Focusing on Depth of Field And Lens Equivalents

Hi! John Hess here from FilmmakerIQ.com. Hopefully you have a fundamental grasp of lenses because today we’re going to dive into the depths of Depth of Field and how sensor size play into this often confusing subject. If you remember back to our course on Optics and the science of lenses - you’ll recall that even the most basic lenses will create a sharp image at some point if the object is more than one focal length away from the lens. Well a photography lens has the same properties except a photography lens has to produce the image on the camera’s sensor. To do so, the lens inside shift about changing the rear nodal point ever so slightly to achieve a sharp image on the lens. The distance which an object is in focus is marked on the lens usually in both feet and meters. So that’s our focus. But now the question is - how close do we have to be so the focus is “good enough” - if the lens says that the object that’s 10 feet away is in focus - will something that’s 11 feet away be acceptably in focus? And that’s basically what depth of field is - how much space do we have on the near and far side of the plane of focus where things are acceptable sharp? A deep depth of field means there’s a lot of space in front and behind the focal plane. A shallow depth of field means there is very little space. Notice how we said “acceptably” sharp. We’ll cover that more deeply in a bit. Also note that the terminology is depth of field - not depth of focus. Depth of focus refers the space you have to move behind the lens - unless you’re working with cameras with a back focus setting, you will not be using depth of focus. Now before we get really deep let’s talk about the key controller of depth of field - the aperture. An Aperture Demonstration A lot has been written and said about Depth of Field using graphics and charts and that’s fine but I really wanted to see the physics of this happening in front of my own eyes. I set up a simple optics experiment using a simple one element lens - a magnifying glass with a focal length of 130mm. Here we can see it projects the light from a bare bulb onto this piece of paper. When the light bulb is 20 inches to the lens - we have a sharp image on the paper. I know I’m mixing metric and imperial units but that’s just how my mind works - we will be talking inches and feet when discussing distance but the lenses will be marked in metric. Now as my assistant moves the light bulb closer to the lens the image becomes blurred - at 17 inches from the lens it looks out of focus. When we pull the lightbulb back to 23 inches it goes out of focus again. This gives us a 6 inch depth of field - 3 inches in front of the focal plane at 20 inches and 3 inches behind. But now watch what happens as we put an aperture in front of this lens. These apertures were just tennis ball can lids that I punched a hole through. Now recall that a the f-stop is simply the focal length divided by the diameter of the aperture. So with the lens having a focal length of 130mm, this first aperture having a diameter of 14, this aperture is about an F9.0. Using this aperture we find that our near boundary is 16 inches and our far is 30 inches - for a new depth of field of 14 inches. But making our aperture smaller, we have increased our depth of field. While we are here - there is only more point to be made about depth of field - that the closer you are to the lens - the shallower your depth of field will be. This works pretty much the same regardless of the focal length or aperture. To demonstrate - I first positioned the bulb 12 inches from the lens and adjusted the paper behind the lens to create a sharp image. The near distance was 10 inches with the far distance being 16 inches - giving us a depth of field of six inches using that same F9 aperture. Now without changing the aperture, I refocused the light bulb at 19 inches - the near was 16 inches and far was 25 inches - giving us a depth of field of 9 inches. If you think back to the thin lens image equation 1/distance to the object plus 1/distance to the image equals 1/focal length you can kind of understand this intuitively. As the distance to the object gets bigger to infinity, 1/distance to object gets closer to zero so that the image distance ends up being the same as the focal length. As you move the object closer the image distance retreats from the focal length - at first very slowly but it takes off to infinity the closer the distance to the object approaches the focal length. But that math is just in regards to the focal plane - what’s in focus. We’re talking about depth of field - which brings us to the question we’ve been dancing around this whole timie - how sharp is sharp enough? When doing those experiments with the lightbulb - I just eyeballed what I thought was “sharp enough”. Mathematically speaking there is only one point in space where the image is perfectly sharp. But our eyes and our recording medium have some leeway - and that leeway is called the circle of confusion. Let’s imagine a single point of light as it travels through the lens. When the single point of light is emanating from the plane of focus, it will hit the sensor as a single point of light creating this cone. As that light moves forward or backward, the cone will shift in space, no longer being single point of light on the imaging sensor but a spot of light. The question is how big can that spot of light be before it becomes noticeable as a blur. And that’s where the The Circle of Confusion confusion comes in. The Circle of confusion is the maximum size that spot of light be to be indistinguishable from a single point to the final viewer - bigger than the circle of confusion and we see a blur - smaller and we see what looks like a focused single dot. This for the most part is subjective - photographers assume the image will be viewed as an 8x10 print and comfortable distances - yielding about .029mm for a Full Frame 35mm sensor and half that for an APS-C sensor with 0.018mm. Cinematographers projecting film onto a big screen use a slightly different set of numbers - the ASC Manual puts the circle of confusion of 35mm film (which is actually about the same size as an APS-C sensor) at 1/1000th of an inch or 0.025mm and 5/10,000th of an inch or 0.013mm for 16mm film. This number can be plugged into this nasty equation to derive depth of field charts. But those numbers are for celluloid film which has incredibly high resolution. In the digital world the sensor is sectioned off into pixels and these pixels put a limit on the size of our circle of confusion - and if you’re still a little confused about the whole circle of confusion thing - this little light experiment might clear things up a bit. Going back to our basic single element lens - I replaced the lightbulb with a flashlight. Now imagine the grid on the paper to be the pixels on the camera sensor. If the light cone falls inside one pixel box - that pixel will activate - it doesn’t matter how small the light cone is, there is no way to capture anything smaller. So in essence the width of one pixel is our circle of confusion. Here the light is focused at 18 inches. As I move the flashlight forward, the light cone gets bigger and starts to spill over to the other pixels around it. Now we’re getting a blur. The close is somewhere around 11 inches and the far of 30 inches which gives us a depth of field using this sensor pixel size of about 19 inches. Now watch what happens as we reduce the size of the pixel - thereby reducing the circle of confusion. Our focus is still at 18 inches but our near is only 13 inches and far is 21 inches - giving us an 8 inch depth of field. Going even tighter with the pixel grid - we get a near of 14 inches and a far of 19 inches - giving us an 5 inch depth of field. So as we increase the resolution - we are going to make the depth of field shallower. This may be rather intuitive. It’s really hard to see what’s in focus when you’re looking at a tiny viewfinder - but once you blow up your image to the big screen you can see all those focusing problems. But there’s one more take away… imagine we’re shooting an HD image - 1920x1080 - as we step down in sensor size from Full Frame to APS-C which is closer to Super 35mm or even down to Micro 4/3rds which is about half that of full frame- our depth of field actually gets shallower. Let me repeat that because it’s a big point. Given identical lenses and apertures, the smaller sensor with it’s smaller circle of confusion will create a shallower depth of field. Smaller sensors have shallower depth of field. Do you hear that - that is the sound of camera nerds all over the world taking to the keyboard to tell me I’m flat out wrong. But the physics of light don’t lie - and we’re not done yet. There’s still a matter of crop factor and lens equivalency. Although it’s true that the Depth of field gets shallower with smaller sensors, there’s a bigger factor involved and that’s crop factor. Basically a smaller sensor will create a more zoomed in image given the identical focal length. And now we’re going to get into a topic which I loathe because it creates so much unnecessarily confusion - Lens Equivalency. In the photography world - 35mm film was the standard that pretty much everyone from hobbyists to professionals shot on. People got used to what a 50mm lens looked like on 35mm film. When digital came along with smaller sensors, they introduced this idea of lens equivalency - where you take the crop factor and multiply it with the lens focal length. A camera with an APS-C sensor which has a crop factor of 1.6 shooting a 50mm would give the same angle of view of an 80mm lens on a full frame sensor. The same field of view - but not the same depth of field given identical settings… But I’m getting ahead of myself. Let’s do a demonstration. Here we have a Full Frame camera - the Canon 5D MkII shooting a scene using an 50mm lens from a distance of 42 inches. We are shooting with ISO 500 and the lens is stopped to F2.0.. This is the resulting image. Let’s measure the depth of field using a focus chart and we find the near is 41 inches and the far is about 43 inches - a really shallow 2 inch depth of field. Now we’ll replace that 5D with a APS-C sensor of the Canon 7D using that same 50mm lens and shooting the same distance, ISO and aperture settings. Here is the image Before we do anything let’s measure the depth of field using our focus chart again and we find a near of about 41 inches and a far of 43 inches - this is about the same as the full frame - Depth of Field calculators show the difference between Full Frame and APS is really only a matter of half an inch or so less depth of field in the smaller sensor from 2 inches down to 1.3 inches - but again such things are very subjective. But the elephant in the room is look how the field of view is smaller with the smaller sensor. So in order to create the same field of view - the same look as the APS-C on the full frame - we have to use a longer lens that full frame. Keeping the exact same distance - here’s that 80mm lens on the Full Frame sensor shooting the same aperture of F2.0. But look at the bokeh of the out of focus lights in the background. They’re different - bigger on the 80mm F2. That’s because if we use the crop factor on the focal length - we have to use it on the fstop as well - because after all fstop is the focal length divided by the diameter of the aperture. So now we get an 80mm shooting at f3.2 or there abouts. which is the crop factor times our original fstop… but now you’ll notice that the image is darker, so we have to increase the the ISO by - you guessed it, the crop factor. So in order to get a full frame equivalent of a 50mm F2.0 and ISO 500 on an APS-C sensor, we need to shoot an 80mm - F3.2 ISO800 on the full frame. So if the lenses are identical and the distances the same - the smaller sensor will have a slightly shallower depth of field but the field of view will be totally different. Using lens equivalency the smaller sensor is shooting the equivalent of a higher focal length on it’s full frame brethren BUT also a deeper depth of field because the full frame camera has to stop down. That’s one way of looking at it, but let’s look at it the way most people would shoot. Going back to our original 50mm image on a FF frame sensor - how far back would we have to move the APS-C camera in order to create the same field of view? The answer is… the distance times the crop factor. So 42 times 1.6 yields 67.5 inches. Here is the resulting picture - again notice how the bloom of the bokeh is smaller than the bloom on the 50mm. Just by adding distance between the lens and the subject, we increase our depth of field just as we demonstrated with the single lens experiment earlier. So because of the crop factor, the smaller sensor will inherently have deeper focus when creating similar field of view even though the sensor has a smaller circle of confusion. If we carry this to the extreme, this is why your cell phone camera with it’s micro sensor can’t produce the same kind of creamy shallow depth of field images that a Full Frame camera can. Does that make smaller sensors inferior - no of course not. It just makes them different. Full Frame sensors have a particular look, and smaller sensors have another look - that’s all it is. So through some demonstration of physics using single lenses and cameras with different sensors I hope we have dispelled some of the of the confusion surrounding depth of field. It still takes some doing to wrap my mind around it, but you’ve seen it right in front of you. Now.. will you find yourself in a position where you need to shoot identical fields of view using two different sized sensors where you’ll need to do the lens equivalency equations? Probably not. For most people, you just need to get used to whatever system you're using. If you’re shooting Super35 APS-C sized sensor, get familiar with what depth of field and field of view you get with your focal lengths - don’t worry so much about what the full frame equivalency is - that’s really only necessary when your jumping between formats - and then if you need to do the math don’t forget to multiply the crop factor into the focal length. The tools are important, but not as important as a mastery of how to use them and how they function. This is the key to making something great. I’m John Hess and I’ll see you at Filmmaker IQ.com