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One of my favorite qualities of large apertures (besides the low light capability) is their characteristic shallow focus that can offer dramatic background blur.

I've been considering how a micro format camera such as a micro four-thirds or even something like a Canon G16 or S120 (with 1/1.7" sensor) might perform with regards to depth-of-field. Both of those cameras boast an f/1.8 ratio. I am of the understanding that the lens won't be as fast as an f/1.8 on an APS-C or fullframe sensor as it obviously won't be capturing nearly as much light, but how does depth-of-field scale down?

To clarify my question consider these scenarios:

  1. a camera body with a fullframe sensor and an appropriately matching f/1.8 lens
  2. a camera body with a micro 4/3 sensor and an appropriately matching f/1.8 lens
  3. a camera body with a 1/1.7" sensor and an appropriately matching f/1.8 lens

How would the depth-of-field compare? Let's also assume for the sake of argument, that all lenses have focal lengths that correspond to the same field-of-view.

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    "I am of the understanding that the lens won't be as fast as an f/1.8 on an APS-C or fullframe sensor as it obviously won't be capturing nearly as much light" - this is not true, since the smaller amount of light is concentrated on a correspondingly smaller sensor area. Aperture numbers are fully comparable across sensor sizes. – Michael Borgwardt Feb 25 '14 at 8:19
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For starters, see Matt Grum's answer here about the phsyical aperture size.

There are two things influencing depth of field: physical aperture size and focusing distance. A larger aperture decreases the depth of field, and a longer focusing distance increases it.

From these two properties, you can extrapolate how a smaller sensor affects the depth of field. While the sensor size has no direct influence on it, smaller sensors have greater crop factors, which means that positioning a subject to take up the same space in the frame requires either a shorter focal length (to expand the field of view) or an increase in focusing distance (i.e., stepping backward so you can see more of the subject).

To use Matt Grum's example, suppose you have a 50mm lens at an aperture of f/4. 50/4 is 12.5mm--that's your physical aperture size (note that sensor size has not entered the picture yet). 1/1.7" sensors have a crop factor of 4.2. If you wanted to use a shorter focal length to get the same field of view, you would need a lens of an approximately 12mm focal length. 12/12.5 is 0.96, or about 1, so to maintain the same depth of field at the same field of view and the same focusing distance, your 50mm at f/4 would have to become 12mm at f/1.

For the other case of increasing the focusing distance/stepping backward, I'm unfortunately not familiar enough with the math to give a concrete example, though suffice it to say that you can verify this relationship between focusing distance and depth of field with a little empirical testing. So if you took the same 50mm lens and mounted it on both full-frame and 1/1.7", you would need to walk backward quite a ways to get the same subject framing on the 1/1.7"--and at that point your depth of field would be much greater, so you would need to open up the aperture quite a bit more to get it back down to the same level as on the full-frame camera.

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  • I kind of like this practical explanation, but the real reason is the circle of confusion (en.wikipedia.org/wiki/Circle_of_confusion). Sorry my English is not good enough to allow me to explain the optical/math, so I'll just let someone else do a full answer. – FredP Feb 25 '14 at 8:27
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Keeping the same f/stop and angle of view, the radius of the background blur scales linearly with the size of the sensor.

The m43rds camera offers half the amount blur as the sensor as the full frame camera as the sensor is half the size. The 1/1.7" camera gives 4.5 times less blur.

Or alternately the m43rds camera at f/1.8 equals the full-frame camera at f/3.6 and the 1/1.7" camera at f/1.8 equals the full-frame camera at f/8!

In terms of the actual depth of field, it's a highly nonlinear relationship, as you approach the hyperfocal distance of the smaller format the difference grows exponentially.

  • The full frame camera with 50mm f/1.8 lens focused to 12m gives total DOF of 6.5m
  • The 1/1.7" camera with 11mm f/1.8 lens focused to 12m gives a total DOF of 96m
  • The full frame camera with 50mm f/1.8 lens focused to 13m gives total DOF of 7.8m
  • The 1/1.7" camera with 11mm f/1.8 lens focused to 13m gives a total DOF of 291m!
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  • I think that with your 1/1.7" sensor examples, it really comes down to quibbling over the acceptable blur/CoC — basically, it's extremely close to converging on infinity. The important thing here is that the full-frame camera does effectively the same jump at 50mm and 12m/13m focus distance at f/8. (Try a CoC of about 0.023 for full frame to see what I mean.) – mattdm Feb 25 '14 at 13:51
  • @mattdm my point was that depth of field is not linear with respect to sensor size, whereas blur radius is. No matter what you choose as the CoC the same non-linearity occurs, just in a different place. I wasn't making a "full frame is better" argument! – Matt Grum Feb 25 '14 at 14:10
  • Yeah, I didn't mean to imply that you were. What I mean is that if you use a CoC small enough to show it, the full frame sensor shows exactly the same non-linearity at exactly the same place at the equivalent aperture of f/8. – mattdm Feb 25 '14 at 15:05
  • @mattdm again I wasn't making any sort of format comparison, just indicating that there's no simple answer to the question "how much more depth of field", as it depends on how close you are to the hyperfocal distance. – Matt Grum Feb 25 '14 at 18:12
  • I get that. :) I just want to make sure that no one takes it the wrong way. – mattdm Feb 25 '14 at 18:19
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I think I am understanding it better now. Thanks to these answers, and a new approach to how I was thinking about it. I think the relationships can all be perfectly linear if you realize that a sensor of smaller dimensions will produce triangles of correspondingly smaller dimensions.

So, if you have a sensor with half the width of another, it will produce half the DOF at half the distance from the focal point.

DOF diagram

At the same distance then, DOF will get considerable larger, quite quickly.

In other words, if I want to get narrow DOF, bigger sensors are the best (all other things being equal).

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