My Superficial View on Depth of Field (DOF)

Firstly, I assume that everyone here knows what is DOF (Depth of Field);
Secondly, I assume that everyone here also knows what is the image sensor (e.g. CCD or CMOS)
Lastly, I expect that everyone here knows I am also a newbie, so, please correct me if I've written wrongly in this article :P

Ok, let's start~

Normally, we'll try to make our subject 'stand-out' from the background when shooting portrait. This is why we always try to blur-out (defocus) those unwanted area and only make the subject clear in focus. To achieve this, we have to get a shallow DOF to be able to selectively 'choose' the subject we desired to be in focused.

The formula to calculate DOF:

h: hyperfocal distance
f: focal_length
s: subject distance
a: aperture
c: circle of confusion
d1: near edge
d2: far edge
DOF: depth of field

h = (f * f)/(a * c)
d1 = (h * s) / (h + (s - f))
d2 = (h * s) / (h - (s - f))
DOF = d2 - d1

According to the formula above, there are mainly 4 factors that affect DOF - Aperture, Subject's Distance, Focal length and the Circle Of Confusion (CoC).

To get shallow DOF, we need:

1. Bigger aperture (smaller F value)
2. Longer focal length
3. Closer to the subject and further away from the background
4. Smaller image sensor!?

I think most people will agree with the first 3 points. The last point, smaller image sensor!? It sounds ridiculous, right? Especially videographer who always blame that they are unable to get shallow DOF with their super small CCD. So, what is wrong with the formula? Is it true that small CCD can really get a shallower DOF than bigger ones? The answer is "YES", and let's see why:

Assuming that:
the height of man = 1.68 meter
the distance between man and camera = 3 meter
aperture = F/1.8
focal length = 50mm

(er!? 50mm F/1.8!? hehe... photographer should know what I mean :P)

We have two different image sensors here :

1. APS (commonly found in Nikon Digital SLR) and
2. 1/3" (commonly used in prosumer camcorder and consumer digital camera)

Let's see what results are:

DOF of APS size sensor = 0.259m, FOV=1.48m(W) x 0.985m(H) (can see top body of the man, from waist and up)
DOF of 1/3" sensor = 0.041m, FOV=0.260m(W) x 0.195m(H) (can see only the head)

Wow!!! You can see that the 1/3" image sensor can get a shallower DOF than APS size!? But, don't be too happy just yet with that result. Let's take a look carefully - we also notice that the Field Of View(FOV) of 1/3" sensor is much smaller than APS size! That means we have to decrease our focal length (widerangle) or increase the subject's distance (further away) to get the same image size with the APS size sensor than 1/3 sensor. In the end, the result will be:

DOF of 1/3" sensor = 1.04m, FOV=1.31m(W) x 0.986m(H)

See? The DOF of 1/3" sensor is deeper than APS size at the same FOV. This is the reason why the bigger sensor, the shallower the DOF.

FOV of APS size sensor	FOV of 1/3" sensor