overlapping orders douglas a. skoog and james j. leary, principles of instrumental analysis,...

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..


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


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


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


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 Criteron Rayleigh Criteron infers:infers: dd ~ s ~ sdd = R = Rddff

W’W’dd

Are you getting the concept?Are you getting the concept?

A grating monochromator with a reciprocal linear dispersion ofA grating monochromator with a reciprocal linear dispersion of1.2 nm/mm is to be used to separate the sodium lines at 589.01.2 nm/mm is to be used to separate the sodium lines at 589.0nm and 589.6 nm. In theory, what slit width would be required?nm and 589.6 nm. In theory, what slit width would be 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


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


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