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/formulasresolution.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/imageformation/gratingdiffraction/index.html

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 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. 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 = 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.

20. 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.

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

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