C[omp]ute

From: "andrew cooke" <andrew@...>

Date: Sun, 23 Dec 2007 16:58:36 -0300 (CLST)

From
http://www.flickr.com/groups/panasonicdmc-lx1/discuss/72157603526533457/#comment72157603525884094

in
http://www.flickr.com/groups/panasonicdmc-lx1/discuss/72157602866039023/#comment72157602895143765
the depth of field in compact p&s cameras was shown to be much greater
than in a 35mm lens at the same aperture (f number).

why is this?

naively i would expect that if you take a lens and put it in a magic
"shrinking machine" that scales it to (say) half size, then you 
would get much dimmer pictures (smaller absolute aperture - 1/4 area of
lens) that cover a smaller area of the focal plane (1/4 area of sensor),
but that  he f number would stay the same (it does, right?).

furthermore, since everything seems to be "the same but smaller"
i would expect the depth of field to be the same (when you make a photo 
smaller or bigger in photoshop the depth of field in the image doesn't 
change).

yet clearly this isn't the case, and it's the thing i miss most in my
camera.  does anyone have a good intuitive explanation why?

[...]

ok, so it's quite simple really :)

in my argument above (which is a "scaling argument") i imagined
taking a lens (well, an entire optical system) and shrinking it.

what i forgot is that when i shrink the camera i also have to shrink the
world it is inside!

less cryptically, there's an extra distance, in the "real world"
that i had forgotten to take into account - the distance from the camera
to the subject.  this may seem unusual, because typical, simple geometric
optics considers subjects that are at an "infinite" distance -
this simplifies things (shrinking infinity is still infinity) and is often
a reasonable assumption.  but depth of field doesn't work "at
infinity", it only works for relatively close objects, so this is not
a good approximation to make.  this is why, incidentally, the first link
above keeps talking about "intermediate distances".

so, once you realise that the distance from the lens to the subject is
important things become a lot clearer.  the shrinking argument is correct,
but you have to shrink the distance to the subject too.

so, for example, the depth of field for a 50mm lens with a 35mm sensor at
10m is the same (in relative terms) as a 25mm lens with a 17.5mm sensor at
5m (we have simply shrunk everything by a factor of 2, geometry - angles
and relative resolutions - stay unchanged).

almost there...

the problem then, of course, is that when we compare depth of field for
different sized sensors we are implicitly talking about taking pictures of
things <em>at the same distance</em>.  and we all know that as you get
closer to the lens depth of field becomes more important (ie smaller). 
conversely, moving further away makes depth of field effects less
pronounced.

so if we want to compare depth of field for two different sensor sizes
<em>with the subject at the same distance</em> then in the smaller sensor
case it is "as if" the subject was futher away (compared to
where it would be if we simply scaled everything).  and, as a consequence,
depth of field for the smaller sensor is larger (less pronounced).

i don't know if that helps anyone except me, but i find that much more
intuitive than looking at formulae...