circular aperture rectangular aperture fraunhofer diffraction
TRANSCRIPT
Diffraction from small and large circular apertures Far-field
intensity pattern from a small
aperture
Far-field intensity
pattern from a large aperture
Airy’s Pattern
http://micro.magnet.fsu.edu/primer/java/imageformation/airydiskbasics/index.html
© Molecular Expression
Diffraction limit of optical microscope!
Pinhole camera pictures
Optimal pinhole size Large pinhole size
Too small a pinhole needs a very long exposure time
Two point sources cannot be resolved if their separation is less than the radius of the Airy disk.
Lord Rayleigh’s Criterion
Central disk is surrounded by dark ring, for which
1 ( ) 0J
According to Rayleigh’s criterion
Angular limit of resolution : D
. 221
Limit of resolution : 1.22F
lD
l=centre to centre separation between images
Arbitrary Aperture
dseR
eE
Aperture
RZzYyikkRti
A
/)()(
A=source strength per unit area
P
(X,Y,Z)R
r
x
y
z
For rectangular aperture with width a and height b
22
0
sinsin
II
R
bz
R
bY
and
dzedyeR
eE
a
a
RikZyb
b
RikYykRti
A
2/
2/
/2/
2/
/)(
http://www.kw.igs.net/~jackord/df/d1.html (Alg C) in circular aperture
http://www.kw.igs.net/~jackord/df/d1.html Rectangular and triangular aperture
Circular aperture
Rectangular and triangular aperture
ProblemA 35 mm camera has a lens with a 50 mm focal length. It is used to photograph a boy of 175 cm in height., such that the image is 30 mm high. How far from the camera should the boy stand?Estimate the best resolution obtainable on the film using light of = 5000 Å, if the lens aperture is 1 cm diameter.
ProblemTwo stars have an angular separation of 1x 10-6 radian. They both emit light of wavelengths 5770 and 5790 Å.How large a diameter of the lens in the telescope is needed to separate the images of the two stars?How large a diffraction grating is needed to separate the two wavelengths present?