Prisms Right AngleEquilateralPentagonalDove

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Right Angle Equilateral Pentagonal Dove

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Interference and DiffractionInterference and 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


sin2

W x


For Destructive For Destructive Interference:Interference:

x = x = /2/2

W sin W sin = =




x = x = /2/2

W sin W sin = 2 = 2

sin4

W x




W sin W sin = m = m

m = m = ±1, ±2, ±3, …±1, ±2, ±3, …



W sinW sin = =

sinsin / W / W

More precisely:More precisely:

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

http://www.microscopyu.com/tutorials/java/imageformation/airyna/index.html

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

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, …


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


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 ())


Intensity is highest when Intensity is highest when matches the angle of matches the angle of specular reflection.specular reflection.

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


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 determine resolution and throughputand throughput

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


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