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Digital Camera
Two factors limit the resolution of the camera as a pho
tographic tool: the diﬀraction by the aperture and the pixel size. For diﬀrac
tion, the inherent angular resolution
θ
R
is the ratio of the wavelength
λ
of
the light and the aperture
D
of the camera,
θ
R
= 1
.
22
λ
D
,
where the standard factor of 1
.
22 reﬂects the circular shape of the aperture.
When taking a picture, the object is generally suﬃciently far away from the
photographer for the image to form in the focal plane of the camera where
the CCD chip should thus be placed. The Rayleigh diﬀraction criterion then
states that two image points can be resolved if they are separated by more
than
3.1
Δ
x
=
fθ
R
= 1
.
22
λ F],
which gives
Δ
x
= 1
.
22
μ
m
if we choose the largest possible aperture (or smallest value
F]
= 2) and
assume
λ
= 500 nm for the typical wavelength of daylight
The digital resolution is given by the distance
`
between the center of two
neighboring pixels. For our 5 Mpix camera this distance is roughly
`
=
L
q
N
p
= 15
.
65
μ
m
.
Ideally we should match the optical and the digital resolution so that neither
aspect is overspeciﬁed. Taking the given optical resolution in the expression
for the digital resolution, we obtain
3.2
N
=
±
L
Δ
x
²
2
≈
823 Mpix
.
Now looking for the unknown optimal aperture, we note that we should
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 Spring '11
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