Smaller sensors do not have deeper DOF

[Alan Emery]

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

[Daniel Browning]

Thanks for the response, Alan.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

[Ben Syverson]

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 Browning]

Originally Posted by Ben Syverson

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.

Originally Posted by Ben Syverson

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.

Originally Posted by Ben Syverson

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,

[Dan Brockett]

Daniel:

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

Dan

[Daniel Browning]

Originally Posted by Dan Brockett

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.

[Alan Emery]

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

[Alan Emery]

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?

[Daniel Browning]

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

[Alan Emery]

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

[Daniel Browning]

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.

Originally Posted by Alan Emery

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.).

[Mike Peterson]

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

[Alan Emery]

Hi Daniel,

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

Alan

[Jeff Donald]

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?

[Daniel Browning]

Originally Posted by Jeff Donald

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-cr...pth-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.