Background correction in rapid scan EPR spectroscopy

Abstract

In rapid scan EPR the rapidly-changing magnetic field induces a background signal that may be larger than the EPR signal. A method has been developed to correct for that background signal by acquiring two sets of data, denoted as scan 1 and scan 2. In scan 2 the external field B₀ is reversed and the data acquisition trigger is offset by one half cycle of the scan field relative to the settings used in scan 1. For data acquired with a cross-loop resonator subtraction of scan 2 from scan 1 cancels the background and enhances the EPR signal. Experiments were performed at an EPR frequency of about 258 MHz, which is in the range that is commonly used for in vivo imaging. Samples include nitroxide radicals, a trityl radical, a dinitroxide, and a nitroxide in the presence of a magnetic field gradient. This method has the advantage that no assumption is made about the shape of the background signal, and it provides an approach to automating the background correction.

Graphical Abstract

Introduction

Pulse, continuous wave (CW), and rapid scan EPR measurements often have significant contributions from background signals due to a wide range of environmental interferences such as extraneous RF signals, temperature variations, vibrations and instrumental artifacts such as switching transients, eddy currents, reflections, ground loops, spins in materials of the resonator and sample holder, and many others. For example, Hyde [1] pointed out that magnetic field modulation introduces background problems due to forces on the wires and due to eddy currents induced in the cavity body. Pulsed EPR suffers deadtime after the pulse due to resonator ring-down, reflections, and switching transients. EPR spectroscopy is designed to minimize these interferences and subtract them from the recorded signal when they are too large to ignore. Poole [2], Alger [3], Buckmaster et al. [4], and Eaton et al. [5], discussed some of these problems.

In rapid scan EPR the magnetic field is scanned through resonance at rates of kHz to MHz [6, 7]. These rapidly-changing magnetic fields interact with metallic components of the resonator and transmission lines analogous to the effects of the magnetic field modulation in CW EPR. For weak samples or broad lines, the background in rapid scan experiments may be many times larger than the amplitude of the desired EPR spectrum. It is proposed that the background is generated primarily from mechanical vibrations produced by the interaction between the current in the scan coils and B₀ (so-called motor effects), between the scanning field and any magnetic material, and between eddy currents and B₀. Many steps have been taken to minimize the background. Resonators have been designed to contain less metal to cut down on eddy currents. A Sorbothane^™ casing surrounding the scan coils of the 258 MHz cross-loop resonator has been shown in some cases to reduce the mechanical movements of the assembly [8], but may also change the symmetry of the response to the modulating field. Off-resonance subtraction is one way to remove background, but this method is limited by the fact that the background is field dependent. Changing B₀ may change the shape and phase of the background as well as the amplitude. Off-resonance subtraction works well for relatively small scans at X-band and higher frequencies, because an off-resonance step is a small percentage of the total field. However, considerable residual background persists after off-resonance subtraction at lower magnetic fields and for wider high-field scans such as for spectra of transition metal complexes where the field offset that is required to be off resonance is a significant fraction of B₀.

Methods of removing rapid scan backgrounds have been described at several stages in the development of this new EPR method [9–12]. In this paper an improved, more general approach to rapid-scan background removal is described that exploits capabilities of cross-loop resonators and power supplies that can reverse the direction of the magnetic field scans. The method is demonstrated at about 258 MHz for triangular and sinusoidal scans for the nitroxide radicals tempone and CTPO, a trityl radical that is used for EPR imaging [13], a nitroxide diradical that can be used as a redox sensor [14], and a nitroxide in the presence of a magnetic field gradient.

Experimental section

Samples

Tempone and CTPO were purchased from Aldrich Chemical (now Sigma-Aldrich). Trityl-CD₃ was obtained from GE Healthcare via Howard J. Halpern, University of Chicago. The dinitroxide is a redox indicator that was a generous gift from Prof. J. P. Y. Kao, University of Maryland [15]. In the oxidized form the two SH groups are linked in a cyclic structure that prevents intramolecular nitroxide-nitroxide collisions and the spectrum is characteristic of noninteracting nitroxides. In the reduced form with two SH groups that was used in this study, intramolecular nitroxide-nitroxide collisions result in spin-spin interaction and a spectrum with alternating linewidths. Samples were in 16 mm OD tubes. The aqueous solution of trityl-CD₃ was deoxygenated by bubbling with nitrogen gas followed by flame sealing the tube. Other samples were air saturated. For data taken in the presence of a gradient, a 1mm divider separated the tube into two halves. Spectra were recorded at microwave powers for which the signal amplitude increases linearly with square root of power.

Instrumentation

The EPR spectrometer that was used for these experiments evolved from the one that is described in [16]. It operates in the range of about 245 to 260 MHz, which is in the band called VHF. When first built, the spectrometer used a Kepco model ATE 36–30M power supply, which was replaced with a Bruker BMC20 system for control via Xepr of the main magnetic field and the magnetic field gradients. This large, 19-inch rack mounted, system was subsequently replaced by smaller, Ethernet controlled power supplies manufactured by CAEN Technologies. A CAENels FAST-PS-1K5 30–50 controls the main magnetic field and a CAENels FAST-PS 2040-600 supply controls field gradients along the z axis. The original gradient coils are described in [17]. Other versions of the gradient coils have been used in conjunction with smaller resonators. The digitizer is a Bruker Specjet II. Data are acquired in quadrature which permits signal phasing in post-processing. Both channels are used in the sinusoidal deconvolution procedure [18]. Each scan was signal averaged. Some scans consisted of multiple full rapid-scan cycles that were combined prior to data processing. In post-processing, the Hilbert transform of the signal in the imaginary channel can be added to the signal in the real channel to improve signal-to-noise. In the final step of post-processing the signals from the two half cycles are combined. The rapid scan driver is described in [19, 20] and the cross-loop resonator that is key to the correction procedure was described briefly in [8]. The amplitude of the rapid scan background is resonator- and frequency-dependent and is smaller at scan frequencies that are not mechanical resonances of the resonator. A chirp scan of frequencies generated by the scan driver showed that the mechanical resonances of the CLR were weaker at frequencies between about 2.2 and 2.8 kHz and above 5.5 kHz (Fig. 1), which was the basis for selection of the scan frequencies that were used in this study. Python computer code interfaced to the Bruker Xepr software facilitated data acquisition and analysis. A graphical user interface was created to allow the user to input scan parameters for both the CAEN supplies and rapid scan coil driver.

Figure 1.

Mechanical resonances of CLR tuned to 262 MHz without a sample, measured with a frequency chirp from 700 Hz to 7 kHz. The current in the coils was 0.62 A which corresponds to a sinusoidal sweep width of about 17 G, incident power = 316 mW, average of 3 scans. Each scan lasted approximately 2.24 minutes. Quiet regions near 1 kHz, 2.3 kHz, 4 kHz are preferable to noisy regions such as 1.5 kHz and 4.5 kHz.

Background correction method

A data acquisition procedure, outlined in Fig. 2, has been developed that takes the difference between two scans that are designated as scan 1 and scan 2. In the difference scan the background cancels and the EPR spectrum is doubled, thereby increasing the signal-to-noise by a factor of square root of 2. The sketches of the method in Fig. 2 are for triangular scans, but the same approach applies to sinusoidal scans. In scan 1 B₀ is along the laboratory +z axis. The timing of the data acquisition trigger is selected such that the current in the scan coils decreases for the first half of the rapid scan cycle and increases in the second half cycle. The net magnetic field therefore decreases in the first half cycle and increases in the second half cycle (Fig. 2, scan 1). Scan 2 is recorded with B₀ reversed such that it is along the laboratory −z axis. The ability to reverse the B₀ direction was made possible by the installation of the CAENels FAST-PS-1K5 30–50 power supply. This supply is bipolar, a capability that was not present in previous DU systems, which permits selection of fields with either polarity. Reversing B₀ is an essential part of the background cancellation procedure. For scan 2 the data acquisition trigger is shifted by one half-cycle such that the current in the coils increases during the first half cycle and decreases in the second half cycle (Fig. 1, scan 2). Since both the direction of B₀ and the sequence for decreasing and increasing current in the scan coils is reversed, the net fields are of the same magnitude, but opposite in sign, relative to that for scan 1. The absolute value of the net field decreases during the first half cycle which is called a ‘down-field scan’ and the absolute value of the net field increases during the second half cycle which is called an ‘up-field scan’. In a single-mode reflection resonator such as a LGR or cavity, if the direction of B₀ is reversed and the scan direction is reversed, the EPR signal is unchanged. If the experiment described in Fig. 2 is performed with a single mode resonator such as a LGR or cavity resonator, scans 1 and 2 are identical, and the background correction described in this paper will not work. The B₀ reversal background correction procedure described in this paper requires a cross-loop resonator (CLR).

Figure 2.

Schematic description of data acquisition for the background correction procedure. B₀ is constant while the rapid scan field varies between +B_m/2 and −B_m/2. In scan 1, the external magnetic field, B₀, is along the +z direction. The current in the scan coils decreases for the first half cycle and increases in the second half cycle. The net field is the absolute value of the vector sum of B₀ and the rapid scan field. It decreases in the first half cycle and increases in the second half cycle. In scan 2, B₀ is along the −z axis. The data acquisition trigger is shifted by one half-cycle such that the current in the coils increases during the first half cycle and decreases in the second half cycle. The magnitudes of the net fields are the same for scans 1 and 2.

An example of data obtained as described in Fig. 2 with triangular scans for a 0.5 mM aqueous solution of the nitroxide radical tempone in a CLR is shown in Fig. 3. Each trace in the figure displays a full scan cycle, analogous to what is shown in Fig. 2. For the data shown in Fig. 3 the RF phase was adjusted such that, in scan 1, one channel contains the positive absorption signal and the quadrature channel contains the dispersion signal. The background correction procedure works for arbitrary phase settings, but the phases for the data in Fig. 3 were selected to visualize the distinctive features of the absorption and dispersion components of the signal. With this phase setting, the dispersion signal goes negative before positive in a down-field scan and positive before negative in an up-field scan. At VHF, even if phasing is arbitrary, the direction of a scan is clearly defined by the unequal spacing of the three nitroxide nitrogen hyperfine lines because of the Breit-Rabi effect. For tempone in water the spacing between the low-field and center lines is 14.3 G and the spacing between the center and high-field lines is 17.2 G.

Figure 3.

Triangular rapid scans for 0.5 mM tempone at 259 MHz. The scan frequency was 2 kHz and the scan width was 50.8 G. The absorption channel is shown in blue and the dispersion channel is shown in orange. The original x axis is in time, which is converted to magnetic field units using the constant scan rate of 2.04×10⁵ G/s. Each scan was averaged 4096 times. (A) Scan 1. (B) Scan 2. (C) Scan 1 – scan 2. Although the scan is triangular, the background signal is approximately sinusoidal at the first harmonic of the scan frequency.

The background signal depends on the time dependence of the net field as is shown in Fig. 2, and is the same for scans 1 (Fig. 3A) and 2 (Fig. 3B). Comparison of the signals in Fig. 3B (scan 2) with those in 3A (scan 1) shows that both the absorption and dispersion signals for scan 2 are multiplied by −1 relative to scan 1. Since the EPR signals in the two scans are inverted and the backgrounds are the same, when scan 2 is subtracted from scan 1, the backgrounds cancel, and the signals add (Fig. 3C). The inversion of the signal, but not the background is due to the structure of the CLR. In a resonator, the phase of the spin magnetization leads B₁ by 90°. The EPR voltage induced into a reflection resonator, which lags the spin magnetization by 90°, is, therefore, in phase with B₁. Reversing B₀ reverses the spin rotation direction, but not the relative phases, so the induced EPR voltage is still in phase with B₁. In a CLR, the spin magnetization, produced by the excitation resonator, induces an EPR voltage in the detection resonator that is mechanically oriented 90° to the excitation resonator. In this case, the phase of the EPR voltage leads B₁ by 90° for B₀ in one direction and lags B₁ by 90° when B₀ is reversed. The result is a 180° phase difference between the EPR signals in scans 1 and 2, which is equivalent to multiplying the EPR signal in scan 1 by −1 to get the signal in scan 2. These features of the CLR impact the EPR signal, but not all background signals. The method applies to background signals that are the same when B₀ and the scan direction are reversed, but not to contributions to background signals that reverse when B₀ and the scan direction are reversed. An analogous example of data acquired for the background correction method using sinusoidal scans on the same nitroxide are shown in Fig. 4. Again, the background signal is the same for scans 1 and 2, but the EPR signal is multiplied by −1. The subtraction scan 1 – scan 2 cleanly removes the background signal.

Figure 4.

Sinusoidal rapid scans for 0.5 mM tempone at 259 MHz. The scan frequency was 10.243 kHz and the scan width was 42 G. Each scan was averaged 5120 times. The absorption channel is shown in blue and the dispersion channel is shown in orange. The x-axis in time units. The scan rate varies through the scan so conversion of the x-axis to magnetic field units requires deconvolution of the driving function, which is done in post-processing. (A) Scan 1 (B) Scan 2 (C) Scan1 – scan 2. The background has contributions from the first and second harmonics of the scan frequency.

Background signals often have contributions at the rapid scan frequency, sin(2πf_mt+ϕ) (the first harmonic) and sometimes at sin(4πf_mt+ϕ′) (the second harmonic) where f_m is the scan frequency and ϕ, ϕ′ are arbitrary phase factors. Our previous method for background removal for sinusoidal scans assumed that the background could be estimated based on fitting sin and cos functions of the first and second harmonics of the scan frequency to background regions in the Fourier domain [10, 18]. That procedure works better for some types of signals and backgrounds than for others. The proposed background correction procedure using reversal of B₀ makes no assumptions about the shape of the background and does not require fitting to the spectrum. It has been observed to work well for a range of shapes of the background. In the example in Fig. 3, the background is dominated by the first harmonic. In Fig. 4 a second harmonic component is present in the background, causing the background to become asymmetric. In both cases the B₀ reversal method removes the background signal very effectively. Note that triangular or other non-sinusoidal scans inherently have multiple harmonics. For example, to have a triangular scan “linear” over about 90% of its amplitude requires designing the frequency response for at least seven times the nominal frequency of the triangular scan. Other arbitrary scan shapes, such as sawtooth or trapezoidal have analogous requirements for the fastest change in the field.

All averages for scan 1 or scan 2 are acquired before changing the polarities of the fields. For the experimental settings used in this paper, the time for a single transient was 0.3 ms to 1.3 ms. The averaging times that were used for either scan 1 or scan 2 ranged from 0.34 s to 13.4 s. To reverse the direction of B_o the setting time of the power supply is about 1.3 s. For imaging experiments, scans 1 and 2 would be acquired for each gradient before changing to the next gradient. The time per scan and the time required to reverse B_o are short relative to kinetics we would expect to monitor with EPR imaging.

Examples for diverse samples

Nitroxide CTPO

Sinusoidal rapid scan data for the nitroxide CTPO are shown in Fig. 5. When our previous background correction procedure was applied to scan 1 (Fig. 5A) the deconvolved spectrum had a residual background contribution (Fig. 5B) that is due to a second harmonic, or possibly higher harmonics, contribution to the experimental background. When the B₀ reversal method was applied to the data for this sample, scan 1 – scan 2 (Fig. 5C) has little residual background. After sinusoidal deconvolution of scan 1 – scan 2, the spectrum in Fig. 5D was obtained. That deconvolution procedure includes additional correction for residual 1^st harmonic background. The result in Fig. 5D has a much cleaner baseline than the spectrum in Fig. 5B that was obtained from data that did not include the B₀ reversal.

Figure 5.

Sinusoidal rapid scans of 0.1 mM CTPO at 259 MHz obtained with 10.242 kHz scan frequency and 40 G scan width. A) Scan 1. B) Spectrum obtained from scan 1 by sinusoidal deconvolution and background correction assuming only a first harmonic. C) Scan 1 – scan 2 obtained by B₀ reversal method. D) Spectrum obtained by sinusoidal deconvolution of scan 1 – scan 2. The total acquisition time for scans 1 and 2 was 0.34 s. Red trace is absorption and blue trace is dispersion for A and C. Black trace is data after linear deconvolution for B and D. The same Gaussian filter was applied to the spectra in parts B and D.

Trityl-CD₃

Triangular rapid scan data for trityl-CD₃ are shown in Fig. 6. The linear deconvolution procedure did not include a background correction routine. When the data from scan 1 (Fig. 6A) are deconvolved there is a substantial residual baseline slope (Fig. 6B). When the data from scan 1 – scan 2 obtained by the B₀ reversal method (Fig. 6C) are deconvolved, the baseline is flat (Fig. 6D). The B₀ reversal procedure preserves the rapid scan oscillations on the narrow trityl signal that are essential for accurate deconvolution. The full-width at half-height linewidth for the trityl signal is 57 mG. The deconvolved spectra include the characteristic ¹³C hyperfine lines [21].

Figure 6.

Triangular rapid scan data for 0.2 mM trityl-CD₃ at 259 MHz obtained with 2 kHz scan frequency and 18.5 G scan width. (A) Scan 1. (B) Spectrum obtained from scan 1 by linear deconvolution and no background correction. (C) Scan 1 – Scan 2 obtained by B₀ reversal method. (D) Spectrum obtained by linear deconvolution of scan 1 – scan 2 without additional baseline correction. The total data acquisition time for scans 1 and 2 was 13.4 s. Red trace is absorption and blue trace is dispersion for A and C. Black trace is data after linear deconvolution for B and D.

Flexible dinitroxide

The linker between the two nitroxide fragments in the dinitroxide for which spectra are shown in Fig. 7 is flexible, which permits collisions between the two paramagnetic centers that results in through-space exchange interaction. For this sample the background correction using sinusoidal deconvolution plus the background correction based on the assumption of a dominant first harmonic (Fig. 7B) is similar to that obtained from the B₀ reversal method (Fig. 7D) following by sinusoidal deconvolution because the background signal is dominated by the first harmonic. The spectrum of the dinitroxide is an example of the alternating linewidth effect that has been known for many years for flexible diradicals [22]. The spectra are in good agreement with simulations [15].

Figure 7.

Sinusoidal rapid scans of 0.5 mM dinitroxide obtained with 2.64 kHz scan frequency and 70 G scan width. (A) Scan 1. (B) Spectrum obtained from scan 1 by sinusoidal deconvolution and background correction assuming only a first harmonic. (C) Scan 1 – scan 2 obtained by B₀ reversal method. (D) Spectrum obtained by sinusoidal deconvolution of scan 1 – scan 2, including background correction for the first harmonic. The total data acquisition time for scans 1 and 2 was 13.4 s. Red trace is absorption and blue trace is dispersion for A and C. Black trace is data after linear deconvolution for B and D. The same Gaussian filter was applied to the spectra in parts B and D. Dashed red trace in B and D is the simulated spectrum.

EPR Imaging

Reversing B₀ has implications for imaging. To maintain the same relationship between a gradient and the location of the sample or voxel, a fourth variable (the polarity of the gradient) should be inverted, along with the main field. This is depicted in Fig. 8 wherein it is shown that reversing the gradient (the slope of the gradient line) along with B₀ ensures that each Scan 1 position in space experiences the same absolute field magnitude as its Scan 2 counterpart. The gradient broadens the spectrum which lowers the ratio of signal amplitude to rapid scan background. A triangular rapid scan for 0.1 mM CTPO in the presence of a 10 G/cm gradient is shown in Fig. 9A. The gradient broadens the signal and splits it into two components from the two sections of the tube that are separated by an approximately 1 mm divider. The rapid scan background dominates the spectrum. For the same sample scan 1 – scan 2 obtained with the B₀ reversal method is shown in Fig. 9B. Although there is still residual background, the signal in Fig. 9B is dramatically improved by the B₀ reversal method. The residual background in Fig. 9B may arise from asymmetric positioning of the resonator relative to the gradient coils.

Figure 8.

Magnetic field strength as a function of distance from the center of the resonator before (blue) and after (red) application of a gradient field. Gradient strength is the slope of the dashed line. Dots highlight the magnetic field strength at 1 cm. (A) Scan 1, with a positive B₀ and positive gradient field. (B) Scan 2 with a negative B₀ and negative gradient field.

Figure 9.

Linear rapid scans of 0.1 mM CTPO at 260 MHz with a gradient of 10 G/cm obtained with a scan frequency of 2 kHz and sweep width of 66 G. The sample tube is divided into two sections by a 1 mm separator. (A) Scan 1. (B) Scan 1 – scan 2 obtained with the B₀ reversal method.

Summary

It is also well-known that when measuring very short relaxation times by pulsed EPR, cavity ringdown, reflections, etc., can result in larger contributions to the detected signal than the EPR signal itself. In these cases, and many others, background signals can confound interpretation of EPR measurements. During development of rapid scan EPR technology, minimizing background has been a central effort. The rapid-scan background signal results from the interaction between the current in the scan coils and B₀ (so-called motor effects), between the scanning field and any magnetic material and between eddy currents and B₀. Depending on many mechanical and electrical aspects of the resonator, scan coils, transmission lines, and many other features of the spectrometer, the result can be a signal that that is largely the first harmonic or more complex. If it is cleanly sinusoidal, the post-processing background removal method for sinusoidal scan [18] works well. When significant higher harmonics are induced, the method reported in this paper is more reliably effective. The B₀ reversal method is effective independent of the shape of the background. The method reported in this paper is a major step toward automatic background elimination so that eventually background need not even be seen by the user.

Research Highlights.

• A new method has been developed to reduce rapid-scan background signals.

• It requires a cross-loop resonator.

• Spectra are acquired with the external field direction and scan direction reversed.

• Subtraction of the two spectra cancel the background and enhances the EPR signal.