Automated test apparatus for bench-testing the magnetic field homogeneity of NMR transceiver coils

Abstract

We describe an automated hands-off bench testing method for measuring the magnetic field profile of transceiver coils for nuclear magnetic resonance (NMR). The scattering parameter (S-parameter) data is measured using a portable network analyzer, and the results are automatically exported to a computer for plotting and viewing. This assay dramatically reduces the time needed to measure the magnetic field (B₁) homogeneity profile of a transceiver coil while also improving accuracy relative to manual operation. Here, we demonstrate the method on a saddle coil of a solution-state NMR probe in comparison to profiles obtained using NMR spectroscopy measurements. We also measure the axial and radial homogeneity of a variable-pitch solenoid.

Introduction

In NMR spectroscopy, interaction with the nuclear spins is achieved using a probe, a specialized radio frequency (rf) circuit with channels tuned to the Larmor frequency of each desired nucleus. A particularly important component is the transceiver coil, which both transmits an excitation pulse to the sample and detects the resulting signal. Although probe design and construction varies considerably, many probes use cylindrical coils of either solenoidal (an axial resonator that generates a magnetic field B₁ along the axis of the coil) or saddle coil (a transverse resonator with B₁ perpendicular to the coil axis) geometry. To maximize performance, the B₁ profile of the transceiver coil must be homogeneous over the central region where the sample is placed. Inhomogeneity in the rf coil causes the distribution of nuclear spin excitation following an rf pulse to be unevenly distributed along the sample, resulting in reduced sensitivity and sometimes phase artifacts as well [1]. Spins found in inhomogeneous regions will not be fully excited and will fall out of phase [2], rapidly decreasing sensitivity, especially in multi-pulse experiments [3, 4]. These effects also reduce the efficiency of heteronuclear [5] and homonuclear [6, 7] decoupling.

A poorly-made coil not only fails to excite the nuclei as intended, observed as longer 90°pulse widths, but also reduces the effectiveness of magnetization transfers. For example, cross-polarization (CP) is a building block of multinuclear solid-state NMR that enables transfer of magnetization from an abundant, high-γ nucleus to a sparser, low γ nucleus when the Hartmann-Hahn conditions are met, matching the angular frequency of the nuclei in the rotating frame [8]. Performing CP using an inhomogeneous rf coil prevents fulfillment of the Hartmann-Hahn condition in areas of the coil where the B₁ amplitude drops, reducing signal enhancement and potentially causing line-shape distortions [9]. Under magic angle spinning (MAS), the most efficient transfer happens not at the Hartmann-Hahn condition, but at a sideband condition where the field mismatch parameter Δ = ω_1I − ω_1S is close to ±ω_r or ±2ω_r, where ω_r is the MAS rate [10, 11]. Under fast MAS, Δ is a significant fraction of the applied field and often exceeds the one-bond heteronuclear coupling, making rf homogeneity particularly important. At moderate magnetic field strength (up to about 500 MHZ ¹H Larmor frequency), CP efficiency is relatively independent of rf homogeneity because both channels share the same inhomogeneity profile. However, this assumption breaks down at higher field strengths because the length of the wire making up the coil is no longer short compared to the wavelength corresponding to the ¹H Larmor frequency [12].

B₁ homogeneity also impacts quantitative NMR, because if it is not accounted for the NMR signal is not directly proportional to the number of spins in the sample. This can be minimized by restricting the sample to a homogeneous region in the center of the coil [13], and/or compensated by mapping the field and calculating a correction factor accounting for the rf inhomogeneity for each coil used [14]. Although the impact of rf inhomogeneity can be compensated, to some degree, by the application of compensatory pulse sequences [15, 16, 17] or frequency-selective pulses [18, 19], optimal results are more likely to be achieved by beginning with a transceiver coil that is as homogeneous as possible over the sample region before applying these corrections.

Experimentally, B₁ field homogeneity can be tested by directly measuring the NMR signal. One commonly reported experimental indicator of the homogeneity is the ratio of signals at 810° / 90°, although this is subject to the effects of radiation damping, inconsistent probe tuning, and variations in linewidth [20]. If gradient coils are installed in the probe, as is typical for solution NMR, a gradient can be applied during a nutation experiment to spatially encode the signal, providing a map of the excited nuclear spins along the coil [21]. In the context of an MAS probe without integrated gradients, other methods must be used. It is possible to obtain a solenoid’s homogeneity profile by sequentially sampling small segments of the coil, filling the rest of the space with inert spacers, and recording nutation curves to map the field amplitude along the rotor axis [22, 12, 23]. Another option is to obtain a 1D image using a gradient applied along the z-axis using the z₀ room-temperature shim coil [24, 23] or by pulling the probe partway out of the magnet [12]. This can also be measured along the axis of the MAS rotor using the correct combination of room-temperature shims [25]. These NMR-based methods for measuring the field profile consume magnet time and can be costly, particularly for laboratories that rely on using facility instruments. Testing a large number of transceiver coils for design improvement studies is not feasible under these circumstances.

An alternative method that enables benchtop testing in a compact apparatus is the ball shift assay, in which a conductive ball is incrementally moved along the coil axis, inducing a frequency shift that is correlated to the B₁ field at each position [12]. A formula derived from Maier and Slater (Eq. 1) describes the signal produced when shifting the ball through the coil. Here, B₁ is the rf field, ω is the unperturbed resonant frequency of the circuit, and ω₁ is the resonant frequency when the circuit is perturbed by a metallic sphere of radius a [26].

$$\frac{{\omega }_1^2-{\omega }^2}{{\omega }_1^2}=-\frac{3}{2}{B}_1^2\left[\frac{4\pi a^3}{3}\right]$$

This approach has long been used by NMR probe builders to perform preliminary coil tests without the need for testing in the NMR instrument.

Advances in miniaturization of computer hardware, including compact transistors and integrated circuits, have made a wide variety of inexpensive yet powerful computing devices available to consumers, driving new innovations in customized laboratory equipment. Compact programmable microcontrollers (MCUs), such as the Arduino system, use a microcontroller mounted on a dedicated printed circuit board (PCB) to create modular devices that are compatible with a wide range of actuators, sensors, PCB shields, drivers, and communication devices. In combination with high-level and low-level programming languages, such as Python and C++, it has become easier to create do-it-yourself (DIY) projects to automate and routinize common laboratory tasks. For example, an inexpensive automated tune and match system for NMR and MRI probes was built using an Arduino Uno board and off-the-shelf components [27]. Further, entire low-cost multi-channel NMR and MRI spectrometers have been developed using an Arduino Due (32-bit processor, 512 KB flash memory, and 96 KB of SRAM) as a digital pulse programmer and means of precisely synchronizing rf and digital signals among multiple devices [28, 29]. This Due board was also used to demodulate acquired signals in NMR experiments, replacing the complicated field-programmable gate array (FPGA) hardware in NMR consoles [30]. Another Arduino spectrometer was built to control laser and microwave pulses to perform pulsed NMR experiments in nitrogen vacancies in diamond [31]. Recently, another single-board, Arduino-based, integrated spectrometer for low-field NMR ( 5–10 kHz) the NMRduino, was introduced [32]. This board can generate rf pulses and resolve the detected NMR data, as initially demonstrated for measurements of ¹H and ¹⁹F in small molecules.

Developments in NMR instrumentation that utilize additive manufacturing, commonly known as 3D printing, have been rapidly increasing due to the high precision of new printers and accessible plastics [33]. For example, in 2018, stereolithography (SLA) was used to 3D print stators for spherical rotors, a newer design that improves signal-to-noise by allowing larger sample volumes, and used in MAS NMR [34]. More recently, fused deposition modeling (FDM) 3D printing was used to manufacture a “double-bearing” MAS stator that is printed as a single piece using a low-cost acrylonitrile butadiene styrene plastic filament [35]. These stators are scalable for various rotor sizes, including 3.5, 4, and 7 mm. For the 4 mm rotor, a turbine cap was 3D printed using polycarbonate (PC), a tougher plastic filament. Drive caps for 2.5 and 1.3 mm rotors can be 3D printed, with only a mild reduction in performance relative to the much more expensive commercial versions [36]. Solid-state MAS stators for 3.2 mm rotors have also been developed using ceramic 3D printing, specifically using zirconia [37]. In this study, larger stator components were printed with zirconia, while more finely detailed components were printed with microfine resin or machined with Vespel for low-temperature experiments. In MAS NMR experiments, a solid or semi-solid sample must be packed into millimeter or submillimeter-diameter rotors and spun at high speeds (sometimes ≥ 100 kHz). As an aid to sample packing small rotors, a 3D printed centrifugal device that transfers rigid solids or viscous slurries into rotor sizes down to 0.7 mm in diameter was created [38, 36]. The use of 3D printing has already proven to be a valuable addition to the NMR maker space, especially in reducing cost and production time for particular components while allowing more groups to participate in improving the methodology.

Here we present the Auto-Ball Shift (ABS) device for performing hands-free transceiver coil mapping. We use the Arduino’s flexible programming capabilities to control mechanical components fabricated using both fused FDM and SLA 3D printing. Although the manual ball shift assay is a useful and inexpensive tool in the NMR maker space, manual operation is time-consuming and introduces deviation among different trials. ABS offers a hands-free experience that streamlines data collection and minimizes human error. The ABS device automatically performs the ball-shift assay while simultaneously collecting the RLC circuit network scattering parameters (S-parameters) at each increment in the form of Touchstone files. We utilize a Python script to parse the obtained parameter files and retrieve the rf coil homogeneity information, dramatically reducing the amount of time sampling each coil and improving the reproducibility of the measurements. We seek to describe the methodology at a level where it can be used by a wide range of NMR labs, including those with limited prior instrumentation expertise; therefore detailed instructions, computer assisted design (CAD) drawings, 3D print files (*.stl), and code are included in the Supplementary Data.

Materials and Methods

ABS apparatus and electronics

The ABS device is controlled by a microcontroller unit, the Arduino UNO Rev3 (Somerville, USA). The MCU is programmed using the Arduino Integrated Development Environment (IDE) and is written in C++. The Pololu A4988 (Las Vegas, USA) stepper motor driver carrier was utilized to control the degree of rotation of the stepper motor. Sequentially, the Arduino board powers the A4988 driver board, that then powers the stepper motor. To connect the components, a breadboard and 22 American Wire Gauge (AWG) jumper wires with 0.7 mm headers were used. The Arduino code we developed for this study (included in the SI as filename ArduinoStepper) enables the user to control the stepper motor’s speed, direction, microstep resolution, number of steps, and action delays.

All mechanical components were designed using Autodesk Inventor CAD software (San Francisco, USA). Once the pieces were modeled, they were exported as stereolithography (STL) files and imported to the appropriate slicer software. Our Formlabs Form 3 (Somerville, USA) stereolithography (SLA) and Intamsys Funmat HT (Eden Prairie, USA) FDM printers use FormLabs’ PreForm and Ultimaker’s Cura slicer software, respectively. The larger components of the apparatus were printed with Polymaker (Shanghai, China) PLA (polylactic acid) using the FDM printer with 0.2 mm z-layering. Smooth rods for the sliding mechanism were printed using the SLA printer with Formlabs’ Clear V4 Resin, using 50-micron z-layer resolution. A light isopropyl alcohol wash was applied at the end to polish and aid in the smoothing process. M6 socket screws and heat sinks were used to fix the rods onto the probe shield adapter. The final 3D-printed component is a sleeve that mounts onto the stepper motor shaft and has a threaded hole (4.2 mm diameter tapped with M5 threading) on the opposite end. Once tapped, the nylon M5 threaded rod (McMaster-Carr, Elmhurst, USA) was inserted. On the opposite tip, the 3 mm diameter copper sphere was mounted and fixed. To properly mount the ball at center, the rod tip was polished flat, then a divot was made at the center with a straight-blade deburring tool. This was then carefully enlarged to create a countersink chamfer. A small amount of Super Weld adhesive (J-B Weld, Marietta, USA) was placed in the chamfer and the ball was lightly pressed in. A second version was also constructed using a 4–40 nylon rod. Upon assembly, the motor converts rotational to linear motion, moving the copper ball along the NMR coil’s central axis.

Data collection

Perturbation data were measured as a tuning frequency shift using a nanoVNA-H network analyzer (Shenzhen, China), and recorded using the desktop-native NanoVNA-App software, created by user OneOfEleven (nanovna.com). The ‘record’ feature in this application takes continuous scans of the S-parameters in the NMR probe circuit. The scan period is dependent on the resolution selected. We divided our span to 3,201 data points and chose a resolution bandwidth (RBW) of 1 kHz, resulting in about 10 seconds per scan. Each individual scan is exported as a Touchstone file, (*.s1p, *.s2p, etc.) and all are automatically saved to the recording path. A Python script (included in the SI as filename ParsingScript) was developed to parse all the individual Touchstone files and retrieve the tuning frequency at each increment. The script compiles all of the frequencies into a single comma-separated value (*.csv), but can be changed to output a text (*.txt) file. The script contains a safety check to ensure that it recognizes and exports the lowest peak, tuning frequency, of the data set.

NMR measurements

The ABS assay was performed on a commercial solution-state NMR probe with a saddle coil (Bruker, Billerica, USA). The probe was then installed in a 400 MHz Ascend magnet and the rf homogeneity was again measured via NMR spectroscopy using TopSpin 4.2.0. First, the rf homogeneity was measured using a gradient-assisted ¹H 1D gradient shimming NMR experiment (imgegp1d). Then, a “pseudo-2D” nutation experiment (imgegp2d) was used to map the rf coil, independent of the gradient. This experiment generates an array of 1D spectra collected using GradShim with increasing excitation pulse (P0) increments as the indirect dimension. From these data, a contour map is generated with respect to P0, where the highest intensity corresponds to the optimal, or shortest, 90° pulse width. The profile length was estimated by converting the parts-per-million (ppm) x-axis to millimeters. The coil length was independently experimentally determined by signal mapping of the ¹H nuclear response using a short-length water sample (5 mm) in a Shigemi tube. This H₂O:D₂O (90%:10%) sample was incremented along the coil length, measuring the NMR signal at each millimeter increment.

Assessing positional accuracy

A “homing”, or positional, test was performed to test whether the A4988 micro-stepping driver was accurately controlling the motor. The stepper motor connected to the A4899 driver was an Adafruit NEMA 17 bipolar motor that takes 200 steps per revolution. Positional accuracy was assessed by placing the conductive ball in an arbitrary position in the solenoid, which shifted the tuning frequency from 400.00 to 401.50 MHz. The motor was operated for 12.5 steps out of 200, or 1/16^th of a revolution, incrementing the ball through the rf coil 22.5° with each clockwise turn. The rod was then retracted counter-clockwise the same number of turns to the starting position. This procedure was repeated fifty times in order to detect any positional inaccuracies coming from inconsistencies in the micro stepping.

Results

In the ball shift experiment, a small conductive ring or disk is moved along the rotor axis in discrete increments defined by the pitch of a finely threaded rod, and the shift in resonance frequency is measured as a function of position [12]. Traditionally, finer-grained measurements can be easily (although tediously) obtained by measuring a data point every half- or quarter turn, at the expense of more experimental time. The auto-ball shift (ABS) apparatus was built to reduce the hands-on time spent measuring B₁ profiles. An overview of the experiment is shown in Figure 1. Figure 1A shows a simulation of the B₁ field of a solenoid coil with a conductive sphere inside it; this frequency shift is schematically depicted in Figure 1B. Figure 1C shows a photo of the device mounted on a standard-bore solution probe.

Figure 1:

(A) A simulation showing the B₁ field perturbation induced by a conductive sphere for a solenoid coil resonating at 400 MHz. (B) A schematic illustrating the frequency shifts induced by perturbing the probe circuit by moving the sphere along the coil. The tuning frequency (f₀) becomes perturbed and shifts (f₁ and f₂) proportionally to the B₁ intensity. (C) A photo of the ABS device mounted on a Varian (Palo Alto, USA) 500 MHz solution NMR probe, ready for use.

The motorized ABS apparatus is more reproducible than manual measurements due to the precision control of the A4988 motor driver. Figure 2 depicts the wiring scheme and components used for the ABS device (more detailed schematics are available in the Supplementary Information). This level of step precision is reached from the A4988 motor driver chip’s “Mixed Decay Operation”, where rising and falling currents in the coil windings of the motor are efficiently switched, changing their magnetic polarity and causing the motor shaft to turn. Without mixed decay, default operation would be either “slow decay” or “fast decay” mode. In slow decay, current in the windings fall slowly, which has the benefit of low ripple current effects. However, this mode cannot decrease current fast enough, and results in the motor skipping from induced EMF. On the other hand, in fast decay, a negative voltage quickly deceases the current — fast falling edge — in the winding, and currents are well regulated between pulses. The major drawback of fast decay is the high ripple currents, which can cause excess vibrations, noise in the motor, overheating, and even possible damage to the circuit. Mixed decay mode uses both fast and slow decay at specific duty intervals to better regulate current spikes and drops and prevent step skipping [39].

Figure 2:

Wiring schematic of the Auto-Ball Shift electrical components. The Arduino board is powered directly by a standard laptop, and its 5V/GND pins are used in turn to power the A4988 driver. The Arduino program commands the driver, which then regulates the stepper motor action. A tactile push button is used to initiate the benchtop experiment. An LED serves as an indicator for when the experiment has started. The motor is powered with an external 9V power supply.

The ABS can be configured to perform measurements at various step resolutions, where finer step modes provide more data points and thus higher resolution in the rf profile, at the expense of increased experimental time. As mentioned previously, a full 360° rotation corresponds to 200 steps and 0.8 mm linear distance traveled when using an M5 thread. If the increment is decreased to 50 steps, this results in a 90° rotation, or quarter revolution, and a distance of 0.2 mm traveled using the same M5 thread. A smaller travel distance can be achieved by either decreasing the number of steps the motor takes or using a finer pitch thread. With the fine step resolutions – resulting in smaller degree rotations – achieved using the stepper motor, more data points can be measured to map out the rf profile much more precisely relative to manual measurements. For example, in our 6-turn solenoids, turning the motor 50 steps (or one quarter of a turn) at each increment yields approximately one hundred data points for the rf field profile. This corresponds to and one hundred individual S-parameter files containing the reflection coefficient (S₁₁), from which the resonant frequency can be extracted. The scripting feature (ParsingScript in the SI) makes it possible to extract the perturbed frequency from each S-parameter file produced at every stepper motor increment. It does so by sweeping through the (S₁₁) data points until it reaches a minimum at resonance, which is then recorded. After running the script, all frequencies were automatically placed into a CSV file in sequence for plotting and viewing of the B₁ profile.

Perturbation measurement

The ABS apparatus measures the B₁ field inside the transceiver coil by moving a millimeter-size copper ball along the coil axis via a threaded rod (here, a metric M5 threaded rod). Perturbations caused by the conductive sphere induce a frequency shift [40] in the tuning of the probe circuit, in this case the 1H channel resonating at 400 MHz. As the position of the ball is incremented, the frequency change relative to the starting value is collected (schematically shown in Figure 1A and B, respectively. This induced frequency shift in the electrical circuit is measured by the nanoVNA-H as the reflection coefficient in dB, which has a minimum at the resonant frequency.As these values are being measured, they are sequentially recorded in the NanoVNA-App at each millimeter increment (Figure 3).The python ParsingScript is utilized to extract the minimum value for each increment. The frequency shifts are normalized and plotted to observe the field distribution along the axis of the resonator, yielding the rf profile of the coil.

Figure 3:

Top Frequency S₁₁ output displayed in the nanoVNA-App desktop interface. Bottom A Smith Chart showing that the measured load impedance of the NMR probe’s matching network at the resonant frequency is approximately 50 Ω.

Homogeneity profiles

In order to test the performance of our ABS apparatus, we measured the homogeneity of a saddle coil inside a commercial solution-state NMR probe (Bruker, Billerica, USA) installed in an NMR system operating at 400 MHz proton Larmor frequency. The homogeneity profile of the 1H rf coil was measured in both 200 step and 50 step increments, providing finer resolution (data shown in 4). Frequency shifts were normalized and plotted against the distance traveled, yielding the B₁ profile (Figure 4A,B).

Figure 4: Comparison of field profiles measured using the auto-ball shift vs. NMR spectroscopy.

B₁ field profiles of a saddle coil measured using ABS are shown above with the motor set to (A) one revolution per data point (200 motor steps) and (B) a half revolution per data point (50 motor steps). B₁ profiles of the same coil are measured by ¹H NMR, using a (C) 1D GradShim and (D) pseudo-2D GradShim spin-density experiment.

For comparison, B₁ profiles were also obtained via 1H NMR signals in a liquid sample (90% H₂O/10% D₂O). Specifically, the gradient shimming experiment [21], included in the TopSpin software, was used. This imaging technique applies a gradient during the acquisition period to encode spatial information in relation to the relative ¹H magnetization, or spin density, along the sample, resulting in a projection of both the ¹H signal and applied gradient (G_z) along the z-axis (Figure 4C). To obtain the isolated rf-dependent component, a pseudo-2D nutation NMR experiment was used. This step-wise acquisition mapped the local magnetization by measuring the NMR signal in a P0 sweep. The applied gradient revealed the spatially-encoded rf along the axis of the transceiver coil (Figure 4D). This experiment not only shows the shape of the rf homogeneity, but also provides insight about how B₁ inhomogeneity affects excitation 90° pulse widths. The coil length is approximately 23.85 mm in length, with an active length, or ideal sample length, of 23.5 mm.

The field maps obtained using the auto-ball shift apparatus are in good agreement with those obtained through NMR experiments. The auto-ball shift maps show a small decrease in the B₁ field on the left side of the profile, corresponding to the top of the transceiver coil. This decrease in B₁ can also be seen in the NMR experiment. The pseudo-2D nutation experiment is displayed as a contour map of excitation pulse times, with the optimal pulse regions in the center axis of the coil. On the left, where the B₁ drops, the optimal pulse region disappears, whereas on the right it is visible as an additional set of contours (indicated by the red arrow in Figure 4D).

Conductor geometries

To determine the optimal probing conductor geometry, we used the ABS device to compare the results for four different conductor shapes. The rf coil measured was a variable-pitch solenoid inside a 3.2 mm MAS probe resonating at 800 MHz. The four geometries compared were a sphere, a ring (band), a cylinder, and a flat disk, each with a 2 mm outer diameter (Figure 5B). Each conductor was placed at the tip of a 4–40 threaded nylon rod. The ABS assay was run at 200 step increments, or one full revolution per increment. The copper ball (sphere) induced the greatest frequency response in the probe circuit, followed by the ring, cylinder, and flat disk (Figure 5C). They induced maximum frequency shifts from 201.0 MHz to 204.3, 203.5, 203.3, and 201.9 MHz, respectively.

Figure 5:

(A) CST radio-frequency models of the four conductor geometries — sphere, ring, cylinder, and flat disk — used to compare perturbations induced on B₁. (B) Picture of the four conductor geometries in this analysis. (C) The four profiles obtained are superimposed. The sphere shows the greatest frequency response and is best suited for detecting finer changes in magnetic fields.

In addition, each conductor geometry was modeled inside the coil using Inventor CAD and imported into the Computer Simulation Technology Microwave Studio (CST MWS) (Darmstadt, Germany) software to analyze the electromagnetic properties and retrieve the B₁ profile along with induced perturbation effects (Figure 5A). Of the shapes tested, the sphere shows the highest effect on the surrounding magnetic fields, consistent with the experimental data.

Assessing positional accuracy

We assessed positional accuracy in repeated measurements by placing the motor in a homing position and observing deviations in tuning frequency after multiple trials. The motor was set to return to the starting position after each trial (Figure 6A). After fifty measurements, each after an ABS run, the measured tuning frequency consistently returned at 401.50 MHz (Figure 6B), indicating excellent reproducibility over multiple trials, allowing for quality control when comparing different coil designs.

Figure 6:

(A) Close-up illustration of a variable-pitch solenoid being tested by the ABS apparatus. An arbitrary starting point was chosen, labeled Homing Position. At this position, a frequency shift from 400.00 MHz to 401.50 MHz was induced. (B) The ABS assay was performed, then the conductor was returned to the homing position fifty times, and the frequency was recorded. A consistent 401.50 MHz is observed for each return value.

Discussion

The NMR experiment is highly dependent on the ability of the rf coil to efficiently and uniformly excite nuclei in the sample. This becomes even more critical with multiple-pulse experiments. Traditional benchtop methods to measure the homogeneity of B₁ are tedious and inefficient when testing many coil designs. The ability to make transceiver coils in the lab setting has improved with the development of dissolvable templates [41] and machined fixtures, however, they are usually still wrapped by hand, which can cause imperfections. Some trial and error may be required before obtaining the optimal rf profile; speeding up this process can facilitate testing of optimized designs and determining the potential limitations of using 3D-printed templates to accurately implement new coil designs.

The Slater Perturbation Theorem [40] describes the relationship between an object’s volume, shape, and material and the frequency perturbation it causes. Moreover, the derivation by Slater and Maier shows how frequency perturbations of different shapes, like for a sphere in Eq. 1, are related to the magnetic fields. Figure 5 illustrates this concept, as the sphere induced the highest frequency shift in the circuit network due to its large volume and non-directional perturbation. To obtain a similar response from a cylinder of equal diameter to a sphere, placing it at the correct angle is essential and requires more meticulous adjustment. In principle, our 2 mm diameter cylinder with its orientation normal to B₁ should display a similar response to our 2 mm diameter sphere; however, in practice its perturbation was not as effective, likely due to the short height of the cylinder and the difficulty of positioning it correctly in a real device.

Overall, the ABS apparatus is a convenient benchtop tool for measuring rf coil profiles consistently and precisely. Further, it is inexpensive to fabricate and can be standardized using 3D printing. We have built our prototype using a Intamsys Funmat HT printer to make the majority of the physical components essential for the ball-shift tests. Including the Arduino controller, the portable network analyzer, and the stepper motor, the total cost is about $150. This apparatus has reduced the time to test rf coils and improved the spatial resolution of B₁ profiles measured on the benchtop. The ABS apparatus can be further customized to improve its form factor and ease of use. Arduino shields, PCBs with dedicated slots and mounts, are commercially available to create a plug-and-play experience. Motor shields have the necessary connections, reducing loose wiring, and have a place to mount an A4988 or other microstep driver. For this study, we intentionally used a breadboard to wire our components to create a user-friendly experience, as it is easier to trace connections and observe their designation in the Arduino code. This is an important consideration, because a major motivation for this building this device was to make it easier for labs less familiar with coil fabrication and testing to use it themselves.

Conclusion

Here, we fabricated an automated device for testing NMR transceiver coils and demonstrated its performance using a 400 MHz solution-state probe and an 800 MHz MAS solid-state probe. The NMR spectroscopy experiments were in good agreement with the ball shift assay. The benefit of the benchtop ABS is the ability to test an rf coil before the probe is installed and calibrated for experimental acquisition, saving magnet time and experimenter effort. With the help of CAD and 3D printing, this apparatus can be modified to fit any NMR probe, whether solid- or solution-state. Further, we see this as the initial step toward 3D printing more probe components such as coil platforms, newer probe head designs, and other automated benchtop tests [42]. With appropriate attention to modularity of the tune and match circuits, this would make it easier to swap stator assemblies designed for different rotor sizes, so that experimenters could benefit from a larger rotor and hence increased signal-to-noise when there is an abundance of available sample, and to be able to use a smaller rotor and appropriately sized coil when sample preparation is a challenge, all in the same probe.