DOF related to f-stop: 1/3", 2/3", APS-C, and 35mm sensors?

[Chris Davis]

Hello,

I'm trying to figure out how the DOF of various sensor sizes relates to various f-stops.

Best I could tell from messing with a DOF calculator, every time you double the width of a sensor, you can stop down by two and get the same DOF.

So that, for example, all these would have about the same DOF (at the same distance at, say, 50mm equivalent focal lengths):

1/3" @ f/2
2/3" @ f/4
4/3" @ f/8
APS-C @ f/11 (?)
35mm (not cropped) @ f/16

Is this about right?

Thanks,
Chris

 

[David Mullen ASC]

More or less, you're about a half-stop off in some cases because you're rounding off to whole f-stops. You can use the magnification factor as a rough guide to the number of stops you have to compensate for to match DOF.

For example, between 2/3" and Super-35, there is about a 2.5X magnification factor because the 2/3" sensor is around 9.5mm wide and the Super-35 sensor is around 24mm wide. If you consider the Full-frame 35mm sensor to be 36mm wide, then that's a 1.5X magnification factor between S35 and FF35.

 

[Chris Kalafarski]

You probably already know this, but I feel like there are at least some people out there who are actually getting confused. When you say "I'm trying to figure out how the DOF of various sensor sizes relates to various f-stops" it sounds like you're saying the sensor size is actually changing the DOF the image the lens is producing has. It's not, a lens's depth of field characteristics at its various aperture sizes is static, regardless of the camera/sensor it's being used with. What's changing is the subject-to-camera distance needed to achieve a certain image with the different sensors, and that change in distance is what alters the DOF in the image.

Again, you probably knew that, and just phrased it that way as a shortcut, but I've had to explain to more than a few people in real life who thought sensor size was actually somehow changing DOF itself.

 

[Miguel "Macgregor" De Olaso]

I have searched for a similar table online and i couldn´t find any.
I wanted to see a comparison, given the same FOV, what would be the shift in DOF depending on different sensor/format/gates sizes. It would be somehow helpful when mixing different formats. Of course they would all have to be calculated regarding one format in particalar, but starting with medium format 6x4.5 and going down sounds good to me.

 

[Chris Davis]

More or less, you're about a half-stop off in some cases because you're rounding off to whole f-stops.

Thanks for your detailed response.

I have searched for a similar table online and i couldn´t find any.
I wanted to see a comparison, given the same FOV...

It's weird that there's not more info on this -- I had to resort to trial and error with a DOF calculator before I started to see a pattern. If you ever come across an actual chart, it would be good to see it.

-Chris

 

[David Mullen ASC]

Have you looked at this page?
http://www.panavision.com/tools.php

 

[Daniel Browning]

I'm trying to figure out how the DOF of various sensor sizes relates to various f-stops.

Here's how to do it:

• Find the sensor size (this is the hard part - many cameras don't put this anywhere in the manual. You can reverse engineer it using the "35mm-equivalent focal length" if they provide one.)
• Crop the sensor size so that the aspect ratio is equivalent to whatever you're comparing it with (e.g. crop 4:3 to 16:9).
• Calculate the crop factor by dividing the widths of the two sensors. For example, if 36x20.3mm = 1.0X, then RED ONE 4K (22.2x12.6mm) = 1.62X.
• Multiply the crop factor by the f-number: f/4 on RED ONE 4K has the DOF of f/6.5 on 36x20.3mm.

Best I could tell from messing with a DOF calculator, every time you double the width of a sensor, you can stop down by two and get the same DOF.

That's correct.

So that, for example, all these would have about the same DOF (at the same distance at, say, 50mm equivalent focal lengths):

1/3" @ f/2
2/3" @ f/4
4/3" @ f/8

The problem here is that "1/3", "2/3", etc. do not refer to the width of the sensor. A typical "2/3" 16:9 is between 9mm and 10mm wide.

 

[Chris Davis]

Late Follow up Clarification

Late Follow up Clarification

...You can use the magnification factor as a rough guide to the number of stops you have to compensate for to match DOF.

For example, between 2/3" and Super-35, there is about a 2.5X magnification factor because the 2/3" sensor is around 9.5mm wide and the Super-35 sensor is around 24mm wide...

So, to get the same DOF at the same FOV, f/1.6 on the Scarlet 2/3" would be about f/4 on the RED ONE?

And f/2.8 on the Scarlet 2/3" would be about f/7 on the RED ONE?

Is this about the same relationship the Panasonic Lumix LX-3 has to a DSLR with a 1.6x crop sensor?

I believe Stu Maschwitz said the DOF would be about the same on a Panasonic Lumix LX-3 as the RED Scarlet 2/3" (both at 16:9, with the same DOF and FOV). Is this about right?

Many thanks,

Chris