In situ erosion measurement tools for electric propulsion thrusters: triangular laser head and telemicroscope

The lifetime of electric propulsion (EP) thrusters depends particularly on the erosion characteristics of operation relevant components, for instance, the grid hole erosion of gridded ion thrusters or the channel wall erosion of Hall effect thrusters. Here two tools for in situ erosion measurements are presented, a triangular laser head for surface profiling and a telemicroscope for high-resolution optical imaging. Both can give access to radial and axial erosion parameters. The measurements can be done in situ without the need for breaking the vacuum and dismounting the thruster, which reduces thruster testing time considerably. In situ measurements can also help to ensure reproducibility of thruster performance conditions and can improve statistics of thruster characterization. The present work describes the fundamentals of both techniques in detail, selected experimental setups are presented, their performance is characterized and critically evaluated. The capabilities and limitations related to erosion measurements of EP thrusters are, exemplary, demonstrated for a gridded ion thruster RIT-22 and a Hall effect thruster SPT-100D.


Introduction
Electric propulsion (EP) thrusters have to undergo extensive testing before flying into space. Predominantly, ion beam and plasma parameters are of interest, because they determine the primary function of the thruster: producing thrust by acceleration of charged particles.
However, secondary parameters are also of interest. For instance, the erosion of operation relevant components must be measured and minimized in order to maximize thruster lifetime. Examples are the grid hole erosion of gridded ion thrusters or the channel wall erosion of Hall effect thrusters.
Erosion measurements can be done by profilometry using mechanical or optical (laserbased) profilers, or imaging techniques, such as white-light interferometry or optical microscopy using high-resolution tabletop microscopes or telemicroscopes.
Typically, erosion measurements are done outside of the vacuum chamber. Here the thruster needs to be removed from the test stand and to be taken apart. If it was possible to do the measurements in situ, i.e. inside the vacuum chamber without breaking the vacuum, venting and evacuating of the vacuum chamber can be avoided. This can save several days per thruster characterization step and, hence, reduces costs. Furthermore, if the thruster does not need to be removed or taking apart, reproducibility of the thruster performance conditions is ensured. Finally, in situ measurements allow to increase the number of experiments, which gives a statistically more reliable thruster performance characterization.
In situ erosion measurements of different EP thrusters were reported using a triangular laser head (TLH, [1,2]) or telemicroscopes [1][2][3][4]. Yuan et al. reported on the use of a telemicroscope for measuring in situ the grid deformation of a gridded ion thruster by videometrics [5].
Measurements of coordinates of the erosion profile points using a microscope provide not only quantitative data about erosion profile as a whole. The use of microscope also allows investigating microstructure of the erosion profile surface [6].
Recently, we were reporting on the advanced electric propulsion diagnostic (AEPD) platform [1,2,7], which consists of a modular, high-precision, five-axis positioning system and several diagnostic tools for ion beam and plasma characterization (Faraday probe, retarding potential analyzer, ExB probe, and active thermal probe), optical inspection (TLH, telemicroscope), and thermal characterization (pyrometer, thermocamera). All measurements can be done in situ, if needed all of them with a firing thruster.
Here, the fundamentals of TLH and telemicroscope measurements are described in detail. Selected experimental setups are presented, their performance is characterized and critically evaluated. The capabilities of the diagnostic tools are demonstrated, exemplary, for two EP thrusters: a gridded ion thruster RIT-22 [8,9] and a Hall effect thruster SPT-100D [10].

Methods/experimental 2.1 Triangular laser head
The TLH is a distance measurement tool. By scanning across an object, a surface profile can be obtained. The TLH utilizes a laser beam which hits the object (see Fig. 1). In general, the surface is rough such that the laser light is scattered in all directions. A portion of the scattered light with a certain emission angle range α ± α enters the detection side of the TLH and is focused by a lens on a position-sensitive detector. If the distance to the object is changed, scattered light with a different detection angle α enters the TLH and the position of the image spot on the detector changes.
Choosing a TLH, the following performance parameters need to be considered: • measurement range, • spot size, • accuracy, • sampling rate, • compactness, • electrical connection/feedthrough, • vacuum compatibility.   Table 1 summarizes performance parameters of selected TLHs. There are many more commercially available, but the numbers given in the table seem to be representative. According to the numbers in Table 1, choosing the right TLH is always a compromise. For instance, choosing a large measurement range, results in an increase of the spot size and of the repeatability. As a consequence, radial and axial resolution are reduced.
The size of the TLH should be chosen as small as possible in order to minimize the interaction with the ion beam if measurements with a firing thruster need to be done. In this case, the TLH and especially the exit and entrance windows for the incident and scattered laser light should be shielded against direct ion impingement (see below).
The electrical connection needs an appropriate vacuum feedthrough. It is desirable to have a standard connection, where a vacuum feedthrough is commercially available. If this is not the case, a customized vacuum feedthrough with standard multi-pin connectors must be designed.
Please note, none of the manufacturers specify vacuum compatibility of their TLH. So check first, if the TLH has vacuum sensitive electronic or mechanical parts. If yes, replace or remove them. In general, the limiting factor seems to be the allowed maximum temperature, which is typically specified to be 50 • C. However, long term tests showed that vacuum compatibility is possible, even if the specified maximum temperature is temporarily exceeded. Still, the operation inside or close to the ion beam of the thruster needs to be minimized in order to avoid extensive external heating of the TLH. In the following experiments, a TLH L-KG152 (Keyence) was chosen. It provides a sufficient measurement range from z = 110 mm up to z = 190 mm (reference distance: z ref = 150 mm) with a small spot size between 0.12 mm at the reference distance and 0.75 mm at the far and near end of the measurement range, and a repeatability of 0.5

μm.
For thruster test campaigns, the TLH is covered by a metal housing (see Fig. 2). The front side is shielded with a graphite plate, and glass or sapphire windows. The dimension of the housing is 95 mm × 47 mm × 127 mm. The TLH uses special connectors. Therefore, a customized vacuum feedthrough with multi-pin connectors (Lemo) was designed and built.
Please note, since the detected, scattered light enters the shielding window at nonnormal incidence, it gets refracted and the direction of the transmitted light is displaced relative to the initial propagation direction (see Fig. 3). As a consequence, the measured distance is smaller than the geometrical distance. The window effect can be calculated using Snell's law α and β are the detection angle and angle of the refracted beam inside the window (see Fig. 3). The distance shift according to the window effect is given by n window and d window are the index of refraction and thickness of the window, respectively. Figure 4 summarizes experimental data of the preliminary characterization of the TLH without and with a window. The data were collected using a manual linear table with high precision (step width 0.01 mm) and a maximum traveling range of 150 mm. Prior to the measurements, the test object was aligned such that its surface is perpendicular to the laser beam propagation direction. Figure 4(a) shows the difference between the set distance and the measured distance. Numbers are given relative to the reference distance of the TLH. It can be concluded that the distance measurement accuracy is better than ±0.03 mm for flat surfaces. Please note, if absolute numbers of different measurement campaigns shall be compared, a fixed reference point must be defined. However, in most cases only relative numbers with respect to a point or plane on the test object are required. In Fig. 4(b) the effect of a window on the measured distance data are shown, exemplary, for a glass window and different test object surfaces. There is a monotonous shift of the distance change by the window if the object distance is varied. But there is only a small scattering of the data with respect to the test object. Still, a good match between experimental and calculated data can be seen.
Please note, the calculation results show that the window effect is very sensitive to the index of refraction or the thickness of the window. Changing the index of refraction by 0.01 or the thickness by 0.05 mm result both in a change of the measured distance by -0.02 mm. Therefore, a window with a reproducible index of refraction and a homogeneous thickness shall be used. Figure 4(c) illustrates that the position of the window has also a small impact on measured distance. However, this change is of less importance since the window will be mounted at a fixed position in the experimental setup for EP thruster characterization.
In order to minimize the window effect, two windows instead of one can be used: one for the incident laser beam and one for the scattered light that enters the TLH. If both windows are positioned such that the respective light enters the windows at normal incidence, refraction is eliminated. Still, to be precise, this is only true for the scattered light that is emitted at a certain distance, preferably the reference distance. Therefore, in all cases, the window effect shall be investigated carefully by experiment before using the TLH.
Furthermore, the data illustrate that different materials (silicon, molybdenum, boron nitride, or graphite) of different color (white, metallic, black) and different surface finishing (mechanically polished, chemically roughened, polycrystalline) can be measured. TLH measurements in the standard configuration (see Fig. 1) requires that the incident laser light is at least partially scattered.
In the following, the object height h with respect to the reference distance z ref instead of the object distance z is given for the TLH data. It holds Thus, the curves describe the upright surface profile of the test object.

Telemicroscope
A telemicroscope is a high-resolution optical camera. It consists of a camera body (with a CMOS or CCD pixel sensor), an optional extension tube, and an objective lens. Regarding its use, the following parameters are of interest: • object area to be imaged, the so-called 'field of view' (FOV), • lateral (or radial) resolution, which is related to the FOV per pixel (see below), • axial resolution, which corresponds to the depth of field (DOF), • signal-to-noise ratio, which scales with light intensity on the detector, • compactness, • electrical connection/feedthrough, • vacuum compatibility.
Concerning compactness, electrical connection, and vacuum compatibility, the same arguments as for the TLH hold (see above).
The other parameters can be, at least in parts, calculated using geometrical optics (see Fig. 5). The imaging of an optical system can be approximated by the lens equation of a thin lens [11][12][13] ( 4 ) Figure 5 Schematic drawing of the imaging with a lens f , s 1 , and s 2 being the focal length, object distance, and image distance, respectively. Focusing is done by moving the lens, which is described by the lens rack out distance s lens 2 (s 2 = f + s lens 2 ). The maximum lens rack out distance s lens 2,max determines the minimum distance of the focal range.
The magnification relates the field of view (object width times object height: w 1 × h 1 ) and the sensor size (image/sensor width times image/sensor height: w 2 × h 2 ). It is given by [11][12][13] Using the lens equation, the magnification can be written as follows This leads to and The lateral (or radial) resolution of a pixel sensor depends on the pixel size. Let's consider two point sources. If they lie close to each other, they might be imaged on the same or neighboring pixels of the sensor, i.e. their images cannot be separated. However, if the spacing between the point sources is increased, they might get imaged on pixels, which are separated by at least one pixel in between (see Fig. 6).
Following that, the lateral resolution can be estimated to be the object width (or height) that corresponds to twice the image width (or height) of a pixel of the sensor. Considering a pixel sensor with m w × m h pixels, the object width w pix 1 and height h pix 1 that is imaged on The axial resolution corresponds to the depth of field (DOF), which describes the object distance range of acceptable sharpness. That is, objects lying within this range appear acceptably sharp at the image plane. The near (s n ) and far distance (s f ) of acceptable sharpness are given by [11][12][13] s 1 and s h are the object distance (in focus) and the hyperfocal distance, respectively. s h defines the minimum object distance at which the range of acceptable sharpness extends to infinity (s f = ∞). It is given by [11][12][13] (13) N and c max are f-number and circle of confusion (CoC), respectively. The depth of field is given by Point sources, which do not lie at the focal point, appear as blurred circle of diameter c on the sensor. The maximum diameter, at which the blurring seems to be acceptable, is the CoC [11]. In this case, the point source is located within the range of acceptable sharpness (see Fig. 7). The circle of confusion depends on the visual acuity, the distance at which the final image is viewed, and the enlargement of the final image [11][12][13]. Additionally, image contrast and illumination [12] play a role. Thus, the CoC depends on the observer and viewing conditions. Hence, any CoC value can only be an approximation.
Therefore and for simplicity, the CoC is often related to the sensor diameter. Typical values range from 1/1000 to 1/2000 of the sensor diameter, but in most cases 1/1500 or 1/1730 are stated [14,15] (sometimes, unofficially called 'Zeiss formula').
Following the above given equations and statements, the performance of the telemicroscope depends on focal length, object distance, sensor size, pixel size, and f-number. According to Eq. (4), the object distance s 1 is determined by focal length f and image distance s 2 . As it was said before, the image distance of an optical camera is given by f ≤ s 2 ≤ f + s lens 2,max . If needed, the imaging distance can be increased by insertion of an extension tube with length l in between the photographic lens and the sensor In the following calculations and experiments with an extension tube, the lens rack out distance was always set to zero ( s 2,max = 0). Focusing was done by high-precision movement of the telemicroscope relative to the test object to be imaged. In order to illustrate the impact of the parameters, Tables 2, 3, and 4 summarize, exemplary for a telemicroscope that is used in the experiments described later, calculation results in dependence on focal length, extension tube length, and f-number, respectively.
The main conclusions can be summarized as follows • Focal length f : Increasing the focal length yields an increase of the object distance (= working distance), an increase of the field of view (per pixel), which corresponds to a reduction of the lateral resolution, and an increase of the depth of field (= axial resolution).
• Extension tube length l: If the length of the extension tube is increased, the working distance, the field of view (per pixel), and the depth of field become smaller. Hence, lateral and axial resolution are improved. • Sensor size:   Increasing the sensor size results in an increase of the field of view (per pixel) and, thus, in a reduction of the lateral resolution. Furthermore, the circle of confusion gets larger and, hence, the axial resolution gets larger.
• Pixel size: The pixel size affects the field of view per pixel and, hence, the lateral resolution. If the pixel size gets larger, the lateral resolution is increased. • F-number: The f-number has only an impact on the depth of field. If the f-number becomes larger, the depth of field increases and, thus, the axial resolution gets worse. The signal-to-noise ratio should be as high as possible in order to improve the image quality. It gets larger if more light falls onto a pixel of the sensor. Therefore, decreasing the f-number, increasing the field of view per pixel or the intensity of the illumination light yields a better signal-to-noise ratio. It also depends on the properties of the test object, namely the amount of light that is reflected or scattered off the object surface: The lighter the object, the more light gets off the sample.
There are many cameras and objective lenses of different size and with different parameters commercially available. Exemplary, an experimental setup with an USB camera DFK 51AU02 (The Imaging Source; dimension: 50.6 mm × 50.6 mm × 56 mm) with an extension tube and an objective lens C5028-M (Pentax; diameter: 29.5 mm; length: 34.0 mm) is shown in Fig. 8.
The telemicroscope is covered by a metal housing (dimension: 60 mm × 70 mm × 210 mm) for EP thruster characterization campaigns. The setup uses a graphite front plate, a sapphire window, four high-power LEDs for illumination (not shown in Fig. 8), and an commercial USB vacuum feedthrough. Experimental data in dependence on the extension tube length are compared with calculation results (see Table 3) in Fig. 9. Calculations are based on the following parameters: The camera has a sensor size of 7.04 mm × 5.28 mm with a resolution of 1600 x 1200 pix- The experimental data were evaluated using two test structures: an eyepiece graticule for measuring the FOV and a laser-scribed line structure for characterizing the lateral resolution. Test structures and test procedures are described elsewhere [2]. There is a very good agreement between experimental and calculated data.
The telemicroscope images in Sect. 3 were recorded with a different setup. It uses a camera DMK 41AF02 (The Imaging Source) with a sensor size of 5.95 mm × 4.46 mm, a resolution of 1280 × 960 pixels, and a pixel size of 4.65μm×4.65μm. The objective lens has a focal length of f = 135 mm and a f-number range from N = 2.8 up to N = 16. An extension tube length of l = 150 mm was used. This setup allows a larger object distance of s 1 = 256.5 mm while keeping a high lateral resolution of 8.4 μm and a small DOF of ∼ 0.1 mm.
As it was said before, the calculated depth of field is an approximation, because it depends on the observer and viewing conditions. Performance characterization experiments with the test line structure yield results close to that. However, these measurements resemble the ideal case, i.e. high optical contrast, sharp and straight edges, flat and smooth object surface, and surface aligned perpendicular to the center axis of the TMS. In the experiments with the thrusters these ideal conditions can often not be fulfilled. Therefore, the achievable axial resolution is estimated to be not better than 0.5 mm.
For completeness, there is a different approach for erosion measurements with a telemicroscope [3,4]: A laser line is projected on the region of interest and imaged. By applying a 3D reconstruction algorithm, the surface profile can be obtained from the shape of the laser line projection. Misuri et al. reported accurate erosion data for the channel wall erosion of a Hall effect thruster, which was operated with different channel wall materials (boron nitride, Macor, Shapal) [3]. Telemicroscope results were verified by caliper measurements. Andreussi et al. used the setup to study the erosion of a high-power Hall effect thruster [4]. A very good agreement with profilometer measurements was reported.

Vacuum test facility and test objects
Thruster test campaigns with the TLH and telemicroscope were performed in the large vacuum test facility (Aerospazio Tecnologie s.r.l.), which has a length of 11.5 m, a diameter The first test object was a gridded ion thruster RIT-22 (ArianeGroup, see Fig. 10(a), [8,9]) with a grid diameter of 22 cm. The RIT-22 is an advanced radio-frequency ion propulsion thruster/engine designed to meet the requirements of commercial and scientific missions. In this study, the thruster was operated at power levels between 1.25 kW  There are also selected data available for a miniaturized gridded ion thruster RIT-μX (ArianeGroup, [2,16]). Figure 11 shows a TLH scan across the diameter of the RIT-22. The grid hole area, rim of the grid, and mounting ring can be clearly identified.

TLH measurements with the RIT-22
A closer look reveals the following artifacts of the TLH measurements: • Depending on the slope of the profile, the TLH cannot measure the distance, which is the reason for the missing data points, for instance, at x ≈ 40 mm and x > 300 mm in Fig. 11(a). This is related to the fact that light, which is usually detected, is blocked by the test object if the slope of the surface is steeper than the detection angle α. In this case, no scattered light can reach the detector. • At sharp edges, as, for instance, at the grid hole edges, upward or downward spikes appear (see Fig. 11(b)). Again, this depends on the slope of the surface. This is related to a different scattering characteristics in comparison to a flat surface. As a consequence, the TLH cannot measure grid hole erosion. However, the data give access to the grid curvature of the outer grid. Figure 12 summarizes grid curvature data for the warm-up and cool-down phase of the RIT-22. Please note, TLH scans during the warm-up phase were done with a firing thruster, i.e. the TLH was moved through the ion beam several times.
It can be seen that switching on the beam results in a sudden drop of the grid curvature, which was tentatively assigned to the electrostatic forces between the grids due to the switched-on high voltages [7]. With increasing operation time, the grid curvature steadily increases and reaches a stable value after about two hours [5,7]. This reflects thermal expansion and thermal equilibrium, respectively. As the thruster is switched off, the behavior is the opposite: the grid curvature increases suddenly and steadily decreases with increasing cool-down time.

Telemicroscope imaging of the RIT-22
Telemicroscope images of the grid holes of the RIT-22 are given in Fig. 13. Images at different operation stages are shown. The grid holes can clearly be resolved if the thruster is switched off (Fig. 13(a)). If the plasma or the beam is on, the edges of the grid holes are blurred. This is related to light from the plasma, that is scattered at the grid hole edges. That means, precise grid erosion measurements can be done only if the thruster is switched-off.  Figure 14 shows a section of a full TLH mapping of the SPT-100D, which was obtained by combining about 150 linescans in x-direction with a shift of y = 1 mm. All characteristic features can be identified: ceramic channel wall rings, anode layer ring at the bottom of the channels, springs and center screw for fixing the ceramic rings at the top.

TLH measurements with the SPT-100D
Selected horizontal TLH linescans across the center of the SPT-100D and radial erosion data are summarized in Fig. 15. The full line scans show again what was already described above for the TLH measurements with the RIT-22: If the edges become too steep, the TLH measurement fails. The detailed view at the top of edge of a channel wall (see Fig. 15(b)) reveals a continuous erosion of the channel wall, at the beginning in radial and axial direction. At a certain point, axial erosion stops and only radial erosion proceeds. Numbers of the radial erosion versus thruster operation time are plotted in Fig. 15(c).

Telemicroscope imaging of the SPT-100D
Selected telemicroscope images of the SPT-100D are shown in Figs. 16 and 17. Figure 16 illustrates the increasing radial erosion versus operation time. Radial erosion data from the telemicroscope images agree well with data from the TLH measurements (see Sect. 3.3).
Additionally, the surface modification can be seen. The top face of the channel wall changes from a flat appearance with grooves from mechanical grinding to a more grainy structure. In contrast to that, the area next to the channel wall becomes brighter, which indicates a coating or polishing.
The axial erosion is illustrated by the telemicroscope images in Fig. 17. By moving the thruster closer to the telemicroscope, the focal point moves steadily from top of the channel wall along the eroded slope. Again, considering the higher uncertainty of ±0.5 mm, the numbers agree well with those from TLH measurements.

Conclusions
This work reports on the use of triangular laser heads and telemicroscopes for in situ erosion measurements of EP thruster components. The fundamentals of both techniques are described in detail. Exemplary, selected experimental setups and their performance characterization is described and critically discussed.
The capabilities and limitations of the TLH and the telemicroscope for in situ erosion measurements were investigated using, exemplary, a gridded ion thruster RIT-22 and a Hall effect thruster SPT-100D. Both techniques can give access to lateral and axial erosion. However, the strength of the telemicroscope is the determination of the radial erosion of Figure 17 Telemicroscope images of a channel wall edge of the SPT-100D at different object distances. As indicated by arrows, the focal point moves along the eroded slope. Images were taken after about 300 hours of operation flat surfaces. Axial erosion with reduced accuracy can be accessed by exploitation of the depth of field. If it comes to 3D surfaces, TLH measurements can provide accurate radial and axial erosion data. However, if steep edges need to be measured, the orientation of the TLH with respected to the edges must be chosen carefully in order to avoid or reduce measurement artifacts.
We believe that this work is of great help for the EP community because testing is a key stage in the development of EP thrusters. Erosion data of selected mechanical parts of the thruster are important since erosion limits thruster lifetime. The tools described here can be operated in situ, i.e. inside a harsh vacuum test environment, which can help to reduce testing time and costs considerably. Extensive testing with thrusters of different types and sizes throughout the last years showed stable and reproducible operation.