Application of a Fizeau Interferometer to
Fast High Resolution Measurements of the
Spectral Line Shapes of Plasma Species
i 
I S Falconer, O Novak, R Sanginé, D R McKenzie and M M M Bilek
School of Physics, University of Sydney, AUSTRALIA
ABSTRACT
An interferometer has been developed for fast, time resolved, high resolution measurements of the shape of
spectral lines emitted by ionized and neutral atoms in pulsed plasmas. This system provides a valuable diagnostic
tool for measuring the pressure broadening and especially the Doppler broadening -- and shift -- for emission lines
from plasma species. As the primary dispersing element is an interferometer, this instrument has a higher
resolution combined with a higher optical throughput than a grating spectrometer of comparable physical
dimensions. This instrument is a combination of a Fizeau interferometer, an intensified CCD camera and a grating
spectrometer, and has been used to obtain time-resolved spectral line shapes for species emitted from the cathode
spots of a high-current cathodic arcs. We will discuss the factors affecting the spectral resolution and optical
throughput of this instrument, give examples of spectral line shapes recorded by it, and discuss its calibration to
determine the shift of the centre of the line profile.
Effect of the inclination of the incident beam on the instrumental function of the
interferometer
The instrumental function of an interferometer is the response of the instrument to a monochromatic beam
of light. When the angle of incidence in the wedge plane of a perfectly collimated beam of light a is varied,
both the position of the maximum and the shape of the instrumental function change. This is illustrated in
Fig. 3 where the angle of incidence of the beam in the
wedge plane is plotted for three different values of a. The
parameters for these calculations are shown in the table
The effect of the inclination of a perfectly collimated beam at
an angle β in the plane perpendicular to the wedge plane is
to increase the effective plate spacing by
Introduction
heff 
An instrument has been developed to measure the spectral line shape of ionized and neutral atoms of
cathode material ejected from the cathode spots of a pulsed cathodic arc, with the objective of determining
the velocity distribution of these species. High spectral resolution is essential if we are to obtain detailed
spectral line profiles for determining the details of the Doppler broadened line profile. For weak light sources
or fast plasma processes the optical system must have a high étendue1 (optical throughput), and in a case
of fast varying plasma such as pulsed magnetron or cathodic arc plasma, it is essential to gate the detector
open for a short time interval to achieve high time resolution. These characteristics are well satisfied with an
interferometer coupled to a gated intensified CCD camera.
Two fundamental quantities characterizing any spectroscopic instrument are its resolving power and
étendue.
•
•
The resolving power is the ratio of the wavelength to the full width at half maximum intensity of the line
profile recorded when the interferometer is illuminated by a monochromatic beam of light.
The étendue is the product of the area of the source and the solid angle subtended by the entrance pupil
of the spectroscopic instrument at the source and is constant for a given instrument.
Fabry-Perot2
It can be shown that the étendue of a
or Fizeau interferometer is between ~30 and ~400 times
greater than that of a grating instrument with the same resolving power, and the same projected area of the
dispersive element as seen by the incident beam of light. A Fizeau interferometer, which produces equally
spaced parallel fringes, was selected for this application as its wavelength dispersion is linear, and thus
analysis of the recorded fringe shapes is straightforward.
h
cos 
Parameters for calculations of the fringe shape
Wavelength of light λ
546.075
Focal length of the collimating lens f
300 mm
Diameter of aperture d
1.8 mm
Wedge angle θ
4x10-5 radian
Reflectance of interferometer
plates R
95.75
Plate separation h
0.56 mm
Beam direction in the wedge plane α
0
Beam direction in a plane normal
to the wedge plane β
0
Fig.3 The effect of the inclination of a
perfectly collimated beam on the
position of the peak and the shape of
Fizeau fringes.
Effect of a source of finite size
In order for sufficient light to be collected by the
instrument it is necessary to use an aperture of finite size
rather than a point source. Each point on this aperture
generates a set of parallel rays illuminating the
interferometer, each of which will have its maximum at a
different position along the interferometer plates (and a
different fringe shape).. The final imperfectly collimated
beam is a superposition of all these perfectly collimated
beams, with their maximum at different positions. The
effect of an aperture of finite size on the finesse of our
system is illustrated in Fig. 4.
Sheddinglight on arc cathode spots
The instrument
The arrangement of the optical components of
the Fizeau interferometer / intensified CCD
camera system developed by our group is
shown in Fig. 1. The light collected from an
area of interest is imaged via a focusing lens on
to a fibre optic bundle which transfers the signal
to an Acton Research SpectraPro 2756
monochromator to select the spectral line of
interest. A variable diameter circular aperture,
typically set to 1.8 mm diameter, was located at
the output focal plane of the monochromator.
This aperture, together with the output of the
fiber optic array – a column of 12 fibers with a
core diameter of 1.2 mm – replaced the slits
and determined the 4 nm spectral resolution of
the monochromator. It is the diameter of this
aperture which, together with the collimating
Fig.1 The Fizeau interferometer / intensified CCD
lens, determines the étendue of the
system. The monochromator selects the wavelength
interferometer.
region of interest, while the circular aperture at the exit
slit defines the angular extent of the imperfectly
The interferometer is formed by two optically
collimated beam of light that illuminates the
flat fused silica plates, nominally flat to λ/200
interferometer. The relay lens and thee camera lens
and with a multilayer dielectric reflective
image the fringes, localized between the plates, on to
coating, inclined at a very small angle.
the intensified CCD array.
The Fizeau fringes are recorded by a PI-MAX
(Princeton Instruments) intensified CCD
camera.
The
fringes
are
imaged
On to the photocathode and release electrons which are intensified by a microchannel plate to produce an
intensified image of the fringes on the output phosphor of the intensifier. This image is transported through
a fused fiber-optic bundle to the input of a 1024x1024 pixels CCD chip. The microchannel plate is both an
intensifier and an ultra fast shutter which can be gated down to an exposure time of 25 ns
Étendue and spectral resolution: finesse and free-spectral range
As the product of étendue and spectral resolution of a Fizeau interferometer is a constant, there is
inherently a trade-off between resolution and optical throughput for interferometer plates of a particular
size. We have explored this trade-off for applications such as our, where photons are in short supply.
The wavelength dispersion is linear along the interferometer plates. The Free Spectral Range (FSR) is
the range of wavelengths between fringes of adjacent order.


FSR


2
2h
h is selected in practical applications so that the feature of interest occupies a substantial part of the FSR,
but that features corresponding to adjacent orders of interference do not overlap.
The finesse (F) of an interferometer is the ratio of the FSR to the spectral resolution  of the
interferometer.
F



The finesse is a measure of the spectral resolution that can be achieved with an interferometer for a
specified FSR – which is determined by experimental requirements.
Ideally the interferometer plates should be illuminated by parallel rays of light and these rays should be in
the wedge plane of the interferometer. To achieve this, a point source is located in the focal plane of the
collimating lens. This is an unrealistic assumption for laboratory conditions: to obtain a sufficiently high
light throughput it is necessary for a source of finite size to be located in the focal plane. The rays from a
particular point on this source will illuminate the interferometer with parallel rays, but these rays will be
inclined both in the wedge plane and at an angle normal to the wedge plane. Different points on the
source will illuminate the plates with parallel rays, but the direction of these rays will be different so that
the beam is imperfectly collimated. In order to discuss the effect of a realistic beam of light
on the fringe profile the contribution to the profile of rays from all points on a source of
finite size must be considered. The results of our analysis of the effect of illuminating the
interferometer with an imperfectly collimated beam of light is presented in this poster.
Fig.2 Resolution of a ray of light into components in the wedge plane – the plane normal
to the vertex of the wedge - and in a plane perpendicular to the wedge plane. The angle
α gives the inclination of the ray in the wedge plane relative to a normal to the second
interferometer plate and the angle β the inclination of the ray in the plane perpendicular
to the wedge plane relative to this normal. The phase shift due to the angle β is the same
as that for - β. In contrast, the angle α has a different effect on the phase shift from the
angle – α of the same absolute value.
Fig. 4. The calculated finesse as a
function of the angular extent of the beam
illuminating the Fizeau interferometer, for
the beam incident normally on the
interferometer plates. The parameters for
these calculations are as given in the
table, except for the diameter of the
circular aperture d.
Fig. 5. The calculated effect of vertical and
horizontal tilt α and β (due to shift of
aperture centre from collimating lens axis)
on the finesse of the interferometer. The
effect of varying the angle α on finesse is
represented by the blue dashed line with
triangles; that due to varying β is
represented by the red dotted line with
squares and that due to simultaneously
changing both α and β is represented by a
black solid line with circles. The
parameters of calculations apart from α
and β are given in the table.
Misalignment of the aperture also give rise to a
decrease in finesse. This is illustrated in Fig. 5.
where the contribution of finite aperture size and
misalignment are calculated
Is it a useful instrument?
We have used this interferometer to study the
broadening of the spectral lines of ionized cathode
material ejected from the cathodes of both a DC
cathodic arc and a pulsed cathodic arc.
DC arc
The experimental line shapes for three species present
in the direct current cathodic arc can be seen in
Fig. 6. There is no strong optical transition of neutral
Fig. 6. Experimental line shapes of neutral
aluminium atoms in wavelength interval λ = 438-581
magnesium atoms (red dotted line) and
nm (the wavelength interval where reflectance of our
singly and doubly ionized aluminium atoms
Fizeau interferometer plates is higher than 90%).
ejected from dc cathodic arc (blue dashed
Because of a magnesium impurity in the cathode,
line and solid black line respectively).
magnesium atoms present in the discharge provided a
suitable Mg I optical transition at 553.840 nm to enable
the investigation of the characteristics of neutral atoms ejected from the cathode spot. The width of the
neutral magnesium line observed at 553.840 nm is virtually identical to that of a reference mercury isotope
lamp line, from which it can be concluded that all effects contributing to line width (pressure, Stark and
Doppler broadening) are beyond the resolution of our instrumental setup (plate separation h = 0.56 mm) for
neutral atoms.
High current pulsed cathodic arc
Extensive examples of fringe shapes recorded for a pulsed cathodic arc are presented in Poster DTP169
(this poster session) at this conference.
Conclusion
This instrument has proved to be a useful tool for measuring spectral line shapes with both high spectral
and time resolution. With a technique we have developed for precisely measuring the plate separation, we
will aklso be able to measure absolute velocity distribution of the ejected species.
References
1.
2
W. H. Steel, Interferometry, (Cambridge University Press, 1967), p. 27-28
P. Jacquinot, J. Opt. Soc. America 44 761-5 (1954)