Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy

A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration.     

The continuous wave electron paramagnetic resonance experiment revisited

When the modulation frequency used in continuous wave electron paramagnetic resonance (cw EPR) spectroscopy exceeds the linewidth, modulation sidebands appear in the spectrum. It is shown theoretically and experimentally that these sidebands are actually multiple photon transitions, sigma(+)+kxpi, where one microwave (mw) sigma(+) photon is absorbed from the mw radiation field and an arbitrary number k of radio frequency (rf) pi photons are absorbed from or emitted to the modulation rf field. Furthermore, it is demonstrated that both the derivative shape of the lines in standard cw EPR spectra and the distortions due to overmodulation are caused by the unresolved sideband pattern of these lines. The single-photon transition does not even give a contribution to the first-harmonic cw EPR signal. Multiple photon transitions are described semiclassically in a toggling frame and their existence is proven using second quantization. With the toggling frame approach and perturbation theory an effective Hamiltonian for an arbitrary sideband transition is derived. Based on the effective Hamiltonians an expression for the steady-state density operator in the singly rotating frame is derived, completely describing all sidebands in all modulation frequency harmonics of the cw EPR signal. The relative intensities of the sidebands are found to depend in a very sensitive way on the actual rf amplitude and the saturation of single sidebands is shown to depend strongly on the effective field amplitude of the multiple photon transitions. By comparison with the analogous solutions for frequency-modulation EPR it is shown that the field-modulation and the frequency-modulation technique are not equivalent. The experimental data fully verify the theoretical predictions with respect to intensities and lineshapes.     

Pseudo field modulation in EPR spectroscopy

This paper develops methodology for computer simulation of the effect on an experimental EPR spectrum that would occur if an additional field modulation were applied followed by eventual phase sensitive detection at the modulation frequency or at one its harmonics. The algorithm, which is called pseudomodulation, transforms the digitized spectrum and also filters the noise. If a second harmonic spectrum is desired in order to make subtle changes in curvature more apparent, it is shown that it is always preferable to obtain an experimental second harmonic spectrum. The signals are identical, but because of the filtering properties of the pseudomodulation algorithm, the noise is lower. Pseudomodulation should be applied to simulated spectra prior to fitting a model to data in order more precisely to simulate the experimental signal. It is argued that such fits ought to involve not only first harmonics but also higher harmonics, since the various harmonics are sensitive in different ways to input parameters in the spin Hamiltonian. Application of pseudomodulation to the EPR spectrum of the blue copper-protein azurin is described.     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.     

ISS protocol for EPR tooth dosimetry

The accuracy in Electron Paramagneetic Resonance (EPR) dose reconstruction with tooth enamel is affected by sample preparation, dosimetric signal amplitude evaluation and unknown dose estimate. Worldwide efforts in the field of EPR dose reconstruction with tooth enamel are focused on the optimization of the three mentioned steps in dose assessment. In the present work, the protocol implemented at ISS in the framework of the European Community Nuclear Fission Safety project “Dose Reconstruction” is presented. A combined mechanical–chemical procedure for ground enamel sample preparation is used. The signal intensity evaluation is carried out with powder spectra simulation program. Finally, the unknown dose is evaluated individually for each sample with the additive dose method. The unknown dose is obtained by subtracting a mean native dose from the back-extrapolated dose. As an example of the capability of the ISS protocol in unknown dose evaluation, the results obtained in the framework of the 2nd International Intercomparison on EPR tooth enamel dosimetry are reported.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

Optical high harmonic generation in C60

High harmonic generation (HHG) requires a strong laser field, but in C60 a relatively weak laser field is sufficient. Numerical results presented here show that, while its low order harmonics result from the laser field, its high order ones are mainly from the multiple excitations. Since high order harmonics directly correlate with electronic transitions, the HHG spectrum accurately measures transition energies. Therefore, C60 is not only a promising material for HHG, but may also present an opportunity to develop HHG into an electronic structure probing tool.     

Online self-calibration for mobile vision based on laser imaging and computer algorithms

A self-calibration technique for mobile three-dimensional vision is presented. This technique determines the vision parameters during the vision task based on computer algorithms and image processing. The three-dimensional vision is performed by a Bezier network based on laser line projection. This network provides the data to perform the online self-calibration when the vision system is modified. Here, the changes of the extrinsic and intrinsic parameters are determined. The structure of the network is performed by the line shifting provided by the surface depth. From this structure, the data for the initial calibration and online self-calibration are deduced. In this manner, the calibrated references and physical measurements are avoided to perform the online self-calibration. Therefore, calibration limitations caused by online modifications are overcome to perform the mobile vision. Thus, the proposed self-calibration improves the accuracy and performance of the mobile vision. It is because online data of calibrated references are not passed to the vision system. This procedure represents a contribution in the field of the online recalibration, which is performed based on calibrated references. To elucidate this contribution, an evaluation is performed based on the self-calibration methods, which are reported in the recent years. Also, the time processing is described.     

Integration of digital signal processing technologies with pulsed electron paramagnetic resonance imaging

The integration of modern data acquisition and digital signal processing (DSP) technologies with Fourier transform electron paramagnetic resonance (FT-EPR) imaging at radiofrequencies (RF) is described. The FT-EPR system operates at a Larmor frequency (L(f)) of 300MHz to facilitate in vivo studies. This relatively low frequency L(f), in conjunction with our approximately 10MHz signal bandwidth, enables the use of direct free induction decay time-locked subsampling (TLSS). This particular technique provides advantages by eliminating the traditional analog intermediate frequency downconversion stage along with the corresponding noise sources. TLSS also results in manageable sample rates that facilitate the design of DSP-based data acquisition and image processing platforms. More specifically, we utilize a high-speed field programmable gate array (FPGA) and a DSP processor to perform advanced real-time signal and image processing. The migration to a DSP-based configuration offers the benefits of improved EPR system performance, as well as increased adaptability to various EPR system configurations (i.e., software configurable systems instead of hardware reconfigurations). The required modifications to the FT-EPR system design are described, with focus on the addition of DSP technologies including the application-specific hardware, software, and firmware developed for the FPGA and DSP processor. The first results of using real-time DSP technologies in conjunction with direct detection bandpass sampling to implement EPR imaging at RF frequencies are presented.     

Background removal procedure for rapid scan EPR

In rapid scan EPR the changing magnetic field creates a background signal with components at the scan frequency and its harmonics. The amplitude of the background signal increases with scan width and is more significant for weak EPR signals such as are obtained in the presence of magnetic field gradients. A procedure for distinguishing this background from the EPR signal is proposed, mathematically described, and tested for various experimental conditions.     

Single crystal and powder EPR study of trivalent gadolinium in Cs2NaBiCl6 in the 30-300 K interval

A crystalline electric field cubic symmetry site has been reported for Gd³⁺ in Cs₂NaBiCl₆ at room temperature. This host exhibits an apparent structural transformation below 100 K that is completely reversible. However, an EPR examination for a powdered sample of Cs₂NaBiCl₆:Gd³⁺ clearly demonstrates that there are no new large crystalline electric field symmetry sites arising between the transition temperature (100 K) and 30 K, suggesting, therefore, that the site symmetry remains predominantly cubic even at temperatures close to 30 K. In order to substantiate this statement, a computer EPR powder simulation was performed using the single-crystal-spin-Hamiltonian parameters obtained from the three different sites that emerge from the original site while observed at 30 K. A remarkable agreement is observed while comparing the computer-simulated data with that of powdered experimental data. It is important to mention here that several attempts were done trying to fit the observed new spectra to lower crystalline field symmetries, however, our best analytical adjustment was obtained with the cubic spin-Hamiltonian.Below 30 K, new structural transitions are present and the lattice loses its original cubic nature. However, at 10 K the EPR spectrum of the crystal again shows only seven lines that are very broad. This new spectrum cannot be fitted with previously used cubic spin-Hamiltonian parameters.     

High spatial resolution multi-site EPR oximetry. The use of convolution-based fitting method

We describe a new method to enhance the spatial resolution of multi-site electron paramagnetic resonance (EPR) oximetry. The method is suitable for any shape (density distribution function) of a solid paramagnetic material implanted in tissue. It corrects distortions of lineshapes caused by the gradient and thus overcomes limitations of previous multi-site EPR oximetry methods that restricted the ratio of the particle size to the distance between sites. The new method is based on consecutive applications of magnetic field gradients with the same direction but with a different magnitude and uses a convolution-based fitting algorithm to derive Lorentzian EPR linewidths of each individual peak of the EPR spectrum. The method is applicable for any particulate EPR oxygen sensitive materials whose EPR spectra can be approximated by a Lorentzian function or a superposition of Lorentzian functions. By incorporating this model of the lineshape in the data processing, we are able to decrease significantly the number of parameters needed for the calculations and to recover the oxygen concentration, even from quite noisy spectra. We (i) describe our method and the data-processing algorithm, (ii) demonstrate our approach in model and in vivo experiments, and (iii) discuss the limitations.     

Estimation of mean and median pO2 values for a composite EPR spectrum

Electron paramagnetic resonance (EPR)-based oximetry is capable of quantifying oxygen content in samples. However, for a heterogeneous environment with multiple pO2 values, peak-to-peak linewidth of the composite EPR lineshape does not provide a reliable estimate of the overall pO2 in the sample. The estimate, depending on the heterogeneity, can be severely biased towards narrow components. To address this issue, we suggest a postprocessing method to recover the linewidth histogram which can be used in estimating meaningful parameters, such as the mean and median pO2 values. This information, although not as comprehensive as obtained by EPR spectral-spatial imaging, goes beyond what can be generally achieved with conventional EPR spectroscopy. Substantially shorter acquisition times, in comparison to EPR imaging, may prompt its use in clinically relevant models. For validation, simulation and EPR experiment data are presented.     

Analysis of the tuning and operation of reflection resonator EPR spectrometers

This paper investigates basic characteristics of the electron paramagnetic resonance (EPR) signal obtained from spectrometers employing reflection resonators. General equations are presented which reveal the phase and amplitude dependence on instrumental parameters of both components of the continuous wave (CW) EPR signal (absorption and dispersion). New phase vector diagrams derived from these general equations are presented for the analysis of the EPR response. The dependence of the phase and absolute value of the CW EPR signal on the local oscillator (LO) phase and on resonator offset and coupling is presented and analyzed. The EPR spectrometer tuning procedures for both balanced and unbalanced heterodyne receivers are analyzed in detail using the new phase diagrams. Extraneous signals at the RF input of the microwave receiver (resulting from circulator leakage and reflections in the resonator transmission line) have been taken into account and analyzed. It is shown that a final tuning condition that corresponds to an extremum of the receiver output as a function of the resonator frequency is necessary and sufficient for the acquisition of pure absorption signal. This condition is universal: it applies to all spectrometer configurations in all frequency ranges. High Frequency EPR spectrometer (130 GHz) data are used to generate experimental phase diagrams that illustrate the theoretical concepts presented in the paper. Conditions are presented under which the absorption signal can be measured with complete suppression of the dispersion, independent of the mutual frequency offset between the microwave source and the EPR sample resonator. Equations describing the approximate relationship between changes of the resonator properties (Q-factor and frequency) and paramagnetic susceptibility are derived and analyzed.     

基于ZEMAX的大视场投影镜头设计

针对大视场投影镜头的设计问题,利用ZEMAX光学设计软件,通过各种操作数对镜头的基本参数和外形尺寸进行限制,并利用镜头架构的方式进行优化及大视场投影镜头的设计。其主要光学参量为:焦距为13.6 mm,全视场角为60°,相对孔径为1/1.6。设计结果表明:镜头的最大畸变量绝对值小于3% ,最大场曲小于0.06 mm,全视场MTF值在空间频率50 lp/mm时高于0.6,基本达到衍射极限。该镜头由10片球面镜组成,光学系统结构紧凑、易加工。     

Object dependent sweep width reduction with spectral-spatial EPR imaging

For spectral-spatial EPR imaging, prior knowledge about the spatial support of an imaged object can be exploited in two ways. We can shrink the spatial field of view (FOV) to closely wrap the object in a sphere or reduce the sweep width in a projection dependent fashion. Use of a smaller spatial FOV with the same number of samples enhances spatial resolution by reducing voxel volume at the expense of signal-to-noise and a consequent degraded line-width resolution. We have developed another approach to define sweep width that prunes away the portions of the projection sweep with no signal. This reduces data acquisition time for the continuous wave (CW) EPR image proportional to the sweep width reduction. This method also avoids voxel volume reduction. Using the reduced-sweep method, we decreased the data acquisition time by 20% maintaining spatial and linewidth resolution.     

Advantages of digital phase-sensitive detection for upgrading an obsolete CW EPR spectrometer

The replacement of the commonly used analog phase-sensitive detection (PSD) by digital PSD for demodulation of electron paramagnetic resonance (EPR) signals is suggested for upgrading of an out-of-date EPR spectrometer. Connection of the microwave bridge output to a fast analog-digital converter (ADC) eliminates some of the spectrometer’s components: the electronics responsible for analog PSD, ADC for sampling of demodulated signals, and a computer, as well as the usage of some of the spectrometer’s settings. The spectrometer is reduced to a magnet, microwave bridge, and personal computer containing an ADC board. EPR signals digitized for a set of magnetic field positions form a two-dimensional array which is stored in a personal computer. Demodulation and filtering are done numerically to produce a conventional EPR spectrum. In comparison with analog PSD, this numerical approach does not eliminate the out-of-phase component of the signal and the signals at the higher harmonics of the modulation frequency. The details of modernizing the Bruker ER200E SRC EPR spectrometer are discussed to demonstrate these and other advantages of digital demodulation.     

Estimation of the in vivo decay rate of EPR signals for a nitroxide radical in rat brains by a region-selected intensity determination method

The region-selected intensity determination (RSID) method was proposed to obtain the temporal changes in electron paramagnetic resonance (EPR) signal intensity from a selected region by a stationary magnetic field gradient. To select the region, the subtraction field that was derived from the distance between the center and the projection of the selected region to the direction of the field gradient was applied to the main field. The directions of the stationary magnetic field gradient at a constant strength were systematically changed in a three-dimensional space after each acquisition of the spectrum. All spectra under the field gradient were accumulated and the resultant spectrum was deconvoluted by a spectrum without the field gradient. The center height of the deconvoluted spectrum indicates the signal intensity of the selected region. To verify this method, a phantom or in vivo study was conducted on a 700 MHz radio-frequency EPR spectrometer equipped with a bridged loop-gap resonator. In the temporal EPR measurements of phantoms including a nitroxide radical aqueous solution with and without ascorbic acid, the selected regions were alternatively changed at the position of the two phantoms. The signal intensity derived from the one phantom showed an exponential decay, and for the other phantom, no temporal changes. The spatial resolution of this method was estimated to be 2.7 mm by using a pinpoint phantom that included diphenylpicrylhydrazyl powder. In the in vivo temporal EPR measurements, the selected regions were alternatively changed at the cerebral cortex and the striatum of rats that had received a blood-brain barrier-permeative nitroxide radical. The decay rate of the signal intensity at each region obtained by this method was consistent with those previously reported.     

High Spatial Resolution Multi-Site EPR Oximetry: The Use of a Convolution-Based Fitting Method

We describe a new method to enhance the spatial resolution of multi-site electron paramagnetic resonance (EPR) oximetry. The method is suitable for any shape (density distribution function) of a solid paramagnetic material implanted in tissue. It corrects distortions of lineshapes caused by the gradient and thus overcomes limitations of previous multi-site EPR oximetry methods that restricted the ratio of the particle size to the distance between sites. The new method is based on consecutive applications of magnetic field gradients with the same direction but with a different magnitude and uses a convolution-based fitting algorithm to derive Lorentzian EPR linewidths of each individual peak of the EPR spectrum. The method is applicable for any particulate EPR oxygen sensitive materials whose EPR spectra can be approximated by a Lorentzian function or a superposition of Lorentzian functions. By incorporating this model of the lineshape in the data processing, we are able to decrease significantly the number of parameters needed for the calculations and to recover the oxygen concentration, even from quite noisy spectra. We (i) describe our method and the data-processing algorithm, (ii) demonstrate our approach in model and in vivo experiments, and (iii) discuss the limitations.     

Post-processing of EPR spectra by convolution filtering: calculation of a harmonics' series and automatic separation of fast-motion components from spin-label EPR spectra

This communication reports on post-processing of continuous wave EPR spectra by a digital convolution with filter functions that are subjected to differentiation or the Kramers-Kr?nig transform analytically. In case of differentiation, such a procedure improves spectral resolution in the higher harmonics enhancing the relative amplitude of sharp spectral features over the broad lines. At the same time high-frequency noise is suppressed through filtering. These features are illustrated on an example of a Lorentzian filter function that has a principal advantage of adding a known magnitude of homogeneous broadening to the spectral shapes. Such spectral distortion could be easily and accurately accounted for in the consequent least-squares data modeling. Application examples include calculation of higher harmonics from pure absorption echo-detected EPR spectra and resolving small hyperfine coupling that are unnoticeable in conventional first derivative EPR spectra. Another example involves speedy and automatic separation of fast and broad slow-motion components from spin-label EPR spectra without explicit simulation of the slow motion spectrum. The method is illustrated on examples of X-band EPR spectra of partially aggregated membrane peptides.