Gratings work on the principles of diffraction
& interference
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Principles and Characteristics of Gratings and Interferometers in Optics, Slides of Analytical Chemistry
An in-depth exploration of the principles, equations, and characteristics of gratings and interferometers in optics. Topics include the grating equation, reflection gratings with non-normal incidence, preparation of reflection gratings, grating efficiency, mountings for gratings, grating characteristics, and the comparison between gratings and interferometers. The document also covers the use of interferometers in ftir and the advantages and disadvantages of both gratings and interferometers.
Typology: Slides
2012/2013
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Gratings work on the principles of diffraction & interference
Grating Equation
m (^) λ (^) = d sin
(^) β
AC = extra distance light travels for first order = d sin Condition for constructive interference
(^) β
For higher orders the distance gets longer
d
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(another view)Reflection grating with non-normal incidence
Φ (^) is fixed
α (or step) normal,relative to facet (^) & (^) β (^) change
normalrelative to gratingincident radiationdepending on
Preparation of reflection gratings – a master grating grooves/mm oraluminum surface on glass (from 20 – 3000is prepared by ruling grooves in a reflective
(^1) 0,000 lines/inch)
Replicate gratings can be prepared from master grating which brings down the cost
diffracted in a particular orderfraction of monochromatic light
Grating Efficiency = ------------------------------------------
fraction specularly reflected
Efficiency is maximum for situation where diffracted wavelength =ray & specularly reflected ray coincide = blaze
(^) λ B = (^) λ (^) of maximum efficiency
- The echellette grating concentrates most of the intensity in the first few orders
- First order efficiency at
(^) λ B is 60 - 70 % and
typically falls off by about half at 2/
(^) λ B (^) and
λ B
- Choose angle for
(^) λ (^) region of interest
- Echellette is the normal grating for UV, vis, IR
- Echelle grating used for atomic emission
- Uses steeper steps– Concentrates intensity in higher orders
Mountings for Gratings – Czerny-Turner
Exit^ Entrance
mirror mirror
Scan
(^) λ
grating by rotating
Φ (^) is fixed
α normalrelative to & β change
as grating moves
Littrow mounting is the same as for prism except use grating in place of prism
Grating Characteristics – Resolution & ruled gratingDispersion are very high for a long, finely
Resolution (theoretical)
R = m N
Combine with grating equation
(^) (given previously)
R = W (sin
(^) β ) / (^) λ
where W (length of ruled area) = N d
The length of ruled area is important
order
illuminatedrulingsnumber of
Dispersion - almost constant with wavelength for grating (an advantage over prisms)
spectrumacrossbandpassget constantchange slits toDon’t have to
1 Methods of reducing stray light: ) Paint interior black
Use baffles to obstruct stray radiation
Use high quality components
Keep out dust and fumes
Can also use double monochromator
Cary
(^1) 4 &
(^1) 7 UV-vis
rejectionvery high stray lightmonochromator with
1 d LD = laser detectorL = laser beamRL = reference laserMM = moving mirrorFM = fixed mirrorB = beamsplitterD = detectorIR = infrared beamS = IR sourceWhere: moving mirror^ = distance to
2 d fixed mirror^ = distance to
Michaelson Interferometer as commonly used in an FTIR
1 d
2 d
Interferometers have no slits so a wide beam of radiation can be used
d Assuming monochromatic radiation (^1) = d
(^2)
- n
λ
constructive interferencefor maximum
d (^1) = d
(^2)
- n
λ (^) + ½
λ
destructive interferencefor maximum
1 d LD = laser detectorL = laser beamRL = reference laserMM = moving mirrorFM = fixed mirrorB = beamsplitterD = detectorIR = infrared beamS = IR sourceWhere: moving mirror^ = distance to
2 d fixed mirror^ = distance to
Michaelson Interferometer as commonly used in an FTIR
1 d
2 d d (^1) = d
(^2)
- n
λ
d (^1) = d
(^2)
- n
λ (^) + ½
λ
Interferogram is a plot of energy vs mirror displacement from zero (i.e. d
(^1) = d
(^2) )
radiationpolychromaticThis is for
Mechanical specifications for mirror movement are very exacting
(^) gets worse
as (^) λ (^) gets shorter, therefore interferometers
feasible in the visible and UV regionsare used in the IR region but are not very
Extracting a conventional spectrum (i.e. I vs
(^) λ )
known as Fourier Transformmathematics of the Fourier integral alsofrom interferogram involves the complex
(^) need
computer to do calculations
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