# Smaller sensors = shallower DOF? No way, right?

Started Jun 1, 2018 | Questions thread
Aliased CoC
2

MrBrightSide wrote: Go to 1:57 on the tape where this editor from Petapixel is calling "BS" and says that "technically speaking smaller sensors have a shallower depth of field because they have a higher pixel density."

Hello MrBrightSide,

I did not watch the video but the quote above taken in isolation is misleading, as Alan has noted. With several simplifying assumptions (some of which you can find here ) Depth of Field can be derived via simple optical geometry:

Depth of Field on a sensing plane of diagonal ds.

with N the effective f-number, ds the length of the diagonal of the sensor, U the distance to the in-focus subject plane and f focal length (ds, U and f all in the same units) - so technically speaking those are the variables that define DOF on the sensing plane. Note that if two cameras with different formats are set up Equivalently, the DOF captured by each is the same.

As Mark noted, one can think of the pixels in a digital camera as simply sampling the area of the Circle of Confusion [diameter = 2.ds.tand(.01)]. In a sense they set a minimum to the practical CoC beyond which strange things may happen to perceived DOF (sometimes perhaps making it appear shallower, sometimes deeper depending on the amount of aliasing). This was also true in the past with film of different grain, though nobody seemed to worry about its effect on DOF then.*

So practically (as opposed to technically) the digital camera with the smaller pixels has a potential advantage in terms of shallow DOF all other things being equal. In a practical equivalent setup however, this advantage is more than canceled by the camera with the smaller potential f-number.

Jack

* Diffraction also places a lower limit on the CoC. You can read more about that in a great paper by Jeff Conrad titled DOF in Depth.

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