Interference and Diffraction

1
Interference and Diffraction
http//en.wikipedia.org/wiki/Diffraction
2
Huygens-Fresnel Principle
What if we block some of the wavelets?
Adapted from Eugene Hecht, Optics,
Addison-Wesley, Reading, MA, 1998.
3
Diffraction
If l is large compared to the aperture, the
waves will spread out at large angles into the
region beyond the obstruction.
Diffraction increases as aperture size ? ?
Eugene Hecht, Optics, Addison-Wesley, Reading,
MA, 1998.
4
Diffraction Pattern From a Single Slit
Ingle and Crouch, Spectrochemical Analysis
5
Diffraction Pattern From a Single Slit
For Destructive Interference
x ?/2
W sin ? ?
Ingle and Crouch, Spectrochemical Analysis
6
Diffraction Pattern From a Single Slit
For Destructive Interference
x ?/2
W sin ? 2 ?
Ingle and Crouch, Spectrochemical Analysis
7
Diffraction Pattern From a Single Slit
For Destructive Interference
W sin ? m ?
m 1, 2, 3,
Ingle and Crouch, Spectrochemical Analysis
8
Diffraction Limited Beam Width
W sinq l
? ? ? / W
More accurately
Ingle and Crouch, Spectrochemical Analysis
sin? 1.22 ? / W
Eugene Hecht, Optics, Addison-Wesley, Reading,
MA, 1998.
9
Diffraction-Limited Resolution
Airy pattern radius from central peak to 1st
minimum
Diffraction-limited resolution
http//www.microscopyu.com/articles/formulas/formu
lasresolution.html
10
Diffraction Gratings
Plane or convex plate ruled with closely spaced
grooves (300-2400 grooves/mm).
Eugene Hecht, Optics, 1998.
http//www.olympusmicro.com/primer/java/imageforma
tion/gratingdiffraction/index.html
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Grating Equation
Two parallel monochromatic rays strike adjacent
grooves and are diffracted at the same angle (b).
Difference in optical pathlength is AC AD.
For constructive interference
m? (AC AD)
m 0, ?1, ?2, ?3,
Ingle and Crouch, Spectrochemical Analysis
12
Grating Equation
m? (AC AD)
AC d sin a
AD d sin b
Combine to give Grating Equation
d(sin a sin b) m?
Grating Equation only applies if d gt l/2
Ingle and Crouch, Spectrochemical Analysis
13
Are you getting the concept?
At what angle would you collect the 1st order
diffracted light with l 500 nm if a broad
spectrum beam is incident on a 600 groove/mm
grating at qi 10? For l 225 nm? For l
750 nm?
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Overlapping Orders
Any equivalent ml combinations will share b
values.
For Example 1st Order 400 nm 2nd Order 200
nm 3rd Order 133 nm
d(sin a sin b) m?
Calculate the free spectral range Dlf l/(m1)
Douglas A. Skoog and James J. Leary, Principles
of Instrumental Analysis, Saunders College
Publishing, Fort Worth, 1992.
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Blaze Angle (g)
Intensity is highest when b matches the angle of
specular reflection.
Gratings often characterized by angular
dispersion (Da)
0th order
the angular separation corresponding to a
wavelength separation
Eugene Hecht, Optics, Addison-Wesley, Reading,
MA, 1998.
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Blaze Angle (?)
Blazed gratings direct most of the light towards
a higher order band.
Optimum Intensity b 2?
Blaze Wavelength (?b) ?b dsin2?
Efficiency drops to 50 at 2/3 ?b and 3/2 ?b.
Ingle and Crouch, Spectrochemical Analysis
17
Czerny Turner Monochromator
Slits determine resolution and
throughput Monochromators often characterized
by linear dispersion (Dl) dx/dl Rd
Reciprocal Dl
Ingle and Crouch, Spectrochemical Analysis
18
Can change angle of grating to focus different ?
on the exit slit.
Take-off angle (?) is constant.
Change q to direct different ? towards F
? a ?
? b - ?
m ? 2 d sin??cos?
Ingle and Crouch, Spectrochemical Analysis
19
Are you getting the concept?
In our monochromator, we have a grating with d
833.33 nm operating in first order with f fixed
at 6.71. At what angles (q) must the grating be
positioned in order to select l 300 nm or 500
nm? What incident angle (a) is achieved for each
l in order to perform wavelength selection?
Sketch the geometry around the diffraction
grating to check your answers.
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Monochromator Characteristics
Czerny Turner Monochromaor
1. Dispersion, Resolution, and Bandpass 2.
Accuracy, Speed 3. Throughput, Imaging Quality 4.
Stray Light
http//www.jobinyvon.com/usadivisions/osd/product/
size_spectrum.pdf
21
Spectral Bandpass and Slit Function
Spectral bandpass sg RdW
Ingle and Crouch, Spectrochemical Analysis
22
Spectral Resolution (l/Dl) with Large W
Q When can I baseline resolve 2 l? A When they
are separated by 2Sg.
Ingle and Crouch, Spectrochemical Analysis
http//www.jobinyvon.com/usadivisions/osd/product/
size_spectrum.pdf
23
Are you getting the concept?
Calculate Da, Dl, Rd and sg for 1st order
diffraction under optimal conditions for the
indicated 0.5 m monochromator with 100 mm slits.
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Spectral Resolution (l/Dl) with Small W
Diffraction-Limited Spectral bandpass sd
Rdlf Wd sd l
DaWd
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Are you getting the concept?
A 1 m scanning grating monochromator with a
reciprocal linear dispersion of 1.2 nm/mm is to
be used to separate the sodium lines at 589.0 nm
and 589.6 nm. Assuming that the slit is
large compared to the wavelengths of interest,
what slit width would be required?
http//en.wikipedia.org/wiki/Diffraction_grating
26
Double and Triple Monochromators

• Use Double or Triple Systems to
• increase spectral resolution
• increase stray light rejection

• Two modes of operation
• additive
• subtractive

http//architect.wwwcomm.com/Uploads/Princeton/Doc
uments/AS_Modes.pdf
27
Additive Multi-Stage Monochromators
All 3 stages contribute to dispersion Grating G1
disperses light Slit S1,2 passes only a narrow
portion Grating G2 further disperses light Slit
S2,3 passes only a narrow portion Grating G3
disperses light before detection
Total dispersion additive dispersion of each
stage Slits open relatively wide in
spectrographs to permit enough light through to
use the entire detector. ?significant stray light
http//architect.wwwcomm.com/Uploads/Princeton/Doc
uments/AS_Modes.pdf
28
Subtractive Multi-Stage Monochromators
1st 2 stages act as a filter Grating G1 disperses
light Slit S1,2 passes only a narrow
portion Grating G2 recombines dispersed
light Slit S2,3 passes filtered light Grating G3
disperses light before detection
Very high stray light rejection Gratings G1 and
G2 must match in groove density, and thus, their
dispersion actions cancel very sharp bandpass
filter.
http//architect.wwwcomm.com/Uploads/Princeton/Doc
uments/AS_Modes.pdf
29
Others Ways to Separate l
Bandpass Filters
High-pass Filters
Notch Filters
Low-pass Filters
www.mellesgriot.com