Download CHAPTER 3 Optical Components of Spectrometers

CHAPTER 3
Optical Components of
Spectrometers
BASIC OPTICAL RELATIONSHIPS
The basic laws in optics include:
• The conservation law,
• The laws of reflection and refraction,
• The absorption law
The Conservation Law
Basic principle of wave motion (conservation law ):
• When a wave strikes a boundary between two media,
a portion of the wave is reflected, a portion is
absorbed, and a portion is transmitted into the new
medium.
• Spectral absorptance,  ()
The fraction of the incident radiant energy lost by
absorption at the interface or surface
• Spectral reflectance, (),
The fraction reflected at the interface or surface
• Spectral transmittance, T()
The fraction transmitted into the entered medium
• The quantitative statement of the conservation law is
 () + () + T() = 1
Laws of reflection and refraction
• Velocity of all electromagnetic waves in free space, c,
depends upon the electric permittivity,and
permeability, , of free space
• Thus, c= 3 x 108 m s-1.
• absolute index of refraction, 
The ratio of the speed of an electromagnetic wave in
vacuum to that in matter
Refers to space
dielectric constant
relative permeability
• Dispersion: variation of refractive index of a medium
with the wavelength of the incident radiation,
• Media that are colorless and transparent have
characteristic frequencies of oscillation (the natural
frequencies of the atomic and molecular oscillators)
in the ultraviolet region
• Glasses, for example, may have char­acteristic
oscillations at wavelengths near 100 nm.
• For these materials, the refractive index increases as
the radiation frequency approaches a natural
oscillation frequency. This behavior is called Normal
dispersion
• For glass and visible wavelengths  is typically
about 1.5
• In a medium of refractive index > 1, a wave of
frequency  undergoes a reduction in wavelength
compared to that in vacuum.
• The wavelength in the medium is
 = v/ = c/  .
• When a wave goes from a medium of refractive index
1 into a medium of refractive index 2 , the ratio of
the wavelengths in the two media is given by
 2/  1 =  1/  2
• The wavelength is thus smaller in the medium of
higher refractive index.
Snell’s law of refraction:
• A ray bends toward the normal (2 <  1) when it
enters a medium of higher refractive index (2 >1)
and away from the normal when it enters a medium
of lower refractive index.
Reflection loss at interfaces
• There are many cases in spectrochemical
instruments where radiant energy must be
transmitted across one or more interfaces
separating dielectric media of different refractive
indices.
• For example, there are two air-glass interfaces to
traverse when EMR is transmitted through a lens.
• In a spectrophotometer cuvette filled with solution
there are two air-glass interfaces and two
glass-solution interfaces to traverse.
• any radiation that is reflected at the interface will
cause a loss in the radiant power transmitted into
the new medium.
Fresnel equation
When the incident beam is monochromatic and
normal to the interface, the reflectance () is
given by Fresnel equation
• The larger the difference in refractive indices,
the larger the reflectance.
• When 1 = 2, there is no reflection.
• For an air-glass interface, where  air = 1 and 
glass = 1.5, approximately 4% of the light
incident perpendicular to the interface is
reflected and 96% is transmitted unless an
antireflection coating is applied
•
Fresnel complete equation
• If a beam strikes the interface at an angle other than
90°, the reflectance varies with the angle of incidence
according to the above eq.
• Reflectance vs. angle of
incidence for a monochromatic
beam traveling from air into glass
• Note that the reflectance changes
only slightly up to an angle of 60°
and then increases rapidly until it is
100% at grazing incidence (90°).
Total internal Reflection
•
•
Consider the transmission and reflection of radiation where the source
is in a medium of refractive index 1 that is larger than the refractive
index 2 of the transmission medium.
Fresnel’s complete equation tells us that the transmitted radiant flux is
a maximum when the incident beam is normal to the surface (1 = 0°)
•The incident beam is in a medium of 1
greater than that of the transmission
medium.
• Hence the refracted beams bend away
from the normal (a).
• As the angle of incidence 1 becomes
larger (b), the reflected beam grows
stronger and the refracted beam grows
weaker.
• At angles of incidence equal to (c) or
exceeding (d) the critical and angle  c,
the transmitted beam intensity goes to
zero.
Absorption Law
• In the absorption process atoms or molecules in the
medium are excited, and the energy absorbed can be
dissipated as thermal energy, radiant energy (e.g.,
luminescence), or chemical energy (e.g.,
photochemical reactions).
• The amount of radiation absorbed depends on the
total number of absorbers that interact with the
beam.
• Thus, the amount of radiation absorbed depends on
the thickness of the medium and the
• Concentration of absorbing species
Radiant flux

 - d
db
Thin slice of absorber
Number of absorbers is 
thickness of the slice, db
• Since number of absorbers is  thickness of the slice, db
Absorption coefficient
Due to beam attenuation
With increasing thickness
• To obtain the absorption in a medium of finite thickness, b,
the above eq. is rearranged and integrated from zero thickness
where the incident flux 0 to thikness b where the transmitted flux
is 
• The absorption coefficient, k, magnitude depends on
the  of the incident radiation, the nature of the
absorber, and the concentration of the absorber.
• In atomic spectroscopy, the absorption law is most
often used in the form shown in the above eq. where k
is conc. dependent
• In molecular spectroscopy, it is common to state
explicitly the concentration dependence of the
absorption coefficient by expressing k as k = k'c,
where k' is a new absorption coefficient independent
of concentration.
• Thus equation becomes
•
• Most often in absorption spectroscopy we
measure the transmittance: T = (/0)°
or the absorbance A = -log T. Thus
a : absorptivity of the absorbing species
When con. of absorber is expressed in M, a will be changed
to  which would be called molar absorptivity.
Thus the absorption law is ,
A = bc
• The absorption characteristics must be carefully
considered in spectrochemical applications.
• The absorption coefficient should be small enough
that attenuation by the material is slight.
• In the UV region quartz (natural silica) or synthetic
silica is used.
• Glass is used in the region 320 nm to 2 m, while
halide salts are employed in the infrared and vacuum
UV region.
Assumptions of the absorption law:
• The incident radiation is monochromatic.
• The absorbers (molecules, atoms, ions, etc.) act
independently of each other.
• The incident radiation consists of parallel rays,
perpendicular to the surface of the absorbing
medium.
• The path length traversed is uniform over the cross
section of the beam. (All rays traverse an equal
distance of the absorbing medium.)
• The absorbing medium is homogeneous and does
not scatter the radiation.
• The incident flux is not large enough to cause
saturation effects. (Lasers can cause such effects,
as discussed later)
INTERFERENCE, DIFFRACTION,AND POLARIZATION
OF ELECTROMAGNETIC WAVES
• The phenomena of interference, diffraction, and
polarization all deal with what occurs when two
or more electromagnetic waves overlap at some
point in space.
Superposition of Waves
• Superposition of sinusoidal
waves.
• In (a) the two constituent
waves E1, and E2 are in phase
and add to produce a larger
amplitude resultant.
• In (b) the two waves are 180°
out of phase and add to
produce a smaller-amplitude
resultant.
• Note in both cases that the
combination wave is of the
same frequency as the
constituent waves.
M = 0, 1, 2, and so on
• Constructive interference occurs
when the optical path length
difference is an integral multiple of
the wavelength.
• Destructive interference occurs when
(OPL) = (2m + 1)0/2.
Interference
• optical interference is the interaction of light waves
to yield a resultant irradiance that is different from
the sum of the component values, as predicted by
the principle of superposition of waves.
• Two waves for which the initial phase difference is
zero or constant for a long time are said to be
coherent.
• Waves emitted by separate sources are incoherent
with respect to one another
• Conditions for interference
1. The light reaching the point of interference comes
from a single source by two different paths.
2. The interfering waves have very nearly the same
frequency composition. This again is readily
achieved if the radiation comes from a single
source.
3. Normal unpolarized light also produces interference
Diffraction
• Diffraction is the deviation of light from rectilinear
propagation when it encounters an obstacle. (A
parallel beam is bent as it passes by a sharp barrier or
through a narrow opening)
• Thus, a parallel beam tend to spread slightly on
passage trough a narrow slit
• Waves of EMR always spread to some extent into the
region which is not directly exposed to the incoming
waves
• The distinction between diffraction and interference is
somewhat arbitrary since diffraction can also result in
the superposition of waves.
• Interference is usually considered to be the
superposition of only a few waves, whereas diffraction
is considered to be that of a large number of waves.
• This optical phenomena can be explained by
assuming that radiation waves move through
space in a linear wavefront
• Each point on the wavefront can be regarded
as a new source of waves called wavelets
• Thus secondary wavelets are propagated in
all directions with the velocity of the original
wavefront.
• This principle (Huygens) in conjunction with
the phenomena of interference is used to
explain the features of diffraction
Diffraction by a slit
Fraunhofer diffraction
• The diffraction pattern observed on a plate or
screen by a slit would be alternate light and
dark bands called fringes
• In the fig next slide the relative intensity of
bands of light is represented as peaks
• The central band has a maximum intensity at
Po because the interference between
wavelets from the slit is constructive for the
direction directly ahead ( = 0)
• However, destructive interference between
wavelets causes intensity minima at points
P1, P2, P3, ….
Source is placed
at long distance
So rays are parallel
single slit of width W
• Rays from the
slit that reach
Po all have
identical optical
path lengths.
• Since they are in
phase in the
plane of the slit,
they are still in
phase at Po and
give rise to a
central maximum
of irradiance
Fraunhofer diffraction by a single slit
(a) parallel source rays illuminate the slit where diffraction occurs.
Observation of the light at a large distance, or focused by a lens,
yields a diffraction pattern. The diffraction is minimum at P1
• Consider two rays that reach P1 on the screen
• The ray originating at the top of the slit must
travel a distance x = (W/2) sin  farther than the
ray from the center of the slit.
• According to earlier discussion, a destructive
interference is expected when the pathlength
difference is /2.
• Thus a minimum irradiance occurs when:
• (W/2) sin  = /2 or W sin  = 
•Other minima can be located by dividing the slit into four parts
as shown above.
•Thus, any two adjacent rays will destructively interfere when
(W/4) sin = /2 or W sin  = 2 .
•By extension, the general formula for diffraction minima is
Optimum slit width
• To achieve maximum advantage of a prism or grating for
separating a mixture of radiation into its component
wavelengths, the entire side of the prism or length of the
grating should be illuminated
• There will be an optimum slit width that will just allow the
central (maximum-intensity) band to be focused on the
entire length of prism or grating
• This eq.: W sin  = 
• When W becomes too narrow, the edges of the central
band
will miss the prism or grating and be wasted
• If W is too wide maximum use of prism or grating will
not be made since the dark regions adjacent to the
central ban will also be focused on the dispersion
Distance between
device. The optimum slit width can be calculated
from slit and
Width of grating or prism
To be illuminated
Wopt
2d

b
grating or prism
•
•
•
•
•
•
•
•
When m = 1, sin  = /W.
As W decreases,  increases, and the beam spreads.
If we consider angle  to be small, then    /W.
The angular half-width (width at half maximum
intensity) of the beam in this case is said to be
diffraction limited.
The width cannot be reduced to zero unless W is
infinite or  is zero.
The total beam half-width W' after the beam travels a
distance b is approximately its original width W plus
b times the angular width  /W.
For large enough b, we can neglect the original width
and W'  b  /W.
A plot of the irradiance of a diffraction-limited beam
upon striking a screen is shown in the Figure
• Fraunhofer diffraction at a single slit.
• The angular half-width is   /W.
• The irradiance of the second maximum is
about 4.4% of that of the principal or central
maximum.
Multiple slit diffraction
• As the number of slits increases, each diffraction
maximum grows in irradiance and becomes
narrower.
• The narrowing occurs because with multiple slits
only a slight change in angle away from that
corresponding to a maximum leads to almost total
destructive interference.
• Diffraction gratings can be considered to consist of
many closely spaced slits. Such gratings are
considered in detail later
Multiple-slit diffraction from six slits separated by distance d
• The difference in OPL between adjacent rays is x = d sin , where d
is the distance between slits.
• Maxima in irradiance occur when this distance is an integral multiple of the
wavelength or d sin  = m m = 0, ±1, ±2, ……
Plane polarized light
• In practice most EMR is unpolarized i.e., has electric
and magnetic vectors at all orientations
perpendicular to the direction of propagation
• The infinite number of vibrational planes are
resolved into two major planes by vector addition
• When the amplitude of the vectors becomes
unsymmetrical, the radiation is polarized
and the elimination of all but one plane
results in plane polarization.
• Thus, plane polarized means that electric
field vector vibrates in a single plane and the
magnetic field vibrates in another plane
perpendicular to the electric field
Polarization of Light
• consider what occurs when we have two
plane-polarized light waves of identical frequency
moving through the same region of space in the same
direction.
• If the electric field vectors of the two waves are aligned
with each other, they will simply combine to give a
resultant wave that is also linearly polarized.
• The amplitude and phase of the resultant depends, on
the amplitude and phase of the two superimposing
waves.
• If the electric field vectors of the waves are mutually
perpendicular, the resultant wave may or may not be
linearly polarized.
• If the waves are of equal amplitude and orthogonal,
superposition can lead to plane-polarized, elliptically
polarized, and circularly polarized radiation;
– which of these is obtained depends on the phase
difference between the two waves, as discussed
below.
Linear Polarization
• Consider two waves with mutually perpendicular
electric field vectors.
• If the two waves have a phase difference that is zero
or an integral multiple of ± 2, they are in phase, and
the resultant wave is linearly polarized, as shown in
the Figure
linearly polarized light of
resultant amplitude E is seen
to be composed of two
or­thogonal components. The
component with amplitude Ey
is polarized in the yz plane,
while that with amplitude Ex is
polarized in the xz plane. The z
axis is the axis of propagation
Circular Polarization
• It arises when the two orthogonal waves are 90° out of phase.
• In such a case a circularly polarized light is obtained because
the resultant traces out a circle.
• When the resultant vector (when the x component lags the y
component by 90°) rotates clockwise, the resultant wave is said
to be right circularly polarized.
• If the x component were to lead the y component by 90°, the
resultant electric field vector would rotate counter­clockwise.
The resultant in this case is said to be left circularly polarized.
• The two oppositely polarized components are often called the l
and d components, where d (right-handed or dex­trorotatory)
refers to clockwise rotation and l (left-handed or levorotatory)
refers to counterclockwise rotation from
• The two oppositely polarized components are often called the l
and d components, where d (right-handed or dextrorotatory)
refers to clockwise rotation and l (left-handed or levorotatory)
refers to counterclockwise rotation
Elliptical Polarization
• If the two superimposing, plane-polarized
waves have a phase difference between 0°
(linear polarization) and 90° (circular
polarization), the resultant traces out an
ellipse and the radiation is said to be
elliptically polarized.
Normal Light
• Light from common sources (filament lamps, the
sun, arc lamps) is emitted by nearly independent
radiators (atoms and molecules).
• Each radiator produces a polarized wave train for a
short time ( = 10-8 s).
• The light propagating in a given direction consists of
many such wave trains whose planes of vibration are
randomly oriented around the direction of
propagation.
• As a result of the random superposition of
independent polarized wave trains, no single
resultant state of polarization is observable, and
natural light is referred to as unpolarized light.
• Unpolarized light can be described as two
orthogonal plane-polarized waves of equal amplitude
with a phase difference between them that varies
randomly in time.
Optical Rotatory Dispersion
• For some substances, the characteristics of optical phenomena
such as absorption, refraction, and reflection depend on the
polarization of the incident radiation.
• Substances that rotate the plane of vibration of plane-polarized
radiation are termed optically active.
• These include anisotropic crystals and liquids or solutes in
solution that can exist as enantiomers (e.g., chiral molecules).
• In the latter case, optical activity is observed if one of the
enantiomers is in excess.
• The rotation of plane polarized light by an optically active
substance can be viewed as being due to the different
propagation rates of the d and l components
• The propagation velocities differ because of the different
refractive indicies for the d and l components,
d and  l,, respectively.
• The rotation in degrees (), also termed the optical rotatory
power, is given by
pathlength
wavelength of incident radiation
• The rotatory power depends not only
on the compound, wavelength, and
pathlength, but also on the
temperature, and for solutions of an
optically active solute, the solvent and
the analyte concentration.
• The rotation can be normalized to a
particular pathlength and concentration
as follows:
Specific rotation
g/mL
decimeters
For pure liquids, c is
Replaced by the density
Polarimetry
• The rotation is measured at one wavelength.
• The temperature and wavelength are
commonly specified by adding a superscript
and subscript to .
• Standard wavelengths include 589 nm (the
Na D(3-26)
line) and 546.1 nm (the green
Hg line).
• In spectropolarimetry, the dependence of the
rotation on wavelength is measured and is
termed Optical rotatory dispersion
Circular Dichroism
•
•
•
•
•
•
•
•
(CD) depends on the difference in molar absorptivities for the d and l
components, d and l, respectively, by optically active materials.
If an absorbing sample of an optically active compound is illuminated
with plane­polarized radiation, the differential absorption results in
one of the circularly polarized components being absorbed more
strongly than the other component
Thus the transmitted radiation is elliptically polarized.
The eccentricity of the ellipse can be characterized by a quantity
termed the ellipticity () in degrees.
() is a measure of the magnitude of CD and is related to the length of
the major and minor axes of the ellipse
The ellipticity cannot be directly measured as the optical rotation.
Rather the absorbance with incident radiation that is circularly
polarized in the d direction (Ad) and the absorbance with l circularly
polarized radiation (Al) are separately measured.
The ellipticity is calculated from these absorbances and the equation
It applies if c is in M units
And b in decimeters
Units are often in degrees
centimeter squared
Per decimole
Circular dichroism
• A circular dichroism curve or spectrum is a plot of molar
elipticity vs wavelength
Modulators
• Devices used to amplitude
modulate a radiation source
• Modulation is based on
mechanical interruption of a
light beam or on electro-optic,
magneto-optic, or
acousto-optic phenomena.
• A rotating wheel or disk
chopper (often called a
toothed wheel chopper) is
usually used.
• A high-quality motor is used to
control the rotation rate of the
wheel.
• The periodic interruption of
the light beam can also be
controlled by other means
Mechanical choppers
• The maximum modulation frequency from a
mechanical chopper is generally in the range 1 to 10
kHz.
• Other choppers are designed to operate at one
frequency (10 to 6000 Hz).
• Choppers can be used for specialized functions by
mounting mirrors, refractor plates, gratings, or filters
to the vanes.
• A chopper with mirrored vanes is commonly used as
a chopping beam splitter, as discussed
• In some applications, it is only necessary to block or
unblock a radiation beam at certain times in an
experiment (e.g., to measure the dark signal).
• Beam blocking can be accomplished by pulling a
vane in an out of the light path
Imaging and beam directing optics
• They produce an image or set of
images of the entrance slit on focal
plane
• Collect and focus radiation from
external source onto sample container
and radiation from container into filter
or entrance slit of a monochromator
• Lenses and mirrors are usually used
for these purposes
Chromatic Aberrations
• As mentioned earlier, the refractive index of a given material is a
function of the wavelength of the incident radiation.
• Because lenses depend on refraction for their imaging properties, they
suffer from chromatic aberrations. Front surface mirrors, which
depend only on reflection, do not.
• The equation for the focal length of a thin lens
1
1
1
 (  1)(  )
f
R1 R2
1
1
R = radius of curvature; 1f =( focal
 1)(  length
)
f
R R
shows that the focal length is also a function of wavelength because 
is a function of wave­length.
Consider, for example, fused silica, which has a refractive index of
1.469618 at  = 404.7 nm and 1.458404 at  = 589.0 nm.
Since 1/f ( - 1), the focal length of a fused silica lens will be 2.4%
longer at 589.0 nm than at 404.7 nm.
Thus in general f decreases with decreasing wavelength.
Chromatic aberrations can be a particular problem if an optical system
is aligned and optimized using visible light and the system is later
used in the ultraviolet region.
Dramatic effects on the size and quality of images and on the
throughput can result.
1
•
•
•
•
•
2
• Chromatic aberrations along the optical axis are
termed axial chromatic aberrations, while in the
vertical direction they are termed lateral chromatic
aberrations.
• As a result of aberrations, a lens illuminated with
white light fills a volume of space with a continuum
of over­lapping images that vary in size and color.
• Chromatic aberrations can be compensated at two
wavelengths by using a combination of a positive
and a negative lens, called an achromatic doublet
• Unfortunately, achromatic lenses are expensive and
impractical in the ultraviolet region of the spectrum.
• Compensation at one wavelength in the red and
another in the blue, for example, is achieved by
selecting glasses of appropriate refractive indices
and choosing their radii of curvature to give the
same f at the two wavelengths.
Monochromatic Aberrations
• Both lenses and mirrors suffer from aberrations
even when the incident light is monochromatic.
• Spherical aberrations are a result of deviations from
the paraxial approximation.
• For converging elements, off-axis rays are focused
closer to the element than paraxial rays, as
demonstrated in the Figure.
• One method to reduce spherical aberrations is to put
an aperture stop in front of or behind the lens so that
off-axis rays are blocked.
• Deviations are also reduced if the lens is used as
illustrated in the Figure.
• Image quality is improved through reduction of
spherical aberrations by use of a spherical optical
components.
• Concave parabolic, ellipsoidal, and hyperboloidal
mirrors form perfect images for pairs of conjugate
axial points.
Spherical aberrations
(a) parallel rays are seen to
produce a circle in the focal
plane, called the circle of
least confusion, due to
spherical aberrations.
(b) Deviations are reduced if
the incident rays makes
nearly the same angle with
the surface as the exiting
ray as shown in
Beam Splitters
• Many applications in spectroscopy call for one
beam to be split into two beams; the
double­beam spectrometer is one example.
• Devices that accomplish this task are called
beam splitters.
• They are available in many different forms for
various applications.
• One simple beam sputter is based on a partially
silvered mirror as shown in Figure 3-31a. They
are usu-
Partially silvered mirror beam splitter
• This type of mirror is
partially transparent
because the metallic
coating is too thin to
make it opaque.
• With such a mirror,
one can both look
through it and see a
reflection simultaneously
• Beam is split into two
beams separated spatially
but temporarily overlapping
Pellicle beam splitter
These are made from very thin nitrocellulose
membranes stretched over a metallic frame
Chopper/beam splitter
• The chopper wheel consists of alternating transmitting and
reflecting segments.
• The transmitting segments are just open slots, while mirrored
surfaces form the reflecting segments.
• The reflected and transmitted beams are temporally separated
as shown.
• it is used to split a beam into two spatially separated beams at
different times
Fiber Optics
• Used in spectrophotometers to transfer light
between various points
• This fiber optic consists of a
core of 1 and a clad of 2
where 1 > 2
• Usually additional jackets
are used to provide
additional strength
• Total internal reflection
occurs when
Light ray entering the core
• Maximum value of 0 for
which total internal
reflection occurs is given by
0 sin 0 = (12- 22 )1/2
• Rays incident at larger angles
are only partially reflected at
core-clad interface and soon
pass out of the fiber
• Numerical aperture (NA) is the cone of light accepted
by the fiber
Fiber optics are used in spectroscopy because:
• Mechanically flexible
• Light can be transmitted over curved paths
• Thus, it replaces several mirrors in directing light rays in a
spectrophotometer (source to monochromator and then detector,
etc.)
• Light can be transmitted over long distance (e.g. 500 m) that allows
remote monitoring in hazardous environment since the more delicate
components can be far from the monitoring site
• A single fiber optic cannot transmit an image because the rays
from different parts of the object are scrambled by multiple
internal reflections
•
Filters, Prisms and Gratings
• Filters attenuate all but the desired wavelength
• Higher resolution systems work on the basis of
dispersing (spreading out the wavelength spatially)
radiation into a spectrum.
Filters
• Filters are used to pass a band of wavelengths (bandpass
filters) or to block wavelengths longer or shorter than
some desired value (cutoff filters)
1. Absorption filters
– Based on absorption by colored glass, crystal, solutions and thin
films
– They are cheap and inactive to the angle of incidence
Bandpass filter
Maximum transmittance
Full width at half maximumheight
 of maximum transmittance
Cutoff filter
short wavelength cutoff
It contains a substance that absorb
all radiation shorter than the given
Cutoff (short wavelength cutoff) or
All radiation at long wavelengths
(long wavelength cutoff)
2. Interference filters
• They are constructed so that the rays from
most wavelengths that strike the filter suffer
destructive interference while only rays
within small wavelength band experience
constructive interference and are passed
• Two main types are used:
– Single layer or Fabry-Perot type
– Multilayer dielectric type
Fabry-Perot type
Material of low 
CaF2
• Ray 1 travels the path
, while ray 2 travels the path
• The two waves will be in phase (constructive interference) at points
g and e if (OPL) is an integral multiple of the wavelength. Thus the
condition for constructive interference is
• In many uses of interference filters, the incident
beam is normal to the plane of the filter, instead of
skewed as in the previous figure.
• In these cases  = 0°, so sin   0.
• The central wavelength passed by the filter m can
be written
The order
How do we obtain filters with variable central wavelengths?
• For a given filter with fixed d and  values, the central wavelength
can be changed by changing the angle of incidence of the filter.
• The new peak wavelength  is related to the central wavelength at
normal incidence by :
• Angle tuning of inter­ference filters is frequently
employed when they serve as wavelength selection
devices in dye laser cavities.
• Filters are commercially available in which the d
spacing varies along the length of the filter.
• Such wedge filters are also available in circular
styles in which d varies with the filter rotation.
Transmission of a typical Fabry­Perot interference filter
• The first-order band has m ~ 720 nm. Note that the
second-order band (m = 360 nm) is narrower, with only slightly
lower peak transmittance. The free spectral range is 360 nm for
the first order.
• An additional broadband filter or cutoff filter is frequently
employed to isolate the order of interest; The range of
wavelengths for which no overlap of adjacent orders occurs is
called the free spectral range.
Multilayer (or multicavity) filters
• They are made with alternating layers of high- and
low-refractive-index dielectrics
• They can be considered to be two to six Fabry­Perot
cavities cemented together.
• The multilayer interference filter can achieve quite
narrow FWHM values (<1 nm) with high peak
transmittances (>50%).
• Single and multicavity filters are available with peak
transmittances in the UV to the IR.
• Bandwidths (FWHM values) in the range 1 to 100 nm
are readily available
Prisms
• In spectroscopy prisms are used to
– change the direction of a beam,
– to split an incident beam into two outgoing beams,
– and to produce polarized light,
– to disperse the incoming beam into a spectrum.
Dispersing Prisms
• Dispersion occurs in a prism primarily because of the wavelength
dependence of the refractive index of the prism material.
• A typical arrangement for dispersion with a prism is shown in the
Figure.
• The angle  that a monochromatic refracted ray makes with the
undeviated incident beam is called the deviation
• The variation of the deviation with the wavelength ( d )
d
is called the angular dispersion, Da
• Da is composed of two factors:
Da
=
d
d
=
d d
d d
dispersion of the prism material;
d d 
d d
This factor varies only slightly
With 
• Dispersion of light of
two wavelengths by a
prism of refractive index
,
• Collimated rays of
wavelengths, 1 (red),
2 (blue) are refracted
upon entering the
prism material and
upon exiting it Normal
• prism materials show
higher refractive
indices at shorter
wavelengths. Hence
blue light of 2 is more
highly refracted than
the red light 1
Reflecting Prisms
• Reflecting prisms are designed to change the direction of
propagation of a beam, the orientation of the beam, or both.
• At least one internal reflection takes place within the prism and
there is no resulting dispersion.
• Several examples of reflecting prisms, including a cube beam
sputter, are shown
Reflecting Prisms
Diffraction Gratings
• A diffraction grating is a plane or concave
plate that is ruled with closely spaced grooves.
• The grating acts like a multi slit source when
collimated radiation strikes it Different
wavelengths are diffracted and constructively
interfere at different angles.
• Gratings are either designed for transmission
of the incident radiation or for reflection.
• Modern spectrometers invariably use
reflection gratings.
Diffraction from a blazed reflection grating
(a) the incident ray makes an angle  with the grating
normal N, while the diffracted ray makes an angle .
The spacing between adjacent grooves is d, and the
blaze angle is . The distance L is called the land.
(b) two mono­chromatic rays are shown undergoing
diffraction at an angle . Ray 1 travels a distance AC
farther than ray 2 in reaching the grating surface and
a distance AD farther than ray 2 on exiting the
grating.
• The condition for constructive interference is given
by the grating formula:
m = order of diffraction = 0, ±1, ±2, ±3, …
• Consider polychromatic light striking a grating.
• Within a given order of diffraction (other than the zero order)
the various wavelengths are spatially dispersed because each
wavelength undergoes constructive interference at a different
diffraction angle.
• For example, consider light composed of two wavelengths, 500
nm and 600 nm, striking a grating at an incident angle of 10°. If
the grating has 1200 grooves per mm, the d spacing is d = 106
nm mm-1/1200 grooves mm-1= 833.3 nm/groove.
• In the first order, the 600-nm radiation is diffracted at an angle:
• for 500 nm radiation the corresponding first order diffraction angle is  = 25.2o
• For a given d spacing and angle of incidence, , the
grating formula predicts that many wavelengths are
observed at a given angle of diffraction , a
phenomenon known as overlapping orders
• With the grating discussed in the example above, the
second order of 300 nm also occurs at a diffraction
angle of 33.1°, as does the third order of 200 nm.
• In fact, wavelengths , /2,  /3, . . . ,  /m all appear
at the same angle in different orders.
• The free spectral range f represents the range of
wavelengths from the source for which no overlap of
adjacent orders occurs
• for  = 600 nm in the first order, the free spectral range is 600 nm/2 or 300 nm.
Monochromators
• Monochromators isolate a small wavelength band
from a polychromatic source.
• Monochromators consist of a dispersive element
(prism or grating) and an image transfer system
(entrance slit, mirrors or lenses, and exit slit).
• Within the monochromator an image of the
rectangular, or sometimes curved, entrance slit is
transferred to the exit slit after dispersion of the
wavelength components of the incident radiation.
Czerny-Turner plane grating monochromator.
S
l
i
t
s
a
r
e
• Slits are of fixed or changeable width
• slit width from 1-10 mm
• In most monochromators the exit slit has the same dimensions as
the entrance slit so that it can be fully illuminated by the entrance slit
image.
• Many monochromators allow both slits to be adjusted in width
simultaneously.
Wavelength Selection
• To change the wavelength
selected by the
monochromator, the dispersive
element is rotated to bring a
different wavelength band
through the exit slit.
• The following equation
expresses the grating formula
in terms of the experimental
variables  and 
• Let us assume that in the monochromator d = 833.3 nm,  is fixed at
6.71° and the grating is operated in the first order.
• The Table gives the grating rotation angle, the angular dispersion Da
calculated from the equation, the linear and reciprocal linear dispersion
and the values of  and  required to isolate 300-, 400-, and 500-nm
radiation.
Angular Dispersion of a prism
Dispersion is breaking apart or separating a mixture
of wavelengths into its component wavelengths
• For a prism
Angular dispersion for a grating
Da is the angular dispersion
 Is the angle of incidence
Dispersive characteristics
• For a monochromator, the dispersion in the focal plane is of
more interest.
• The linear dispersion, Dl = dx/d tells how far apart in distance
two wavelengths are separated in the focal plane.
• The Figure illustrates how Dl is determined for a dispersion
element illuminated by collimated radiation of wavelengths
1and  2.
• For the configuration shown, the linear dispersion is
given by
Dl = fDa
• where f is the focal length of the focusing element.
• The linear dispersion Dl is expressed in units of mm nm-1
in the UV-visible region of the spectrum.
• Most often it is the reciprocal linear dispersion Rd that
is specified for a spectrometer.
• The reciprocal linear dispersion represents the number
of wavelength intervals (e.g., nm) contained in each
interval of distance (e.g., mm) along the focal plane
• For a prism monochromator the reciprocal linear
dispersion is usually wavelength dependent because
of the variation of Da with wavelength.
• Some prism monochromator configurations provide
dispersion that is wavelength independent.
Spectral Bandpass and Slit Function
• The spectral bandpass s (nm) is the half-width of the
wavelength distribution passed by the exit slit.
• Except at small slit widths, where aberrations and
diffraction effects must be considered, the spectral
bandpass is controlled by the monochromator
dispersion and the slit width.
• Under these conditions the spectral bandpass is
equal to the geometric spectral bandpass sg, given
by
sg = Rd W
• For a mononchromator with Rd =1 nm mm-1; a slit
width of 100 m give a spectral bandpass of
• Many monochromators have equal entrance and exit slit
widths.
• The slits determine the spectral profile of the output
observed at the exit slit.
• If we illuminate the entrance slit with monochromatic
light, for example, the image transfer system produces a
monochromatic image of the entrance slit in the plane of
the exit slit (focal plane).
• As we rotate the dispersion element, the entrance slit
image is swept across the exit slit as illustrated in the
Figure.
• The resulting convolution of the entrance and exit slit
images is a triangular shaped function called the slit
function.
Wavelength setting
• Slit function
Incident wavelength
• Slit function of a monochromator
with equal exit and entrance slits.
• In (a) the slit function is shown
as the convolution of the entrance
and exit slit images.
• For a broadband (continuum) source, the focal plane
contains a distribution of overlapping slit images.
• If the monochromator is fixed at a single wavelength 0,
the five images shown in the Figure could represent the
focal plane images from five different wavelengths out of
the source spectrum.
• Each wavelength is passed to a degree that depends on
the overlap of its image with the exit slit.
• Thus for a broadband source, t() represents the
fractional transmission vs. wavelength of the continuum
spectrum impingent on the focal plane.
• From equation above the image of wavelength  = o ±
sg)/2 would overlap 50% with the exit slit and thus be
transmitted 50% compared to the image with  = o
b) the slit function is shown as a function of wavelength
(
Resolution
• While the dispersion determines how far apart two
wavelengths are separated linearly or angularly,
• the resolution determines whether the separation
can be distinguished.
• In many cases the resolution is determined by the
monochromator spectral bandpass.
• If the slit width W is large enough that we can
neglect aberrations and diffraction (s = sg), a scan of
two closely spaced monochromatic lines of peak
wavelengths 1 and 2 would appear as ideal
• Clearly the two lines will be just
separated if 2 - 1 = 2s
• Thus the slit width limited resolution  s is
• If
the monochromator wavelength control is adjusted
to that 0 = 1 and the slit width has been adjusted so
that /Rd , the image of 1 will be completely passed
while that of 2 will be just at one side of the exit slit
Resolving power
•
•
The Resolving power is another way to express the ability to
distinguish two wavelengths.
The experimental resolving power of a monochromator is
The average of two wavelengths to be resolved
•
Rexp = /smin
The theoretical resolving power is
Rth =  / d
d the diffraction limited slit width (the slit width equal to the
half –width of the central maximum)
•
•
If the monochromator is free of aberrations, the experimental
resolving power at smin is equal to the theoretical value.
Normally, monochromators are operated at slit widths
considerably larger than the diffraction-limited width.
Stray Radiation
• Stray radiation or stray light in a monochromator is
considered to be any radiation passed outside the
interval o ± s where o is the wavelength setting and
s is the spectral bandpass.
• Stray radiation is usually specified as the percentage
of the total radiation passing the exit slit at a given
wavelength over a specified wavelength range. Thus
Source radiant power
Passed by the monochrom.
Over o ± s
• Stray radiation is very difficult to measure accurately
because it depends on the wavelength, the spectral
bandpass, and the type of source used.
• There are many possible causes of stray radiation.
For example, room light can leak into the
monochromator or radiation can be reflected
internally from walls, optics and baffles. Scattering
from dust particles, and fluorescence from optical
materials are also sources of stray radiation. An
overlapping grating order, grating imperfections, and
diffraction from slit edges can also produce stray
radiation.
• With gratings, some stray radiation appears at all
wavelengths because there is not complete
destructive interference between diffraction orders.
• Stray radiation can be reduced in several ways
• Good instrument design, including appropriate
baffles to intercept various reflected and scattered
rays, is one obvious way.
• Holographic gratings provide much lower stray
radiation factors than do ruled gratings.
• Stray radiation figures can vary from 0.1% to
10-5°. Typical values are 10-3% for ruled gratings and
10-4% for holographic gratings.
• Broad absorption filters are often employed in front
of the entrance slit to narrow the source bandwidth.
These can also serve as order-sorting filters.
• Double monochromators or two monochromators in
tandem can achieve extremely low stray radiation
figures.