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There is a lot of confusion surrounding the effect of sensor size on DoF, some articles say crop bodies have more DoF, others say they have less.
The truth is that sensor size doesn't change the DoF at all.
DoF is a function of magnification and aperture. If the subject is resolved to the same size in the frame (ignoring cropping) and you use the same aperture then it doesn't matter what the focal length or sensor size is, the DoF will be the same. It's as simple as that.... almost.
There are a few scenarios we need to examine to understand what is happening.
Firstly, same shot, same lens, different sensor size.
Let's say our subject is a ruler, a few feet away. Regardless of crop factor 10cm on the ruler will be the same size on the sensor. For this example we'll assume 10cm on the rules is 1mm on the sensor.
If we printed both shots 30cm high then the FF image needs less enlargement than the crop sensor image. This is obvious when we look at the print, the ruler and our 10cm sample will be smaller on the FF print (remember the 10cm sample is 1mm on both sensors). In order to get our 10cm sample the same size on both prints the one from the FF sensor would need to be enlarged by a factor of around 1.6.
Next, same shot, different lenses.
This time the focal length for the FF is 1.6x longer than the crop body. The 10cm sample from the ruler would now be 1.6mm on the FF sensor but the prints would be identical in terms of scale. The real difference here is that we've increased the magnification on the FF shot.
Finally, same lens, different shooting distance.
This is actually the same as the last example but instead of changing lens we've moved the FF sensor 1.6x closer to the subject. The 10cm sample is still 1.6mm on the FF sensor and the prints are again identical.
Circles of Confusion
The CoC is the size of a point on a print that, when viewed under normal conditions appears to be in sharp focus. The CoC changes depending on the size of the sensor. The smaller the sensor the greater the enlargement of the image for a given print size. A 10 print is 254mm, a FF sensor is 36mm and a crop sensor might be 22.5mm.
254mm / 36mm = 7.05
254mm / 22.5mm = 11.28
Clearly a crop sensor needs more enlargement than a FF sensor for a given print size. Going back to the first example. The 10cm sample on the print was 1mm on the sensor so it would be 7.05mm on the FF print and 11.28mm on the crop sensor print. If we printed the FF image 1.6x larger then then 10cm sample would also be 11.28mm on the print (7.05 x 1.6 = 11.28).
How does this affect DoF?
How sharp or blurred detail on a print will be is defined by the CoC, the more you enlarge the more blurred the CoC will become. If we print so the 10cm sample is the same physical size then the DoF will also be the same, as we saw earlier to get the 10cm sample printed the same size as the crop we needed to enlarge it another 1.6x in effect making the CoC the same size. In reality the DoF (optically) hasn't changed but the size of the printed details changes our perception of what is or isn't in focus.
Back in the real world...
In reality we print to a particular size no matter what the sensor size might be. This means that a 10x8 print a from crop sensor will have its CoC enlarged more than a print from a FF sensor which will give less apparent DoF than a shot from a FF camera.
When you start trying to match the framing (subject size on the sensor or print) between crop and FF then the DoF will be same. If you crop the FF image to match you also reduce the CoC size. If you increase magnification on the FF (either by moving closer or using a longer lens) then you decrease the DoF but that will be offset by the CoC size when printing. The FF image no longer needs cropping so for a given print size the FF CoC will be enlarged 1.6x less than the print from the crop sensor.
Hopefully I haven't made this too confusing, if it helps you can just summarise it as:
The truth is that sensor size doesn't change the DoF at all.
DoF is a function of magnification and aperture. If the subject is resolved to the same size in the frame (ignoring cropping) and you use the same aperture then it doesn't matter what the focal length or sensor size is, the DoF will be the same. It's as simple as that.... almost.
There are a few scenarios we need to examine to understand what is happening.
Firstly, same shot, same lens, different sensor size.
Let's say our subject is a ruler, a few feet away. Regardless of crop factor 10cm on the ruler will be the same size on the sensor. For this example we'll assume 10cm on the rules is 1mm on the sensor.
If we printed both shots 30cm high then the FF image needs less enlargement than the crop sensor image. This is obvious when we look at the print, the ruler and our 10cm sample will be smaller on the FF print (remember the 10cm sample is 1mm on both sensors). In order to get our 10cm sample the same size on both prints the one from the FF sensor would need to be enlarged by a factor of around 1.6.
Next, same shot, different lenses.
This time the focal length for the FF is 1.6x longer than the crop body. The 10cm sample from the ruler would now be 1.6mm on the FF sensor but the prints would be identical in terms of scale. The real difference here is that we've increased the magnification on the FF shot.
Finally, same lens, different shooting distance.
This is actually the same as the last example but instead of changing lens we've moved the FF sensor 1.6x closer to the subject. The 10cm sample is still 1.6mm on the FF sensor and the prints are again identical.
Circles of Confusion
The CoC is the size of a point on a print that, when viewed under normal conditions appears to be in sharp focus. The CoC changes depending on the size of the sensor. The smaller the sensor the greater the enlargement of the image for a given print size. A 10 print is 254mm, a FF sensor is 36mm and a crop sensor might be 22.5mm.
254mm / 36mm = 7.05
254mm / 22.5mm = 11.28
Clearly a crop sensor needs more enlargement than a FF sensor for a given print size. Going back to the first example. The 10cm sample on the print was 1mm on the sensor so it would be 7.05mm on the FF print and 11.28mm on the crop sensor print. If we printed the FF image 1.6x larger then then 10cm sample would also be 11.28mm on the print (7.05 x 1.6 = 11.28).
How does this affect DoF?
How sharp or blurred detail on a print will be is defined by the CoC, the more you enlarge the more blurred the CoC will become. If we print so the 10cm sample is the same physical size then the DoF will also be the same, as we saw earlier to get the 10cm sample printed the same size as the crop we needed to enlarge it another 1.6x in effect making the CoC the same size. In reality the DoF (optically) hasn't changed but the size of the printed details changes our perception of what is or isn't in focus.
Back in the real world...
In reality we print to a particular size no matter what the sensor size might be. This means that a 10x8 print a from crop sensor will have its CoC enlarged more than a print from a FF sensor which will give less apparent DoF than a shot from a FF camera.
When you start trying to match the framing (subject size on the sensor or print) between crop and FF then the DoF will be same. If you crop the FF image to match you also reduce the CoC size. If you increase magnification on the FF (either by moving closer or using a longer lens) then you decrease the DoF but that will be offset by the CoC size when printing. The FF image no longer needs cropping so for a given print size the FF CoC will be enlarged 1.6x less than the print from the crop sensor.
Hopefully I haven't made this too confusing, if it helps you can just summarise it as:
- Subject size the same on the print, DoF is the same regardless of sensor size.
- Print to a particular size (subject bigger on crop) then crop sensors have less (apparent) DoF.