Before I start, let me clarify the subject line. When smaller sensors are used at the same f-number (e.g. f/2.8), they do indeed have deeper DOF. But large formats can always stop down to get the same DOF, so small sensor are not capable of deeper DOF than the large sensor, and that is what I mean by the subject line. Now, on to the meat.

When comparing two different sensor sizes, it makes sense to assume that all the other variables will be equal:


Same scene.
Same light.
Same perspective.
Lenses with the same field of view
Sensors with the same technology (read noise per area)
The same raw conversion / post processing.
Displayed at the same size and resolution.


It so happens that the 5D2 and 7D have very similar technology, so it's very easy to compare them in these conditions.

In ample light, the large sensor is capable of:


Less noise for any given DOF.
The same amount of diffraction for any given DOF.
The same deep DOF 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 does not have a deep DOF advantage.
The large sensor will not have less noise unless you have more light or thinner DOF.


If you shoot in low light and can not handle thinner DOF, then the large sensor will be more expensive with no noise benefit. (There may be other benefits, such as contrast.) 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.

For example, the 7D with 50mm 1.8 ISO 160 has the same DOF and noise as 80mm f/2.9 ISO 400.


This is easy to prove to yourself with a simple experiment using any raw camera, such as a DSLR.

Take picture A with whatever settings you want. It will simulate the smaller format. For example:


Focal length = L (e.g. 50mm)
F-number = N (e.g. 2.8).
ISO = I (e.g. 100)


Then decide on the crop factor that you want to simulate. For example, 5D2 -> 7D is a crop factor of 1.6X. And take a second picture with the same camera in the same position with the same focus distance and same lighting:


Simulated crop factor C (e.g. 1.6X)
Focal length of L * C (e.g. 50mm * 1.6 = 80mm)
F-number of N * C (e.g. 2.8 * 1.6 = f/4.5)
ISO of I * C^2 (e.g. 100 * 1.6^2 = ISO 250)


Now you have one picture at 50mm f/2.8 ISO 100 and another at 80mm f/4.5 ISO 250. Now:


Apply the exact same raw conversion and post processing to both photos
Crop Picture A by the crop factor.
This will cause both pictures to have the exact same field of view
Now you can compare noise, DOF, diffraction, etc. in both pictures.


What you will find is that they are the same. Again, this simple experiment can be done by anyone with a single raw digital camera. The sensor technology is the exact same, so we know that isn't a factor.

One way to look at it is to consider just two variables: sensor size and f-number.

1. Sensor size:


Bigger sensor = less noise and thinner DOF
Smaller sensor = more noise and deeper DOF


2. F-number:


Faster f-number = less noise and thinner DOF
Slower f-number = more noise and deeper DOF


Here's what I think happens when one or both of the factors are changed in some way:


Bigger sensor size but keep f-number the same: less noise but thinner DOF.
Faster f-number but keep sensor size the same: less noise but thinner DOF.
Bigger sensor and compensate with f-number: same noise and same DOF.
Smaller sensor and compensate with f-number: same noise and same DOF.
Smaller sensor with same f-number: more noise and deeper DOF.
Same sensor with slower f-number: more noise and deeper DOF.


F-number scales with sensor size.

What about lens weight? This one is much trickier, because every lens design tends to be unique. But if you if assume the exact same lens design, then you find that larger formats do not, in fact, have heavier lenses.

For example, compare the 300mm f/2 lens on Nikon FX (FF35), which has the same angle of view as 200mm f/2 on Nikon APS-C (~S35):


Nikon 200mm f/2 - 6.4 pounds
Nikon 300mm f/2 - 16.6 pounds
Nikon 300mm f/2.8 - 6.3 pounds


Then consider that you only need 300mm f/3 to get the same DOF, diffraction, and light gathering power as the 200mm f/2 on ASP-C. The 300 f/2.8 has the same weight!

Here's another example, again with Nikon (because their crop factor of 1.5X just happens to align very closely with their lens selection):


Nikon 400mm f/2.8 on DX (similar to S35) - 10.2 pounds
Nikon 600mm f/4 on FF35 - 11.2 pounds


Here we see it is 10% heavier, but not significantly. (The difference may be due in part to the fact that the 600mm only needs to be f/4.2, not f/4.0, to get the same DOF, light, diffraction, etc.)

The reason why I'm comparing these expensive superteles is because they have optical designs that are similar. When you compare other focal lengths, it is very hard to find a lens in one format (e.g. APS-C) that has the same design (just scaled up) for another format (e.g. FF).

It's true, of course, that larger-format lenses *tend* to be heavier, but that's because they tend to have the same f-number. And as established, they don't need to have the same f-number in order to get the same results.

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.


The field of view is just as important in composition as perspective, and can't be compensated other ways for the same reasons.


Sensors with the same performance 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 (at low ISO). 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 same raw conversion and post-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.

The reason why this is true essentially comes down to apparent iris diameter. (I am not using the word "aperture" because it is often confused with f-number.) When the per-area performance of the sensor is the same (as in assumptions above and many real life situations), then the DOF, light gathering ability, and noise all depends on only one thing: the aperture of the lens.

The iris diameter of 32mm f/1.2 is 26.6mm. The iris diameter of 50mm f/2.0 is 25mm. They both provide the same FOV on S35 (e.g. 7D) and FF35 (e.g. 5D2), 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, etc. 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):


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 iris diameter despite the 7-stop difference in f/numbers. Another way to see it is like this:


2/3": 15mm iris diameter, 14mm focal length
4/3": 15mm iris diameter, 24mm focal length
Super35: 15mm iris diameter, 34mm focal length
Still FF35: 15mm iris diameter, 49mm focal length
645: 15mm iris diameter, 76mm focal length
617: 15mm iris diameter, 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 iris diameter. 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 iris diameter.

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 iris diameter 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.

F-number scales with sensor size.

In practice, the smaller sensor will show more DOF. Two parameters impact the depth of focus: the lens focal length & aperture setting. For the same field of view, the smaller sensor will have a shorter focal length, therefore the resultant DOF will be larger, using the same f-number. BTW, The crop factor does not apply to the lens aperture.

In practice, the smaller sensor will show more DOF.

You are talking about using both at the same f-number. This thread explains that it's also possible to use them at different f-numbers to arrive at the same DOF, and increasing gain (ISO) to get the same brightness and noise.


For the same field of view, the smaller sensor will have a shorter focal length, therefore the resultant DOF will be larger, using the same f-number.


Yes. But what happens when you stop down the f-number so that both have the same DOF, then increase the gain (ISO) so that they both have the same brightness?

BTW, The crop factor does not apply to the lens aperture.

The surprising truth is that it does! May I kindly suggest that you try the very simple experiment outlined above to prove it for yourself?

F-number scales with sensor size.

I went ahead and did some comparison shots to demonstrate the principle:

Images demonstrating how f-number scales with sensor size (http://thebrownings.name/images/2009-10-5d2-equivalence/)

This image was taken with 70mm f/4 ISO 640 on a 1.6X sensor similar to the 7D:

http://thebrownings.name/images/2009-10-5d2-equivalence/a-1.6x-ambient/a2-70mm-f4.0-ISO640-crop-half-100crop-2.png

And this one was taken at 111mm f/6.4 ISO 1600 on a FF35 sensor (5D2):
http://thebrownings.name/images/2009-10-5d2-equivalence/a-1.6x-ambient/a1-111mm-f6.3-ISO1600-resize-half-100crop-2.png

Follow the link above for the rest of the shots.

This has to be the most confusing, convoluted and misconstrued explanations of DoF and the relationship to sensor size I have ever read.

Usually, threads on this subject mention circle of confusion, subject to camera distance, field of view, f/stop and focal length. I don't think I've ever seen "lens weight" described as a contributing factor...

"...This has to be the most confusing, convoluted and misconstrued explanations of DoF and the relationship to sensor size I have ever read..."

Succinct and too the point, Liam! :)

This has to be the most confusing, convoluted and misconstrued explanations of DoF and the relationship to sensor size I have ever read.


If you let me know which part was too confusing for you, I will be happy to explain it.


Usually, threads on this subject mention circle of confusion, subject to camera distance, field of view, f/stop and focal length.

In order to learn something new, sometimes it's necessary to stop disqualifying new information solely on the basis of being different from your old information.


I don't think I've ever seen "lens weight" described as a contributing factor...

Let me try to clarify. There is a common misconception that lenses for larger formats have to be heavier than smaller formats. The post explains why that is only true if the lens is built to be capable of thinner DOF. When DOF is the same, weight, too, tends to be the same.

Daniel, I fully understand depth of field and all of the determining factors.

I find it extraordinary that you write, "In order to learn something new, sometimes it's necessary to stop disqualifying new information solely on the basis of being different from your old information." The laws of physics don't change because Canon bring out a new consumer camera!

I know the point you are trying to make, but with respect, your opening post is a confused mess. Yes, you can stop down to maintain a similar DOF between formats, but the simple truth is all things don't remain equal and there's a hell of a lot of difference between shooting at f/1.4 on one camera and f/5.6 on another.

Anyway, here's a simple explanation with a rather neat calculator to show the relationship between sensor size and depth of field.

http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

It is worth noting that even though the numbers add up, the images will not look the same.

I find it extraordinary that you write, "In order to learn something new, sometimes it's necessary to stop disqualifying new information solely on the basis of being different from your old information." The laws of physics don't change because Canon bring out a new consumer camera!


There is no contradiction with the laws of physics. It is true for all linear raw cameras, not just the 7D.


Yes, you can stop down to maintain a similar DOF between formats, but the simple truth is all things don't remain equal and there's a hell of a lot of difference between shooting at f/1.4 on one camera and f/5.6 on another.

You are mistaken. As I said, they will not have different brightness, different noise, different diffraction, etc. They are actually the same. For example, all of the following have the same diffraction angle of view, DOF, brightness, diffraction, etc.:


7mm f/1.6 ISO 50 on a 1/4" Bayer sensor (3.6x2.0mm)
18.6mm f/4.7 ISO 360 on a 2/3" Bayer sensor (9.6x5.4mm)
21.6mm f/4.9 ISO 480 on the RED ONE in 2K mode (11.1x6.2mm)
43mm f/9.8 ISO 1900 the RED ONE (22.1x12.4mm)
70mm f/16 ISO 5000 on FF35 (36x20.3mm)



It is worth noting that even though the numbers add up, the images will not look the same.


Please direct your attention to the images I posted above that do indeed "look the same":

Images demonstrating how f-number scales with sensor size (http://thebrownings.name/images/2009-10-5d2-equivalence/)

Please direct your attention to the images I posted above that do indeed "look the same":

Daniel, image two is clearly sharper and appears to have greater depth of field than the first. Also, it serves little purpose in a test of this kind because there's not much depth in the shot.

You are mistaken. As I said, they will not have different brightness, different noise, different diffraction, etc. They are actually the same.

I'm not mistaken at all. Stopping down to match depth of field will affect lens contrast, edge sharpness and bokeh. It can result in a similar depth of field, but there's more to it than that. Look at your own test, they're not the same at all. If you don't believe me go shoot at test.

What exactly is this point to this thread?

To say X sensor/film size with Y focallength and Z F-stop with W light conditions with respect to ASA sensitivity will give different looking images but that if you adjust any of these variables you can get the same DOF and same grain for each image?

Isn't that a DUH?

Daniel, image two is clearly sharper and appears to have greater depth of field than the first. Also, it serves little purpose in a test of this kind because there's not much depth in the shot.


The purpose of the test is not to establish that DOF is the same. Such an obvious fact can be proven quite simply with a DOF calculator, as you did yourself above. The purpose of the image is to establish something else: that the noise is the same. Sharpness doesn't enter into it.


Stopping down to match depth of field will affect lens contrast, edge sharpness and bokeh.


Of course it's possible for two different lenses to have different bokeh or aberration correction. For example, if you compare the 50mm f/1.2 on the 7D to the 85mm f/1.8 on the 5D2, you'll find the former to have greatly undercorrected spherical aberration, giving it smoother bokeh. But of course that does not mean smaller formats always have better bokeh! You need to realize that bokeh at a given DOF and sensor size is arbitrary. If you change a variable, of course it will affect the image. But what I'm talking about is different. I'm talking about what happens when the variables are controlled, so that the impact of format size can be understood.


It can result in a similar depth of field, but there's more to it than that. Look at your own test, they're not the same at all. If you don't believe me go shoot at test.

Again, the test was not meant to show the same sharpness, aberration, or bokeh between the two focal lengths. It is assumed that the reader already knows that it's possible for these things to be the same among different sensor sizes, so it's not necessary to demonstrate that in the test. Rather, the test shows something less obvious: that noise and diffraction are the same.

What exactly is this point to this thread?

That large sensors are capable of everything that small sensors are when it comes to DOF, diffraction, and noise. I ran into a DP that wanted to switch from the 5D2 to the 7D because he thought it had an advantage in deep DOF. This thread explains why that is incorrect.


To say X sensor/film size with Y focallength and Z F-stop with W light conditions with respect to ASA sensitivity will give different looking images but that if you adjust any of these variables you can get the same DOF and same grain for each image?


It's not about adjusting "any" of these variables. It's about scaling f-number and ISO (gain) with sensor size to get the same DOF, noise, and diffraction.

Isn't that a DUH?

Perhaps it should be, but based on the number of people who are shocked and amazed when they find out it's true, I'd say it's not an obvious fact to most. For example, many have a very hard time believing that 112mm f/6.3 ISO 1600 on the 5D2 has the same noise as 70mm f/4 ISO 640 on the 7D, just as the image above shows.

Uhm.. the 5Dm2 image is at least a 1/2 stop brighter.

I ran into a DP that wanted to switch from the 5D2 to the 7D because he thought it had an advantage in deep DOF. This thread explains why that is incorrect.

I have to say Daniel that is sad to hear and does explain you posting all this I guess. To me I expect people to have at least photo 101 knowledge base here especially if they are forking over $1k on just a camera body. But alas, I see threads about not even understanding basic f-stop and focal-length concepts on this and other forums and it freaks me out (changing F-stop changes DOF? really? But why then does the images get so dark when you increase the f-stop number? I don't get it. - posts like this). But then that reminds me that when I've guest lectured in a photo dept at a predominate (not going to say which school) in NYC, that I've had 2nd-3rd year students in the class who still have never stepped in to a darkroom and never used a light meter.

The new way of being a "pro" photographer is(and I see this all the time): shoot, look down at LCD, spin a wheel, shoot, look down at LCD, spin a wheel, look at subject really confused since the screen isn't showing what they see in real life, spin a wheel, shoot, give up and put it on P and put a flash on the camera.

Uhm.. the 5Dm2 image is at least a 1/2 stop brighter.

When I open the a2 PNG file in my image editor, the neutral 3.5 patch (the one below black) has an average RGB value around 87. The same patch in the a1 PNG file has an average around 87. Are you looking at different files? Or a different part of the file?

Hi Daniel,

I have a couple of questions that your thread sparked.

1) For those of us who use and consider using 1/3" and 1/2" camcorders, it might be useful to get a theoretical statement of what settings on a 1/3" camcorder would match the same settings on a 1/2" camcorder. If possible can you make this comparison using the actual specifications for a Sony EX3 (XDCAM EX) with a Canon XL H1s (HDV)? I presume you will need to take into account both the sensor size and the resolution (which determines the size and therefore light-gathering capacity of each pixel). I presume the different codecs will also affect the answer.

To make the example useful to me (if its OK to be selfish!), can you suggest what I would need to have as the f number on the Canon to compare to the Sony if the two cameras are shooting the same scene at 1/60th of a second 1080i? The Sony in this scene is using f5.6.

To make the answer even more interesting, and I presume a little easier to calculate, what would be the comparison if you assumed there was no difference in the codec, let's say by using uncompressed output from the HD-SDI port on each camera?

2) Is there an optimum resolution to pixel number (optimum density) to balance sharpness with noise? For example let's compare a large sensor and a huge number of pixels (with let's say a pixel density per square mm of "100x" and a pixel size of "y") and a smaller sensor with a smaller number of pixels (with a pixel density of "10x" and a pixel size of "2Y"). In this case I have a large sensor with small pixels close together increasing noise and sharpness compared to a small sensor with pixels twice as big, but not as many of them, thereby reducing sharpness and noise.

I ask the question because I sometimes wonder if the increasing resolution on large sensors runs the risk of increasing noise to the detriment of sharpness created by the large number of pixels.

Many thanks,

Alan

Thanks for the response, Alan.


1) For those of us who use and consider using 1/3" and 1/2" camcorders, it might be useful to get a theoretical statement of what settings on a 1/3" camcorder would match the same settings on a 1/2" camcorder. If possible can you make this comparison using the actual specifications for a Sony EX3 (XDCAM EX) with a Canon XL H1s (HDV)?


Sure thing. I'll throw in 2/3" just for kicks. Here are some example sensor sizes (YMMV):


1/3" 5.0x2.8mm sensor (Canon XL H1s, 1.92X)
1/2" 6.7x3.8mm sensor (Sony EX3, 1.34X)
2/3" 9.6x5.4mm sensor (1.00X)


If we set aside noise for a moment, and look at just angle of view (AOV), depth of field (DOF), and diffraction, here are some settings that would be equivalent:


4.5mm f/1.6 on 1/3"
6.0mm f/2.1 on 1/2"
8.6mm f/3.1 on 2/3"


And here is how they compare at telephoto:


50mm f/3.4 on 1/3"
65mm f/4.5 on 1/2"
95mm f/6.5 on 2/3"


Now the question of how they compare for noise is a little more complicated. The biggest reason is software processing. For example, if the software on one camera is configured for more highlight headroom than the other, it can make it look noisier than if it were set to the same. I don't if it's possible to configure them to be similar enough to achieve the same level of noise.

The other reason is the difference in sensor technology. If your baseline comparison is +0 db on 1/3", then it's very unlikely that there will be any visible difference due to sensor technology on 1/2" or 2/3". The reason is that in such settings the entire dynamic range is dominated by photon shot noise, which depends only on light collection (quantum efficiency, or QE), not read noise. Since all the sensors in this range have had similar QE for years, the photon shot noise, too, will be the same, even at +6 db on the 2/3". Differences in sensor technology only become significant at larger sensor sizes (or higher gain settings on small sensor sizes) because of read noise.


I presume you will need to take into account both the sensor size and the resolution (which determines the size and therefore light-gathering capacity of each pixel).


Actually, pixel size has absolutely no effect on noise for this size of sensor. The reason is the same as above: the entire dynamic range of the image is dominated by photon shot noise. So even if the 1/2" camera had 4K resolution (9 MP), the noise would be the exact same as 1080p sized pixels (2 MP).

It's only when read noise becomes significant that it is possible for smaller pixels to have more noise. But even then it does not happen nearly as often as most people think. For example, at low gain, the pixel size with the lowest noise in modern cameras is 2.0 microns. The LX3, for example, has less than 5 electrons read noise compared to 23 electrons in the 5D2 (6.4 micron). High gain is another story, however, with large pixels under 2.5 e- read noise at 6.4 micron size.


I presume the different codecs will also affect the answer.


Most certainly. There are many image-processing-related factors that can affect the image:


Raw preconditioning (changes to the data before a raw file is written)
Raw conversion (white balance, color matrix, black clip, noise reduction, etc.)
Post processing (tone curve, saturation, sharpening, etc.)
Compression, and more.


If you could somehow equalize all these factors between the two cameras, I think you would find that the f-numbers given above would provide an equal amount of noise; however, I don't know if it is possible to get them that similar.


2) Is there an optimum resolution to pixel number (optimum density) to balance sharpness with noise?


If read noise is significant in the conditions under consideration, and if read noise does not scale in perfect proportion with pixel pitch, then yes, there is a trade-off between resolution and noise. However, there are many circumstances where read noise is not significant (e.g. 1/3" at 0db gain), and many cases where read noise does scale in perfect proportion with pixel pitch (e.g. 7D and 5D2). So in those cases the smaller pixel provides higher resolution and the same amount of noise. Other times, read noise does not scale (e.g. 5D2 vs T1i), and therefore there is a small trade off between noise and resolution.


I ask the question because I sometimes wonder if the increasing resolution on large sensors runs the risk of increasing noise to the detriment of sharpness created by the large number of pixels.


Generally, no. For one, for the last few years there has no significant rdifference in QE between pixels of any size. Other factors have varied greatly, though, like read noise at high/low gain and full well capacity. As such, images that are already dominated by photon shot noise (like 1/3" at 0db) have no difference in noise from smaller pixels.

Second, even in the types of images where read noise is a contributing factor (e.g. ISO 6400 on the 5D2), sensor designers have been able to scale read noise in perfect proportion with pixel size. That's why the 4.3 micron pixels in the 7D can match the performance of the 5D2 pixels, even though they have over 2 times less area. Now perhaps sensor designers could have done an even *better* job if they had left pixel size the same, but at least you can rest easy that things aren't getting *worse*.

Hope that helps.

Daniel, your basic point is correct, but you're missing the larger issue: larger sensor allow shallower DOF because you can generally create a larger aperture for a given FOV than you could with a smaller sensor.

In other words, there's no way to create the DOF & FOV of a 24mm f/1.4 lens on FF using a 1.6X sensor, because there's no 14mm lens fast enough (there isn't even a f/1.4, let alone what you would need to mimic the FF). So the smaller sensor has deeper DOF by virtue of lens limitations.

By the same token, smaller sensors allow deeper DOF when you want it, because you can use a larger aperture for the same FOV/DOF as a large sensor. So you might be able to get everything in focus at f/16 on a 1.6X sensor, whereas on 8x10 film, even stopping down to f/64 might not give you enough DOF. You're again limited by the lens -- in this case, by the minimum aperture.

Daniel, your basic point is correct, but you're missing the larger issue: larger sensor allow shallower DOF because you can generally create a larger aperture for a given FOV than you could with a smaller sensor.


My perception is that most people are already aware that larger sensors are usually (but not always) capable of thinner DOF than smaller sensors. Therefore, to me, it is not a "larger issue" to start a thread emphasizing something that most people already know. Instead, I would prefer to start a thread about something that I think is not so widely known.

By the way, I noticed that you used the correct definition of the word "aperture" (diameter, not f-number). Be warned that you may get into trouble for that, as I have before. The colloquial definition of aperture (f-number, not diameter) has gained such a strong hold here and everywhere on the Internet that using the correct definition will cause immense confusion and even anger. Personally, I have settled on using "iris diameter" as a substitute for the real definition of aperture, and "f-number" as a substitute for the colloquial definition of aperture. Just FYI.


In other words, there's no way to create the DOF & FOV of a 24mm f/1.4 lens on FF using a 1.6X sensor, because there's no 14mm lens fast enough (there isn't even a f/1.4, let alone what you would need to mimic the FF). So the smaller sensor has deeper DOF by virtue of lens limitations.


Agreed.


By the same token, smaller sensors allow deeper DOF when you want it, because you can use a larger aperture for the same FOV/DOF as a large sensor. So you might be able to get everything in focus at f/16 on a 1.6X sensor, whereas on 8x10 film, even stopping down to f/64 might not give you enough DOF. You're again limited by the lens -- in this case, by the minimum aperture.

You're right, of course. But there are two important considerations to keep in mind. First, this will only be a problem for applications where *extremely* deep DOF is needed (and *extremely* strong diffraction is acceptable). At such f-numbers the iris diameter is into pinhole territory (10mm f/16 on APS-C is about one half of a millimeter).

Lenses for almost all formats provide "reasonably" deep DOF (i.e. to the point where diffraction is very strong and most people would not use it). For example, f/22 on 35mm, f/14 on 1.6X, f/5.9 on 2/3", etc. There are some applications where even more DOF is needed, but I think they are few and far between.

Second, and more importantly, there is an important difference between your two examples. One is due to theoretical limits and practical limits, the other is simply a design choice. There are at least three factors that affect the maximum and minimum f-numbers:


Theoretical limits
Practical limits
Design choices


When you try to make a smaller-format lens fast enough to match the DOF in the larger format, you will run into practical limits and theoretical limits. No matter how much you *want* to make an f/0.45 air-spaced lens, it's not even theoretically possible, to say nothing of the practical limitations.

On the other hand, when you try to make a larger-format lens *slow* enough to match the DOF in a smaller format, there are *no* theoretical limits. It's quite possible to make an 8x10 lens that stops down to the f/181 that would be needed to get the same DOF as f/16 on APS-C. But of course most 8x10 lenses only stop down to f/64 - f/128 as a design choice.

This design choice plays out in other format sizes as well. For example, some four thirds lenses stop down to f/22, the same limit as many FF lenses. This means that four thirds will be capable of 2 stops deeper DOF and 2 stops more diffraction than FF. But that's not because of any fundamental limitation in the FF format. The designers could have built the lenses to stop down to f/44 if they wanted to, and in fact, some FF lenses do indeed stop down to f/44. But for most lenses the designers decided that it wasn't worth the extra manufacturing cost since no one would use it.

Thanks for bringing it up,

Daniel:

I am just ribbing you but jeez, are you working these days?

Dan

I am just ribbing you but jeez, are you working these days?


:) It helps that I've had this discussion several times already on other forums. I just copy and paste. (Shhh!) Typing 120 WPM helps too.

Hi again Daniel,

If I understand your replies, they imply that the larger sensor and the smaller sensor will have equivalent noise if they have equivalent light (all other things being equal). To calculate equivalent light, one would take the square root of the ratio of the areas of the two sensors and apply that to the f number??? So for example (again assuming all other things equal) an exposure of f5.6 on a 1/2" sensor would be equal to approximately f4.15 on a 1/3" sensor. If I understand correctly, this is true even at moderately higher gain settings such as +6db.

The context for this question is the potential to capture the data directly from the sensor without using the camera recording or processing mechanisms (such as with a nanoFlash). Clearly the larger sensor has the advantage in lower light, but it would appear to be only by about one f number. Is that correct?

Many thanks,
Alan

I forgot to ask if there is a difference in the efficiency of light gathering between a CCD and CMOS sensor.

Is there any significant difference and would that also affect the noise levels?

If I understand your replies, they imply that the larger sensor and the smaller sensor will have equivalent noise if they have equivalent light (all other things being equal).


Precisely.


To calculate equivalent light, one would take the square root of the ratio of the areas of the two sensors and apply that to the f number???


Yes. You'll find that the result is the same as the so-called "crop factor". If there is a difference in aspect ratio, cropping to the same as a first step is a good idea. Also, since the linear dimension also scales with the square root of the area, you can use that instead, (e.g. 9.6mm / 5.0mm).

After applying the crop factor to the f-number, one must also apply it to the gain (or "ISO") in order to have the same brightness. For ISO, multiply by the crop factor squared. ISO 100 with a 1.6X crop factor becomes ISO 256. ISO 100 with a 7X crop factor (e.g. 1/3" vs FF 35mm) becomes ISO 4900.


So for example (again assuming all other things equal) an exposure of f5.6 on a 1/2" sensor would be equal to approximately f4.15 on a 1/3" sensor. If I understand correctly, this is true even at moderately higher gain settings such as +6db.


Exactly.


The context for this question is the potential to capture the data directly from the sensor without using the camera recording or processing mechanisms (such as with a nanoFlash). Clearly the larger sensor has the advantage in lower light, but it would appear to be only by about one f number. Is that correct?


Yes.

I forgot to ask if there is a difference in the efficiency of light gathering between a CCD and CMOS sensor.

Is there any significant difference and would that also affect the noise levels?

It really depends on the specific implementation. In general, CMOS are better in low light thanks to pretty amazing read noise levels (under two electrons). CCD have higher electronic (bare sensor) fill factors, which would normally give them much better light gathering capability and full well capacity, but CMOS have long had microlenses that give them in the same (or better) "effective" (or optical) fill factor. Theoretically it's possible for CCD to have much higher full well capacity thanks to the higher electronic fill factor, but that only affects dynamic range in ample light, not noise in low light. The other generalization is that at low gain, CCD tends to have lower read noise, again giving them more dynamic range in ample light. But again, all these generalizations can be easily overshadowed by the individual characteristics of a specific image sensor.

Hi Daniel,

Very helpful information -- thank you so much. I seem to find another question each time.

You comment that in addition to a crop factor on the f number which gives equivalent light on the sensors; to get equivalent brightness, I also need to multiply the "gain" by the same factor.

Is this because there is a smaller source sending the image to the recording mechanism or to my eye, both of which want a final product that is "the same size"?

So does this mean, for example, that between the 5D2 and the 7D (or any two sensors of different sizes) there is both an f number difference and an effective ISO (gain) difference to achieve the same brightness in the recorded image presented at the same sizes (print or projected image) of the same scene and field of view?

In general is this why the available ISO range of cameras with larger sensors tends to be greater -- they can add the range without compromising the noise factor as much as would be the case with smaller sensors?

If so, it seems the complete advantage of the larger sensor is both the f number and the gain crop factors.

Once again, many thanks,
Alan

Is this because there is a smaller source sending the image to the recording mechanism or to my eye, both of which want a final product that is "the same size"?


Yes. If instead of showing both images at the same size you showed the small sensor at 720p and the large sensor at 1080p, the difference in gain would not be necessary. But to me, keeping the display size and resolution the same is important for a comparison of sensor sizes.

I should also perhaps mention that it applies more to ISO than it does to gain. Gain itself may actually be the same if the pixel size scales with sensor size. In other words, the larger pixel will output the same light value even with a lower exposure and the same gain. In that case, the "base ISO" will be higher on the larger format, even though gain is the same.


So does this mean, for example, that between the 5D2 and the 7D (or any two sensors of different sizes) there is both an f number difference and an effective ISO (gain) difference to achieve the same brightness in the recorded image presented at the same sizes (print or projected image) of the same scene and field of view?


Yes. the crop factor is 1.6X, so f/10 ISO 160 on the 7D has the same DOF and diffraction as f/16 ISO 400 on the 5D2.


In general is this why the available ISO range of cameras with larger sensors tends to be greater -- they can add the range without compromising the noise factor as much as would be the case with smaller sensors?


Yes.


If so, it seems the complete advantage of the larger sensor is both the f number and the gain crop factors.


Yes, there is no advantage in DOF or noise to smaller sensors, as long as technology stays the same. There may be other advantages, though (e.g. cost, lens availability, compression technology, etc.).

I'm giving this thread my own personal award of being the most confusing thread of all time.

Hi Daniel,

Many thanks again. Very illuminating (bad pun!).

Alan

Hi Daniel,

I seem to recall that you and I had a discussion late last year about many aspects of DOF and one of your premisses was that different size sensors (Nikon D700 and D300) have different DOF. What caused the change of thinking?

Hi Daniel,

I seem to recall that you and I had a discussion late last year about many aspects of DOF and one of your premisses was that different size sensors (Nikon D700 and D300) have different DOF. What caused the change of thinking?

Hi Jeff! Good to see you back, I hope all is well and I'm really looking forward to our next big discussion.

There has been no change in my thinking. My central point in last year's thread was that the camera system with the widest iris diameter is the one with the thinnest DOF. (For a given angle of view, subject distance, display size, bellows factor, etc.)

http://www.dvinfo.net/forum/still-crazy/140533-more-about-dof-depth-field.html

I still think that's correct, and I don't see any contradiction with this thread. The post here tries to deal with the situation of using two camera systems at the same iris diameter, and discuss the effect on noise and diffraction.

Perhaps the thread title is confusing. What I mean by "Smaller sensors do not have deeper DOF" is this: "Large sensors can always stop down to achieve the same DOF as smaller sensors, and will even then achieve a similar level of noise and diffraction; therefore, smaller sensors do not have any advantage of deeper DOF". The thread title is the best way I could think of to shorten that down.

Current thread Title:

Smaller sensors do not have deeper DOF

Statement from prior thread:

My central point was the format with the larger sensor was capable of thinner DOF, because it requires a longer focal length in order to keep perspective and field of view the same.


Statement from current thread:

That large sensors are capable of everything that small sensors are when it comes to DOF, diffraction, and noise. I ran into a DP that wanted to switch from the 5D2 to the 7D because he thought it had an advantage in deep DOF.

In one case large sensors are capable of thinner DOF and in another thread large sensors are capable of the same DOF as small sensors. Needless to say you've created some confusion.

Current thread Title:
Smaller sensors do not have deeper DOF


That's the best summary of the thread emphasis that I could think of.


In one case large sensors are capable of thinner DOF and in another thread large sensors are capable of the same DOF as small sensors. Needless to say you've created some confusion.

I still don't see where the confusion is. Both statements are correct and happily coexist. Large sensors are indeed capable of both the same DOF as well as thinner DOF.

I, for one appreciate this thread. Thanks Daniel, for the insight here. I guess gather that your point is, if you can afford it and don't need a tiny camcorder, you're not giving up any advantages by getting the largest sensor camcorder possible.

If you get a large sensor camcorder, and wind up stopping it down to get the most DOF you can, are you risking a soft image because of diffraction? I experience a big drop in image quality with my EX1 when I go above 5.6 or so. With a larger sensor is less of an issue?

Thanks again.

Thanks, Keith.


If you get a large sensor camcorder, and wind up stopping it down to get the most DOF you can, are you risking a soft image because of diffraction?


No, because diffraction scales with DOF. So no matter what method you use to get the DOF, whether fast f-number on a small sensor or slow f-number on a large sensor, the diffraction will be the same.


I experience a big drop in image quality with my EX1 when I go above 5.6 or so. With a larger sensor is less of an issue?


It will be less of an issue at the same f-number. But it will be the same issue at the same DOF. Essentially, the relationship between DOF and diffraction is the same for all sensor sizes.