then they are both capable of the same DOF at their narrowest f/stop. But if the S35 can also activate f/32, then the FF35 will never be able to achieve that very deep DOF. In practice, this is usually not an issue because few people shoot at the very narrowest stop.
Modern sensors have been within 1/3 stop of the same sensitivity for the last few years. Read noise, on the other hand, has more variety among manufacturers and models. Generally, the smaller the sensor, the less read noise per area. The same is true for FWC. So the amount that a given sensor is better in this area will change the results, even as much as 1/3 stop just for a lower read noise.
The resolution requirement is just to simplify DOF calculations. A higher resolution sensor is capable of thinner DOF if the lens is. You can compensate for that in post processing by softening the image or displaying it at a size that has low enough resolution that the capture resolution is the same as the compared camera. For the purpose of discussion, it's easier to assume they're both the same.
Raw recording is important, because underexposure only works if response is linear (or curve is well tuned). A nonlinear response (like film) will lose more than 4 stops of information if it is 4 stops underexposed, because it is nonlinear.
The same processing is pretty obvious, as sharpening, demosiac, etc. can have a big effect on DOF.
If a sensor has larger capture resolution, and displayed at a larger size and resolution, then it will be capable of thinner DOF. For that reason, a smaller sensor with the same aperture and higher resolution actually has thinner DOF than a larger sensor.
So it basically comes down to money. Larger sensors are capable of the same DOF and noise as smaller sensors, so they are only worth the extra money if you are going to have more light or thinner DOF.
To make the point easier to illustrate, I've simplified the conditions. Below there is a discussion of the effect of the simplifications, but generally they match reality to within 1/3 to 2/3 stop.
Given any number of cameras all matching the following conditions:
- The same scene and perspective.
- Lenses with the same field of view and maximum f/stop.
- Lenses with the same DOF at narrowest f/stop.
- Sensors with the same sensitivity per area.
- Sensors with the same read noise per area.
- Sensors with the same full well capacity per area.
- Sensors with the same total resolution and relative OLPF.
- The same raw recording and processing.
- Displayed at the same size and resolution.
- Distance is large enough to avoid bellows factor.
In ample light, the large sensor is capable of:
- Less noise for any given DOF.
- The same amount of diffraction for any given DOF.
- Even the very deepest DOF are the same with less noise.
In low light, the large sensor is capable of:
- The same DOF and same noise.
- Thinner DOF and less noise.
General conclusions:
- The large sensor is capable of everything the small sensor is.
- The small sensor is not capable of deeper DOF.
- The large sensor will not be better unless you have more light or thinner DOF.
So it all comes down to money. If you shoot in low light and can not handle thinner DOF, then the large sensor will be more expensive with no benefit. But at least it will be able to do everything the small one did, including the same DOF. On the other hand, if you shoot in ample light or you can handle thinner DOF, then the large sensor will provide a benefit.
The reason why this is true essentially comes down to aperture. Not the f/number (which is "relative" aperture), but the the physical aperture, absolute opening, or "hole in space". When the per-area performance of the sensor is the same (as in assumptions above and most real life situations), then the DOF, light gathering ability, and noise all depends on only one thing: the aperture of the lens.
The physical aperture of 32mm f/1.2 is 26.6mm. The physical aperture of 50mm f/2.0 is 25mm. They both provide the same FOV on S35 and FF35, respectively, and the DOF is the same because the physical aperture is also the same (~25mm). Light gathering ability and noise, too, are the same: one focuses the light in a smaller space with more intensity, the other spreads it out over a larger space with less intensity. In either case, the total amount of light is the same.
This is true of all formats when given the above assumptions. From 1/3", 2/3", S35, FF35, 645, all the way up to 617. Larger sensors get the same DOF/light/noise by through longer focal lengths, narrower f/numbers, and smaller reproduction ratios. Smaller formats have the same DOF/light/noise through shorter focal lengths, wider f/numbers, and larger reproduction ratios. For example, with a 16.4-foot subject distance, all of the following camera/lens combinations will have the same 40 degree horizontal AOV and 6.7 feet DOF (using h/CoC=1200):
Code:
2/3": 14mm f/0.9
4/3": 24mm f/1.6
Super35: 34mm f/2.2
Still FF35: 49mm f/3.2
645: 76mm f/5.0
617: 220mm f/14
They all have approximately 15mm physical aperture despite the 7-stop difference in f/numbers.
Another way to see it is like this:
Code:
2/3": 15mm aperture, 14mm focal length
4/3": 15mm aperture, 24mm focal length
Super35: 15mm aperture, 34mm focal length
Still FF35: 15mm aperture, 49mm focal length
645: 15mm aperture, 76mm focal length
617: 15mm aperture, 220mm focal length
For a given capture and display resolution, they all have the same level of diffraction as well, since that, too, depends on physical aperture. Smaller sensors are magnified very much for display, so diffraction is visible at wider f/stops. Larger sensors are not magnified as much, so it takes a much narrower f/stop to get the same effect of diffraction. When the focal length is equalized for field of view, the amount of diffraction is perfectly described by the physical aperture.
The f/number is inversely proportional to the reproduction ratio for any amount of DOF or diffraction for any sensor size.
So as you can see, the physical aperture is a big factor in a lot of things. Many photographers tend to focus on f/number ("relative" aperture), whereas other fields (e.g. astronomy) use the word "aperture" in the correct sense, which is physical aperture.
How what happens when the conditions/assumptions vary?
- The same scene and perspective.
The same scene should always be given. There are many times when perspective cannot be changed, such as when a cliff prevents forward movement or a wall prevents backward movement. Other times, it is possible to change the perspective, but it is undesirable for artistic reasons (e.g. distortion/compression). In any case, changing perspective is like changing angle of view, scene, or lighting: it's a fundamental element of composition that must be kept constant for any comparison to make sense.
- Lenses with the same field of view and maximum f/stop.
The field of view is just as important in composition as perspective, and can't be compensated other ways for the same reasons. The same maximum f/stop condition is only necessary for larger formats to be capable of thinner DOF. If instead the condition was "same maximum physical aperture (not f/number)", then all formats would be capable of the same DOF. In some comparisons, the smaller format is capable of much thinner DOF (e.g. FF35 vs. MFDB) due to wider physical apertures.
- Lenses with the same DOF at narrowest f/stop.
This condition basically states that lenses for larger formats can stop down smaller than lenses of smaller formats, but that's not necessarily the case. For example, if a FF35 lens can activate f/32, and a S35 lens can activate f/20, then they are both capable of the same DOF at their narrowest f/stop. But if the S35 can also activate f/32, then the FF35 will never be able to achieve that very deep DOF. In practice, this is usually not an issue because few people shoot at the very narrowest stop.
- Sensors with the same sensitivity per area.
- Sensors with the same read noise per area.
- Sensors with the same full well capacity per area.
Modern sensors have been within 1/3 stop of the same sensitivity for the last few years. Read noise, on the other hand, has more variety among manufacturers and models. Generally, the smaller the sensor, the less read noise per area. The same is true for FWC. So the amount that a given sensor is better in this area will change the results, even as much as 1/3 stop just for a lower read noise.
- Sensors with the same total resolution and relative OLPF.
The resolution requirement is just to simplify DOF calculations. A higher resolution sensor is capable of thinner DOF if the lens is. You can compensate for that in post processing by softening the image or displaying it at a size that has low enough resolution that the capture resolution is the same as the compared camera. For the purpose of discussion, it's easier to assume they're both the same.
- The same raw recording and processing.
Raw recording is important, because underexposure only works if response is linear (or curve is well tuned). A nonlinear response (like film) will lose more than 4 stops of information if it is 4 stops underexposed, because it is nonlinear.
The same processing is pretty obvious, as sharpening, demosiac, etc. can have a big effect on DOF.
- Displayed at the same size and resolution.
If a sensor has larger capture resolution, and displayed at a larger size and resolution, then it will be capable of thinner DOF. For that reason, a smaller sensor with the same aperture and higher resolution actually has thinner DOF than a larger sensor.
So it basically comes down to money. Larger sensors are capable of the same DOF and noise as smaller sensors, so they are only worth the extra money if you are going to have more light or thinner DOF.