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# Overlapping Orders

Overlapping Orders. Any equivalent m l combinations will share b values. For Example: 1 st Order = 400 nm 2 nd Order = 200 nm 3 rd Order = 133 nm. d(sin a + sin b ) = m . Calculate the free spectral range: Dl f = l /(m+1).

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## Overlapping Orders

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1. 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.

2. 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.

3. 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

4. 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

5. 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

6. 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.

7. 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

8. Spectral Bandpass and Slit Function Spectral bandpass: sg = RdW Ingle and Crouch, Spectrochemical Analysis

9. Spectral Resolution (l/Dl) with Large W Ingle and Crouch, Spectrochemical Analysis http://www.jobinyvon.com/usadivisions/osd/product/size_spectrum.pdf

10. Are you getting the concept? Calculate the angular dispersion, linear dispersion, and reciprocal dispersion for third order diffraction of l = 650 nm from a diffraction grating 6 cm wide with 3500 grooves/cm rotated 17° from normal. The take off angle to reach the exit mirror is 6.5 ° and the spectrometer focal length is 150 cm.

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

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