Compact 1 GHz Electron Paramagnetic Resonance Spectrometer and Imager

Abstract

A 1 GHz preclinical electron paramagnetic resonance spectrometer and imager has been developed to study low concentrations of radicals using rapid-scan detection. The design focuses on minimizing the losses between the resonator and the first-stage low-noise amplifier. The adjustable-frequency source with the lowest available noise was selected and the output was amplified to provide sufficient power for experiments with relatively rapidly-relaxing nitroxide radicals. For resonators with similar geometries and efficiencies, improved signal to noise was demonstrated relative to our previous instrument that operates at 700 MHz, consistent with predictions for frequency dependence. System performance was demonstrated for solutions of nitroxide radicals in resonators that contain 8 mm or 25 mm diameter cylindrical tubes. For ¹⁵N-d₁₆ tempone in aqueous solution and a signal averaging time of 3.8 s a signal-to-noise of 3 required 2×10¹⁴ spins in the 8 mm resonator or 4.5×10¹⁵ spins in the 25 mm resonator. 3D spatial imaging was demonstrated with a phantom consisting of three tubes containing solutions of a nitroxide radical.

I. Introduction

Many labs have demonstrated important applications of electron paramagnetic resonance (EPR) spectroscopy and imaging at frequencies at or below L-band.^1–11 Approximately 1 GHz microwave frequency appears to be optimum in the tradeoff between depth of penetration and signal-to-noise (S/N) for preclinical imaging of mice and other small animals.^12–14 Rapid-scan signal detection has been shown to give substantially improved S/N for a wide range of radicals, including nitroxides.¹⁵ In this paper we describe a 1 GHz spectrometer designed to minimize noise in rapid-scan EPR. Nitroxide radicals, which have many applications in biological systems, have shorter relaxation times¹⁶ than the trityl radicals that have been widely used for in vivo oximetry.^{2, 17} Shorter relaxation times permit use of higher rf powers to record optimized signals. For the relatively high incident powers that are useful for studies of nitroxide radicals, source noise may dominate. Recently, low-noise microwave sources have become available at 1 GHz, so we evaluated several adjustable-frequency sources.

A central design goal is to create a benchtop EPR imager for applications in preclinical research. Consistent with this goal, compact overall size guides some decisions. The progress reported in this paper builds upon the 700 MHz spectrometer described by Buchanan et al. 2018.¹⁸ The potential improvement in S/N while still having good depth of penetration for in vivo imaging of mice by increasing the frequency to 1 GHz stimulates the engineering effort reported in this paper. If components are broad-band, only the resonator has to change to increase frequency from 700 MHz to 1 GHz. However, many microwave components must be carefully selected because 1 GHz is an upper or lower frequency limit for some designs and narrow band components may offer better performance with reduced noise.

II. System design

The magnet, gradient coils, rapid-scan coils and rapid-scan current driver have been described previously.^{18, 19} Although the scan driver has options for various waveforms, sinusoidal scans were used exclusively in this study because of the lower power requirements for a given scan width. The rapid-scan coils are on a 3D printed plastic form that fits inside the gradient coils. The scan frequency is selected by changing capacitors in a plug-in capacitor box in-line with the coils, which resonates the circuit. Sinusoidal scans of 70 G at 26 kHz require, for example, 8.25 V_RMS and 1.28 A_RMS, hence 10.6 W are dissipated in the coils. The power needed to drive the coils is significantly increased by eddy currents in the resonator and other coils. If the resonator shield is too conductive, eddy currents can overheat it. Air cooling was provided by a small fan that directed air along the bore of the magnet. The major modifications relative to the 700 MHz system¹⁸ are in the rf bridge, resonators, and software.

A. Bridge

The 700 MHz spectrometer described in Buchanan et al.¹⁸ was designed for maximum flexibility, with multiple excitation and signal paths selectable with switches. As stated there, the additional components in the signal detection path added about 6.7 dB of loss after the resonator in the detection system. The new 1 GHz spectrometer design goals include maximizing sensitivity for small numbers of radicals as expected for in vivo experiments. Removing components that are not necessary for the experiment that the user wants to perform lowers the overall noise figure (NF) and gives the highest possible S/N. A decision was made to use a reflection resonator due to its ease of tuning. Use of a reflection resonator also permits removal of much of the switching present in the 700 MHz bridge,¹⁷ resulting in the design of the 1 GHz bridge that is shown in Fig. 1.

Figure 1.

Circuit for the 1 GHz bridge. Descriptions of the components are given in Table 1. The input labeled as ‘RF Source’ is the output from the Rohde & Schwarz SMA100B.

Unlike a pulse experiment, the rf source is on during CW or rapid-scan data acquisition so it may be a significant contributor to experimental noise. The data analysis for the rapid scans uses both the I and Q components of the detected signal, so it is important to have a source with the lowest possible noise in both channels. The amplitude and phase noise for a Rohde & Schwarz SMA100B (Rohde & Schwarz USA, Columbia, MD), a MicroLambda MLVS (Micro Lambda Wireless, Fremont, CA), a Holtzworth HSX 9004A (Holtzworth Instrumentation, Boulder, CO), a Tektronix AWG70002A (Tektronix, Beaverton, OR), a Berkley Nucleonics (BNC) Model 986 (Berkeley Nucleonics Corporation, San Rafael, CA), and a SP Teledyne SDR14TX-PCIe (Teledyne Lecroy, Chestnut Ridge, NY) were determined (Fig. 2). The powers incident on the resonator were measured with a Ladybug LB559A (www.ladybug-tech.com). The L-band EPR signal for 2,2-diphenyl-1-picrylhydrazyl (DPPH) does not saturate with available powers, so it was used to phase adjust the signals in the I and Q channels. When the signal has been adjusted to have absorption in one channel (I) and dispersion in the second channel (Q), amplitude noise is in the I channel and phase noise is in the Q channel. The rms noise (mV) was calculated based on baseline regions of the spectrum for DPPH in a 4 mm loop gap resonator (LGR) (Table 2) and was corrected for number of half-cycles averaged. Of the sources studied, the Rohde & Schwarz SMA100B has the lowest noise in both channels at high powers so it was selected for input to the bridge. For this source the noise is approximately independent of power up to 0.0067 W. The source is operated at constant power of 0.10 W, which is the maximum available. At the maximum power at the resonator the noise is approximately 3 times the baseline value. Amplification by A1 (15.6 dBm), losses in the system, and the need to avoid saturation of components in the detection path in the bridge limited the power incident on the resonator to 0.165 W. When comparing source noise for the same power at the resonator no advantage was found in decreasing the source output and increasing the amplification by A1.

Figure 2.

Rms noise as a function of log (power (W)) for the six rf sources. Noise in the baseline of a spectrum, acquired with 2000 averages and 2 half cycles per cycle, was divided by √4000 to obtain the average value for a single scan. Source power output was measured after attenuation (SA1) and amplification (A1).

Table 2.

Resonators used for experiments reported.

Resonator designation	Type	Frequency Range (MHz)a	Diameter (mm)b	Height (mm)c	Q water	Efficiency (mT/√W)	Incident power (W) for a B1 of 0.006 mT
8 mm	Reflection, LGR	1030–1080	9	10	45±6	0.051±0.002	0.014
25 mm	Reflection saddle coil	1010–1040	25.5	24.5	33±4	0.0067±0.0002	0.80
UHF-4 mm	Reflection Alderman-Grant	695.7	4.5	4.6	71	0.103	0.0034
L-4 mm	Reflection Alderman-Grant	1070–1080	4.5	4.6	97	0.106	0.0032

^aThe low and high frequencies listed in the table are for the resonator with a tube containing an aqueous sample and without a sample, respectively. For the frequency ranges and ‘Q with water’ the inner diameters of the tubes containing water were 7 mm, 21 mm, 3 mm, and 3 mm respectively.

^bInterior diameter of resonator

^cHeight of the active volume

Bridge components are listed in Table 1. Microwave source power is directed with a 30 dB coupler. The through-path of the coupler, which is the excitation path, is then attenuated by SA1 and amplified by A1. The coupled output is amplified by A3 and A4 to supply the phase-coherent local oscillator (LO) side of the mixers, which is constant, independent of the power incident on the resonator. Nitroxides in fluid solution have relaxation times that are less than a μs²⁰ so higher B₁ can be used for nitroxides than for trityl radicals²¹ without saturating the spins. The large resonators that are used in this study have relatively low efficiencies (Table 2) so high powers are required to achieve B₁ of about 0.006 mT. This B₁ maximizes the signal for air-saturated aqueous solutions of ¹⁵N-d₁₆-tempone within the range where signal increases linearly with square root of power. The loop gap resonators typically have about 30 dB coupling so if the A1 maximum of 22 dBm power incident is used, −8 dBm will be reflected which is then amplified to 10 dBm by A2. There is 3 dB of loss in the splitter, so 7 dBm of power is output to each of the mixers. To allow for imperfect tuning and additional reflected power, high-power mixers are necessary. The Marki MM1–0115HS mixers were chosen, which can handle a maximum of 33 dBm of power. The LO side was operated at constant power of 17 dBm, which is within the requirement for less than 21 dBm. After the mixers only the DC EPR signal is left, which is usually in the mV range and needs to be amplified prior to the digitizer. Careful accounting of the microwave power is needed throughout the bridge using actual measured powers and not just manufacturer specifications to ensure that all components are operating within their specified power range.

Table 1.

Parts list for 1 GHz bridge

Reference Designator	Device Type	Manufacturer	P/N	Gain	NF	Linear Output Level
(A1)/(A4)	Amplifier	MiniCircuits	ZX60-P103LN+	15.6 dB	0.5 dB	22.4 dBm
(A2)/(A3)	Amplifier	MiniCircuits	ZX60-P33ULN+	17.7 dB	0.4 dB	17.4 dBm
(DC1)	Directional Coupler	MiniCircuits	ZX30-30-4
(DC2)	Directional Coupler	MiniCircuits	ZX30-20-4
(CIR)	Circulator	UTE	CT2004-O
(SA1)	Step Attenuator	JFW	50DR-001SMA
(SW1)	Electronic Switch	MiniCircuits	ZX80-DR230-S+
(LIM1)	Limiter	MiniCircuits	VLM-33-S+	−0.2 dB
MIXER	Mixer	Marki	MM1–0115HS
0° SPLITTER	Splitter	MiniCircuits	ZFSC-2–5+	−3.0 dB
90° HYBRID SPLITTER	Splitter	MiniCircuits	ZX10Q-2–13-S+	−3.0 dB
VIDEO AMPLIFIER	Amplifier	Femto	HVA-10M-60-B	40.0 dB	12
LOW PASS FILTER	Filter	MiniCircuits	SLP-5+

The digitizer selected is the 14-bit Teledyne SP Devices ADQ14, which has the advantage of PCIe interface providing rapid data transfer. Fewer than 14 bits would not provide adequate dynamic range for weak signals superimposed on a large rapid-scan background. The output from the digitizer, in arbitrary units (a. u.) was converted to mV using the conversion factor of 0.029 mV/a.u. provided by the vendor.

The video amplifiers described previously,¹⁸ which had a noise figure of 15, were replaced with Femto amplifiers that have a noise figure of 12. The adjustable gain of the Femto amplifiers was set at 40 dB. The bandwidths of the Femto amplifiers are larger than signal bandwidths, so Mini-Circuits SLP-5+ low pass filters were added to decrease noise at frequencies above 5 MHz. The bandwidth of these filters is selected to be large enough to capture the full bandwidth of the rapid scan signals.²² To permit the use of a DC coupled digitizer a simple homebuilt 80 Hz RC high pass filter is used to remove the DC component so that the digitizer is not overwhelmed.

Modern EPR spectrometers use microwave circulators to direct the microwave energy to the resonator and from the resonator to the detection path. In circulators the microwaves can go in the reverse direction, albeit with about 20 dB attenuation. The microwave power that leaks through the circulator can add to the EPR signal. Most commercial spectrometers use an attenuated and phase-shifted path around the circulator that is then mixed with the EPR signal path to cancel the leakage. To hopefully mitigate any leakage a directional coupler was tried in place of the circulator because the directivity measured was 35 dB compared to the 20 dB in the circulator. It was found that there was a negligible difference with the circulator giving a S/N of 540 and the coupler giving a S/N of 530. These tests used a UTE CT2004-O circulator and Pasternack PE2201–10 10dB directional coupler. The 4 mm L-band reflection resonator was used (Table 2). Data were collected for a 0.2 mM trityl-CD₃ sample²¹ at approximately 5×10⁻⁵ W averaging 1,000 scans, with a scan rate of 2.85 kHz. A post-acquisition 0.05 G line width filter was applied to the deconvolved data, and the S/N was corrected to account for the minor variation in insertion loss. This paragraph updates information in the PhD dissertation of Lukas B. Woodcock.²³

B. Resonators

Resonator construction is more challenging at 1 GHz than at significantly lower or higher frequencies because the wavelength is similar to resonator component sizes.²⁴ The characterization of the resonators used in this study is summarized in Table 2. The 8 mm (Fig. 3) and 25 mm (Fig. 4) resonators use the same design of a sliding inductively coupled loop for tuning. In the 8 mm resonator the interior is a coil of wire that is split in half with a bridging capacitor to make the field more uniform. In the 25 mm resonator the coil is shaped like saddles and a small piece of coax is used to bridge instead of a chip capacitor. A polylactic acid plastic housing is 3D printed, and the inside is coated with silver paint to shield the resonator. A minimal layer of coating was used because too thick a coating can result in eddy currents that heat the shield and increase the voltage requirements for a scan. The 4 mm resonators are Alderman-Grant style resonators cut from a piece of copper tubing (Fig. 5). This style of inductive coupling²⁵ and differences in geometries have been described.²⁴

Figure 3.

Pictures of 8 mm inductively coupled loop gap resonator. Two small chip capacitors are soldered across the gap. The left panel shows the resonator in the upright position that it is in when inserted into the magnet. The right panel shows the gear mechanism that moves the green coupling coil to adjust for critical coupling. A list of dimensions is in Table S1 of Supplementary Materials.

Figure 4.

Pictures of 25 mm inductively coupled saddle coil resonator. The left panel is the complete resonator, with the shield lowered. The middle panel shows the coupling assembly. The small pieces of coax are used as capacitors. A screw attached to the green knob moves the coupling loop up and down. The two right panels are views rotated by 90^o of the resonator coils. A list of dimensions is in Table S1 of Supplementary Materials.

Figure 5.

Pictures of 4 mm inductively coupled Alderman-Grant resonator. The left panel shows all components. The center panel is the assembled resonator without the outer shield. A small chip capacitor is soldered across the coils. The mechanism to move the coupling loop is the same as in the 25 mm resonator. The two right panels are the coils, without and with, the capacitor. A list of dimensions is in Table S1 of Supplementary Materials.

The Q = ν/Δν of the resonators was measured with an Anritsu Vector Network Analyzer MS46122A. The Q can be estimated as Δν at the 3 dB points. A more accurate calculation for where on the dip (in dB) Δν should be measured is given in eq 1, where dB_o is the value at the center of the dip.²⁶

$${dB}_{\Delta \nu }=10\text{log}\left(1-\frac{1-{10}^{\frac{{dB}_{°}}{`10}}}{2}\right)$$ (1)

To measure the resonator efficiency a standard sample was characterized on an X-band Bruker EMXnano. A single crystal of BDPA was selected because its relaxation times are independent of frequency between L- and X-band. When the EPR signal for the same sample is saturated to the same extent (≈ 20%) in the X-band and L-band resonators, the B₁ is the same. The efficiency of the Bruker SHQE resonator is known (0.2 mT/√W)²⁷ and the power incident on both resonators is known, so the efficiency of the L-band resonator can be calculated. The BDPA sample does not saturate in the 25 mm L-band resonator because the efficiency is too low, so a power saturation curve for the E’ center in irradiated fused quartz was recorded with the 8 mm resonator and that was used as a transfer standard to find the efficiency of the 25 mm resonator.

Materials with a high dielectric constant, such as water, distort the microwave distribution in a resonator when the sample dimensions are significant relative to the rf wavelength.²⁸ This is known as the “lens effect” and can result in increased B₁. At 1.0 GHz λ is ~ 30 cm so the 25 mm resonator has a dimension that is significant relative to λ. To test for the lens effect power saturation curves were measured for a sealed de-oxygenated sample of LiPc (lithium phthalocyanine) with dimensions approximately 1 cm by 0.1 cm. The sample was positioned in an empty 25 mm tube and also centered in the 25 mm tube filled with water. The power saturation curves are shown in Fig. 6. The decrease in power required to cause signal deviation from linearity, the criterion for power saturation, showed that the B₁ was about 3.5 times larger inside the aqueous sample than in air. The Q with an aqueous sample is 33 and without is 127. Since resonator efficiency is proportional to √Q this decrease in Q is expected to decrease B₁ by a factor of about 2. Thus, for the 25 mm resonator the increase in B₁ (rather than a decrease) shows that the lens effect dominates over the effect of lower Q. In the smaller 8 mm resonator Q decreased from 72 to 45 when the tube was filled with water. This decrease in Q is expected to decrease B₁ by a factor of 1.26 times, and a factor of 1.35 was observed. Thus, for the 8 mm resonator the lens effect has minimal effect because of the smaller size of the aqueous sample. For imaging a mouse or other small animal the lens effect will be minimal because of the heterogeneity of the tissue.²⁹

Figure 6.

Comparison of power saturation curves in the presence and absence of water. The data were taken at a scan frequency of 2.55 kHz. Orange: LiPc sample in 25 mm tube filled with water. Purple: Same LiPc sample in empty 25 mm tube in 25 mm resonator. Blue: Same LiPc sample in 8 mm tube filled with water. Green: Same LiPc sample in empty 8 mm tube in 8 mm resonator. The y axis is linear in signal amplitude. The colored dashed lines are the best fits to the linear regions of the curves, extrapolated to higher power. The vertical dashed lines mark the powers at which the signal intensity deviates from linearity by about 20% due to power saturation. Points for higher powers are omitted. Since the dispersion signal saturates less readily than the absorption signal, and deconvolution uses both channels, the amplitude of the deconvolved signal is distorted at powers that saturate the absorption signal. The uncertainty in resonator efficiency is estimated at ±5%; error bars are omitted for clarity.

The lower efficiency for larger resonators (Table 2) is typical for EPR resonators²⁴ but means that higher incident power is needed to achieve the same B₁ at the sample in larger resonators. In air-saturated solution the amplitude of the signal for a 275 μM ¹⁵N-d₁₆-tempone in aqueous solution with a scan rate of 26 kHz was observed to increase linearly with square root of power up to a B₁ of about 0.006 mT in the 8 mm resonator. If there were no limits on power, one would acquire spectra with B₁ = 0.006 mT in any resonator. However, to achieve the same B₁ = 0.006 mT requires about 56 times higher incident power in the 25 mm resonator than in the 8 mm resonator because of the differences in efficiencies (Table 2). This would require 0.80 W, which exceeds the available power, so spectra in the 25 mm resonator were acquired at lower B₁ than in the 8 mm resonator, which decreases the S/N that can be obtained for the same number of spins.

1. Resonator Tuning

In the 700 MHz system a Tektronix AWG or a Teledyne SP Devices SDR14TX was used as the source of a chirp pulse for resonator tuning.¹⁸ Since a design goal is to make a smaller and more transportable imager the Tektronix AWG had disadvantages of high cost and large size. The SDR14TX solves the size issue as it is a PCie device that fits in the workstation, but a large and expensive Teledyne LeCroy Wavesurfer oscilloscope was still used to detect the resonator response. In the new system the synthusb3 from Windfreak technologies (windfreaktech.com) was selected as the source for the frequency chirp because it is accurate, inexpensive and small. Instead of direct detecting the response to the chirp pulse at 1 GHz, a diode detector was added to the bridge, which rectifies the reflected chirp signal. The DC signal from the diode can be input either to a low frequency scope or to the digitizer that is used for the signal. To digitize both the EPR and tune signals on the same device we selected the DC coupled version of the ADQ14 because the AC version of the same digitizer cuts off at 80 Hz. To generate the trigger a 555 timer in the astable configuration mode was used with a transistor line driver as described in Figure S1 of the Supplementary Material. The resonator dip is read from the digitized frequency sweep. The frequency from the Rohde & Schwarz source is adjusted to match the resonator frequency by sending a command to the source.

C. Software

The software is written in MATLAB (MathWorks, Natick, MA). Depending on the capabilities of the digitizer/averager and the host PC there are two strategies for extensive signal averaging – (i) acquire a long array in the digitizer then segment and co-add scans after transfer to the PC or (ii) perform signal averaging in the digitizer and then transfer to the PC. In the previous iteration of the system¹⁸ the digitizer with the base data acquisition (DAQ) firmware could not signal average. The memory was filled with many sequential rapid-scan cycles, after which all of the data was transferred to MATLAB. Within MATLAB the long array was separated into rapid-scan cycles, and then added to previous blocks of data, which slows down the data acquisition. The current system uses the advanced time domain option (ATD) of the Teledyne SP Devices ADQ14 which can sum data for individual rapid-scan cycles directly on the digitizer and transfer the summed data. To communicate with the device a C-language layer, provided by SP Devices, is used to translate MATLAB commands. In this mode there is a 5 s fixed overhead to send the acquisition parameters to the digitizer, arm the digitizer, and receive a response so that data collection can start. This is a fixed overhead so once it is set up spectra can be taken much more quickly, which means that when taking an image there is virtually no overhead beyond the initial set up time. For example, to capture 10 k averages of a full cycle of a 26 kHz rapid-scan signal requires 38.46 μsec (=1/26000 sec) multiplied by 10 k which is about 0.3846 seconds and has negligible overhead. This approach uses data acquisition time more efficiently.

Each full sinusoidal rapid-scan cycle consists of an up-field scan and a down-field scan through the signal which were deconvoluted using the published algorithm and combined.³⁰ Correction for the rapid-scan induced sinusoidal background was performed as previously reported.³¹ Additional correction was performed using the MATLAB backcor function as described in the Supplementary Material. The final step in the data workup uses a Gaussian filter with a standard deviation that is selected to decrease noise with no more than 5% broadening of the line. Rms noise was calculated in baseline regions of the spectra.

III. EPR samples

DPPH (1,1-diphenyl-2-picryl-hydrazyl, Sigma-Aldrich, St. Louis, MO) and ¹⁵N-tempone-d₁₆ (4-oxo-2,2,6,6-tetramethylpiperidine-d₁₆-1-¹⁵N-1-oxyl, CDN Isotopes, Pointe-Claire, Quebec, Canada)) were used as received. Solutions of ¹⁵N-d₁₆-tempone were prepared gravimetrically in deionized water. Concentrations were checked on an X-band EMXnano using the Bruker software. BDPA (1:1 α,γ-bisdiphenylene-β-phenylallyl complex with benzene 1:1, Sigma-Aldrich, Saint Louis, Missouri) was used as received. LiPc (lithium phthalocyanine, Dartmouth College, Hanover, New Hampshire) was used as received. The irradiated fused quartz sample with 26 MRad dose was described previously.³² 0.2 mM trityl-CD₃ was described previously.²¹

IV. Performance Tests

A. Comparison of S/N with 700 MHz

A test of whether there was a real advantage to moving from 700 MHz to 1 GHz was performed using a particle of BDPA, whose relaxation times at room temperature are not frequency dependent in this region. Spectra obtained in two similar 4 mm resonators (Table 2) are compared in Figure 7. For the same data acquisition parameters the signal amplitude increased and the S/N improved from 295 to 595, which is a factor of 2.1. Signal is predicted to be proportional to magnetic susceptibility χ”, filling factor η, and resonator Q (Eq. 2).³³ The χ” is proportional to frequency, ω. If noise is assumed to be frequency independent, then S/N is proportional to V_s. The efficiencies of the two resonators were nearly identical (Table 2). The ratio of S/N at L-band and 700 MHz is then predicted to be proportional to the ratio (Q_L ω_L)/ (Q₇₀₀ ω₇₀₀). Using the values of Q from Table 2 and the frequencies at which the comparison was made (1074 and 696 MHz) this ratio is 2.1, which is excellent agreement with experiment.

Figure 7.

BDPA spectra recorded at 1 GHz (blue) and 700 MHz (red). The same BDPA sample was used in both cases, as its spectral properties are not field-dependent within this frequency range. Measurements were performed using a pair of similarly designed 4 mm diameter resonators, as described in Table 2.

$$V_s=\frac{1}{2}x”ƞQ\sqrt{Z_{0}P}$$ (2)

B. Magnetic field scan widths and field homogeneity

The coil constant for the rapid-scan coils was calibrated using the well-defined ¹³C hyperfine coupling constants for trityl-CD₃³⁴ at a scan frequency of 2.55 kHz and verified at higher scan frequencies with the ¹⁵N-d₁₆ tempone nitrogen hyperfine coupling constant of 2.25 mT.³⁵ For I = 0.5 (¹⁵N) the Breit-Rabi corrections are the same for the two nitrogen hyperfine lines,³⁶ and the spacing between the two hyperfine lines is equal to the nitrogen hyperfine coupling at both X-band and L-band. The coil constant decreases with increasing scan frequency and sweep width, which is attributed to the effects of eddy currents that tend to oppose the rapidly oscillating fields. For example, the coil constant for a 4.0 mT scan at 26 kHz is about 0.94 times the value at slow scans and narrow sweeps. In the data workup sweep widths were corrected based on the known value of the nitrogen hyperfine coupling constant.

To test the field homogeneity four samples of deoxygenated LiPc with dimensions of about 0.5 × 3 mm were positioned about 1 cm apart along the three Cartesian axes. In a rapid-scan spectrum acquired with 20 mT scan width and 2.55 kHz scan frequency a single line was detected with a full-width at half-maximum (FWHM) linewidth of 0.0075 mT, which is in good agreement with the linewidth observed at X-band for these samples. Assuming that a field inhomogeneity greater than about 10 % of linewidths would be detectable, this result confirms excellent magnet homogeneity. However, when samples of ¹⁵N-d₁₆-tempone were recorded in 8 mm or 25 mm tubes, the linewidths were dependent on scan frequency. At X-band the ΔB_pp is 0.025 mT for 0.12 mM ¹⁵N-d₁₆-tempone equilibrated with air at Denver’s atmospheric pressure of about 0.82 atm. Relaxation times for tempone are about the same at X-band and L-band,³⁵ so similar linewidths are expected at X- and L-band. The rapid-scan spectra are displayed as absorption spectra, for which the FWHM is √3∙ΔB_pp which would be 0.043 mT. At L-band for 4.0 mT scans with a scan frequency of 2.55 kHz the FWHM was 0.048 mT in both the 8 mm and 25 mm resonators, which is in reasonable agreement with expectations. However, when the scan frequency was increased to 17.6 or 26 kHz the FWHM increased to 0.055 or 0.062 mT, respectively, even after correcting the scan widths for changes in the coil constant. The increases in linewidth are attributed to increasing effects of eddy currents impacting magnetic field homogeneity, in addition to the effect on the coil constant for the sweep coils.

C. Noise figure of detection system

Noise figure (NF, dB) = 10 log (F, unitless) where F is called the noise factor. These parameters are measures of the noise added by a device. The NF for the detection system includes components extending from amplifier A2 to the digitizer (Fig. 1). The Friis equation (Eq. 3) calculates F, based on the gains (G) and the losses in the components; for each stage F-1 is divided by the product of the gains of the previous stages. Gains and losses of the various stages in the bridge were measured by inputting a known power at 1 GHz and measuring the output with the Ladybug LB559A. From Eq. 3 it can be seen that the first amplifier sets the noise floor of the device which is why A2 was moved closer to the resonator in this system (Fig. 1) relative to our previous system.¹⁸ Cable lengths and connectors also introduce loss so decreasing cable lengths and removing any unnecessary components decreases loss. To measure the NF of the detection system the Y factor technique was used. A Pasternak noise source (PE85N1001) was put in place of the resonator and used to inject a known level of noise into the system (ENR) of 29.34 dB. To measure the noise the output of the video amplifiers was connected to a Rohde & Schwarz spectrum analyzer FPC1000, with low-noise preamp option. The ratio, Y, of the noise with the noise source on (N_on) to the noise source off (N_off) was measured (Eq. 4). The NF is calculated using Eq 5. A perfect amplifier would have F = 1 and NF = 0 dB (Eq 5). In making the measurements it was determined that the noise floor of the spectrum amplifier was sufficiently low, that it did not dominate the noise and that the input was not saturated at high gains.

$$F_{12\dots n}=F_1+\frac{\left(F_2-1\right)}{G_1}+\frac{\left(F_3-1\right)}{G_1{G}_2}+\dots \frac{\left(F_n-1\right)}{G_1{G}_2\dots G_{n-1}}$$ (3)

$$Y=\frac{N_{on}}{N_{off}}$$ (4)

$$NF\left(dB\right)=ENR\left(dB\right)-10\text{log}\left(Y-1\right)$$ (5)

The NF calculations were performed for the DU-built video amplifier used in the previous system (NF = 15.)¹⁸ and the Femto amplifiers (NF = 12.) For example, with the Femto amplifiers and ENR = 29.34 dB, Y = 283, which gives NF = 4.8 dB. The results measured with the Y-factor method and calculated with the Friis equation are in good agreement (Table 3). The data indicates that the actual NF of the DU amplifiers is likely lower than 15 which was reported previously. The Femto amplifiers are better shielded and appear to be less susceptible to pickup of stray signals than the DU amplifiers. For signals from dilute nitroxide solutions the replacement of the older video amplifier by the Femto amplifier improved the S/N by about 20%. This small change in S/N is consistent with the similarity in calculated performance, within estimates of uncertainty.

Table 3.

Impact of video amplifier on noise in the detection system

VA	Y factor NF	Friis NF	Measured Gain (dB)a	Bandwidth (MHz)b
Femto	4.8	4.8	49.5	5
DU18	5.6	6.8	49.5	3

^aMeasured with Ladybug LB559A.

^bBandwidth of filter after amplifier

D. Noise in baseline of spectra

The data (Figure 2) that were used to compare noise performance of sources were obtained with a previous configuration of the bridge. To define the baseline noise with the current bridge configuration (Figure 1), spectra of BDPA at low power (1×10⁻⁶ W) and 4.0 mT sweep width were acquired. The bandwidth of the Gaussian filter that is used in the final step of data workup was set to 0.02 mT, which is equivalent to omitting it. The limiting bandwidth is then the 5.0 MHz of the hardware filter in the bridge. With this bandwidth and including the G (49.5) and NF of the system (4.8), the thermal noise power in spectra calculated using Eq. (6)³⁷ is −52.7 dBm. In a 50-ohm circuit the P_n from eq. (6) can be converted to rms voltage using Eq. (7) which gives 0.52 mV at 295 K.

$$P_n=-174+10\text{log}\left(\mathit{\text{bandwidth}}\right)$$ (6)

$$V_n=\sqrt{P_n{Z}_0}$$ (7)

The rms noise in the baseline of spectra obtained in the 4 mm resonator with a scan frequency of 2.7 MHz was 0.55 mV, which is in good agreement with the prediction for thermal noise propagated through the detection system. The noise increases with increasing scan frequency and resonator size, up to 1.0 mV in the 25 mm resonator with a scan frequency of 24.9 kHz, as discussed in the Supplementary Material. The baseline noise at the powers used to acquire spectra of nitroxides is discussed in the following section.

E. Signal and noise for ¹⁵N-d₁₆-tempone samples in 8 and 25 mm resonators

The rapid-scan EPR signal for aqueous air-saturated solutions of ¹⁵N-tempone with a scan frequency of about 2.55 kHz are linear in square root of power up to a B₁ of about 0.006 mT, so that B₁ was used for the S/N tests with the 8 mm resonator (Fig. 8). Spectra were signal averaged 100 k times, which requires about 7.5 s. This B₁ requires incident power of 0.014 W which is in the range where the contribution from source noise is small (Fig. 2). The S/N that was obtained with samples of ¹⁵N-d₁₆-tempone in an 8 mm OD tube in the 8 mm resonator was 801 for 275 μM, 167 for 50 μM, and 90 for 20 μM. The efficiency of the 25 mm resonator is lower than for the 8 mm resonator by about a factor of 8 (Table 2), which means that the incident power on the resonator would need to be 56 times larger to achieve the same B₁. The spectra in the 25 mm resonator were obtained at a power which gave the maximum S/N, which was at 0.077 W (B₁ of 0.002 mT). This power is in a range where source power dominates (Fig. 2) and increasing power increases noise. For this resonator increasing power above 0.077 W increases both S and N for the ¹⁵N-d₁₆ tempone sample and does not improve S/N. Although the S/N for the samples in the two resonators are similar in Fig. 7, the volume of sample in the 25 mm resonator is about 17 times larger than for the 8 mm resonator. Larger numbers of spins are required to achieve the same S/N in the two resonators (Table 4).

Figure 8.

Comparison of S/N for air-saturated solutions of ¹⁵N-d₁₆-tempone in the 8 mm (P = 0.014 W (B₁ of 0.006 mT)) and 25 mm (P = 0.077 W (B₁= 0.002 mT)) resonators. The y axis scales are in mV. To calculate the signal amplitude for a single scan the arbitrary units are divided by number of half cycles co-added. To calculate the noise for a single scan the value is divided by the square root of the number of half cycles co-added.

Table 4.

¹⁵N-d₁₆-tempone spins in active volume of resonators

Resonator	High Concentrationa	Low Concentrationb	Average Spins required for S/N = 3	Concentration required for S/N = 3
8 mm	6.4×1016 spins	4.6×1015 spins	2.0×1014 spins	0.8 μM
25 mm	1.1×1018 spins	6.3×1016 spins	4.5×1015 spins	1.1 μM

^aThe high concentration samples were 275 μM for both resonators

^bThe low concentration samples were 20 and 15 μM for the 8 mm and 25 mm resonators, respectively

The noise in the baseline of the spectra in Fig. 8 is higher than what was observed at 1×10⁻⁶ W for the same resonators and scan frequencies (see Supplementary Material). Increasing power may increase noise by introducing more source noise. Higher power also increases deviations of the background signal from a simple sinusoid, which makes background removal more difficult, and introduces residual baseline variation that contributes to higher baseline noise. The 0.4 G Gaussian filter that is used in the final step of the data workup removes some high frequency noise but does not remove lower frequency baseline variation that makes substantial contributions at higher scan frequencies. Microphonics in the resonator may also contribute to noise at higher scan frequencies.

The biggest uncertainties in predicted signal intensities using Eq (2) is in the filling factors, η. As discussed in the Supplementary Materials, the calculated signal intensities are in reasonable agreement with the experimental intensities. The noise in the baseline of the spectra is highly dependent on pickup of the scan frequency, incomplete removal of the rapid scan background and injection of source noise. To account for some of the rapid scan background a smaller region of noise can be used in calculations. Using this method, the 8 mm resonator gives a minimum value of 2.0 mV. This increases up to 3.8 mV with the 25 mm resonator.

F. 3-D spatial imaging

The imaging capabilities of the system, using the 25 mm resonator, were demonstrated with a phantom that was constructed from two 8 mm o.d. tubes sandwiching a 4 mm thick flat rectangular tube as shown in Fig. 9. Each of the three tubes contained 1.1 mM ¹⁵N-d₁₆-tempone and was filled to a height greater than the active volume of the resonator. Data acquisition parameters were as follows; 100 k averages, scan frequency of 26.25 kHz with 2 mT scan widths, 0.5 mT/cm maximum gradient with equal solid angle sampling, and 15 steps in θ for a total of 142 projections.³⁸ Projections were acquired at 77 mW which gives B₁ of 0.002 mT. Filtered back projection was used to reconstruct the image based on the low-field nitrogen hyperfine line. Slices through the image show the expected sample geometry.

Figure 9.

Slices through 3D images of the phantom, reconstructed from one nitroxide line.

G. Background Removal

A problem inherent to rapid scan is the background oscillation that is induced by the rapidly fluctuating magnetic field. The background signal typically is dominated by a sinusoid at the scan frequency and its first harmonic, which can be removed relatively effectively in software.³⁹ However, there are residual artefacts possibly arising from pickup signals and eddy current induced microphonics that may be significant for weak signals. At 250 MHz when using a bimodal cross loop resonator the background removal was improved by a combination of reversal of field direction and scan direction.⁴⁰ However, that method requires a bimodal resonator. The spectra at 1 GHz were obtained with reflection resonators so other background removal methods were tested. The background signals have components that are independent of B₀ and incident power. Other components increase with increasing power. If the background is independent of signal, then acquisition of two scans in which the rf phase is flipped by 180⁰ then calculating the difference between the two signals should reinforce signal and null the background. This can be done with a phase shifter inserted between the rf coming from the bridge and the circulator (Fig. 10). To test the effectiveness of this method a manual phase shifter (360° per GHz) by ARRA INC. with model number 3428B, serial 1213, was added on port 1 of the circulator to shift the input RF signal by 180^o. An example of the subtraction for a signal with an unusually large background that is coherent with the rapid field scan and can be removed with a 180^o phase shift is shown in Figure 11. Subtraction of data set 2 (blue) from data set 1 (red) gives the black trace with greatly reduced background sinusoid. Data acquisition was performed at a B₁ of 2.7×10⁻⁴ mT with a 100 μM nitroxide sample. The acquisition parameters were as follows: center field of 36.347 mT, scan frequency of 25.65 kHz, scan width of 7 mT, 5000 data points, 15 ns resolution, 40 dB video amplifier gain, 32x digital gain, and 100,000 scans. The reported amplitudes of background intensities are peak-to-peak.

Figure 10.

Circuit modification to implement 180^o phase shifts.

Figure 11.

Spectra of 100 μM nitroxide showing impact of 180^o phase shift. The red and blue traces are 180^o out of phase and black is the difference. (left) Absorption, with amplitude of the background, Red: 9×10⁶, Blue: 8.2×10⁶, Black: 0.8×10⁶. (right) Dispersion, with amplitudes of the background, Red: 2.9×10⁷, Blue: 2.5×10⁷, Black: 0.4×10⁷.

The data in Fig. 11 shows that a substantial portion of the background is removed, but there are residuals. For most data sets the fraction of the background signal that is removed by the 180^o phase shift is relatively small. It was concluded that the 180^o phase shift method was a useful trouble-shooting tool, to identify pickup contributions to the background. However, since a substantial portion remained after the phase shift, it was not worth sacrificing S/N to put in more components when other approaches would still be required to remove the residual background. Improved software methods to remove background contributions are being explored.

H. Conclusions

The primary improvement in S/N for the current system relative to the 700 MHz instrument is due to the removal of components between the resonator and the first-stage low-noise amplifier, which has reduced the noise figure. The current system has baseline noise at low power that is close to thermal noise. However, even with the high-performance Rohde & Schwarz source, source noise is a significant contribution at the high powers that are required to generate the optimum B₁ for nitroxides in the larger resonators that will be needed for in vivo studies. Sources with lower noise would be beneficial. Fixed frequency sources are available with lower source noise than variable frequency sources. However, using a fixed frequency source requires resonators that can be tuned to match the source frequency. One approach to tuning resonator frequency is a varactor, but these have been found to introduce substantial noise.⁴¹ At the high scan frequencies that are needed for acquisition of large numbers of projections for images, the baselines contain scan-induced microphonics. More robust resonator designs could potentially lower this effect. The amplitude of the scan-induced background signal depends on scan frequency and amplitude and includes harmonics of the sinusoidal scan frequency. Incomplete removal of these induced background signals result in baseline “noise” after deconvolution that dominates at high scan frequencies. The main limitation on rapid scan is the scan-induced background signal, which can be larger than the EPR signal. Efforts to identify the main contributors to the background and remove it via more robust resonators and via signal processing are underway.

Future efforts will include creating a pulsed EPR version of the 1 GHz imager and further decreasing the overall size to increase practical applications.

Supplementary Material

Trigger circuit for tuning timing, dimensions and parameters for resonator parts, calculation of absolute signal intensity and comparison with experimental data, calculation of thermal noise and comparison with experimental data

Data Availability:

The datasets generated in the current study are available from the corresponding author upon reasonable request.