Smaller sensors do not have deeper DOF

[Daniel Browning]

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.

[Bert Na]

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.

[Daniel Browning]

Originally Posted by Bert Na

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.

Originally Posted by Bert Na

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?

Originally Posted by Bert Na

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?

[Daniel Browning]

Originally Posted by Daniel Browning

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

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



And this one was taken at 111mm f/6.4 ISO 1600 on a FF35 sensor (5D2):


Follow the link above for the rest of the shots.

[Liam Hall]

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...

[Tony Davies-Patrick]

"...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! :)

[Daniel Browning]

Originally Posted by Liam Hall

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.

Originally Posted by Liam Hall

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.

Originally Posted by Liam Hall

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.

[Liam Hall]

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/tut...ensor-size.htm

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

[Daniel Browning]

Originally Posted by Liam Hall

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.

Originally Posted by Liam Hall

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)

Originally Posted by Liam Hall

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

[Liam Hall]

Originally Posted by Daniel Browning

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.

Originally Posted by Daniel Browning

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.

[Christopher Lovenguth]

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 Browning]

Originally Posted by Liam Hall

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.

Originally Posted by Liam Hall

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.

Originally Posted by Liam Hall

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.

Originally Posted by Christopher Lovenguth

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.

Originally Posted by Christopher Lovenguth

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.

Originally Posted by Christopher Lovenguth

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.

[Kin Lau]

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

[Christopher Lovenguth]

Originally Posted by Daniel Browning

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.

[Daniel Browning]

Originally Posted by Kin Lau

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?