1

First assignment of Experimental Physics Lab "The

use of spectromter"

Name : RUBEL MIA

Student ID: 5096190105
Department of Textile Engineering
Date :28/04/2020
Course Number: BTE1901
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2. Introduction:

A spectrometer is a scientific instrument used to separate and measure spectral components of

a physical phenomenon. Spectrometer is a broad term often used to describe instruments that
measure a continuous variable of a phenomenon where the spectral components are somehow
mixed. In visible light a spectrometer can separate white light and measure individual narrow
bands of color, called a spectrum. A mass spectrometer measures the spectrum of the masses
of the atoms or molecules present in a gas. The first spectrometers were used to split light into
an array of separate colors. Spectrometers were developed in early studies of physics,
astronomy, and chemistry. The capability of spectroscopy to determine chemical composition
drove its advancement and continues to be one of its primary uses. Spectrometers are used in
astronomy to analyze the chemical composition of stars and planets, and spectrometers gather
data on the origin of the universe.
Examples of spectrometers are devices that separate particles, atoms, and molecules by their
mass, momentum, or energy. These types of spectrometers are used in chemical analysis and
particle physics.

Number of rulings inch on the grating = 15,000

1 inch= 0.0254 meter
Number of rulings per meter on the grating, N=15,000/0.0254
=590551
=5.9×105 lines/meter

Least count of spectrometer

Leas count= 1 M.S.D − 1 V.S.D
20 M.S.D =10”

VALUE OF M.S.D = 1⁄2 "or 30’

If there are 60 divisions in the Vernier scale than,

60 V.S. D=59 M.S.D

60 V.S. D= 59× 1⁄2

1 V.S.D- (59/60) ×1⁄2

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1° 60°
Least count =1⁄2 −(59⁄60)× 1⁄2 = = = (1⁄2)" half minute
120 120

3. Procedure:

▪ Apparatus required

1. spectrometer

2. HG lamp

3. Grating
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4. Reading lens

5. sprit level
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6. Telescope

7. Collimator

FORMULA :

Wavelength of prominent lines of mercury spectrum is given by

𝝀=𝒔𝒊𝒏𝜽𝒎𝑵
Where

𝝀 – wavelength of prominent line of mercury spectrum(m)

𝜃- angle of diffraction (degree)

N- number of lines per meter length of the given grating (lines/m)

m- order of the spectrum (no unit)

OBSERVATIIONS:
No. of rulings per meter on the grating, N= 5.9×105 lines/meter
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Least count of spectrometer=(1⁄2)′

Order of spectrum m = 1

If there are 60 divisions in the Vernier scale than,

60 V.S. D=59 M.S.D

60 V.S. D= 59× 1⁄2

1 V.S.D- (59/60) ×1⁄2

1° 60°
Least count =1⁄2 −(59⁄60)× 1⁄2 = = = (1⁄2)" half minute
120 120

4. Data and Data Analysis

Over the past 20 years, miniature fiber optic spectrometers have evolved from a novelty to the
spectrometer of choice for many modern spectroscopists. People are realizing the advanced
utility and flexibility provided by their small size and compatibility with a plethora of sampling
accessories.

The basic function of a spectrometer is to take in light, break it into its spectral components,
digitize the signal as a function of wavelength, and read it out and display it through a computer.
The first step in this process is to direct light through a fiber optic cable into the spectrometer
through a narrow aperture known as an entrance slit. The slit vignettes the light as it enters the
spectrometer. In most spectrometers, the divergent light is then collimated by a concave mirror
and directed onto a grating. The grating then disperses the spectral components of the light at
slightly varying angles, which is then focused by a second concave mirror and imaged onto the
detector. Alternatively, a concave holographic grating can be used to perform all three of these
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functions simultaneously. This alternative has various advantages and disadvantages, which
will be discussed in more detail later on.

Once the light is imaged onto the detector the photons are then converted into electrons which
are digitized and read out through a USB (or serial port) to a computer. The software then
interpolates the signal based on the number of pixels in the detector and the linear dispersion
of the diffraction grating to create a calibration that enables the data to be plotted as a function
of wavelength over the given spectral range. This data can then be used and manipulated for
countless spectroscopic applications, some of which will be discussed here later on.

In the following sections we will explain the inner-workings of a spectrometer and how all of
the components work together to achieve a desired outcome.

I’ll first discuss each component individually so that you have a full understanding of their
function in the workings of a spectrometer, then we’ll discuss the variety of configurations that
are possible with those components, and why each of them has a different function. We’ll even
touch on some of the accessories used to make your application as successful as it can possibly
be.

Part 1: The Slit

Overview

A spectrometer is an imaging system which maps a

plurality of monochromatic images of the entrance slit onto the detector plane. This slit is
critical to the spectrometer’s performance and determines the amount of light (photon flux)
that enters the optical bench and is a driving force when determining the spectral resolution.
Other factors are grating, groove frequency and detector pixel size.
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The optical resolution and throughput of a spectrometer will ultimately be determined by the
installed slit. Light entering the optical bench of a spectrometer via a fiber or lens is focused
onto the pre-mounted and aligned slit. The slit controls the angle of the light which enters the
optical bench.

Slit widths come in a number of different sizes from 5µm to as large as 800µm with a 1mm
(standard) to 2mm height. It is important to select the right slit for your application since they
are aligned and permanently mounted into a spectrometer and should only be changed by a
trained technician.

The most common slits used in spectrometers are 10, 25, 50, 100 and 200 μm. For systems
where optical fibers are used for input light coupling, a fiber bundle matched with the shape of
the entrance slit (stacked fiber) may help increase the coupling efficiency and system
throughput.

Technical Details

The function of the entrance slit is to define a clear-cut object for the optical bench. The size
(width (Ws) and height (Hs)) of the entrance slit is one of the main factors that affect the
throughput of the spectrograph. The image width of the entrance slit is a key factor in
determining the spectral resolution of the spectrometer when it is greater than the pixel width
of the detector array. Both the throughput and resolution of the system should be balanced by
selecting a proper entrance slit width.

The image width of the entrance slit (Wi) can be estimated as:

Wi = (M2×Ws2+Wo2 )1/2

Where M is the magnification of the optical bench set by the ratio of the focal length of the
focusing mirror (lens) to the collimating mirror (lens), W s is the width of the entrance slit, and
Wo is the image broadening caused by the optical bench. For a CZ optical bench, W o is on the
order of a few tens of microns. So reducing the width of the entrance slit below this value won’t
help much on improving the resolution of the system. The axial transmissive optical bench
provides much smaller Wo. Thus it can achieve a much higher spectral resolution. Another
limit on spectral resolution is set by the pixel width (W p) of the array detector. Reducing
Wi below Wp won’t help to increase resolution of the spectrometer.
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Under the condition that the resolution requirement is satisfied, the slit width should be as wide
as possible to improve the throughput of the spectrograph.

Part 2: Diffraction Grating

Overview

The diffraction grating of a spectrometer determines the wavelength range and partially
determines the optical resolution that the spectrometer will achieve. Choosing the correct
grating is a key factor in optimizing your spectrometer for the best spectral results in your
application. Gratings will influence your optical resolution and the maximum efficiency for a
specific wavelength range. The grating can be described in two parts: the groove frequency and
the blaze angle, which are further explained in the sections below.

There are two types of diffraction gratings: ruled gratings and holographic gratings. Ruled
gratings are created by etching a large number of parallel grooves onto the surface of a
substrate, then coating it with a highly reflective material. Holographic gratings, on the other
hand, are created by interfering two UV beams to create a sinusoidal index of refraction
variation in a piece of optical glass. This process results in a much more uniform spectral
response, but a much lower overall efficiency.

While ruled gratings are the simplest and least expensive gratings to manufacture, they exhibit
much more stray light. This is due to surface imperfections and other errors in the groove
period. Thus, for spectroscopic applications (such as UV spectroscopy) where the detector
response is poorer and the optics are suffering more loss, holographic gratings are generally
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selected to improve the stray light performance of the spectrometer. Another advantage of
holographic gratings is that they are easily formed on concave surfaces, allowing them to
function as both the dispersive element and focusing optic at the same time.

Groove Frequency:

The amount of dispersion is determined by the amount of grooves per mm ruled into the
grating. This is commonly referred to as groove density, or groove frequency. The groove
frequency of the grating determines the spectrometer’s wavelength coverage and is also a major
factor in the spectral resolution. The wavelength coverage of a spectrometer is inversely
proportional to the dispersion of the grating due to its fixed geometry. However, the greater the
dispersion, the greater the resolving power of the spectrometer. Inversely, decreasing the
groove frequency decreases the dispersion and increases wavelength coverage at the cost of
spectral resolution.

For example, if you were to choose a Exemplar™ spectrometer with a 900g/mm, it would give
you a wavelength range of 370 nm, with an optical resolution as low as 0.5nm. Comparably, if
you were to choose a Exemplar™ with a 600g/mm grating, it would instead give you up to
700nm of wavelength coverage with an optical resolution as low as 1.0nm. As this example
shows, you are able to increase your wavelength coverage at the sacrifice of optical resolution.

When the required wavelength coverage is broad, i.e. λmax > 2λmin, optical signals in
wavelengths from different diffraction orders may end up at the same spatial position on the
detector plane, which will become evident once we take a look at the grating equation. In this
case, a linear variable filter (LVF) is required to eliminate any unwanted higher order
contributions, or perform “order sorting”.

For fixed grating spectrometers, it can be shown that the angular dispersion from the grating is
described by

where Βeta is the diffraction angle, d is the groove period (which is equal to the inverse of the
groove density), m is the diffraction order, and λ is the wavelength of light as shown in Figure
1-1.
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By taking into account the focal length (F) of the focusing mirror and by assuming the small
angle approximation, equation 2-1 can be rewritten as

which gives the linear dispersion in terms of nm/mm. From the linear dispersion, the
maximum spectral range (λmax - λ min) can be calculated based upon the detector length (LD),
which can be calculated by multiplying the total numbers of pixels on the detector (n) by the
pixel width (Wp) resulting in the expression

Based on equation 2-3, it is clear that the maximum spectral range of a spectrometer is
determined by the detector length (LD), the groove density (1/d) and the focal length (F).

The minimum wavelength difference that can be resolved by the diffraction grating is given
by

where N is the total number of grooves on the diffraction grating. This is consistent with
transform limit theory which states that the smallest resolvable unit of any transform is
inversely proportional to the number of samples. Generally, the resolving power of the grating
is much higher than the overall resolving power of the spectrometer, showing that the
dispersion is only one of many factors in determining the overall spectral resolution.

It should also be noted that the longest wavelength that will be diffracted by a grating is 2d,
which places an upper limit on the spectral range of the grating. For near-infrared (NIR)
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applications, this long wavelength limitation may restrict the maximum groove density allowed
for your spectrometer.

Blaze Angle:

As a grating diffracts incident polychromatic light, it does not do so with uniform efficiency.
The overall shape of the diffraction curve is determined mainly by the groove facet angle,
otherwise known as the blaze angle. Using this property, it is possible to calculate which blaze
angle will correspond to which peak efficiency; this is called the blaze wavelength. This
concept is illustrated in figure 2-1, which compares three different 150g/mm gratings blazed at
500nm, 1250nm & 2000nm.

Figure 2-1

Gratings can be blazed to provide high diffraction efficiency (>85%) at a specific wavelength,
i.e. a blaze wavelength (λB). As a rule of thumb, the grating efficiency will decrease by 50% at
0.6×λB and 1.8×λB. This sets a limit on the spectral coverage of the spectrometer. Generally,
the blaze wavelength of the diffraction grating is biased toward the weak side of the spectral
range to improve the overall signal to noise ratio (SNR) of the spectrometer.
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Part 3a: The Detector

Overview

In the previous sections, we discussed the

importance of the entrance slit and the diffraction grating in forming a spectral image of the
incident light in the image plane. In traditional spectrometer (monochrometer) designs, a
second slit is placed in the image plane, known as the exit slit. The exit slit is typically the same
size as the entrance slit since the entrance slit width is one of the limiting factors on the
spectrometer’s resolution (as was shown in Part 1). In this configuration, a single element
detector is placed behind the exit slit and the grating is rotated to scan the spectral image across
the slit, and therefore measure the intensity of the light as a function of wavelength.

In modern spectrometers, CCD and linear detector arrays have facilitated the development of
“fixed grating” spectrometers. As the incident light strikes the individual pixels across the
CCD, each pixel represents a portion of the spectrum that the electronics can then translate and
display with a given intensity using software. This advancement has allowed for spectrometers
to be constructed without the need for moving parts, and therefore greatly reduce the size and
power consumption. The use of compact multi-element detectors has allowed for a new class
of low cost, compact spectrometers to be developed: commonly referred to as “miniature
spectrometers.”

Detector Types:

While photodetectors can be characterized in many different ways, the most important
differentiator is the detector material. The two most common semiconductor materials used in
miniature spectrometers are Si and InGaAs. It is critical to choose the proper detector material
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when designing a spectrometer because the bandgap energy (Egap) of the semiconductor
determines the upper wavelength limit (λ max) that can be detected by the following relationship

where h is Plank’s constant and c is the speed of light. The product of Plank’s constant and the
speed of light can be expressed as 1240 eV•nm or 1.24 eV•µm to simplify the conversion from
energy to wavelength. For example, the bandgap energy of Si is 1.11eV which corresponds to
maximum wavelength of 1117.117nm. InGaAs, on the other hand, is an alloy created by mixing
InAs and GaAs, which have a bandgap of 0.36eV and 1.43eV respectively, and depending on
the ratio of In and Ga the bandgap energy can be tuned in between those two values. However,
due to a variety of factors, not all ratios of In and Ga are easily fabricated, therefore 1.7µm (or
0.73eV) has become the standard configuration for InGaAs detector arrays. It is also possible
to use extended InGaAs arrays which can detect out to 2.2µm or 2.6µm, but these detectors are
much more expensive and are much nosier than traditional InGaAs detectors.

The lower detection limit of a material is slightly harder to quantify because it is determined
by the absorbance characteristics of the semiconductor material, and as a result can vary widely
with the thickness of the detector. Another common method of lowering the detection limit of
the detector is to place a fluorescent coating on the window of the detector, which will absorb
the higher energy photons and reemit lower energy photons which are then detectable by the
sensor. Figure 3-1 below shows a comparison of the detectivity (D*) as a function of
wavelength for both Si (CCD) and InGaAs.
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CCDs, BT-CCDs, and PDAs:

While currently InGaAs detector arrays are only available in one configuration, Si multi-
element detectors are readily available in three different subcategories: charge coupled devices
(CCDs) back-thinned charge coupled devices (BT-CCDs), and photodiode arrays (PDAs).

CCD technology allows for small pixel size (~14µm) detectors to be constructed because it
eliminates the need for direct readout circuitry from each individual pixel. This is accomplished
by transferring the charge from one pixel to another, allowing for all of the information along
the array to be read out from a single pixel. CCDs can be constructed very inexpensively which
makes them an ideal choice for most miniature spectrometers, but they do have two drawbacks.
First, the gate structure on the front of the CCD can cause the incident light to scatter and
therefore not be absorbed. Second, CCDs need to have a relatively large P-Si substrate to
facilitate low cost production, however, this also limits the efficiency of the detector (especially
at shorter wavelengths) due to absorption through the Player.

To mitigate both of these issues in spectroscopy applications where very high sensitivity is
needed, BT-CCDs are ideal. BT-CCDs are made by etching the P-Si substrate of the CCD to a
thickness of approximately 10µm. This process greatly reduces the amount of absorption and
increases the overall efficiency of the detector. This process also allows the detector to be
illuminated from the back side (P-Si region) which eliminates the effects from the gate structure
on the surface of the detector. Figure 3-2 below shows a typical comparison of the quantum
efficiency between a traditional front illuminated CCD and a back illuminated BT-CCD.

While there are distinct advantages to the use of BT-CCDs in spectroscopy, there are also two
major drawbacks that should be noted. First, this process greatly increases the cost of
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production, and second (since the detector is so thin ) there can be an etaloning effect caused
from reflections off the front and back surfaces of the detector. The etaloning phenomena
associated with BT-CCDs can be mitigated by a process known as deep depletion, but once
again this adds additional cost to the production process.

PDA detectors are more traditional linear detectors which consist of a set of individual
photodiodes that are arranged in a linear fashion using CMOS technology. These detectors,
while not having the small pixel size and high sensitivity, have several advantages over CCD
and BT-CCD detectors. First, the lack of charge transfer eliminates the need for a gate structure
on the front surface of the detector, and greatly increases the readout speed. The second
advantage of PDA detectors is that the well depth is much higher than the well depth of a CCD;
a typical PDA detector well depth is ~156,000,000e- as compared to ~65,000e- for a standard
CCD. The larger well depth of PDA detectors causes them to have a very large dynamic range
~50,000:1 as well as an extremely linear response. These properties make PDAs ideal for
applications where it is necessary to detect small changes in large signals, such as LED
monitoring.

Part 3b: The Detector

In Part 3a, we discussed several different types of detectors and the role they play in miniature
spectrometers. No discussion of detectors would be complete without covering noise sources
and how they can be mitigated by the use of TE Cooling.

Detector Noise:

The main noise sources found in an array detector

include: readout noise, shot noise, dark noise, and fixed pattern noise.
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Readout noise is caused by electronic noise in the detector output stage and related circuitry,
which largely dictates the detection limit of the spectrometer.

Shot noise is associated with the statistical variation in the number of photons incident on the
detector, which follows a Poisson distribution. Therefore, shot noise is proportional to the
square root of the incident photon flux.

Dark noise is associated with the statistical changes in the number of electrons generated in a
dark state. A photo detector exhibits a small output even when no incident light is present. This
is known as the dark current or dark output. Dark current is caused by thermally generated
electron movements and is strongly dependent on ambient temperatures. Similar to shot noise,
dark noise also follows a Poisson distribution; as a result, dark noise is proportional to the
square root of the dark current.

The fixed pattern noise is the variation in photo-response between neighboring pixels. This
variation results mainly from variations in the quantum efficiency among pixels caused by non-
uniformities in the aperture area and film thickness that arise during fabrication.

The total noise of an array detector is the root square sum of these four noise sources.

TE Cooling:

Cooling an array detector with a built-in thermoelectric cooler (TEC) is an effective way to
reduce dark noise as well as to enhance the dynamic range and detection limit. For Si detectors,
dark current doubles when the temperature increases by approximately 5 to 7°C and halves
when the temperature decreases by approximately 5 to 7°C. Figure 3-3 shows the dark noise
for an un-cooled and cooled CCD detector at an integration time of 60s. When operating at
room temperature, the dark noise nearly saturates the un-cooled CCD. When the CCD is cooled
down to only 10°C by the TEC, the dark current is reduced by about four times and the dark
noise is reduced by about two times. This makes the CCD capable of operating at a longer
integration time to detect weak optical signals. When a CCD based spectrometer is involved in
non-demanding high light level applications such as LED measurement, the dark noise
reduction due to TE cooling is minimal because of the relatively short integration time used.
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As a rule of thumb, when the integration time of a CCD spectrometer is set to less than 200ms,
the detector is operating in a read noise limited state. Therefore, there is no significant noise
reduction due to the TE cooling; although the temperature regulation under these conditions
will be beneficial for long term baseline stability.

Part 4: The Optical Bench

Overview

As stated in Part 1: The Slit, a spectrometer is an

imaging system which maps a plurality of monochromatic images of the entrance slit onto the
detector plane. In the past 3 sections, we discussed the three key configurable components of
the spectrometer: the slit, the grating, and the detector. In this section, we will discuss how
these different components work together with different optical components to form a complete
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system. This system is typically referred to as the spectrograph, or optical bench. While there
are many different possible optical bench configurations, the three most common types are the
crossed Czerny-Turner, unfolded Czerny-Turner, and concave holographic spectrographs
(shown in Figures 4-1, 4-2, and 4-3 respectively).

Czerny-Turner

The crossed Czerny-Turner configuration consists of two concave mirrors and one plano
diffraction grating, as illustrated in Figure 4-1. The focal length of mirror 1 is selected such
that it collimates the light emitted from the entrance slit and directs the collimated beam of
light onto the diffraction grating. Once the light has been diffracted and separated into its
chromatic components, mirror 2 is then used to focus the dispersed light from the grating onto
the detector plane.

Figure 4-1 Crossed Czerny-Turner Spectrograph

The crossed Czerny-Turner configuration offers a compact and flexible spectrograph design.
For a diffraction grating with given angular dispersion value, the focal length of the two mirrors
can be designed to provide various linear dispersion values, which in turn determines the
spectral coverage for a given detector, sensing length and resolution of the system. By
optimizing the geometry of the configuration, the crossed Czerny-Turner spectrograph may
provide a flattened spectral field and good coma correction. However, due to its off-axis
geometry, the Czerny-Turner optical bench exhibits a large image aberration, which may
broaden the image width of the entrance slit by a few tens of microns. Thus, the Czerny-Turner
optical bench is mainly used for low to medium resolution spectrometers. Although this design
is not intended for two dimensional imaging, using aspheric mirrors (such as toroidal mirrors)
instead of spherical mirrors can provide a certain degree of correction to the spherical
aberration and astigmatism.
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To minimize image aberrations, the Czerny-Turner optical bench is generally designed with an
f-number of >3, which in turn places a limit on its throughput. The f-number of an optical
system expresses the diameter of the entrance pupil in terms of its effective focal length. The
f-number is defined as f/# = f/D, where f is the focal length of the collection optic and D is the
diameter of the element. The f-number is used to characterize the light gathering power of the
optical system. The relation of the f-number with another important optical concept, Numerical
Aperture (NA), is that: f/# = 1/(2•NA), where the numerical aperture of an optical system is a
dimensionless number that characterizes the range of angles over which the system can accept
or emit light.

The relatively large f/# of Czerny-Turner optical benches, in comparison to a typical multimode
fibers (NA ≈ 0.22), can cause a fairly high level of stray light in the optical bench. One simple
and cost-effective way to mitigate this issue is by unfolding the optical bench as shown in
Figure 4-2 below. This allows for the insertion of “beam blocks” into the optical path, greatly
reducing the stray light and, as a result, the optical noise in the system. This issue is not as
damaging in the visible and NIR regions where there is an abundance of signal and higher
quantum efficiencies, but it can be a problem for dealing with medium to low light level UV
applications. This makes the unfolded Czerny-Turner spectrograph ideal for UV applications
that require a compact form factor.

Figure 4-2 Unfolded Czerny-Turner Spectrograph

Concave Holographic:

The third most common optical bench is based on an aberration corrected concave holographic
grating (CHG). Here, the concave grating is used both as the dispersive and focusing element,
which in turn means that the number of optical elements is reduced. This increases throughput
and efficiency of the spectrograph, thus making it higher in throughput and more rugged. The
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holographic grating technology permits correction of all image aberrations present in spherical,
mirror based Czerny-Turner spectrometers at one wavelength, with good mitigation over a
wide wavelength range.

Figure 4-3 Concave-Holographic Spectrograph

In comparison with a ruled grating, the holographic grating presents up to over a 10x reduction
in stray light, which helps to minimize the interferences due to unwanted light. A ruled
diffraction grating is produced by a ruling engine that cuts grooves into the coating layer on
the grating substrate (typically glass coated with a thin reflective layer) using a diamond tipped
tool. A holographic diffraction grating is produced using a photolithographic technique that
utilizes a holographic interference pattern. Ruled diffraction gratings, by the nature of the
manufacturing process, cannot be produced without defects, which may include periodic errors,
spacing errors and surface irregularities. All of these contribute to increased stray light and
ghosting (false spectral lines caused by periodic errors). The optical technique used to
manufacture holographic diffraction gratings does not produce periodic errors, spacing errors
or surface irregularities. This means that holographic gratings have significantly reduced stray
light (typically 5-10x lower stray light compared to ruled gratings) and removed ghosts
completely.

Ruled gratings are generally selected when working with low groove density, e.g., less than
1200 g/mm. When high groove density, low stray light, and/or concave gratings are required,
holographic gratings are the better choice. It is important to keep in mind that the maximum
diffraction efficiency of concave holographic gratings is typically ~35% in comparison to plano
ruled gratings, which can have peak efficiencies of ~80%.
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Part 5: Spectral Resolution

Introduction

One of the most important characteristics of a

spectrometer is the spectral (or optical) resolution. The spectral resolution of a system
determines the maximum number of spectral peaks that the spectrometer can resolve. For
example, if a spectrometer with a wavelength range of 200nm had a spectral resolution of 1nm,
the system would be capable of resolving a maximum of 200 individual wavelengths (peaks)
across a spectrum.

In dispersive array spectrometers, there are 3 main factors that determine the spectral resolution
of a spectrometer: the slit, the diffraction grating, and the detector. The slit determines the
minimum image size that the optical bench can form in the detector plane. The diffraction
grating determines the total wavelength range of the spectrometer. The detector determines the
maximum number and size of discreet points in which the spectrum can be digitized.

Measuring Spectral Resolution

It is important to understand that the observed signal (So) is not solely dependent on the spectral
resolution of the spectrometer (R) but it is also dependent on the linewidth of the signal (Sr).
As a result, the observed resolution is the convolution of the two sources,

Equation 5-1
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When the signal linewidth is significantly greater than the spectral resolution, the effect can be
ignored and one can assume that the measured resolution is the same as the signal resolution.
Conversely, when the signal linewidth is significantly narrower than the spectrometer
resolution, the observed spectrum will be limited solely by the spectrometer resolution.

For most applications it is safe to assume that you are working in one of these limiting cases,
but for certain applications such as high resolution Raman spectroscopy, this convolution
cannot be ignored. For example, if a spectrometer has a spectral resolution of ~3cm -1 and uses
a laser with a linewidth of ~4cm -1, the observed signal will have a linewidth of ~5cm -1 since
the spectral resolutions are so close to each other (assuming a Gaussian distribution).

For this reason, when attempting to measure the spectral resolution of a spectrometer it is
important to assure that the measured signal is significantly narrow to assure that the
measurement is resolution limited. This is typically accomplished by using a low pressure
emission lamp, such as an Hg vapor or Ar, since the linewidth of such sources is typically much
narrower than the spectral resolution of a dispersive array spectrometer. If narrower resolution
is required, a single mode laser can be used.

After the data is collected from the low pressure lamp, the spectral resolution is measured at
the full width half maximum (FWHM) of the peak of interest.

Calculating Spectral Resolution

When calculating the spectral resolution (δλ) of a spectrometer, there are four values you will
need to know: the slit width (Ws), the spectral range of the spectrometer (Δλ), the pixel width
(Wp), and the number of pixels in the detector (n). It is also important to remember that spectral
resolution is defined as the FWHM. One very common mistake when calculating spectral
resolution is to overlook the fact that in order to determine the FWHM of a peak, a minimum
of three pixels is required, therefore the spectral resolution (assuming the Ws = Wp) is equal to
three times the pixel resolution (Δλ/n). This relationship can be expanded on to create a value
known as resolution factor (RF), which is determined by the relationship between the slit width
and the pixel width. As would be expected, when Ws ≈ Wp the resolution factor is 3. When Ws ≈
2Wp the resolution factor drops to 2.5, and continues to drop until Ws > 4Wp when the
resolution factor levels out to 1.5.

All of this information can be summarized by the following equation,

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Equation 5-2

For example, if a spectrometer uses a 25µm slit, a 14µm 2048 pixel detector and a wavelength
range from 350nm – 1050nm, the calculated resolution will be 1.53nm.

Part 6: Choosing a Fiber Optic

Overview

When configuring a spectrometer for a given

experiment, one of the commonly overlooked considerations is in choosing the best fiber optic
cable. Although there are many different factors to consider for this choice, this section will
focus on the following two key factors: core diameter and absorption.

First, we will briefly review what a fiber optic cable is and how it is used to direct light into a
spectrometer. Then, we will discuss the two characteristics stated above and why they are
important for determining the throughput of the fiber optic.
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Technical Details:

A fiber optic can be thought of as a “light pipe”. If you consider how the pipes in a home direct
water from one location to another by guiding it through twists and turns to the desired location,
you can recognize that fiber optics guide light waves in a similar fashion. Instead of directing
light to a bathroom or kitchen, though, we are interested in guiding the light into a spectrometer
or other optical detection system. This is achieved by a process known as total internal
reflection.

In order to understand how total internal reflection is achieved, we must first look at the optical
property known as refraction. Refraction arises because the speed of light varies based on the
material it is traveling through. As a result, when light transitions from one medium to another,
the angle at which the light is traveling is retarded relative to the interface.

The refracting power of a material is defined as

Equation 6-1

where n is the index of refraction, v is the speed of light in the medium of interest, and c is the
speed of light in a vacuum. For example, the index of refraction of air is 1.000293, which shows
that the speed of light in air is almost exactly the same as it is in a vacuum, whereas the index
of refraction of water is 1.333, showing that light travels 25% slower in water than in a vacuum.

The relationship between the index of refraction and the angle at which light travels is defined
by Snell’s law

Equation 6-2

From this equation, we can see that the refracted angle (θ2) is dependent on the ratio of the
indices of the two materials (n1/n2) as well as the incident angle (θ1). As a result, by controlling
the ratio of the indices, one can engineer the refracted angle such that all of the light is reflected
back from the interface. This is known as total internal reflection and is the method that allows
for light to be contained and guided inside of a fiber optic.
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Figure 6-1

Figure 6-1 illustrates how a fiber optic is designed to facilitate total internal reflection by using
two different types of glass, a lower index cladding, and a higher index core in order to trap the
light within the core of the fiber and guide it through the fiber optic. This ability to collect light
from one place and direct it to another is the reason fiber optic cables are the ideal solution for
coupling light into a spectrometer.

Core Diameter:

Since all of the light in a fiber optic is collected in the core, the diameter of the core directly
correlates to the amount of light that can be transmitted. Based on this principle, it would seem
intuitive that a larger core diameter will improve the sensitivity and signal-to-noise ratio of a
spectrometer. While this is true to a certain extent, there are other limiting factors that need to
be considered when selecting the right fiber optic.

The first thing to consider is the pixel height of the detector. As shown in previous sections,
the optical bench of a spectrometer is designed to form an image of the slit onto the detector
plane. If the detector pixels are only 200µm in height and you select a 400µm core fiber, 50%
of the light incident on the detector is wasted. In this case, there appears to be no advantage
gained from having a larger core, but there is a way to get around this issue by adding a
cylindrical lens into the optical bench in front of the detector.
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Figure 6-2 Signal Intensity for Various Core Diameters with a Cylindrical Lens Installed

The cylindrical lens focuses the image of the slit in the axis orthogonal to the array without
distorting the image along the axis parallel to the array in the detector plane. This allows for
the light from the entire core to be directed onto the pixel, greatly increasing the sensitivity of
the overall setup. Figure 6-2 shows that this approach works quite well up to a 600µm core
fiber.

Absorption:

Another important factor to consider is the absorption properties of the fiber optic. If the light
is absorbed by the fiber, it will never be detected by the spectrometer.

During the traditional manufacturing process for fiber-optics, OH- ions are inadvertently doped
into the glass by the plasma torches used to soften the bulb so that it can be drawn into fibers.
The presence of these ions creates very strong absorption bands (known as water peaks) in the
NIR, which can greatly interfere with the ability to make broad band measurements through
this region. In order to avoid this when using fiber optics for NIR spectroscopy, fiber optics
need to be manufactured using special low OH - plasma torches.
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Figure 6-3

Inversely, there are also severe absorption properties in the UV spectrum. This property arises
from a photo-chemical effect known as solarization, which worsens over time with extended
UV exposure, especially below 290nm.

For these reasons, it is extremely important to pay close attention when selecting a fiber for a
specific application. When operating in the NIR spectra, make sure to choose low OH - fibers
optics (also commonly called NIR fiber optics). When working in the visible and near UV
spectral region, standard fiber optics commonly referred to as UV fiber optics are acceptable.
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Part 7: Fiber Optic Bundles

Overview

For many spectroscopic applications, proper

sampling requires more than just a simple fiber optic patch cord. In cases that require you to
measure various samples simultaneously or those that require improved signal to noise ratio
(as in the case of weak signals), the use of fiber optic bundles are required. In this section, we
will discuss the advantages and disadvantages of some common fiber optic bundle
configurations.

Fiber Optic Bundles:

A fiber optic bundle is defined as any fiber optic assembly that contains more than one fiber
optic in a single cable. The most common example of a fiber optic bundle is known as a
bifurcated fiber assembly. The goal of using a bifurcated fiber assembly is either to split a
signal or to combine signals. Figure 7-1 shows an example of a typical bifurcated fiber
assembly.
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Figure 7-1 Example of a Bifurcated Fiber Assembly

Some of the most common applications for bifurcated fiber assemblies are those that require
you to direct light from a sample into two different spectrometers. This is generally used to
extend the spectral coverage of the measurement, either to maintain higher resolution, or to
cover an extended range. For example, if someone is looking to make a broadband
measurement from 350 – 1700nm, they need to use both an InGaAs and a Si detector array. By
using a bifurcated fiber assembly with one UV fiber and one NIR fiber to direct light into each
spectrometer, they can make a simultaneous measurement. Figure 7-2 shows an example
spectrum of this type of measurement.

Figure 7-2 Spectrum of a Tungsten Halogen Lamp from 350 – 1700nm

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A bifurcated fiber can also be used to couple the signal from multiple samples into the same
spectrometer. When using a bifurcated fiber in this fashion, only one sample can emit light at
a time, or special care should be taken to make sure the signals do not have spectral overlap.

The same basic principal and applications can be scaled up to trifurcated and quadfurcated fiber
assemblies as well. An example of a trifurcated fiber assembly is shown in Figure 7-3 below.

Figure 7-3 Trifurcated Fiber Assembly

Another common bundled fiber optic assembly is called a “round to slit” configuration. This
configuration consists of multiple small core fibers (typically 100µm) that are put into one fiber
assembly with fibers bundled tightly in a circular fashion on one end, and stacked linearly on
top of each other on the other end. The end with fibers stacked linearly on top of one another
form a pattern to match the entrance slit of the spectrometer, as shown in Figure 7-4 below.

Figure 7-4 “Round to Slit” Fiber Optic Bundle

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This configuration allows for much higher throughput into the spectrometer, as opposed to
simply using a larger core fiber. As shown in Figure 7-5 below, when a large core fiber is
placed in front of the entrance slit of a spectrometer, the majority of the light is vignetted and
doesn’t make it into the spectrometer. By contrast, when the smaller fibers are stacked along
the entrance slit, significantly more light enters into the spectrometer. This allows for much
higher sensitivity and signal to noise, while maintaining resolution, since the slit can remain
relatively narrow.

Figure 7-5 Comparison of Stacked Fiber to Single Large Core Fiber

When using a fiber optic assembly with a slit configuration, it is important to remember two
important details. First, in order to get any benefit from the fiber stacking, a cylindrical lens
must be used to prevent the vast majority of the light to be imaged above and below the
detector. Second, it is important to properly align the fiber stack to the entrance slit, which can
be done by shining light into the round end of the assembly and monitoring the signal as the
fiber is rotated in the SMA905 connection port. When peak signal is achieved, the fiber can
then be screwed down to lock the position. One very common application using this kind of
fiber optic assembly is NIR transmission spectroscopy, where there are very few photons and
photon energy is extremely low. An example of a transmittance setup is shown below in Figure
7-6.
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Figure 7-6 Example Transmittance Setup Utilizing a “Round to Slit” Fiber Bundle

By combining various combinations of single, round, and stacked configurations with regular,
bifurcated, trifurcated, and quadfurcated fiber assemblies, there are countless options available
to suit any application. In the next section, we will discuss how to combine fiber bundles with
other various opto-mechanical components to create more specific applications.

5. Discussions:
Firstly: initial adjustment telescope. We need get clear to the object then its ready to get parallel
race.
Secondly: we need to make prepare collimator to get sharp image of the slit.
Thirdly: prism table will be done with sprit level. Sprit level put over on the prism table there
has three screw to move center of the sprit level.

Now the telescope is ready to gating normal incidence.

The slit adjusted to consider with the vertical crosswire in this position the main scale will be
reading, so main scale is 10
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Now I have to more the telescope 90 and fixed. Now value of the main scale 100
Grating holder is rotated slowly tell the reflexed image from the grating consider with the
vertical crosswire. In this position grating table fixed. Now the angle of the incidence 45 then
turn the Vernier table exactly 54. Now the main scale reading 55. Now the greeting normal
adjust to the light. Now it’s okay. We can rotate the telescope directly. Now we are able to
measure different color just move the telescope and read the scale.

In order to take a reading of the angle at which the spectrometer is set, do the following:

1. Take a reading from the main scale: read the number opposite the marking "0" on the
vernier scale. ...
2. Take a reading from the vernier scale, which gives the number of arcminutes away from
the half-degree determined above.

6. Conclusion:
The semiconductor spectrometer proved its capability to characterise the dosimetric
characteristics of complex radiation fields on-board aircraft. Of course, additional effort is
needed to improve its performance. Further calibration of it in the CERN-EC reference fields
is necessary. The accumulation of further on-flight data is also necessary; particularly it would
be important to perform on-board measurements in situations when the relative contributions
of both components are sufficiently different (comparison of routes close to geomagnetic poles
and to the equator). Both these approaches are in further progress in our laboratories.
The future of spectrophotometry lies especially in the improvement of pathological diagnostics,
disease detection and general clinical research as “uv-vis spectroscopy enables safer, non-
invasive analysis of soft tissue, and can enhance accuracy and speed in clinical diagnostics and
medical research