Interference and Diffraction .

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Interference and Interference and Diffraction Diffraction http://en.wikipedia.org/wiki/Diffraction
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Transcript of Interference and Diffraction .

Interference and DiffractionInterference and Diffraction

http://en.wikipedia.org/wiki/Diffraction

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.

Others Ways to Separate Others Ways to Separate

Bandpass FiltersBandpass Filters

www.mellesgriot.comwww.mellesgriot.com

Notch FiltersNotch Filters

High-pass FiltersHigh-pass Filters

Low-pass FiltersLow-pass Filters