Asian in a Strange Land

This is a continuation of my previous post about Depth of Field (DOF).

How then does sensor size affect DOF? Again there is much confusion here because of a lack of fundamental understanding of what DOF actually is and how it works. Assuming my previous post made sense and is acceptably clear, let’s use that as a starting point.

It is often claimed that given the same lens, aperture, and focus distance, the resulting DOF is the same regardless of sensor size. There is a grain of truth in this but it ultimately depends on what you’re trying to achieve. Say you take a picture with a fullframe (FF) camera like a Canon 5D with a 50mm lens at f/4, 10 feet away from the subject. Then you take a photo with a Micro 4/3 (m4/3) camera like an Olympus E-P1 also with a 50mm lens at f/4, also 10 feet away from the subject. It is true that the physical size of the projected image of the subject will be the same size on both sensors. It is also true that the degree of blurriness of the areas not in the focus plane will be the same in both shots. The composition will be very different with the E-P1 shot looking more “zoomed in”.

If you then print both images to the same size (not same size of subject but same size of print) the DOF will be different because you must enlarge the E-P1′s image more to reach the same print size as the 5D. In this case the E-P1′s print will actually have less DOF than the 5D’s because you’re enlarging it more. Remember: the larger the print the smaller the DOF. That seems counter-intuitive but if you have the equipment you can try it yourself and you’ll see that it’s right. You can also check the DOF calculator at http://www.dofmaster.com/dofjs.html to see for yourself. The math and the practice match up.

If however you print both images to where the subject is the same size in both, which means the 5D’s image is twice the length and height of the E-P1′s, then the DOF will be the same because you have enlarged both the same amount. (the 5D’s sensor is twice the length and height of the E-P1′s [more or less, close enough for our discussion anyway]).

But let’s be honest: this isn’t how most photographers work. This is interesting on a theoretical level and for our own understanding, but in practical terms it’s not very useful in my opinion. A photographer usually has in mind a particular composition and tries to achieve it by any means necessary. Photographers who are mostly equipment constrained (sports and wildlife, for instance) have other concerns and probably aren’t interested in this at all, but for most other types of photography we start from a composition and go from there.

So let’s say you have a composition in mind–subject a certain size and position in the frame, certain amount of background included in the shot, certain level of perspective distortion, certain amount of DOF–and are trying to figure out the equipment needed to achieve it. You figure out that you can do so with a Canon 5D, 50mm at f/4, 10 feet away. To achieve the exact same composition with an E-P1 you can only do so from the same position (10 feet away) with a 25mm lens at f/2. When I say “same composition” I mean all of the elements I mentioned above: size and position of subject, background, perspective distortion, and DOF. To achieve this you have to take the photo from the same position with the same angle of view, which is achieved by the respective configurations I described above. You can get a similar shot by moving closer and using a wider lens or moving further and using a longer lens, but neither will achieve the exact composition you’re after.

Why 50mm on 5D and 25mm on E-P1? Because each produces the same angle of view (more or less, manufacturer specification might be slightly off) for its respective sensor format, thus creating the same composition. The E-P1′s 2x crop sensor is 1/2 the size in either dimension compared to the 5D’s FF sensor, which means it essentially crops the middle 1/2 of the image length and height that the 5D would capture. So using a 25mm lens on an E-P1 results in the same angle of view as a 50mm on a 5D, which is 2x the focal length.

Why f/4 on the 5D and f/2 on the E-P1? Honestly that’s a bit technical and beyond my capacity to explain in a concise manner. The rule of thumb is since the E-P1 is m4/3 and has a 2x crop sensor, to achieve the same composition and DOF you use a lens 1/2 the focal length (25mm vs. 50mm) and 2 stops larger (f/2 vs. f/4) than FF. I believe the technical explanation involves a lot of optical physics, which I’m not prepared to take a stab at, although again the literature is out there if you care to read it.  Intuitively it makes sense–shorter lens gives larger DOF so we compensate by using a larger aperture to decrease DOF, although that might not necessarily line up with the purely technical explanation.  And again if you just want to see the numbers in action you can and should check out http://www.dofmaster.com/dofjs.html just to play around and see how the numbers work out.

Back to the 1st example with a 50mm lens on both cameras: you actually have to stop down the lens 2 stops on the E-P1 to get the same DOF, so it would be f/4 on the 5D vs. f/8 on the E-P1. Remember enlargement. Or you could think of the 50mm acting as a 100mm when mounted to the E-P1, which might help remind you to stop down more to get the same DOF. Then again you would get a completely different composition so I’m not sure how useful that is. In my opinion for how most photographers work the process of figuring out equivalent equipment in 2 different sensor formats is more useful than figuring out how DOF will differ using the same lens on 2 different sensor formats, but others might feel differently and I’d like to hear some feedback on that to see what kind of rationale there is behind that line of thinking.

All of that to say what exactly? Well, take what you will from it, hopefully something useful and meaningful to you. I know my attempt at simplifying wasn’t nearly as successful as I hoped. Perhaps it’s just too complicated to boil down to simple terms. Perhaps I’m just not at good at explaining. Regardless I hope you’ve benefited in some measure.

Yesterday I got involved in a bit of a messy discussion about Depth of Field (DOF):
http://forums.dpreview.com/forums/read.asp?forum=1041&message=40360410

Then again when is a discussion about DOF ever not messy, right? There’s so much misunderstanding and misinformation out there, and when you try to point it out people get offended. That motivated me to step back and try to put together some information on the subject away from the heat of the moment without replying to anybody in particular. I’m not an expert but I’ve learned a lot about DOF over the years from people much more knowledgeable than me, and hopefully this sharing of information will be helpful to others out there. I might even learn something new myself from the ensuing discussion I hope occurs, which would be icing on the cake.

The main reason there is so much debate over what should be a straightforward topic is that people often don’t know what DOF actually is. If you want some excellent technical articles on the topic here are some links:

http://www.cambridgeincolour.com/tutorials/depth-of-field.htm
http://en.wikipedia.org/wiki/Depth_of_field
http://www.dofmaster.com/equations.html
http://toothwalker.org/optics/dof.html
http://www.largeformatphotography.info/articles/DoFinDepth.pdf

Some of that will probably make your eyes water. I was a math and computer science double major in college and reading some of that stuff takes me 2-3 tries to fully grok. So here is my attempt at simplifying it, and if you don’t believe my synthesis of said info you can always go back to the sources.

So what is DOF? DOF is perception. It is the perception of what is acceptably in-focus to the viewer. By the laws of physics when you focus rays of light onto a flat surface like film or a sensor, there is a 2-dimensional plane that is actually in focus and everything else is out of focus to varying degrees. Remember using a magnifying glass to start a fire as a kid? You adjust the position of the magnifying glass until you get the smallest point of concentrated light. If you then moved even slightly closer or further, that focused point of light got bigger, that is to say it went out of focus. So in the captured image there is actually no depth to the focus plane, hence there is no such thing as DOF in the captured image itself–only a single in-focus plane and everything else is out of focus to varying degrees. That’s not to say that the captured image doesn’t influence the final DOF because it does, but we’ll get to that in a moment. For now what’s important to know is that there is only a 2-dimensional plane that is actually in focus; nothing else in the captured image is in focus but that plane.

How does the captured image affect DOF? As stated above, everything but the focus plane in the image is out of focus, with different areas being out of focus to varying degrees. It’s this “varying degrees” that affects final DOF. Let’s call it “blurriness”. Some areas of the image have more blurriness than others. The more you stop down your lens aperture the less blurry you make the areas that aren’t perfectly in-focus. You can also make areas less blurry by moving further back or using a lens with a shorter focal length. The less blurry these areas are the more likely they will look to be within DOF in the final output, be it print or screen.

Why then when we look at images can we see a depth to the area that is in-focus? This is DOF. We perceive more than just a 2-dimensional plane to be in focus in the image–the areas with less blurriness than others will look in focus–due to a variety of factors including print/viewing size, viewing distance, visual acuity (how good one’s eyesight is), lighting conditions, etc. Let’s take visual acuity and lighting conditions out of the mix to simplify a bit. After all if you’re trying to determine DOF for yourself, your own visual acuity and lighting conditions won’t change when you flip back and forth between 2 images you’re comparing. That leaves print size and viewing distance.

Assuming the same source image and same viewing distance, the larger the print size the smaller the DOF. Here is an excellent example by fellow forum-goer Sean Nelson:
http://forums.dpreview.com/forums/read.asp?forum=1041&message=40362365

You can easily see the effect of enlargement/print size there.  The smaller image looks all in focus while the larger image shows that the flower is in focus but the leaves in the background are not.  This is the effect of print size on DOF in action.  Why is this the case?  In short it’s because the smaller the image the harder it is for us to differentiate between blurry and sharp areas in the image.  I refer you back to the technical articles for a more detailed explanation.  In practical terms it’s sufficient to know that this is the case, and the test is easy to replicate for yourself.

Viewing distance works the same way. Assuming the same source image and same print size, the closer the viewing distance the smaller the DOF.

So there are 2 parts to DOF: the captured image and the viewing conditions of the final output. Both influence DOF, and you can’t figure out absolute DOF without taking into account both factors. Having said that, when comparing relative DOF of 2 different formats (for instance fullframe [FF] vs. Micro 4/3 [m4/3]) it’s usually possible to ignore viewing conditions because they are typically constant. Your eyesight and lighting conditions stay the same, as are the size of your monitor and viewing distance to it. I believe this is also often a source of confusion when discussing DOF, leading people to believe that DOF is only inherent in the image instead of a combination of the captured image and the viewing conditions of the final output.

Why is this important to know? One reason is if you want to know how sensor size affects DOF. I’ll try to tackle that in the next post.