Overlapping Orders Notes | EduRev

Created by: Vikas Sharma

: Overlapping Orders Notes | EduRev

 Page 1


Overlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, 
Saunders College Publishing, Fort Worth, 1992.
d(sin a + sin ß) = m?
For Example:
1
st
Order = 400 nm
2
nd
Order = 200 nm
3
rd
Order = 133 nm
Any equivalent m? combinations will share ß values.
Calculate the free spectral range:
??
f
= ?/(m+1)
Page 2


Overlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, 
Saunders College Publishing, Fort Worth, 1992.
d(sin a + sin ß) = m?
For Example:
1
st
Order = 400 nm
2
nd
Order = 200 nm
3
rd
Order = 133 nm
Any equivalent m? combinations will share ß values.
Calculate the free spectral range:
??
f
= ?/(m+1)
Blaze Angle (?)
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Intensity is highest when ß
matches the angle of 
specular reflection.
Gratings: often characterized 
by angular dispersion (D
a
)
ß ?
ß a
ß ?
ß
cos
sin sin
cos
+
= = =
d
m
d
d
a
D
the angular separation corresponding 
to a wavelength separation
0
th
order
Page 3


Overlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, 
Saunders College Publishing, Fort Worth, 1992.
d(sin a + sin ß) = m?
For Example:
1
st
Order = 400 nm
2
nd
Order = 200 nm
3
rd
Order = 133 nm
Any equivalent m? combinations will share ß values.
Calculate the free spectral range:
??
f
= ?/(m+1)
Blaze Angle (?)
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Intensity is highest when ß
matches the angle of 
specular reflection.
Gratings: often characterized 
by angular dispersion (D
a
)
ß ?
ß a
ß ?
ß
cos
sin sin
cos
+
= = =
d
m
d
d
a
D
the angular separation corresponding 
to a wavelength separation
0
th
order
Blaze Angle (?)
Blazed gratings direct most of the
light towards a higher order band.
Optimum Intensity:
ß = 2?
Blaze Wavelength (?
b
):
?
b
= dsin2?
Ingle and Crouch, Spectrochemical Analysis
Efficiency drops to ~50% at 
2/3 ?
b
and 3/2 ?
b
.
Page 4


Overlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, 
Saunders College Publishing, Fort Worth, 1992.
d(sin a + sin ß) = m?
For Example:
1
st
Order = 400 nm
2
nd
Order = 200 nm
3
rd
Order = 133 nm
Any equivalent m? combinations will share ß values.
Calculate the free spectral range:
??
f
= ?/(m+1)
Blaze Angle (?)
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Intensity is highest when ß
matches the angle of 
specular reflection.
Gratings: often characterized 
by angular dispersion (D
a
)
ß ?
ß a
ß ?
ß
cos
sin sin
cos
+
= = =
d
m
d
d
a
D
the angular separation corresponding 
to a wavelength separation
0
th
order
Blaze Angle (?)
Blazed gratings direct most of the
light towards a higher order band.
Optimum Intensity:
ß = 2?
Blaze Wavelength (?
b
):
?
b
= dsin2?
Ingle and Crouch, Spectrochemical Analysis
Efficiency drops to ~50% at 
2/3 ?
b
and 3/2 ?
b
.
Ingle and Crouch, Spectrochemical Analysis
Czerny – Turner 
Monochromator
Slits: determine resolution and 
throughput
Monochromators: often 
characterized by linear 
dispersion (D
l
) – dx/d?
R
d
: Reciprocal D
l
a l
fD D =
Page 5


Overlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, 
Saunders College Publishing, Fort Worth, 1992.
d(sin a + sin ß) = m?
For Example:
1
st
Order = 400 nm
2
nd
Order = 200 nm
3
rd
Order = 133 nm
Any equivalent m? combinations will share ß values.
Calculate the free spectral range:
??
f
= ?/(m+1)
Blaze Angle (?)
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Intensity is highest when ß
matches the angle of 
specular reflection.
Gratings: often characterized 
by angular dispersion (D
a
)
ß ?
ß a
ß ?
ß
cos
sin sin
cos
+
= = =
d
m
d
d
a
D
the angular separation corresponding 
to a wavelength separation
0
th
order
Blaze Angle (?)
Blazed gratings direct most of the
light towards a higher order band.
Optimum Intensity:
ß = 2?
Blaze Wavelength (?
b
):
?
b
= dsin2?
Ingle and Crouch, Spectrochemical Analysis
Efficiency drops to ~50% at 
2/3 ?
b
and 3/2 ?
b
.
Ingle and Crouch, Spectrochemical Analysis
Czerny – Turner 
Monochromator
Slits: determine resolution and 
throughput
Monochromators: often 
characterized by linear 
dispersion (D
l
) – dx/d?
R
d
: Reciprocal D
l
a l
fD D =
Can change angle of grating to
focus different ? on the exit slit.
Take-off angle (F) is constant.
Change ? to direct different ?
towards F ?
?= a + F
F = ß - ?
m ? = 2 d sin? cosF
Ingle and Crouch, Spectrochemical Analysis
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