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The introduction of video-enabled large-sensor still cameras (so-called VDSLRs) has really shaken up the camcorder landscape in terms of the access to shallow depth of field. Just a few short years ago a 2/3" sensor was the largest sensor commonly available in the video world... and now, substantially larger sensors (such as those found on the Panasonic Lumix GH1, Canon EOS 7D, and EOS 5D Mark II) are much larger than anything we've had access to before. The sensor in a GH1 is 4x as large as a 2/3" camera! The 7D's sensor is as large as a frame of 35mm movie film, and the 5D's sensor is as large as a frame of 70mm movie film!
Larger sensors can have many benefits over smaller sensors, if all other things are equal (such as pixel count, etc). When comparing a 1/3" sensor to a 2/3" sensor, all other things being equal, typically the 2/3" sensor would have better sensitivity, better noise performance, and higher latitude. However, what we're discussing here in this article is strictly the effect the sensors have on the attainable depth of field you can achieve.
Before we get into the numbers, let's take a small side trip into pedantry: strictly speaking, sensor size in and of itself doesn't have a direct relationship to the depth of field; the depth of field is established in the lens, regardless of what sensor the lens projects its image onto. The lens focuses the image, and what's in-focus or out-of-focus is determined by the lens, not by the sensor it's attached to! Whether you attached the lens to a 1/3" camera, or a VistaVision camera, what's in-focus and what's out-of-focus would remain the same. What changes is instead the Field of View; larger sensors see wider fields of view. Accordingly, to get an equivalent field of view on a smaller-sensor camera, you'd have to use a wider-angle lens than you would on the bigger sensor. It is the wider-angle lens, not the sensor size, that is giving the deeper depth of field.
However, there is one aspect of sensor size that is involved in the perception of depth of field, and that's the ever-confusing Circle of Confusion size. The Circle of Confusion is the mathematical diameter of how tightly a pinpoint of light would need to be focused so that when the image is magnified to viewing size, that pinpoint still looks sharply focused. The Circle of Confusion causes people to become confused (aptly named!) because people seem to think that there's one set diameter for each format, and that's simply not true. The size of the Circle of Confusion is entirely dependent on how much magnification you're going to subject the image to. For theatrical projection, your image will become much larger than it would for television viewing, and incredibly larger than it would become for web viewing. Accordingly, your calculations should technically be using three different Circle of Confusion sizes, based on each intended display. Something that looks tightly focused on your iPod Touch might be grossly out of focus when it's magnified and blown up on a theater screen. And your lushly out-of-focus backgrounds (on theater projection) might be quite a bit sharper and in-focus on the iPod Touch. So there's no definitive size of Circle of Confusion for each format, but it is fair to say that the relative size is constant between formats (i.e., a format that requires 4x more magnification to display, will need a proportionally-tighter Circle of Confusion in order to maintain crisp focus). So the exact size of the Circle of Confusion isn't definitive, but the larger the sensor, the looser (i.e., bigger) the Circle of Confusion you can use in your calculations, because the larger the sensor, the less the image will need to be magnified to fill any particular display device.
Okay, so back on the subject -- how can you compare formats to see how the Depth of Field differs between them? My approach is to use the concept of a fixed camera position, and a fixed subject position (the subject is 10 feet away), and we would change the lens so that we had the equivalent field of view on each camera. Then, after arbitrarily assigning an f-stop to the smallest-sensor camera, I calculated how deep the depth of field for that camera would be, and I set out to match that depth of field with each of the other cameras, by changing their iris values. The larger the sensor, the more I would have to close down the iris in order to achieve comparable depth of field.
Note: this is not an actual field test, this is a mathematical simulation using an angle-of-view spreadsheet and an online depth-of-field calculators.
I ran the figures for all the most-common video sensor sizes ranging from 1/4" up to "Full Frame" 35mm still-photography size. I set the lens field of view at 45 degrees, using a subject that was 10' away, and I settled on having 40 feet of total depth of field.
I also calculated the Circle of Confusion for a common viewing size, using 3 microns for Full Frame, all the way down to 1/3 of a micron for the 1/4" chip camera.
For those wanting to follow along, here are the values I used:
1/4" sensor
5.5mm lens
0.0033 CoC
1/3" sensor
7.25mm lens
0.0044 CoC
1/2" sensor
10.25mm lens
0.0062 CoC
2/3" sensor
13.25mm lens
0.0080 CoC
4/3 sensor (Panasonic GH1)
26mm lens
0.0150 CoC
APS-C sensor (Canon 7D)
32.5mm lens
0.0190 CoC
Full-Frame or 35mm Still or VistaVision sensor (Canon 5D Mk II)
52.25mm lens
0.0300 CoC
Now, based on the calculations, you should be able to achieve the exact same field of view on all cameras using all these sensor sizes, pointing at a subject 10 feet away, using the lens focal lengths I indicated. And if you used a common aperture (such as f/2) the depth of field would be very different between all the shots. But if you compensate using the iris, you should be able to create equivalent shots in terms of field of view and depth of field.
Here are the iris values that I calculated, for each camera to deliver approximately 40' of depth of field on a subject 10' from the film plane:
1/4":...F/2.4
1/3":...F/3.1
1/2":...F/4.4
2/3":...F/5.6
u4/3:...F/12
APS-C:..F/14.4
FF:.....F/24
Now, those are some odd f-stop numbers, so I've calculated the f-stop difference value so you know just how much you'd have to open-up a smaller-sensor camera, or how much you'd have to stop down a larger-sensor camera, to get the same field of view.
Here are the iris differences I derived, to get the same DOF at the same field of view at the same subject distance, on different-sized sensors:
A 1/4" sensor would need to be 3/4 of a stop more open to match a
1/3" sensor, which would need to be 1 stop more open to match a
1/2" sensor, which would need to be 2/3 of a stop more open to match a
2/3" sensor, which would need to be 2 1/4 stops more open to match a
4/3 sensor, which would need to be 1/2 stop more open to match an
APS-C sensor, which would need to be 1 1/2 stops more open to match a
Full-frame sensor.
Okay, so... put another way, here are some tables based on each camera size, showing the difference in stops you'd have to use in order to get them to look visually equvalent:
For a 1/4" camera to match to
1/3" - open up 3/4 of a stop
1/2" - open up 1 3/4 stops
2/3" - open up 2 1/2 stops
4/3 or GH1 - open up 4 3/4 stops
APS-C or 7D - open up 5 1/4 stops
Full frame - open up 6 3/4 stops
For a 1/3" camera to match to
1/2" - open up 1 stop
2/3" - open up 1 2/3 stops
4/3 or GH1 - open up 4 stops
APS-C or 7D - open up 4 1/2 stops
Full frame - open up 6 stops
For a 1/2" camera to match to
2/3" - open up 2/3 of a stop
4/3 or GH1 - open up 3 stops
APS-C or 7D - open up 3 1/2 stops
Full frame - open up 5 stops
For a 2/3" camera to match to
4/3 or GH1 - open up 2 1/4 stops
APS-C or 7D - open up 2 3/4 stops
Full frame - open up 4 1/4 stops
For a movie camera or APS-C-sized camera like the Canon 7D, to match to
a full frame - open up 1.5 stops
These numbers have been rounded slightly to make for easier presentation, and please remember this cannot be an absolutely exact science -- sensor sizes vary, even within class designations; a 1/3" JVC HD100 has a smaller sensor than a 1/3" HVX200, and they're both smaller than a 1/3" HVX200A, for example. And APS-C is a different size depending on whether you're discussing Nikon or Canon, and on and on. But the general relative sizes and stop differences here should certainly go a long way towards equalizing out the depth of field performance between these various camera sizes.
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