Download optical design of an echelle grating based atomic emission

ICOP 2009-International Conference on Optics and Photonics
CSIO, Chandigarh, India, 30 Oct.-1 Nov. 2009
OPTICAL DESIGN OF AN ECHELLE GRATING BASED ATOMIC EMISSION
SPECTROMETER FOR SIMULTANEOUS SPECTRO-CHEMICAL ANALYSIS.
D V Udupa and Sanjiva Kumar
Spectroscopy Division
Bhabha Atomic Research Centre, Mumbai 400 085
Email: [email protected]
Abstract: The optical design of an atomic emission spectrometer useful for simultaneous spectrochemical analysis of up to 51 elements is presented. The spectrometer consists of two concave spherical
mirrors, an echelle grating having frequency of 79 lines/mm, and a CCD detector for recording the
spectral lines in two-dimensional format. The instrument has a wavelength range of 2000 - 4000 Å with a
resolving power of 15000. The range of grating orders used is 60 – 120. Fused silica Littrow prism is
used to sort the different spectral orders to avoid their overlapping in the focal plane of the instrument.
The focal lengths for the collimating mirror and focusing mirror have been calculated to be 250 mm and
175 mm respectively for covering the full wavelength range with minimum repetition over the detector
area of 13 mm X 13 mm. The reciprocal linear dispersion of the instrument is 3.49 Å/mm at a wavelength
of 3000 Å.
1. INTRODUCTION
An optical spectrometer is the core of an analytical
system based on atomic emission spectroscopy (AES).
The spectrometer records the intensities of various
spectral lines in the emission spectrum, which is then
used for the determination of the concentration of
different elements simultaneously. Traditionally a
Rowland
circle
mounted
concave
grating
polychromator consisting of multiple exit slits and
photo-multiplier detectors (PMT) is used for
simultaneous multi-element analysis[1-2]. This type of
instrument has several drawbacks such as the number
of spectral lines recorded are limited due to physical
limitations in mounting many exit slits. The instrument
also lacks the flexibility of changing the analytical lines
at will since the slits are positioned permanently. An
echelle grating based spectrometer with a charge
coupled device (CCD) detector overcomes these
limitations by allowing continuous recording of lines in
the entire wavelength band of the instrument. A higher
signal to noise and the simplicity in data acquisition
due to the use of a single detector are added
advantages. The echelle grating spectrometer is also
much more compact than a concave grating
polychromator of equivalent resolution.
We describe here the optical design and development
of an echelle grating spectrometer useful for
simultaneous spectrochemical analysis of 51 impurity
elements using AES.
2. OPTICAL DESIGN
The basic principle of an echelle spectrometer is to
record the spectrum dispersed by a diffraction grating
at a high order of interference[3-4] in order to have a
higher dispersion and hence a higher resolution for the
same size of the instrument. A low dispersing element
(order sorter) is employed in order to separate out the
overlapping orders of diffracted light, which is present
in higher orders by dispersing in a direction
perpendicular to the grating dispersion. We have used
a fused silica prism as an order sorter in our instrument.
Focusing
Mirror
2-D CCD
Detector
(M2)
Order Sorter
Prism
(P)
Entrance
Slit
φ
(G)
Echelle
Grating
Collimating
Mirror
(M1)
Fig. 1. Schematic optical layout of the echelle
spectrometer.
A schematic diagram of the echelle spectrometer is
shown in Fig. 1. The design employs a CzernyTurner[5] type of configuration with the addition of a
Littrow prism as another dispersing element. Light
from an entrance slit is collimated by M1 and is
dispersed by a littrow prism and an echelle grating in
mutually perpendicular directions. The dispersed light
is focused on a 2-D detector to record an echellogram.
The focal length of mirror M2 has been calculated
based on the dispersions of the echelle grating and the
size of the detector so that all the wavelengths in the
range of 2000-4000 Å are covered with minimum
overlap from different orders. The prism has been
designed to give a proper dispersion to separate the
overlapping orders in the full wavelength range.
3. GRATING AND PRISM DISPERSION
The general theory of the echelle grating has been
discussed by Harrison[6]. The diffraction of the grating
is described by the grating equation as follows:
d (sin α + sin β) = mλm
(1)
where, m is the spectral order number, d is the
groove spacing, and α and β are the angles of
incidence and diffraction, respectively, measured from
the grating normal. It follows from eq. (1) that all the
wavelengths λk diffracted in spectral order k, and
satisfying the condition
k . λk = m . λm
(2)
emerge from the grating in the same direction and
hence will overlap. An order-sorter having a low
dispersion in the perpendicular direction is essential for
separating overlapping spectral orders in echelle
gratings. The reciprocal linear dispersion is given by:
dλ / dl = d . cos β / m . f2
(3)
where f2 is the focal length of the focusing mirror in the
instrument.
In order to record the complete spectral range on the
detector plane with minimum overlap, we calculate the
angular spread ∆β in the grating diffraction. If φ is the
angle between incident and refracted ray at the grating
(See Fig. 1), we have from eq. (1)
ΨC = d(sin(θB + φ/2) + sin(θB - φ/2))
(4)
where θB is the blaze angle and ΨC = mC λC for the
central wavelength. The maximum and minimum
orders diffracted at the same angle are related to
maximum and minimum wavelength as
mmax = ΨC /λ min and mmin = ΨC /λ max
(5)
The parameter Ψ varies from Ψmax to Ψ min in the
grating dispersion direction. The values of Ψmax and
Ψmin must be such that all wavelengths in the range
must be covered with minimum overlap. This is
possible if we have the wavelengths corresponding to
Ψmin for all orders to be less than or equal to the
wavelengths corresponding to Ψmax for the next
consecutive order. Since wavelength dispersion is
largest for the highest wavelength, we have the
condition:
Ψmax / (mmin +1) = Ψmin / mmin
(6)
To the first approximation if we assume a nearly linear
dispersion we have
Ψmax + Ψmin = 2ΨC
(7)
For an echelle grating of ruling frequency 79 lines/mm,
θB = 74°, and choosing minimum possible φ = 14° from
physical considerations, we get the parameters :
mmin = 60, mmax = 120, Ψmax = 243539 Å, Ψmin =
239547 Å and ∆β = 4.45°. For a detector size of 13.3
mm X 13.3 mm the focal length f2 of M2 is calculated
to be 175 mm from the relation:
f2 =L / (2 tan (∆β /2))
(8)
where L = 13.3 mm.
The prism apex angle has been calculated to be 22.5°
for dispersion of light from 2000-4000 Å over a length
of 13.3 mm.
4. ABERRATIONS
The major aberration in the system is astigmatism,
spherical aberration and coma. While coma is corrected
to a large extent due to the use of off-axis angles of the
focusing and collimating mirrors in opposite directions
as in a Czerny-Turner mount[5], spherical aberration is
reduced due to the use of f/9 system design. The effect
of astigmatism elongates the spectral lines on the
detector plane, which is at the tangential image plane of
M2 and is again restricted by the limiting of sagittal
field by means of an aperture stop.
4. ASSEMBLY AND ALIGNMENT
The echelle grating used in the instrument has 79
lines/mm, a ruled area of 254 mm X 128 mm, and a
blaze angle of 740. The entrance slit is a square aperture
of 40 µm X 40 µm. Mirrors M1 and M2 are 250 mm
and 175 mm focal length respectively with aluminium
high reflection coatings. The Littrow prism is 35 X 70
X 40 mm3 made of fused silica with aluminium high
reflection coating. The mirrors and the prism, which
were fabricated in-house have a surface accuracy of
λ/8 and angle accuracies of 30 arc-seconds. The
grating dispersion is horizontal and the prism
dispersion is vertical. A CCD detector of 13.3 mm X
13.3 mm having 1024 X 1024 pixels has been chosen
to record the spectra in 2-dimensional format. All the
components are mounted rigidly to avoid any relative
vibrations between them. The slit was placed precisely
at the focal point of M1. This was ascertained by
checking the collimation of a laser beam focused at the
slit aperture using Murty’s interferometer[7]. The
precise alignment of the grating and the prism at the
desired angles were verified by recording spectrum
from a mercury spectral lamp. A reciprocal linear
dispersion of 3.49 Å/mm for 3000 Å corresponds to a
resolution of 0.15 Å considering at least three pixels
necessary for resolving.
5. CALIBRATION AND TESTING
6. CONCLUSION
The wavelength calibration of the spectrometer is
complicated due to superposition of two different
dispersions with multiple orders. Consequently, many
known wavelengths in each diffraction orders are
needed. Emissions from several standard singleelement hollow-cathode lamps of various elements
such as Fe, Mg, Mn, Be, Co, Cu etc were utilized for
the wavelength calibration. Exact pixel positions on
the detector plane were identified for many prominent
and easily identifiable spectral lines emitted by the
lamps. This data is then utilized for assigning the exact
wavelengths and their diffraction orders corresponding
to other emission lines covering the entire area of the
detector. Figure 2 shows the emission spectra of the
element Tungsten as recorded by the echelle
spectrometer. The grating dispersion is in horizontal
direction whereas prism dispersion is the vertical
direction.
An echelle spectrometer useful for simultaneous
spectro-chemical analysis of 51 elements has been
designed and developed indegeneously. The instrument
has a wavelength range of 2000 - 4000 Å with a
resolving power of 15000. The optical design of the
instrument incorporating a two dimensional spectra to
be recorded on a CCD detector is presented. The
resolution at 2500 Å has been measured to be 0.17 Å.
REFERENCES
[1] R. P. Shukla et. al. “Design, Fabrication and
Performance Evaluation of a 22-Channel Direct
Reading Atomic Emission Spectrometer using
Inductively Coupled Plasma as a Source of Excitation”
Sadhana 25 (1), 57 (2000)
[2] Skoog, D. A., Hollar, F.J., Nieman, T.A.,
“Principles of Instrumental Analysis”, 5th edition, ,
Haircourt Brace & Co. 237 pp (1998)
[3] Skoog, D. A., Hollar, F.J., Nieman, T.A.,
“Principles of Instrumental Analysis”, 5th edition, ,
Haircourt Brace & Co. 160, 236, 240 pp (1998)
[4] Rudolf Kingslake (1969). Applied Optics and
Optical Engineering Vol.5, Part 2, Academic Press,
New York, 41, 43, 56 pp.
Fig. 2. Spectra of the element tungsten in the 2100 –
3000 Å region recorded using the echelle spectrometer.
As a test of resolution, two close emission lines of
beryllium having wavelength separation of 0.17 Å
(λ=2494.73 Å and 2494.56 Å) was recorded and seen
to be well resolved as shown in Fig. 3. The image is
recorded with an entrance slit size of 20 µm X 40 µm.
Fig. 3. An enlarged section of the beryllium spectrum
showing the resolved image of emission lines (2494.73
Å and 2494.56 Å) separated by 0.17 Å.
[5] M.V.R.K. Murty, “Theory and Principle of
Monochromators, Spectrometers and Spectrographs”,
Optical Engineering, 13 (1), 23 (1974)
[6] G. R. Harrison, J. Soc. Opt. Am. 39, 522 (1949)
[7] M V R K Murty, “The use of a single plane parallel
plate as a lateral shearing interferometer with a visible
gas laser source”, Appl. Optics, 3 531 (1964).