Demonstration of confocal laser induced fluorescence at long focal lengths

Laser induced fluorescence (LIF) has proven to be a reliable, non-perturbative diagnostic method for measuring plasma ion and neutral velocity distribution functions (I/NVDF) since its introduction by Stern and Johnson¹ in 1975. Conventional LIF arrangements require intersecting injection and collection optical paths for spatially localized measurements. Typically, fluorescent emission is collected with a set of optics oriented perpendicularly to the laser injection path. The overlap of the two optical paths then defines the measurement volume. The requirement of intersecting injection and collection paths prevents the application of LIF to many experimental devices, e.g., Hall thrusters,² which have opaque channel walls.

Confocal optical systems were originally developed for ophthalmological and biomedical sciences to diagnose sub-surface conditions in the cornea or dermis.^3,4 However, the distances between the optical assembly and measurement location in those applications were typically on the order of millimeters. A half century later, Kajiwara et al. implemented a confocal optical system for two-photon laser induced fluorescence (TALIF) measurements in a thermonuclear fusion plasma.⁵ Because TALIF signals scale with the square of the injected laser intensity, the spatial localization of confocal TALIF measurements is tightly constrained by the focal volume of the injected laser. Confocal single-photon fluorescence measurements, in which LIF signal scales linearly with the injected laser intensity, require a more sophisticated optical design to achieve high spatial localization.

Recently, Thompson et al. demonstrated an implementation of the confocal method that achieves millimeter-scale spatial localization at a focal length f = 150 mm. The localization is determined via the zeroth moment of the metastable velocity distribution function—the relative metastable density—which spatially averages the injection and collection overlap region. Relative metastable density profiles were obtained across the diameter of a centrally peaked plasma column. If the confocal localization is narrow, the profiles obtained with this method agree well with the profile obtained from the highly localized conventional method. Degraded localization results in a profile that is artificially broad. Quantitative estimates of the localization were obtained by comparing the confocal and conventional profiles using response functions from an optical model.

Here, we extend the confocal method in two ways. First, we report relative density profile measurements in the Hot hELicon eXperiment (HELIX) plasma source (with coordinates represented by lowercase letters) that confirm marked improvements in confocal LIF localization from the insertion of an obscuration in the collection path. This result was anticipated by the optical model of Thompson et al. but was not addressed experimentally in their work. Second, an enlarged obscuration is used to demonstrate localized confocal LIF at a focal length of f = 500 mm. The extension of the focal length in this way permits LIF measurements in a plasma region enclosed by a helicon antenna, a region typically inaccessible to conventional LIF methods. Measurements of neutral velocity distribution functions (NVDFs) in this region of the Compact Helicon for Waves and Instabilities Experiment (CHEWIE) plasma source (with coordinates represented by uppercase letters) are presented.

Optimization of the f = 500 mm confocal telescope was accomplished on the hot hELicon eXperiment (HELIX) at West Virginia University. HELIX is a linear helicon plasma experiment that creates an argon plasma with a copper strap, half-turn m = +1 helicon rf antenna. A complete description of the experiment is available in a recent review.⁶ The maximum rf power for plasma creation is 1 kW. Fill pressures range from 0.1 to 20 mTorr, and the maximum magnetic field strength in the plasma is 0.12 T. Typical electron temperatures and densities in the steady-state plasma are T_e ≈ 4 eV and n ∼ 1 × 10¹³ cm⁻³.

LIF optical access is provided by a 4-way cross-port centered 690 mm downstream from the helicon antenna. Conventional optics mounted to the vacuum chamber translate in three directions and provide millimeter-scale localization for relative density profiles across the plasma column diameter. The diameter profile is recorded by translating the focus of the collection optics along the collimated laser beam. The laser defines the x-axis of the measurements, whose origin occurs where the laser intersects the mechanical axis of the chamber. In the demonstration measurements on HELIX, the confocal laser is aligned to the same axis. The entire confocal assembly translates as a unit so that the sample volume moves with the shared focal point of the injection and collection optics.

Once the localization is known, the antenna region of the Compact Helicon for Waves and Instabilities Experiment (CHEWIE) provides an opaque-walled test bed for confocal LIF measurements at long focal lengths. A schematic of the CHEWIE facility is shown in Fig. 1 along with the coordinate directions and notations. Plasma is generated in CHEWIE through an m = +1 half-turn Shoji-type helicon antenna, with maximum rf powers, magnetic fields, and fill pressures reaching 1 kW, 0.15 T, and 20 mTorr, respectively. Argon gas is fed into the top of a Pyrex tube (D = 5 cm, L = 60 cm) through a mass-flow controller. The plasma is confined by two water-cooled electromagnetic coils. Pressure is maintained at a constant rate by using a turbomolecular drag pump attached to the chamber at the opposite end from the gas inlet. The measurement region underneath the helicon antenna is rendered inaccessible by the tight-fitting electromagnets and the helicon antenna. To obtain measurements directly under the helicon antenna, the confocal telescope is aligned parallel to the long axis of CHEWIE and to the axial magnetic field. The origin of this dimension, denoted Z, is located at the center of the helicon antenna, with negative locations occurring toward the gas inlet. The radial direction, perpendicular to Z and centered on the mechanical axis of the chamber, is denoted X.

Detailed reviews of conventional, intersecting optical path LIF measurements are available in the literature.^7,8 In LIF, a narrow-bandwidth laser is used to excite an electronic state of an atom or ion to an upper, more energetic state. Relaxation emission from the deexcitation of the upper state to a third, lower energy state is observed. Measurement of the fluorescent emission intensity as a function of laser frequency provides a measurement of the Doppler broadened velocity distribution function (VDF). From the VDF, such as the one shown in Fig. 2, the relative metastable state density, species temperature, and species bulk velocity are obtained.

For Ar ii velocity distribution function (IVDF) measurements, a ring dye laser is tuned to 611.662 nm (vacuum wavelength) to pump the Ar ii 3d²G_9/2 metastable state and observe the resulting 460.96 nm fluorescence upon relaxation to the 4s²D_5/2 state. As the laser frequency is swept over as much as 60 GHz, the fluorescent emission from the excited state is recorded with a filtered (1 nm bandwidth) narrowband, high-gain, Hamamatsu photomultiplier tube (PMT). Perpendicular injection with linear polarization along the magnetic field direction yields a single peak VDF from the ∆m = 0 Zeeman-split cluster. Injection parallel to the magnetic field produces two Zeeman split and shifted peaks centered on the rest frame absorption wavelength. The laser output of 1300 mW passes through a chopper and is then coupled into a 5 μm core, single-mode, optical fiber connected to the confocal optics.

For Ar i LIF, the 4s²[3/2]^o metastable state is pumped to the 4p²[1/2]^o state at 696.7352 nm, and the resultant fluorescence to the 4s²[3/2]^o state at 727.4940 nm is measured. The initial metastable argon neutral state has a lifetime estimated in the 10s of seconds.⁹ The fluorescence collected from the confocal optics enters a 1 mm multi-mode optical fiber before passing into a McPherson 1.33 m scanning spectrometer, which serves as a bandpass filter centered around the fluorescent wavelength. The light then enters an infrared-sensitive Hamamatsu photomultiplier tube (PMT). The PMT signal is digitized after passing through a Stanford Research Systems SR830 lock-in amplifier referenced to a mechanical chopper.

The confocal assembly used here and imaged in Fig. 3 is a modified version of the f = 150 mm, 12.7 mm obstructed system described previously. For the bulk of the measurements, the apparatus uses a 50 mm diameter, f = 500 mm achromatic doublet objective lens and a 38.1 mm diameter obstruction (see Fig. 3). A detailed theoretical analysis of the optics is provided in Ref. 3. In that work, Thompson et al. theoretically determined that there is a trade-off between the maximum signal-to-noise ratio and longitudinal (i.e., along the optical axis) spatial localization achievable for a fixed objective lens diameter. This trade-off hinges on the diameter of the obscuration disk placed in the collection path, as shown in Fig. 4. The coordinate system for these optimization measurements is described in Sec. II A. The obscuration disk creates a cone of exclusion that limits the collection volume overlap with the laser beam. However, a larger obstruction reduces the total throughput of the optics, thereby reducing the signal-to-noise of the instrument.

In the confocal arrangement, the objective lens depth of field plays a critical role in limiting the overlap between the injection laser and the non-Gaussian collection volume. The depth of field (DOF) for a Gaussian beam is¹⁰ 

where λ is the wavelength, F is the focal length of the lens, and D is the lens diameter. Thus, for very long focal length lenses, good spatial localization, i.e., narrow DOF, requires a large diameter lens.

Measurements of relative ion metastable density, from the zeroth moment of IVDFs, are obtained on HELIX to determine the effect of obscuration diameter on the spatial localization. Plasmas were generated in 650 W of rf power at 9.5 MHz, a neutral fill pressure of 3.5 mTorr, and a magnetic field of 70 mT. Shown in Fig. 5 are relative density profiles measured across the HELIX plasma diameter. Measurements are shown for an f = 500 mm lens with a 38.1 mm (red circles) or 12.7 mm (blue squares) diameter obstruction. Both confocal arrangements are compared to the conventional (2D Stage) LIF data, using perpendicularly intersecting optics which have a known spatial localization of 1.1 mm. Comparing the confocal LIF integrated signal (relative absorber density) to conventional LIF data provides a measure of the spatial localization of a confocal arrangement, i.e., for a specific obscuration diameter and objective focal length. As shown in Fig. 5, the larger (red circles) obstruction produces a density profile that more closely resembles the test profile from the intersecting, conventional optics.

To quantify the spatial localizations of the f = 500 mm confocal systems used to produce the density plots in Fig. 5, a simulated ideal plasma profile is estimated from the conventional LIF data and a model of the conventional optical response. The ideal profile is convolved with a model of the confocal optical response, and the result is compared to the confocal data. Each test confocal profile is derived using a simulation space encompassing ±120 mm around the focal point of the objective lens. The full width half maximum (FWHM) of the confocal optical response provides a measure of the longitudinal spatial localization of the arrangement.

Example response functions of the confocal and conventional optics are shown in Fig. 6(a). For f = 500 mm, increasing the obstruction from 12.7 mm to 38.1 mm in the model results in a significant improvement in the localization of the measurement. Qualitatively, this result is confirmed by the measurements in Fig. 5. The larger obstruction [Fig. 5(a)] clearly produces a measured radial profile in better agreement with the profile measured with the intersecting optics. The 38.1 mm obstruction yields a 7.3 mm spatial localization at FWHM which accounts for 68% of the intensity in the overlap volume. Also shown in Fig. 6(a) is the predicted effect on the response when the obstruction diameter is increased to 45 mm. While this constitutes a modest narrowing of the optical response, experiments with a 45 mm obstruction yielded no measurable LIF signal. Shown in Fig. 6(b) are theoretical response functions for a 100 mm diameter lens with f = 1000 mm. As predicted from Eq. (1), increasing both the focal length and lens diameter narrows the theoretical optical response to the width of the f = 500 mm objective when large diameter obstructions are used.

The shape of the confocal response approaches a Gaussian shape for long focal length arrangements. Shown in Fig. 7 is a comparison of the responses obtained by treating the f = 500 mm, 38.1 mm obstruction case using both the complete theoretical model of the response function and a simplified Gaussian model to decrease computational expense. The Gaussian model yields a localization width of 14 mm, while the full model yields a value of 7.3 mm. While the response function appears Gaussian for f = 500 mm, it is clear that the full theoretical model is still required to accurately determine the spatial localization of the confocal arrangement.

Radially resolved argon NVDF measurements were acquired with the optimized long focal length confocal arrangement in CHEWIE, in a plasma generated using 160 W of rf power, 8.2 mTorr of fill pressure, and 0.12 T of background magnetic field. The zeroth-moment of the NVDF provides a measurement of the relative neutral metastable state density. In Fig. 8, cylindrical symmetry is assumed, and the measurements are depicted reflected about X = 0 cm, using the coordinate scheme discussed in Sec. II B.

Measurements are consistent with a hollow neutral metastable density profile.¹¹ The neutral metastable state density is smallest directly under the antenna and increases with increased distance from the antenna. The minimum in neutral metastable state density suggests a ∼40% depletion from the outermost radius to the center of the argon discharge. Because the neutral metastable state density is strongly coupled to the electron density profile (which is peaked on-axis in these discharges), even a flat neutral metastable density profile would indicate a hollow ground state neutral density profile. That the profiles are hollow in Fig. 8 suggests a very depleted neutral density on-axis. Observations of strong neutral depletion on-axis are consistent with several studies of neutral populations in linear plasma devices.^12,13

Predicted spatial localization improvements from large diameter collection path obscurations are confirmed in relative metastable density profiles. This improvement allows the confocal telescope to be used as a single-photon LIF diagnostic at experimentally viable focal lengths (f ≥ 150 mm), as was predicted theoretically. These results confirm that an increase in obscuration diameter minimizes the volume over which the collection and injection paths overlap, thereby improving the spatial localization of the measurements until the theoretical depth of field of the collection lens is reached. The N/IVDF LIF measurements demonstrate that excellent signal-to-noise is still achievable for confocal designs with large obstructions in the collection path. In regions that are inaccessible by conventional optical techniques, this new, long focal length confocal optical arrangement provides high-quality, spatially resolved measurements that yield new insights about the spatial distributions of neutrals in helicon sources. With accurate knowledge of the confocal optical response, any confocally measured profile can be corrected to recover the true source profile.

This work was supported by NSF award PHYS 1360278 and the KY-WV Louis Stokes Alliance for Minority Participation.