Overlapping Orders Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, d(sin  + sin  ) = m d(sin  + sin  ) = m For Example: 1 st Order = 400 nm 2 nd Order = 200 nm 3 rd Order = 133 nm Any equivalent m combinations will share  values. Calculate the free spectral range:  f = /(m+1)

Blaze Angle (  ) Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Intensity is highest when  matches the angle of specular reflection. Gratings: often characterized by angular dispersion (D a ) the angular separation corresponding to a wavelength separation 0 th order

Blaze Angle (  ) Blazed gratings direct most of the light towards a higher order band. Optimum Intensity:  = 2  Blaze Wavelength ( b ): b = dsin2  b = dsin2  Ingle and Crouch, Spectrochemical Analysis Efficiency drops to ~50% at 2/3 b and 3/2 b.

Ingle and Crouch, Spectrochemical Analysis Czerny – Turner Monochromator Slits: determine resolution and throughput Monochromators: often characterized by linear dispersion (D l ) – dx/d Monochromators: often characterized by linear dispersion (D l ) – dx/d R d : Reciprocal D l

Can change angle of grating to focus different on the exit slit. Take-off angle (  ) is constant. Change  to direct different towards    =  +   =  -  m = 2 d sin  cos  Ingle and Crouch, Spectrochemical Analysis

Are you getting the concept? In our monochromator, we have a grating with d = nm operating in first order with  fixed at 6.71 °. At what angles (  ) must the grating be positioned in order to select = 300 nm or 500 nm? What incident angle (  ) is achieved for each in order to perform wavelength selection? Sketch the geometry around the diffraction grating to check your answers.

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

Spectral Bandpass and Slit Function Ingle and Crouch, Spectrochemical Analysis Spectral bandpass: s g = R d W

Spectral Resolution (  ) with Large W Ingle and Crouch, Spectrochemical Analysis

Are you getting the concept? Calculate D a, D l, R d and s g for 1 st order diffraction under optimal conditions for the indicated 0.5 m monochromator with 100  m slits.

Spectral Resolution (  ) with Small W Diffraction-Limited Spectral bandpass: s d = R d f s d = R d f W’ d W’ d s d = s d = D a W’ d D a W’ d Rayleigh Criteron infers:  d ~ s d = R d f  d ~ s d = R d f W’ d W’ d

Are you getting the concept? A 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. In theory, what slit width would be required?

Double and Triple Monochromators Use Double or Triple Systems to: 1.increase spectral resolution 2.increase stray light rejection Two modes of operation: 1.additive 2.subtractive

Additive Multi-Stage Monochromators All 3 stages contribute to dispersion Grating G 1 disperses light Slit S 1,2 passes only a narrow portion Grating G 2 further disperses light Slit S 2,3 passes only a narrow portion Grating G 3 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

Subtractive Multi-Stage Monochromators 1 st 2 stages act as a filter Grating G 1 disperses light Slit S 1,2 passes only a narrow portion Grating G 2 recombines dispersed light Slit S 2,3 passes filtered light Grating G 3 disperses light before detection Very high stray light rejection Gratings G 1 and G 2 must match in groove density, and thus, their dispersion actions cancel – very sharp bandpass filter.

Others Ways to Separate Others Ways to Separate Bandpass Filters Notch Filters High-pass Filters Low-pass Filters