1. Interference and 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:

10. Diffraction Gratings
Plane or convex plate ruled with closely spaced grooves ( grooves/mm).
Eugene Hecht, Optics, 1998.

11. 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 only applies if:
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 > 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?

14. Calculate the free spectral range:
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/(m+1)
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.

15. 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.

16. 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 = 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.

20. Czerny – Turner Monochromaor
Monochromator Characteristics
Czerny – Turner Monochromaor
1. Dispersion, Resolution, and Bandpass
2. Accuracy, Speed
3. Throughput, Imaging Quality
4. Stray Light

21. Spectral Bandpass and Slit Function
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

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.

24. Spectral Resolution (l/Dl) with Small W
Diffraction-Limited Spectral bandpass:
sd = Rdlf
W’d
sd = l
DaW’d
Rayleigh Criterion infers:
Dld ~ sd = Rdlf
W’d

25. 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 nm and nm. Assuming that the slit is large
compared to the wavelengths of interest, what slit width would be
required?

26. Double and Triple Monochromators
Use Double or Triple Systems to:
increase spectral resolution
increase stray light rejection
Two modes of operation:
additive
subtractive

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

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.

29. Others Ways to Separate l
Bandpass Filters
High-pass Filters
Notch Filters
Low-pass Filters