1. Introduction

Arcjet reactors are used for chemical vapor deposition (CVD) of diamond, GaN, and other materials. Diagnostics of these processes are useful for understanding the physics and chemistry involved in the plasma expansion, for assisting in the design of arcjet systems and establishing operating conditions, and for process control. Beam deflection is a sensitive, yet simple technique for monitoring fluid flows and plasmas. We have studied how well beam deflection tomography performs for characterization of the free stream of a low power (1 kW) dc arcjet. This work was motivated by the desire to gain understanding of the arcjet plasma plume and to test the practicality of beam deflection measurements for process control of arcjets.

ARCJETS

An arcjet is a high-pressure discharge wherein an arc is struck in a flowing, high-pressure gas that expands into low-pressure, forming a luminous plume of reactive gas with increased enthalpy and kinetic energy. Arcjet plasmas were developed as electric propulsion devices for satellite station keeping; the electric arc heats feedstock gas to high temperature, and this heating increases the specific impulse [1–3]. During the past decade, the highly reactive exhaust from these devices has been exploited for the deposition of exotic materials. The most rapid growth rates reported for diamond thin film [4,5] use an arcjet plasma similar to the one reported here. More recently, similar arcjet plasmas have been used as a source of reactants for the deposition of group III nitrides [6–8]. Commercial viability of these deposition processes requires stable arcjet operation for many hours. Thus, the development of in situ diagnostics for real-time process control of arcjet plasmas is quite desirable.

BEAM DEFLECTION TOMOGRAPHY

We have investigated the use of beam deflection tomography as a diagnostic for an arcjet reactor. When a laser beam passes through a medium with variations in refractive index, the beam is deflected by refractive index gradients. This deflection is the physical basis for the mirage effect, and is used in the photothermal deflection technique [9–11]. Beam deflection measurements are simple to implement, and can be very sensitive. Sensitivity of 35 nrad, equivalent to a change of 23,000th of a fringe across the laser beam, has been achieved [12]. Beam deflection measurements provide path-integrated measurements of the gradient in the index of refraction. Using tomographic reconstruction, multi-path beam deflection measurements at multiple positions and angles can be inverted to provide images of the index of refraction or density [13]. For the measurements reported here, we measured beam deflection angles at multiple positions but at a single angle. Such a set of measurements is called a single projection. In this case we assumed axial symmetry and performed tomography with identical projections, which is essentially a form of Abel inversion.

Beam deflection measurements and tomography are a good combination. When deflections or gradients are measured parallel to the image plane, the tomographic reconstruction inversion corrects for the gradient, directly providing images of refractive index. In addition, the filter function for reconstruction of in-plane beam deflection measurements is flat; all spatial frequencies are given equal weighting [12]. This contrasts with scalar measurement reconstruction in which low spatial frequencies are attenuated and high spatial frequencies are amplified. Tomographic reconstruction effectively differentiates the projection data when ordinary scalar measurements are used, but with beam deflection measurements the derivative has already been performed.

Beam deflection tomography has been applied to probing subsurface defects [14], three-dimensional reconstruction of gas density in cold supersonic flows [15], diffusion flames and gas mixing [16], laser-produced plasmas [17], selfoc lenses [18], liquids [19], and turbulent flames [20]. Beam deflection provides a direct electrical output proportional to the deflection angle. Thus no processing of fringe data is required, as is the case for interferometry and holography. No reference beam is required for beam deflection measurements. Differential or shearing interferometry [21] has similar advantages to beam deflection measurements.

In the arcjet the refractive indices of the plasma plume and background gas differ due to temperature and compositional variations. The arcjet plume is hotter than the background gas, leading to a lower density and refractive index in the plume. Thus the plume acts as a weak convex lens, deflecting the beam away from the plume center. When hydrogen is used, dissociation of hydrogen also causes a refractive index change as H atoms and H₂ molecules have different refractive indices [22]. Further refractive index changes can occur due to changes in the ground state population or ionization at high temperatures. For our measurements in argon, which has a very large ionization potential, changes in population distribution and ionization are small, and refractive index images can be related directly to argon density. Because of the dissociation of hydrogen, we have not attempted to relate refractive index images to density when argon/hydrogen mixtures were used.

2. Experimental Apparatus

Arcjet Reactor

The dc-arcjet reactor is the same as used for previous work [23–28]. A dc arc is struck in a gas mixture at a pressure of 6 atmospheres; this mixture ranged from pure argon to 45% argon/ 55% hydrogen. The effluent from this arc expands through a converging/diverging nozzle into a reactor maintained at a constant pressure of between 4 and 30 Torr. The free-stream flow impinges on a water-cooled molybdenum substrate normal to the flow of the plume. A blast plate shields the bottom of the chamber from the hot gas effluent. When methane at 0.5% of the hydrogen flow is injected into the diverging section of the nozzle, high quality diamond film grows at a rate of approximately 1 mm/hour. Measurements were performed using both pure argon and argon/hydrogen/methane mixtures in the arcjet reactor at a variety of reactor chamber pressures. Total gas flow rates were 7.1 to 7.5 standard liters per minute (slpm) for pure argon, and 5.8 to 6.5 slpm for the mixtures. The gas plenum pressure was 90 psi. The arcjet nozzle is mounted on a vacuum translation stage, allowing the jet to be moved vertically and enabling beam deflection measurements at different distances from the jet exit.

Heating of the windows by the arcjet plume can cause spurious beam deflections due to window distortion. To minimize these effects, we moved the windows 50-cm from the arcjet plume using 10-cm diameter stainless steel pipes with vacuum fittings. To further isolate the windows from convective and radiative heating, aluminum baffles with 2.5-cm by 10-cm slots were placed where these pipes join the main vacuum chamber at 15 cm from the jet axis.

Scanning Beam Deflection Measurement System

Previous implementations of beam deflection measurements used static laser beams with, variously, scanning of the measured object or flow field [12,14–16], time-resolved measurement of a pulse-driven expansion [17], a scanning slit [18], or multiple laser beams [19,20]. For this work, we have developed a system in which the optical beam is scanned. Scanning of a laser beam can be performed using a rotating or oscillating mirror, or acousto-optic (AO) or electro-optic (EO) deflectors. We have performed scanning beam deflection using both a rotating mirror and an acousto-optic deflector. We chose the acousto-optic deflector for all of the measurements presented here because the width of the scanning region can be easily adjusted using electronics to match the clear viewing region through the arcjet reactor. Electro-optic deflectors can scan much more rapidly than AO deflectors can, but the deflection angles are smaller and the devices are more expensive.

 

Fig. 1. Experimental apparatus for scanned beam deflection measurements.

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A schematic of the beam deflection system is given in Fig. 1. The deflection and scanning angles are exaggerated for clarity. The scanned beam is shown as a dashed line. Note that there are two types of beam deflection occurring. The first type is the large deflection in the AO deflector, which produces the swept beam. The second type is the small deflection produced by refractive index gradients in the arcjet plume. The term beam deflection tomography refers to the second type of deflection, which is the signal source for the reconstructed images.

The light source is a HeNe laser (Melles Griot 05-LHP-321; 2 mW, 0.79 mm 1/e² beam diameter, 1 mrad full angle beam divergence). The beam is swept using an AO deflector (IntraAction Corp. model ADM-40 deflector and model DE-40M deflector driver). To avoid saturating the detector, the laser beam is attenuated with a neutral density filter. Light passing through the deflector is deflected at an angle proportional to the acoustic frequency provided by the driver. The driver acoustic frequency is swept using a voltage ramp (sawtooth wave) from a function generator (Wavetek model 21).

The AO deflector provides a beam sweep angle of only 3.25 mrad. To make larger deflection angles using an AO deflector, and to maximize the number of resolvable spots, the beam is expanded using a cylindrical telescope (6.4-mm and 150-mm focal length lenses) to fill the 20 mm clear horizontal aperture of the deflector. After passing through the modulator, the beam is reduced with a second telescope (600-mm focal length spherical lens and 12.7-mm focal length cylindrical lens) as shown in Fig. 1. The resulting beam sweeps through an angle of approximately 150 mrad.

The angle-swept beam produced by the AO deflector is converted to a scanned parallel beam by a first, collimating, camera lens (400 mm focal length, f/6.3). This results in a scanning distance of about 60 mm. The scanned parallel beam passes through the arcjet chamber perpendicular to the plasma flow direction. Gradients in the path-integrated refractive index in the plasma jet produce small angular deviations (beam deflections) from the parallel set of rays. The windows on either end of the arcjet chamber were anti-reflection coated glass windows, 123 mm diameter and 6 mm thick. After passing through the chamber, the scanned parallel beam strikes a second camera lens (400 mm focal length, f/6.3) that serves two purposes. First, it collects the beam from each parallel position onto the split detector (also called a bi-cell or dual-element detector), which is at the focal plane of the lens. Second, it converts the small angular deviations from each parallel ray position into deviations in position at the split detector. Although the two camera lenses are multi-element lenses, for clarity only single lenses are shown in Fig. 1.

The split detector (Advanced Photonix, Inc. SD 113-24-21-021) comprises two identical detectors separated by a small gap. The voltage difference between each detector side is amplified using a differential amplifier, acquired using a digital oscilloscope, and stored on a personal computer. As the beam moves away from the detector center, a voltage is produced that is linear with position for small deviations. The sign of the voltage indicates the direction of deviation. Because the second, transform, camera lens converts angular deviations into position deviations at the detector, the detected signal is linearly proportional to the angular deviation at each point in the plasma jet. The split detector is oriented to measure angular deviations in the same plane as the beam scanning. The beam is scanned at a one kHz repetition rate. For the measurements described here, we averaged 256 scans, which corresponds to a measurement time of 0.26 s.

The split detector is attached to an x-y translation stage, allowing the detector to be accurately positioned at the transform lens focal plane, both longitudinally, and transversely in the scanning plane. These adjustments were performed while the beam was scanning and the arcjet was off. During a scan the signal is flattest during a scan when the detector is at the focal position longitudinally, and is closest to zero when the detector is centered on the laser beam transversely.

The second lens in the optical train (150-mm focal length cylindrical lens) was also mounted on a x-y translation stage. Longitudinal adjustment was used to adjust the focus of the beam in the arcjet chamber, and transverse adjustment was used to center the beam through the remainder of the optics train. Care was taken that the second order diffracted beam from the AO deflector was not detected, as interference between this beam and the first order beam can produce spurious deflection measurements.

There are tradeoffs in adjusting the focus through the chamber. A tighter focus in the chamber leads to better spatial resolution; however, the spot size at the detector is larger, leading to lower deflection sensitivity. A larger beam at the chamber reduces the effects of scratches on the chamber windows. Attenuation due to scratches produces spikes on the beam deflection traces. The beam was typically defocused to produce a beam width of roughly 2 mm at the chamber.

Two effects were found to be important for scanned beam deflection measurements: reflections and spherical aberrations. Reflected light that reaches the detector produces interference fringes. Light intensity changes from these fringes are a source of spurious beam deflections. We minimized the effects of reflections by using anti-reflection coatings on the optics; all optics were anti-reflection coated except for the 150-mm focal length cylindrical lens. In principle, the effects of interference fringes could also be reduced by tilting the optics or by using a broadband light source. We have not investigated these approaches.

Spherical aberrations in the collimation and transform lenses prevent the exact conversion of angle to position and position to angle expected for an ideal lens. These spherical aberrations produce small deviations at the split detector, which appear as spurious angular deflections. To reduce the effects of spherical aberrations, we used camera lenses as the collimation and transform lenses, and carefully centered all lenses in the optical train. Still, spurious angular deviations from spherical aberrations can be as large or larger than the beam deflections produced by the arcjet plume when operating at low chamber pressures. This can be compensated by measuring baseline deflection signals with the arcjet off, and subtracting these values from the signals measured with the arcjet on.

One advantage of rapidly scanned beam deflection measurements is a reduced sensitivity to vibrations. Our beam deflection measurements are performed as differential measurements across the arcjet plume. The refractive index in the plume is measured relative to the background index, and thus the measurements can be performed with ac coupling. Performing the measurements at a scan rate of 1 kHz eliminated most acoustic vibrations from the measurement.

Conversion of the measured split detector voltage to deflection angle requires calibration. Using the transverse translation stage for the detector, we measured the sensitivity of the split detector/differential amplifier combination in V/µm displacement. This factor is influenced by the laser beam size and intensity, and was measured each day. A calibration factor in V/mrad is found by multiplying the sensitivity in V/µm by focal length of the transform lens in µm.

3. Results and Discussion

An example of the measured deflection signal with the arcjet off is shown as the dashed line in Fig. 2(a). This background trace is curved due to aberrations in the lenses. Linear slopes in the background can be removed by adjusting the longitudinal position of the split detector (putting it in the transform lens focal position). We have not explored the use of correction optics to remove the background curvature.

A trace taken with the arcjet turned on using a mixture of 1 : 1 : 0.01 argon/hydrogen/ methane at a chamber pressure of 24 Torr and a distance of 24 mm from the nozzle exit is shown as the solid line in Fig. 2(a). The trace in Fig. 2(b) shows the corrected signal obtained by subtracting the background from the raw signal and using the calibration factor to produce a scale in µrad. As expected, the beam is deflected in opposite directions on either side of the plume center.

Note that the raw signal is dominated by the curvature of the background deflection signal. However, the background variations are stable. It takes approximately a half hour to acquire a full image of the arcjet plume by manually scanning the nozzle position. Comparison of background traces taken before and after acquiring an image show little change during this time, which is ample for any heating of the windows to produce changes in the background traces. Furthermore, data taken during arcjet operation also show no evidence of background changes. This can be seen from the corrected data shown in Fig 2(b). The flat baseline and the symmetry of this signal indicate that there is little change between the background beam deflection signals taken with the arcjet on and off.

 

Fig. 2. (a) Background and raw signals, (b) corrected signal (raw signal minus background) and (c) reconstructed refractive index as a function of radial distance for arcjet using a mixture of 1 : 1 : 0.01 argon/hydrogen/methane at a chamber pressure of 24 Torr and a distance of 24 mm from the nozzle exit.

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The beam deflection data can be converted to refractive index using the convolution backprojection technique, with a modified filter function appropriate for beam deflection measurements [12]. For this work we have only a single projection. Assuming axial symmetry, we perform the tomographic inversion using the same projection at 100 evenly spaced angles covering 180°. Fig. 2(c) shows the radial variation in refractive index in the arcjet plume reconstructed from the data in Fig. 2(b).

Images can be formed by acquiring line scans such as shown in Fig. 2 at different distances from the jet orifice. The optical arrangement is held stationary, and the jet nozzle is moved vertically. A set of such measurements is shown in Fig. 3(a) for pure argon and Fig. 3(b) for an 1 : 1 : 0.01 argon/hydrogen/methane mixture at chamber pressures of 31.2 and 24 Torr, respectively. These measurements were performed at a 6 mm vertical interval from the jet exit (top) to the substrate surface (bottom).

For measurements in argon, the refractive index can be directly related to gas density. Examples of reconstructed refractive index and argon density are shown in Fig. 4(a) and 4(b), respectively, for cold argon flow (argon flowing, but the arc not lit) and for argon with the arc on at chamber pressures of 5.1, 15, and 30.4 Torr. All measurements were taken at a distance of 24 mm below the jet exit. The refractive index of argon was calculated using the Sellmeier expression of Leonard [29]. For the cold gas flow there is a higher density at the center of the flow. This is the opposite of the case with the arc on where the higher temperatures of the plume create a lower density in the plume center. Note that the reconstruction provides the refractive index or density variation across the jet, but not the baseline (large distance) values of the refractive index or density. To visualize the approximate total density variation in Fig. 4(b), we calculated the background densities in Fig. 4(b) from the measured chamber pressure and approximate temperature of the background gas estimated from thermocouple measurements at the chamber wall.

We estimate the error in the reconstructed refractive index Δn to be [(0.05Δn)²+(2×10^-7)²]^1/2, which reflects the combined contributions of a 5% uncertainty in the relative refractive index (dominated by uncertainty in the deflection calibration) and minimum refractive index error of 2×10^-7 (due to noise). The errors in relative gas concentration scale accordingly. These errors are shown as the error bars in Figs 4(a) and 4(b). The uncertainty in background gas temperature results in larger error bars for measurements in Fig. 4(b) with the arcjet on.

 

Fig. 3. Reconstructed refractive index profiles as functions of distance from the nozzle exit for argon 3(a) and a 1 : 1 : 0.01 argon/hydrogen/methane mixture 3(b). The chamber pressures are 31.2 and 23.9 Torr for Figs 3(a) and 3(b), respectively.

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Fig. 4. Refractive index 4(a) and density 4(b) of argon for cold gas flow (arc off, chamber pressure of 5.2 Torr) and with the arc on at chamber pressures of 5.1, 15, and 30.4 Torr.

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Multiple line scans such as shown in Fig. 2, may also be displayed as refractive index or density images. A number of these images are shown in Figs. 5–12. The images are composed of individual line reconstructions at a vertical spacing of 2 mm.

An image of cold gas flow using pure argon is shown in false color in Fig 5. The color code is shown at the right of the image; red is high density and violet is low density. Diamond-shaped regions of alternately high and low density occur along the jet. This familiar pattern is produced by oblique shocks and expansion fans reflected from the jet boundary. Although the pressure in the jet is alternately above and below the chamber pressure, the jet density remains above the chamber density because of the lower temperature in the jet. The density increases abruptly just above the substrate due to a shock wave.

 

Fig. 5. Argon density with arcjet off and a chamber pressure of 5.2 Torr. Density range is 3.40×10¹⁷ atoms/cm³.

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Images with the arc on are shown in Figs. 6(a)–12(a). Also shown are photographs of the arcjet plume taken under the same conditions and at the same scaling [Figs. 6(b)–12(b)]. Significant differences are seen between the reconstructed and emission images. It is known that the optical emission from the luminous plume does not describe either the density or temperature distributions in the plasma plume [30–33].

The density gradients and the fluid dynamics in the arcjet plume are easier to interpret with pure argon feedstock. Therefore, our initial tests of beam deflection tomography were made on argon plumes. Images of density and optical emission for the arcjet plume using pure argon feedstock are shown for a reactor pressures of 5.3 Torr (Fig. 6), 15 Torr (Fig. 7), and 30.4 Torr (Fig. 8). Optical emission from the argon appears blue in the photograph due to the strong argon emission lines between 450 and 480 nm. Regions of intense emission appear white because argon has emission lines all across the visible spectrum and the photographic film has limited dynamic range.

The flow pattern of the plume is evident in the tomographic reconstruction of density. In general, the tomographic reconstruction of gas density gives a very different picture of the radial transport of hot plume gases than does the optical emission photograph. Diamond-shaped density variations similar to that of Fig. 5 are quite apparent in Figs. 6(a) and 6(b) and the upper portion of Figs. 7(a) and 7(b). The locations of these variations are well correlated in the density images and the photographs. Note that each diamond region has a lower density than the previous one in Figs. 5–7. This is expected as the stagnation pressure drops across shock waves while the stagnation temperature remains constant [34]. The diamond patterns are clearly seen all the way to the substrate at chamber pressures near 5 Torr (Figs 5 and 6) but only evident in the upper half of the flow at 15 Torr (Fig. 7). There is little evidence of these patterns at 30.4 Torr (Fig. 8). Apparently, turbulent mixing with the background gas is causing the flow to become subsonic. The transition to subsonic flow should occur at shorter distances as the chamber pressure increases, which is what we have observed. The fact that the flow is supersonic all the way to the substrate near 5 Torr is confirmed by the presence of shock waves just above the substrate [Figs. 5(a) and 6(a)]. The higher pressure measurements [Figs. 7(a) and 8(a)] show no shock waves over the substrate, and the flow responds to the presence of the substrate well upstream (about 1 cm above the substrate). Both facts are consistent with subsonic flow at the substrate. Figures 7(a) and 8(a) show the lowest density just above the substrate. Increased local velocities when the subsonic flow changes direction at the substrate or heating by the substrate may produce the lower gas density in this region.

Figs. 9–12 show images of the arcjet plume with a mixture of hydrogen and argon in the feedstock and 1% methane added in the exit nozzle. Diamond film is deposited on the water-cooled molybdenum substrate for these conditions. The interpretation of the index of refraction is more complicated with hydrogen feedstock because the refractive index image is influenced by both density and hydrogen dissociation. Again, we find significant differences between the tomographic reconstruction of refraction index and the optical emission photograph.

Fig. 9(a) demonstrates that images from beam deflection tomography are possible at reactor pressures as low as 4 Torr with a feedstock of 45% argon and 55% hydrogen. The addition of hydrogen significantly alters the flow behavior. The plume at 4 Torr rapidly expands in radius after exiting the nozzle. The substrate influence on radial transport does not extend as far above the substrate as it does in Fig. 6–8.

Fig. 10 shows the plume for an 11.4 Torr reactor pressure with a feedstock of 60% argon and 40% hydrogen. The substrate-induced radial transport begins only 8 mm above the substrate surface. However, in contrast to the case at 4 Torr, the plume at this higher pressure is much more sharply defined. Again, the optical emission photograph does not depict the physical dimensions.

Figs. 11 and 12 show the plume for a 30.4 Torr reactor pressure with hydrogen content of 32% and 51%, respectively. At the higher pressure, the substrate influence on radial transport is reduced and extends only 5 mm above the substrate surface. The plume becomes even more sharply defined, and the density/hydrogen-dissociation is nearly uniform between the nozzle exit and the substrate. The addition of hydrogen increases radial transport in Fig. 12(a) as compared with Fig. 11(a).

4. Summary and Conclusions

We have demonstrated a new scanning beam deflection technique and applied this technique to imaging a 1 kW arcjet reactor. Good images are obtained at chamber pressures as low as 4 Torr. Measurements can be performed at a 1 kHz scan rate, which is adequate for process control. It appears that the techniques can be scaled to larger arcjet reactors provided that care is taken regarding window quality and isolating the windows from thermal effects from the plume.

Acknowledgments

This work was supported by the U.S. Defense Advanced Research Projects Agency. We thank Professor Mark Cappelli of Stanford University for the design and loan of the dc arcjet nozzle. We acknowledge helpful conversations with Dr. Donald Eckstrom of SRI International.

 

Fig. 6. Argon density 6(a) and optical emission 6(b) for pure argon and a chamber pressure of 5.3 Torr. Density range in Fig 6(a) is 1.41×10¹⁷ atoms/cm³.

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Fig. 7. Argon density 7(a) and optical emission 7(b) for pure argon and a chamber pressure of 15.0 Torr. Density range in Fig 7(a) is 3.09×10¹⁷ atoms/cm³.

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Fig. 8. Argon density 8(a) and optical emission 8(b) for pure argon and a chamber pressure of 30.4 Torr. Density range in Fig 8(a) is 5.53×10¹⁷ atoms/cm³.

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Fig. 9. Refractive index 9(a) and optical emission 9(b) for a 1 : 1.2 : 0.01 argon/hydrogen/ methane mixture and a chamber pressure of 4.1 Torr. Refractive index range in Fig 9(a) is 1.55×10^-6.

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Fig. 10. Refractive index 10(a) and optical emission 10(b) for a 1 : 0.6 : 0.01 argon/ hydrogen/methane mixture and a chamber pressure of 11.4 Torr. Refractive index range in Fig 10(a) is 2.85×10^-6.

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Fig. 11. Refractive index 11(a) and optical emission 11(b) for a 1 : 0.5 : 0.01 argon/ hydrogen/methane mixture and a chamber pressure of 24 Torr. Refractive index range in Fig 11(a) is 5.47×10^-6.

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Fig. 12. Refractive index 12(a) and optical emission 12(b) for a 1 : 1 : 0.01 argon/ hydrogen/methane and a chamber pressure of 24 Torr. Refractive index range in Fig 12(a) is 5.21×10^-6.

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References and Links

1. J. G. Liebeskind, R. K. Hanson, and M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993). [CrossRef]   [PubMed]  

2. I. J. Wysong and J. A. Pobst, “Quantitative two-photon laser-induced fluorescence of hydrogen atoms in a 1 kW arcjet thruster,” Appl. Phys. B 67, 193–205 (1998). [CrossRef]  

3. D. G. Fletcher, “Arcjet flow properties determined from laser-induced fluorescence of atomic nitrogen,” Appl. Opt. 38, 1850–1858 (1999). [CrossRef]  

4. K. Kurihara, K. Sasaki, M. Kawarada, and N. Koshino, “High rate synthesis of diamond by dc plasma jet chemical vapor deposition,” Appl. Phys. Lett. 52, 437–438 (1988). [CrossRef]  

5. N. Ohtake and M. Yoshikawa, “Diamond film preparation by arc discharge plasma jet chemical vapor deposition in the methane atmosphere,” J. Electrochem. Soc. 137, 717–722 (1990). [CrossRef]  

6. D. H. Berns and M. A. Cappelli, “Cubic boron nitride synthesis in low-density supersonic plasma flows,” Appl. Phys. Lett. 68, 2711–2713 (1996). [CrossRef]  

7. F. J. Grunthaner, R. Bicknell-Tassius, P. Deelman, P. J. Grunthaner, C. Bryson, E. Snyder, J. L. Giuliani, J. P. Apruzese, and P. Kepple, “Ultrahigh vacuum arcjet nitrogen source for selected energy epitaxy of group III nitrides by molecular beam epitaxy,” J. Vac. Sci. Technol. A 16, 1615–1620 (1998). [CrossRef]  

8. L. J. Lauhon, S. A. Ustin, and W. Ho, “Large area supersonic jet epitaxy of AlN, GaN, and SiC on silicon,” in III-V Nitrides. Symposium, edited by F.A. Ponce, T.D. Moustakas, and I. Akasaki et al. (Mater. Res. Soc., Pittsburgh, PA, 1996), pp. 277–282.

9. W. B. Jackson, N. M. Amer, A. C. Boccara, and D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981). [CrossRef]   [PubMed]  

10. W. Zapka and A. C. Tam, “Noncontact optoacoustic determination of gas flow velocity and temperature simultaneously,” Appl. Phys. Lett. 40, 1015–17 (1982). [CrossRef]  

11. M. Bertolotti, G. Liakhou, R. Livoti, F. Michelotti, and C. Sibilia, “Method for thermal-diffusivity measurements based on photothermal deflection,” J. Appl. Phys. 74, 7078–7084 (1993). [CrossRef]  

12. G. W. Faris and R. L. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212 (1988). [CrossRef]   [PubMed]  

13. G. W. Faris and R. L. Byer, “Beam-deflection optical tomography,” Opt. Lett. 12, 72–74 (1987). [CrossRef]   [PubMed]  

14. D. Fournier, F. Lepoutre, and A. C. Boccara, “Tomographic approach for photothermal imaging using the mirage effect,” J. Phys. Colloque 44 (C6), 479–482 (1983).

15. G. W. Faris and R. L. Byer, “Quantitative three-dimensional optical tomographic imaging of supersonic flows,” Science 238, 1700–1702 (1987). [CrossRef]   [PubMed]  

16. G. W. Faris and R. L. Byer, “Beam-deflection optical tomography of a flame,” Opt. Lett. 12, 155–157 (1987). [CrossRef]   [PubMed]  

17. G. W. Faris and H. Bergstrom, “Two-wavelength beam deflection technique for electron density measurements in laser-produced plasmas,” Appl. Opt. 30, 2212–2218 (1991). [CrossRef]   [PubMed]  

18. O. Sasaki and T. Kobayashi, “Beam-deflection optical tomography of the refractive-index distribution based on the Rytov approximation,” Appl. Opt. 32, 746–751 (1993). [CrossRef]   [PubMed]  

19. Y. A. Andrienko, “Optical ray deflection tomography with fan-shaped beams,” Proc. SPIE 2122, 217–225 (1994). [CrossRef]  

20. K. Gerstner, A. Fehl, J. Otten, D. Neidhardt, and T. Tschudi, “Continuous temperature measurements in turbulent combustion by laser beam deflection tomography,” Proc. SPIE 3172, 400–404 (1997). [CrossRef]  

21. G. W. Faris and H. M. Hertz, “Tunable differential interferometer for optical tomography,” Appl. Opt. 28, 4662–4667 (1989). [CrossRef]   [PubMed]  

22. J. Gardiner, W. C., Y. Hidaka, and T. Tanzawa, “Refractivity of combustion gases,” Combustion and Flame 40, 213–219 (1981). [CrossRef]  

23. G. A. Raiche and J. B. Jeffries, “Laser-induced fluorescence temperature measurements in a dc arcjet used for diamond deposition,” Appl. Opt. 32, 4629–4635 (1993). [CrossRef]   [PubMed]  

24. E. A. Brinkman, G. A. Raiche, M. S. Brown, and J. B. Jeffries, “Optical diagnostics for temperature measurement in a DC arcjet reactor used for diamond deposition,” Appl. Phys. B 64, 689–697 (1997). [CrossRef]  

25. W. Juchmann, J. Luque, and J. B. Jeffries, “Atomic hydrogen concentration in a diamond depositing dc arcjet determined by calorimetry,” J. Appl. Phys. 81, 8052–8056 (1997). [CrossRef]  

26. J. Luque, W. Juchmann, and J. B. Jeffries, “Absolute concentration measurements of CH radicals in a diamond-depositing dc-arcjet reactor,” Appl. Opt. 36, 3261–3270 (1997). [CrossRef]   [PubMed]  

27. J. Luque, W. Juchmann, and J. B. Jeffries, “Spatial density distributions of C₂, C₃, and CH radicals by laser-induced fluorescence in a diamond depositing dc-arcjet,” J. Appl. Phys. 82, 2072–2081 (1997). [CrossRef]  

28. W. Juchmann, J. Luque, and J. B. Jeffries, “Flow characterization of a diamond-depositing dc arcjet by laser-induced fluorescence,” Appl. Opt. 39, 3704–3711 (2000). [CrossRef]  

29. P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14, 21–37 (1974). [CrossRef]  

30. P. V. Storm and M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma. I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996). [CrossRef]  

31. P. V. Storm and M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma. II. Plume region diagnostics through radial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 919–932 (1996). [CrossRef]  

32. J. C. Cubertafon, M. Chenevier, A. Campargue, G. Verven, and T. Priem, “Emission spectroscopy diagnostics of a d.c. plasma jet diamond reactor,” Diamond Relat. Mater. 4, 350–356 (1995). [CrossRef]  

33. J. Luque, W. Juchmann, E. A. Brinkman, and J. B. Jeffries, “Excited state density distributions of H, C, C₂, and CH by spatially resolved optical emission in a diamond depositing dc-arcjet reactor,” J. Vac. Sci. Technol. A 16, 397–408 (1998). [CrossRef]  

34. H. W. Liepmann and A. Roshko, Elements of Gasdynamics (John Wiley & Sons, Inc., New York, 1957), pp. 57–61.