ABSTRACT

1. Parameters for calculations of the fringe shape Parameters for calculations of the fringe shape Application of a Fizeau Interferometer to Fast High Resolution Measurements of the Spectral Line Shapes of Plasma Species 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 lighta 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 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. It can be shown that the étendue of a Fabry-Perot2 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. • 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 lens, determines the étendue of the interferometer. The interferometer is formed by two optically flat fused silica plates, nominally flat to λ/200 and with a multilayer dielectric reflective coating, inclined at a very small angle. The Fizeau fringes are recorded by a PI-MAX (Princeton Instruments) intensified CCD camera. The fringes are imaged 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.1 The Fizeau interferometer / intensified CCD system. The monochromator selects the wavelength region of interest, while the circular aperture at the exit slit defines the angular extent of the imperfectly collimated beam of light that illuminates the interferometer. The relay lens and thee camera lens image the fringes, localized between the plates, on to the intensified CCD array. 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 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 αon finesse is represented by the blue dashed line with triangles; that due to varying βis represented by the red dotted line with squares and that due to simultaneously changing both αand βis represented by a black solid line with circles. The parameters of calculations apart from αand βare given in the table. 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. 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. 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 • 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 aluminium atoms in wavelength interval λ = 438-581 nm (the wavelength interval where reflectance of our Fizeau interferometer plates is higher than 90%). Because of a magnesium impurity in the cathode, magnesium atoms present in the discharge provided a suitable Mg I optical transition at 553.840 nm to enable Fig. 6. Experimental line shapes of neutral magnesium atoms (red dotted line) and singly and doubly ionized aluminium atoms ejected from dc cathodic arc (blue dashed line and solid black line respectively). • 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. 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 hasa different effect on the phase shift from the angle – α of the same absolute value. References 1. W. H. Steel, Interferometry, (Cambridge University Press, 1967), p. 27-28 2 P. Jacquinot, J. Opt. Soc. America 44761-5 (1954)