Circular aperture Rectangular aperture Fraunhofer Diffraction.

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Circular aperture Rectangular aperture Fraunhofer Diffraction

Transcript of Circular aperture Rectangular aperture Fraunhofer Diffraction.

Circular aperture

Rectangular aperture

Fraunhofer Diffraction

Fraunhofer Diffraction pattern which you have observed in your lab for circular aperture

Circular aperture

qRa

Bessel function of order m

2( v cos v)

0

( ) v2

mi m u

m

iJ u e d

I = I0 [2 J1(γ) / γ]

[ J1(γ) / γ]

γ = kaq/R=k a Sin

3.83

Airy disk : high irradiance circular spot

2 1.22R

qa

Diffraction from small and large circular apertures Far-field

intensity pattern from a small

aperture

Far-field intensity

pattern from a large aperture

1 1.22F

qD

With a lens of focal length F and aperture diameter D

Airy’s Pattern

http://micro.magnet.fsu.edu/primer/java/imageformation/airydiskbasics/index.html

© Molecular Expression

Diffraction limit of optical microscope!

Diffraction limit of Camera

q

Resolution of imaging system

Just resolvedNot resolved Well resolved

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

R.P. = 1.22 λ / DD= Diameter of the telescope objectiveTelescope

Single slit – Two point sources

ws

Rayleigh’s criterion and Sparrow’s criterion

Arbitrary Aperture

dseR

eE

Aperture

RZzYyikkRti

A

/)()(

A=source strength per unit area

P

(X,Y,Z)R

r

x

y

z

Rectangular aperture

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

Circular aperture

Rectangular aperture

Triangular aperture

Pinholes

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?

ProblemA camera lens of 60 mm focal length is accurately focused for objects at 15 m. For what aperture will diffraction blur of visible light be roughly the same as the defocus blur for a star (at )