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Huygens-Fresnel PrincipleHuygens-Fresnel Principle
Adapted from: Eugene Hecht, Adapted from: Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.
What if we block some of What if we block some of the wavelets?the wavelets?
Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.
Diffraction increases as aperture Diffraction increases as aperture size size
If If is large compared to the aperture, is large compared to the aperture, the waves will spread out at largethe waves will spread out at largeangles into the region beyond theangles into the region beyond theobstruction.obstruction.
DiffractionDiffraction
Diffraction Pattern From a Single SlitDiffraction Pattern From a Single Slit
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Diffraction Pattern From a Single SlitDiffraction Pattern From a Single Slit
sin2
W x
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
For Destructive For Destructive Interference:Interference:
x = x = /2/2
W sin W sin = =
Diffraction Pattern From a Single SlitDiffraction Pattern From a Single Slit
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
For Destructive For Destructive Interference:Interference:
x = x = /2/2
W sin W sin = 2 = 2
sin4
W x
Diffraction Pattern From a Single SlitDiffraction Pattern From a Single Slit
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
For Destructive For Destructive Interference:Interference:
W sin W sin = m = m
m = m = ±1, ±2, ±3, …±1, ±2, ±3, …
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.
W sinW sin = =
/ W/ W
More accurately:More accurately:
sinsin = 1.22 = 1.22 / W / W
Diffraction Limited Beam WidthDiffraction Limited Beam Width
1.22
2( )Airyr NA
0.61resolution
NA
Airy pattern radius from centralAiry pattern radius from centralpeak to 1peak to 1stst minimum: minimum:
Diffraction-limited resolution:Diffraction-limited resolution:
http://www.microscopyu.com/articles/formulas/formulasresolution.html
Diffraction-Limited ResolutionDiffraction-Limited Resolution
Eugene Hecht, Eugene Hecht, OpticsOptics, 1998., 1998.
Diffraction GratingsDiffraction Gratings
Plane or convex plate ruled with Plane or convex plate ruled with closely spaced grooves (300-closely spaced grooves (300-2400 grooves/mm).2400 grooves/mm).
http://www.olympusmicro.com/primer/java/imageformation/gratingdiffraction/index.html
Two parallel monochromatic Two parallel monochromatic rays strike adjacent grooves rays strike adjacent grooves and are diffracted at the and are diffracted at the same angle (same angle ().).
Difference in optical Difference in optical pathlength is AC + AD.pathlength is AC + AD.
For constructive For constructive interference:interference:
mm = (AC + AD) = (AC + AD)
m = 0, m = 0, 1, 1, 2, 2, 3, …3, …
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Grating EquationGrating Equation
mm = (AC + AD) = (AC + AD)
AC = d sin AC = d sin
AD = d sin AD = d sin
Combine to give Grating Equation:Combine to give Grating Equation:
d(sin d(sin + sin + sin ) = ) = mm
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Grating EquationGrating Equation
Grating Equation only applies if:Grating Equation only applies if:d > d > /2/2
Are you getting the concept?Are you getting the concept?
At what angle would you collect the 1At what angle would you collect the 1stst order diffracted light with order diffracted light with = 500 nm if a broad spectrum beam is incident on a 600= 500 nm if a broad spectrum beam is incident on a 600groove/mm grating at groove/mm grating at ii = 10 = 10°°? For ? For = 225 nm? For = 225 nm? For = 750 nm? = 750 nm?
Overlapping OrdersOverlapping Orders
Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Saunders College Publishing, Fort Worth, 1992.
d(sin d(sin + sin + sin) = ) = mmFor Example:For Example:11stst Order = 400 nm Order = 400 nm22ndnd Order = 200 nm Order = 200 nm33rdrd Order = 133 nm Order = 133 nm
Any equivalent mAny equivalent m combinations will share combinations will share values. values.
Calculate the free spectral range:Calculate the free spectral range:ff = = /(m+1)/(m+1)
Blaze Angle (Blaze Angle ())
Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.
Intensity is highest when Intensity is highest when matches the angle of matches the angle of specular reflection.specular reflection.
Gratings:Gratings: often characterized often characterized by angular dispersion (Dby angular dispersion (Daa))
cos
sinsin
cos
d
m
d
daD
the angular separation corresponding the angular separation corresponding to a wavelength separationto a wavelength separation
0th order
Blaze Angle (Blaze Angle ())
Blazed gratings direct most of the Blazed gratings direct most of the light towards a higher order band.light towards a higher order band.
Optimum Intensity:Optimum Intensity: = 2= 2
Blaze Wavelength (Blaze Wavelength (bb):):
bb = dsin2 = dsin2
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Efficiency drops to ~50% at Efficiency drops to ~50% at 2/3 2/3 bb and 3/2 and 3/2 bb..
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Czerny – Turner Czerny – Turner MonochromatorMonochromator
Slits:Slits: determine resolution and determine resolution and throughputthroughput
Monochromators:Monochromators: often often characterized by linear characterized by linear dispersion (Ddispersion (Dll) – dx/d) – dx/d
RRdd: Reciprocal D: Reciprocal Dll
al fDD
Can change angle of grating to Can change angle of grating to focus different focus different on the exit slit. on the exit slit.
Take-off angle (Take-off angle () is constant.) is constant.
Change Change to direct different to direct different towards towards
= = + +
= = - -
m m = 2 d sin = 2 d sincoscos
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Are you getting the concept?Are you getting the concept?In our monochromator, we have a grating with d = 833.33 nm In our monochromator, we have a grating with d = 833.33 nm operating in first order with operating in first order with fixed at 6.71 fixed at 6.71°°. At what angles (. At what angles ())must the grating be positioned in order to select must the grating be positioned in order to select = 300 nm or = 300 nm or500 nm? What incident angle (500 nm? What incident angle () is achieved for each ) is achieved for each in order in orderto perform wavelength selection? Sketch the geometry aroundto perform wavelength selection? Sketch the geometry aroundthe diffraction grating to check your answers.the diffraction grating to check your answers.
http://www.jobinyvon.com/usadivisions/osd/product/size_spectrum.pdfhttp://www.jobinyvon.com/usadivisions/osd/product/size_spectrum.pdf
Czerny – Turner Czerny – Turner MonochromaorMonochromaor
1. Dispersion, Resolution, and Bandpass1. Dispersion, Resolution, and Bandpass2. Accuracy, Speed2. Accuracy, Speed3. Throughput, Imaging Quality3. Throughput, Imaging Quality4. Stray Light4. Stray Light
Monochromator CharacteristicsMonochromator Characteristics
Spectral Bandpass and Slit FunctionSpectral Bandpass and Slit Function
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Spectral bandpass:Spectral bandpass: ssgg = R = RddWW
Spectral Resolution (Spectral Resolution () with Large W) with Large W
http://www.jobinyvon.com/usadivisions/osd/product/size_spectrum.pdfhttp://www.jobinyvon.com/usadivisions/osd/product/size_spectrum.pdf
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Q: When can I baseline resolve 2 ?A: When they are separated by 2Sg.
Are you getting the concept?Are you getting the concept?Calculate Da, Dl, Rd and sg for 1st order diffraction under optimalconditions for the indicated 0.5 m monochromator with 100 m slits.
Spectral Resolution (Spectral Resolution () with Small W) with Small W
Diffraction-Limited Diffraction-Limited Spectral bandpass:Spectral bandpass: ssdd = R = Rddff
W’W’dd
ssdd = = DDaaW’W’dd
Rayleigh Criterion Rayleigh Criterion infers:infers: dd ~ s ~ sdd = R = Rddff
W’W’dd
Are you getting the concept?Are you getting the concept?
A 1 m scanning grating monochromator with a reciprocal linearA 1 m scanning grating monochromator with a reciprocal lineardispersion of 1.2 nm/mm is to be used to separate the sodium linesdispersion of 1.2 nm/mm is to be used to separate the sodium linesat 589.0 nm and 589.6 nm. Assuming that the slit is largeat 589.0 nm and 589.6 nm. Assuming that the slit is largecompared to the wavelengths of interest, what slit width would becompared to the wavelengths of interest, what slit width would berequired?required?
http://en.wikipedia.org/wiki/Diffraction_grating
Double and Triple MonochromatorsDouble and Triple Monochromators
http://architect.wwwcomm.com/Uploads/Princeton/Documents/A&S_Modes.pdf
Use Double or Triple Systems to:1. increase spectral resolution2. increase stray light rejection
Two modes of operation:1. additive2. subtractive
Additive Multi-Stage MonochromatorsAdditive Multi-Stage Monochromators
http://architect.wwwcomm.com/Uploads/Princeton/Documents/A&S_Modes.pdf
All 3 stages contribute to dispersionGrating G1 disperses lightSlit S1,2 passes only a narrow portionGrating G2 further disperses lightSlit S2,3 passes only a narrow portionGrating G3 disperses light before detection
Total dispersion = additive dispersion ofeach stage
Slits open relatively wide in spectrographsto permit enough light through to use theentire detector.→significant stray light
Subtractive Multi-Stage MonochromatorsSubtractive Multi-Stage Monochromators
http://architect.wwwcomm.com/Uploads/Princeton/Documents/A&S_Modes.pdf
1st 2 stages act as a filterGrating G1 disperses lightSlit S1,2 passes only a narrow portionGrating G2 recombines dispersed lightSlit S2,3 passes filtered lightGrating G3 disperses light before detection
Very high stray light rejection
Gratings G1 and G2 must match in groovedensity, and thus, their dispersion actionscancel – very sharp bandpass filter.