Array theorem and convolutions
Derive array theorem from convolution theorem
( ', ') 2 x xF g h x y g h
individualaperture1
x n y nN
ik x y
array x y x yn
E z e E z
, , * , ,
Review: Sketch the diffraction pattern of this rectangular slit
A) I got it mostly rightB) I got it mostly wrong but I tried
The E-field at the screen due to one slit is (centered at the origin)
A) I got it mostly rightB) I got it mostly wrong but I tried
sinc2 2o x y
ka kbE
Find and sketch the E-field at the screen due to due slits centered at y = ±h/2.
Diffraction of the light from a distant flashlight viewed through a black umbrella fabric.
2-slit Fraun. diffraction pattern
How many minor peaks are between the major peaks?
N-slits diffraction features
http://optics.byu.edu/animation/fraunhof.mov
N-slits, grooves,mirror-strips diffraction grating
2 2
1 2 2
2
2
x x
x n
x x
kh khi N i N
xNi x
kh khi in
x
khN
e ee
khe e
'
sin
sin
2
2peak
2 2
sinsinc
sin
hN
aI I
hN
major peaks occur when:
minor peaks occur when:
N-slits, grooves,mirror-strips diffraction grating
2
2peak
2 2
sinsinc
sin
hN
aI I
hN
u m
Nu
u
sinlim
sinRatio of major to minor peak in I:a) N b) N2 b) N1/2
Width of major peak decreases as what power of N?a) 1/N b) 1/N2 b) 1/N1/2
Diffraction grating orders
Diffraction grating orders
Reflective gratings are “blazed”
Reflective gratings most common: lines cut in glass, replicated onto plastic blanks, coated with metal (aluminum)
Typical grating for visible to UV light: 1000-2000 grooves/mm, 10 cm wide105
lines.
Modern methods
Blazed gratings put more light into a nonzero order
Resolving power of a grating
2
2peak
2 2
sinsinc
sin
hN
aI I
hN
peakRP mN
How much must l change so peak moves by half its width?
Spectrometer
Put slits at f from mirrors. Grating in center