Sensor Size vs. Depth of Field vs. Exposure Time

[Pat in San Jose]

I have a question about depth of field. DoF is something I want lots of (bokeh is not for me) and it will be a major consideration in choosing a new camera. I read the CiC tutorial on Digital Camera Sensor Sizes, which stated at one point that “if depth of field is the limiting factor, the required exposure time increases with sensor size for the same sensitivity”. I wasn’t able to follow the reasoning.

In the part of the tutorial I did follow, it is approximately true (except for macro shots) that for equivalent fields of view, to maintain the same depth of field requires an f-number inversely proportional to the sensor width. To use a convenient example, a camera with a 4/3” sensor would need f/8 to get the same depth of field as a camera with a 2/3” sensor at f/4. My purchase-related question is, is this a disadvantage for the larger sensor? According to the quote above, the answer would be yes (presuming I haven’t taken it out of context): to compensate for the smaller aperture, I would need a longer exposure time. This makes some sense, given the exposure equation, in which the luminance is proportional to fn^2/(ISO)(t), where t is the exposure time and fn the f-stop. In fact, I would have to have an exposure four times as long to keep the same ISO sensitivity. But …. if (again to make a simplifying assumption) the two sensors have the same number of pixels, the pixel on the 4/3” sensor is 4x as large as that on the 2/3” sensor, so the luminance should be 4x as great, exactly canceling the effect of doubling the f-number. It should be a wash. I should be able to get the same shots, with the same depth of field and the same shutter speed, on the larger sensor camera by reducing the aperture, with no sensitivity penalty. In fact, since the larger sensor will probably have better high-ISO performance, it would have an even better compromise between low light and DoF.

Or would it? Did I goof in my calculation? Or my assumptions? I’m very new to this and it doesn’t make sense that I would catch something the CiC tutorial writers hadn’t.

[epmi314]

Pat I'm a bit of a rookie myself and some of the more experienced will certainly chime in one this. If you wish to eliminate all bokeh then I think you can save some math and do some research on HDR. This is more a post processing technique than equipment deal. Look up some stuff done by FrankMI on this site he has it down quite well.

Perhaps a better questions is what do you want to shoot? If you are shooting everything at settings that uber maximize DoF then your subject will be somewhat limited due to the delicate balance of the exposure, IMO.

[Colin Southern]

If you wish to eliminate all bokeh then I think you can save some math and do some research on HDR.

Err, HDR are a set of techniques for handling ranges of brightness that are too great to capture in a normal single exposure -- nothing to do with Depth of Field I'm afraid.

[epmi314]

I just looked at that and I am totally wrong!!! Maybe I should stick to what I know. I did qualify by saying a more experienced individual would chime in soon.... How would you answer his question though? If he is trying to essentially eliminate bokeh does he not significantly eliminate what he is shooting?

[epmi314]

By the bye Colin. Thanks for the correction. It is how one learns!

[epmi314]

Just thinking... If HDR is a solution to "brightness ranges" relative to what settings are needed to get a good exposure acrosss the board then why isn't HDR prosessing a solution to his issue? I realize I may be trying to solve two equations (DoF and Exposure) with one solution... but if he is trying to take shots with a tremendous DoF then isn't he going to have an issue with brightness, exposure and blowing things out given the aperature needed and other settings used to compensate? Is his solution to do so in post processing rather than camera settings or equipment? This is sublte but good to know.... Experts?

[epmi314]

What are you shooting Pat? This would be good to know....

[Colin Southern]

I just looked at that and I am totally wrong!!!

It's happened to me 1000 times ...

... and that's just this week!

[Colin Southern]

Just thinking... If HDR is a solution to "brightness ranges" relative to what settings are needed to get a good exposure acrosss the board then why isn't HDR prosessing a solution to his issue? I realize I may be trying to solve two equations (DoF and Exposure) with one solution... but if he is trying to take shots with a tremendous DoF then isn't he going to have an issue with brightness, exposure and blowing things out given the aperature needed and other settings used to compensate? Is his solution to do so in post processing rather than camera settings or equipment? This is sublte but good to know.... Experts?

Hi Scott,

No, exposure doesn't really come into it. For maximum depth of field one would normally use a narrow aperture (ie "high F-Stop number"), but the "balance" to that in the exposure triangle is that the camera will then choose a slow shutter speed to compensate for the reduced amount of light hitting the sensor. The actual exposure remains exactly the same, so HDR doesn't enter into it.

Probably the closest thing would be focus stacking where a number of shots are taken (at the same exposure), but at different focus points, and then software used to blend the "in focus" portions together into one composite image.

Sean will probably pop in a reply later on, but the short answer to Pat's question is "yes, for a given amount of light, bigger sensors are at a disadvantage to smaller sensors when it comes to depth of field". Having said that though, the application of proper techniques will probably make an even bigger difference. At the end of the day, it's all about the ratio of camera to subject -v- subject to background distances; the greater the ratio, the more out of focus the background will be (assuming that the focus is on the subject). Normally it's not a big issue to solve (when one understands depth of field charts / calculations) ... at worst, all it's probably going to mean is shooting at narrow apertures, which may often require the use of a tripod.

It's going to depend a lot on the subject though -- generally, an in-focus background with portraiture (for example) is a bad thing as it doesn't allow the eye to be drawn to the subject, as it should be, but that's only a generalisation -- really need to know more about what's being shot to comment much further.

[epmi314]

Yes! Focus stacking may have been what I meant to the whole time. Good point and well put! I get it... I think!

[Colin Southern]

Yes! Focus stacking may have been what I meant to the whole time. Good point and well put! I get it... I think!

Both HDR and focus stacking involve taking multiple shots - with the former, one varies the exposure; with the latter, one varies the focus point. It's a useful technique, but it has it's limitations ... it's not going to work in a situation where there is movement for example.

[epmi314]

Thanks Colin. That defines a good deal! I do appreciate it.

[FrankMi]

Although this reply is really 'off track' from Pat's original question, but it may help address the questions about Image Stacking. There are five situations that I can think of where multiple exposures (image stacking) can provide a benefit in limited circumstances. There may be others I am not aware of, but as Colin points out, they have limited usefulness.

Ghosting - Identical Image Stacking - There may be a better name for this but if you need to take an image where there are people moving about in front of your subject, you can take multiple identical images and combine then to mask out the people with parts of an image where the people have moved to another location. Doesn't help if a person simply won't move out of the way or you can’t get a clear shot of a particular part of the subject. If the exposure is long enough but the people move slowly you can see their 'ghost' in the image.

Excessive Contrast - Exposure Stacking - Taking multiple exposures in aperture priority can be combined to increase the ability to recover detail in shadows and/or highlights typically by using Tonemapping software. Drawback? Tonemapped images usually require additional post processing and doesn't work well with moving objects although in limited circumstances, single image Tonemapping may work.

Limited DoF - Focus Stacking - Changing on the focus point can increase the DoF but again doesn't work well if the subject moves, even the tiniest bit.

Noise Reduction - Identical Image Stacking – Blending multiple images at different opacities can be used to help reduce image noise but it is far easier to just get a good noise reduction program for most situations.

Panoramic Stitching - Multiple Overlapped Images - This can be used to stitch together a larger panoramic image than even a wide-angle lens can provide.

One of the drawbacks to any image stacking process is that it can take a lot of work, skill and may require specialized software to accomplish the goal. Couple that with the inherent limitations of each process and you have a set of techniques that may produce a result that is not possible any other way but - and I'll let you fill in the butts.

I hope this helps!

[Colin Southern]

Hi Frank,

Image stacking is also useful to give a psudo extended shutterspeed (kinda what you were saying with your paragraph about removing people from an image, but from a different angle); it actually works a treat for lowering the noise content of those type of images too. The downside is the camera needs to be rock-steady if one is already doing extended exposures (often I'll be shooting multiple 30 or 60 second exposures).

Stacking isn't a lot of work in CS5 - they have a command that does it automatically - then all one needs to do (for identical images anyway), is just change the opacity (from the bottom, 100%, 50, 33, 25, 20, 16.66 etc) (or repeat as required, and then "stack the stacks" (I think my record is around 100!). In terms of noise - a rough guide is "divide the ISO by 100, and that's the number of shots you need to take to get about the same noise as an ISO 100 shot".

In terms of excessive contrast - a lot of people employ (read "struggle") with HDR techniques, not realising that a typical (and correctly exposed) RAW capture captures around 12 stops of dynamic range anyway (even though we only print 4 and display 6 on our screens) -- so often all that's needed to capture sufficient DR is a one-click & drag movement of any RAW converter's fill light control.

[McQ]

if depth of field is the limiting factor, the required exposure time increases with sensor size for the same sensitivity”. I wasn’t able to follow the reasoning.

In the part of the tutorial I did follow, it is approximately true (except for macro shots) that for equivalent fields of view, to maintain the same depth of field requires an f-number inversely proportional to the sensor width. To use a convenient example, a camera with a 4/3” sensor would need f/8 to get the same depth of field as a camera with a 2/3” sensor at f/4. But …. if (again to make a simplifying assumption) the two sensors have the same number of pixels, the pixel on the 4/3” sensor is 4x as large as that on the 2/3” sensor, so the luminance should be 4x as great, exactly canceling the effect of doubling the f-number.

Hi Pat, thanks for the careful look! I don't see a mistake in the above comparison, but that sentence is a little out of context, because right after it the article goes into how larger sensors generally have better sensitivity (for similar pixel counts). To summarize:

Scenario 1. 4/3" sensor at f/8 with a 100mm lens
For the equivalent depth of field and angle of view (ie, an identically composed image), one would need:
Scenario 2. 2/3" sensor at f/4 with a 50mm lens

This means that both camera setups will end up letting in the same amount of light, since the physical aperture opening for each is 12.5mm (since this is calculated by dividing the focal length by the f-number, which is 100/8 for scenario 1 and 50/4 for scenario 2).

Therefore, at the same ISO speed, the larger sensor needs a longer exposure time to compensate for the fact that its light is spread over a much larger area. This is what I mean by the statement in the tutorial that you quoted above. Since one sensor is 4X larger, the exposure needs to be 4X as long. Alternatively, as you say, it could have 4X larger pixels and therefore achieve 4X the sensitivity (in theory, at least). This is all consistent with what you've said.

This is an oversimplification, but is probably enough to give you a feel for how the camera sensor choice might impact your photography. In reality though, image noise is unfortunately more complicated. The larger sensor will need a much higher ISO speed, and this could mean that read-out/"dark current"/banding or other causes of noise could creep in and make the resulting image worse off than it would have been in the example above.

Hope this helps.

[FrankMi]

In terms of noise - a rough guide is "divide the ISO by 100, and that's the number of shots you need to take to get about the same noise as an ISO 100 shot".

Ah! I didn't know that! Thank you for the information. That will make it easier next time I need to deal with this issue!

I have experimented with this but have not taken the opportunity as yet to compare the results with a noise reduction program. As a result, I'm not too sure where it's a benefit to apply this technique over using noise reduction software.

[Pat in San Jose]

Thank you, Sean, both for the clarification and for the original, very enlightening tutorial. Your example makes the comparison more concrete and allows me to phrase my question a bit differently. Given that the physical apertures in your two scenarios are exactly the same and therefore both cameras let in the same amount of light, then, again assuming the pixel count for both sensors is the same (and it probably wouldn't make much difference if they weren't), the light per pixel is the same in both cameras if the exposure time is the same. So to keep the same depth of field with the camera with the bigger sensor, you don't need to change the exposure time, you don't need to change the ISO sensitivity, you only need to adjust the aperture to let in the same amount of light.

If I am right (and I have little confidence that I am), I could go ahead and spring for the larger format camera and still keep things in focus throughout the picture just as well as I can with a small format camera. Maybe even better in low light. However, that is not the conclusion one would get from your tutorial or almost any other site that deals with depth of field. Everyone notes that small format sensors give you a larger depth of field for an equivalent field of view, but then they seldom carry the comparison further to compare one sensor to another with equivalent depth of field and equivalent exposures. I was happy to see that you at least broached the subject.

I'm mainly interested in photos as memories - travel, restaurants, family gatherings, other occasions, often indoors. My oranizational habits in the past were atrocious, and I now find myself trying to, for example, enlarge the street sign just barely visible through the restaurant window, to try to figure out where the heck we were. That's actually more fun than it sounds, but I'm always wishing everything were in better focus.

[McQ]

Given that the physical apertures in your two scenarios are exactly the same and therefore both cameras let in the same amount of light, then, again assuming the pixel count for both sensors is the same (and it probably wouldn't make much difference if they weren't), the light per pixel is the same in both cameras if the exposure time is the same. So to keep the same depth of field with the camera with the bigger sensor, you don't need to change the exposure time, you don't need to change the ISO sensitivity, you only need to adjust the aperture to let in the same amount of light.

Ah, OK, this is the sticking point. You would need to increase the ISO speed from say 100 to 400 in order to compensate for the 4X larger sensor. Even though both sensors receive the same amount of light, this light is spread over a larger area with the larger sensor, so the larger sensor receives a lower *flux* of light. Since ISO speed is flux-based (ie, the rate at which light hits a unit area), the ISO speed needs to increase in order to achieve the same exposure with the larger sensor.

As you say though, in theory ISO 400 on the larger sensor should produce the same noise as ISO 100 in the smaller sensor (presuming the same sized print).

[Pat in San Jose]

We may be zeroing in on the errors in my comprehension. But now I'm confused about ISO sensitivity. Let's continue with the comparison of 2/3" sensor with a 50 mm focal length at f/4 and 4/3" sensor with a 100 mm focal length at f/8, each sensor with, say, 10 megapixels. Each corresponding pixel in the two sensors gets the same flux in, say, photons per second. But the bigger sensor gets a lower flux if measured in photons per unit area. The ISO number, as I understand it, represents a voltage applied to the sensor to get a higher or lower electron current (but also dark noise) from the same photon flux. Does the gain have to increase on the large sensor because the photons are spread out over a larger area, or is the whole pixel just one bin responding to the number of photons, meaning the gain applied to the two sensors could be the same, and generate the same signal at each pixel, because the same number of photons for corresponding pixels is always the same?

[rpcrowe]

Hi Pat in San Jose...

I wonder if the following information might help clear things up a bit. Please accept my apologies if this information is too basic or if it doesn't pertain to your query...

You mentioned, "DoF is something I want lots of (bokeh is not for me)" I am interpreting this to mean that you do not like images in which areas are out of focus (OOF) such as when the photographer uses selective focus to isolate specific subjects leaving the rest of the frame OOF. A quick mention of terminology is that the term bokeh refers to the quality of the OOF are, not the size or depth. Bokeh is a subjective label while DOF, meaning the area between the closest point and farthest point of focus is objective.

DOF is controlled by the following inter-connected parameters and changing any one of these parameters impacts one or more the other parameters and or the resulting DOF...

FOCAL LENGTH: This refers to the actual focal length of the lens you are using. It doesn't refer to the equivalent focal length. Normally (the other parameters being the same), shorter focal lengths will provide greater DOF while longer focal length lenses will provide a shorter DOF.

F/STOP: The smaller the aperture of the lens, the greater the depth of field. If the other parameters are consistent, the smaller aperture (larger f/number) will provide a greater DOF and the larger aperture (smaller f/number) will provide a more narrow DOF. The shutter speed has absolutely no impact on the DOF except that shutter speed is linked (or visa-versa) to your f/stop for correct exposure...

DISTANCE FOCUSED ON: The greater lens to subject distance (all other parameters being the same) will provide a greater DOF.

SENSOR OR FILM FORMAT: The size sensor you are using is a parameter you must consider in determining DOF. The formula for DOF takes the size of "Circle of Confusion" (COF) into consideration. The physics behind determining the COF is relatively complicated and need not be understood. Simply stated, a larger sensor will require the image to be enlarged to a lesser degree to obtain the final result so the smaller sensor (which needs to be enlarged to a greater degree) must be sharper than the image captured by the larger sensor.

A wonderful website which allows you to play with these interrelated parameters is: DOFMaster online Depth of Field Calculator at
( http://www.dofmaster.com/dofjs.html ). Entering values for the various parameters will allow you to see how each parameter will impact the DOF.

You can enter the camera or film format, focal length, selected f/stop and distance focused on. The results will provide the extent of DOF along with the distance in front (usually 1/3 of the DOF) and the distance to the rear (usually 2/3 of the DOF) of the point focused on.

If you enter the Canon 5Dii (which is a full frame camera), 50mm focal length, f/4 and 10 feet for the distance focused on: the results will be a total DOF of 2.94 feet (1.26' in front and 2.94' to the rear of point focused on)...

If you change the camera to a 7D (which is a 1.6x crop) and retain the same focal length, f/stop and distance focused on; the results will be: a DOF of 1.84 feet (.84' in front and 1.0' to the rear of the focus point).

WAIT A SECOND! We always hear that the larger format will have a shorter DOF than the smaller format but, the DOF for the 5D is wider than that of the smaller format 7D. Why is that?

In order to get the exact same framing on a full-frame camera as we would get on a 1.6x camera; we would either need to get closer to our subject or to use a longer focal length lens. Changing either of these parameters would change the DOF. As an example, to get equivalent framing with a 1.6x camera using a 50mm lens, you would need to increase the focal length of the lens you are using on your full frame camera to 80mm (1.6x x 50mm = 80mm). Using an 80mm lens on a full frame camera (like the 5Dii) at f/4 focused at 10 feet would provide a DOF of 1.12 feet (.53' in front and .59' to the rear of the point focused on).

If both lenses were focused on 10 feet and you wanted to exactly match the DOF of the 7D using a 50mm lens with the 5D using an 80mm lens, you would have to open the 50mm lens on the 7D to around f/2.8 (giving you a DOF of 1.29').

However both the 80mm lens on the 5D and the 50mm lens on the 7D were set at f/4 the same shutter speed would get the same exposure results. However, if you wanted to use an 80mm lens on the 5D and a 50mm on the 7D and if you demanded the same DOF, you would need to open the 50mm lens approximately one stop to f/2.8 which would require a shutter speed of 1/2 the duration of your exposure at f/4. The relative exposures of these two images would, however, be the same despite one being on a full frame camera at 50mm and the other on a crop camera at 80mm.

Now to muddy the waters slightly... Although a 50mm prime lens is 50mm in focal length all the time; the only time a zoom lens, if set at 50mm, is actually 50mm in focal length is when the zoom is focused at infinity. The differences at 50mm are so small that the variation of focal length in a zoom is not worth considering. However if you are using a prime 400mm lens and a zoom lens which is marked at 400mm; the only time that the zoom is actually 400mm in focal length is when it is focused at infinity.

IMO, calculating the exact DOF is "Much Ado About Nothing". When I want a shallow DOF, I open up the lens or use a longer focal length. When I want a wider DOF, I simple stop down and or use a shorter focal length. I never calculate to the foot or meter what my DOF will be...