A microwave resonator for limiting depth sensitivity for electron paramagnetic resonance spectroscopy of surfaces.

A microwave Surface Resonator Array (SRA) structure is described for use in Electron Paramagnetic Resonance (EPR) spectroscopy. The SRA has a series of anti-parallel transmission line modes that provides a region of sensitivity equal to the cross-sectional area times its depth sensitivity, which is approximately half the distance between the transmission line centers. It is shown that the quarter-wave twin-lead transmission line can be a useful element for design of microwave resonators at frequencies as high as 10 GHz. The SRA geometry is presented as a novel resonator for use in surface spectroscopy where the region of interest is either surrounded by lossy material, or the spectroscopist wishes to minimize signal from surrounding materials. One such application is in vivo spectroscopy of human finger-nails at X-band (9.5 GHz) to measure ionizing radiation dosages. In order to reduce losses associated with tissues beneath the nail that yield no EPR signal, the SRA structure is designed to limit depth sensitivity to the thickness of the fingernail. Another application, due to the resonator geometry and limited depth penetration, is surface spectroscopy in coating or material science. To test this application, a spectrum of 1.44 μM of Mg(2+) doped polystyrene 1.1 mm thick on an aluminum surface is obtained. Modeling, design, and simulations were performed using Wolfram Mathematica (Champaign, IL; v. 9.0) and Ansys High Frequency Structure Simulator (HFSS; Canonsburg, PA; v. 15.0). A micro-strip coupling circuit is designed to suppress unwanted modes and provide a balanced impedance transformation to a 50 Ω coaxial input. Agreement between simulated and experimental results is shown.


I. INTRODUCTION
One fundamental issue of surface magnetic resonance spectroscopy, particularly in vivo, is limiting the depth sensitivity to the volume of interest. Ikeya et al. designed an aperture resonator for Electron Paramagnetic Resonance (EPR) X-band in vivo tooth dosimetry by cutting an iris, either a hole or slot, in a rectangular TE 102 cavity. 1,2 Aperture resonator geometries use the cavity resonator as a coupler to an evanescent wave at a localized region. Similarly in Magnetic Resonance Imaging (MRI), Song et al. used a small 1 cm surface coil at 1.5 T to increase the magnetic field at the surface of the skin to image the cutaneous surface. 3 From reciprocity, a small surface coil has a near field close to the coil. Therefore, the vector reception field of a small surface coil will minimize coupling to deep tissue regions. Ikeya et al. and Song et al. use the size of their probes to minimize losses and coupling to unwanted volumes surrounding the sample.
Counter-rotating current (CRC) surface coils were introduced in the field of MRI for limiting depth sensitivity. 4,5 Froncisz et al. showed that two fundamental modes exist when two resonant coils are placed on axis. The first, Fig. 1(a), is a solenoid mode with a magnetic field profile similar to a single coil with total length of the two coils plus the separation. Here, the currents are parallel to each other and thus, the fields add. The second mode, and the focus of this work, occurs when the two coils have opposite vector currents (anti-parallel) which create a magnetic field that rapidly falls in intensity as shown in Fig. 1(b). The axis of the coils is parallel to the sample which is known as the edge-on configuration. Edge-on coils have depth sensitivity approximately half the distance between the coil centers. The design of Fig. 1(b) was extended to include an even number of coaxial loops with alternating currents, which provided an extended area of sensitivity for MRI. 5 Separately, Bohnign et al. 6 used surface coil meanderline and parallel array technology to study 31 P on surface tissues using Magnetic Resonance Spectroscopy (MRS). Similar to a CRC surface coil, meander-line and parallel array surface coils set up equal and opposite parallel currents. Bohnign et al. found that 81% of the MRS signal came from tissues 1.9 mm deep with a meander-line geometry of eight turns, 2.0 mm apart with 1.5 mm trace thickness.
A surface resonator array (SRA) of CRC surface coils is proposed to operate at X-band (9.5 GHz). 7 The SRA has the advantage of an edge-on CRC pair by restricting the field depth sensitivity to the sample region of interest and reducing the electric field in surrounding lossy material. By designing multiple CRC surface coils in parallel a larger surface area is realized which increases the area of sensitivity linearly with excited volume. In designing an SRA, the transmission line Depth sensitivity in the sample (gray) is reduced to approximately half the distance between the coil centers in the anti-parallel mode.
is bent away from the surface and cross-element bridges are included at the open end to create a distributed network of capacitances and suppress other unwanted modes, including the solenoidal mode. One advantage of this geometry over the previously cited geometries is that the electric field is designed to be farther from the sample surface. With the SRA geometry, higher Q-value and higher EPR signal intensity are realized with lossy samples. This is especially important at higher microwave frequencies. The SRA geometry can be designed to limit the depth sensitivity to a region of interest on a surface. Each element in the array is described by a transmission line model that incorporates the self-resonant condition from the distributed inductances and capacitances of the geometry. The electric and magnetic fields of a shorted transmission line resonator are illustrated in Figs. 2(a) and 2(b), respectively. If the length of the transmission line is less than a quarterwavelength, no discrete elements are needed for this structure to resonate.
One potential application for the SRA is to measure stable free radicals formed by ionizing radiation of an individual's fingernails and toenails by EPR in vivo dosimetry. When the human nails are exposed to ionizing radiation, chemical bonds are broken in keratin and stable free-radicals are formed. The EPR signal has been found to be proportional to radiation dosage. [8][9][10] Three body tissues contain the protein keratin: fingernail, toenails, and hair. This work focuses on the fingernails and toenails.
Previous studies use cut nails placed in a rectangular TE 102 EPR cavity to measure radiation dosage. However, the clipping of the nails has been found to create a mechanically induced signal (MIS) that overlaps the radiation induced signal. 11,12 It is proposed here to use the SRA on irradiated fingernails to measure the radiation dosage in vivo, thus elim- inating the need to use nail clippings and removing the accompanying and interfering MIS. One challenge to in vivo studies is the coupling of fields into surrounding tissue under and around the sample. Fields that couple to non-signal producing tissue will cause losses and degrade resonator efficiency. Concentrating the magnetic field near the surface of the sample increases filling factor and EPR signal intensity.
The SRA resonator is designed, fabricated, tested and compared to a Bruker Super High-Q (ER 4122SHQE EPR) cavity for relative signal intensity. Simulations of signal intensities of the SRA are in excellent agreement with experimental values.

II. METHODS
Finite-element simulations were performed with Ansys (Canonsburg, PA) High Frequency Structure Simulator (HFSS; Version 15.0) on a Dell Precision T7500 workstation with dual hex-core Xeon X5675 3.0 GHz processors with 12 MB of L2 Cache per chip and 96 GB of total system RAM. The operating system is Windows 7 64-bit. Simulations were stored on 16 GB of system RAM reserved for a RAMDisk. This allows maximum input-output transfer for better disk performance. Typical simulation time was 10 min. Both eigenmode, where the solution is based on lowest energy states, and driven-mode, where power is coupled into a port, were used in the design process. The SRA was designed for X-band (9.5 GHz) where both the nail material ( r = 4.3 + j0.0172) and surrounding tissue (35% acrylamide, polyacrylamide gel, r = 49.5 + j25.839) were modeled. 13,14 Ansys Maxwell 3D was used to profile the 100 kHz field-modulation magnetic field. Calculations of the analytical transmission line model were performed using Wolfram (Champaign, IL) Mathematica (v. 9.0) on the same computer.
Fabrication of the resonator structure was completed using electric discharge machining (EDM) at Integrity Wire EDM (Sussex, WI), where ultra precision machining can give positional tolerances of 1 μm with features down to 0.05 mm. The cross-element bridges and coupling structure were fabricated using printed circuit (PC) board techniques by Polyflon (Norwalk, CT) on a 0.254 mm thick polytetrafluoroethylene (PTFE) ( r = 2.1 + j0.0021) PC board with copper traces. Components were soldered together using a Zephytronics (Pomona, CA) precision air solder station. Field modulation coils were matched for a Bruker Elexis spectrometer and wound using AWG-34 magnet wire on a custom saddle coil holder.
Experiments were performed on a Bruker Elexis X501 X-band spectrometer. A nail phantom was fabricated from a blend of L-α-alanine (>98%) and polystyrene flakes, both available from Sigma-Aldrich (St. Louis, MO). The L-αalanine was ground into a fine powder using a mortar and pestle and thoroughly mixed into a solution of polystyrene in chloroform. The mixture of L-α-alanine to polystyrene was 80:20 ratio by weight, respectively. The sample was pressed in a Pyrex petri-dish to the desired thickness (1.5 mm thick) and left to dry overnight, evaporating off the chloroform. The alanine-polystyrene phantom was then cut to accommodate the size of the SRA active region (12 × 6 mm). Irradiation was performed using a Cs-137 animal irradiator at a dose rate of 0.90 Gy/min. The alanine-polystyrene standard samples were left out overnight to allow for the known initial decrease in irradiated alanine signal. [15][16][17] Finally, the standard samples were placed in a mylar bag with desiccants, sealed under nitrogen, and placed in the freezer until testing. A polyacrylamide gel finger sized slab is formed from 35% acrylamide and the alanine-polystyrene standard samples were affixed creating the full-finger phantom, shown in Fig. 3. The phantom finger was positioned in the SRA structure and held in place firmly to reduce vibrations.

III. THEORY
The SRA structure can be modeled as an array of twoconductor transmission lines arranged in parallel, illustrated in Fig. 4(a). Each line is fed from one end and shorted on the other. The backbone, shown in Fig. 4(a), is a shorted line connecting the two transmission lines and providing mechanical support for the structure at a point of zero potential. The total length of each line is just less than one-quarter wavelength, which makes the line inductive. The rf magnetic field strength is cosinusoidal along the line and peaked at the short. The electric and magnetic fields are perpendicular to the conductors and the standing wave is transverse electric and magnetic (TEM) as illustrated in Fig. 2. The inductance of the line resonates with a capacitance formed by conductors on a PC board bridge that connect the transmission lines together in parallel and permit them to be driven by a matching network and input transmission line, shown in Fig. 4(b). Because the lines are alternately driven, the magnetic field reverses direction in every other line. For n total conductors, there are n/2 − 1 two-conductor transmission lines in parallel. The current flows primarily on the conductor surfaces that face nearby conductors. The entire structure is mirrored at the backbone. From the insight achieved from this model, Ansys HFSS can be used to perform a full-wave optimization on the SRA structure from a reduced parameter space.

A. SRA circuit and transmission line model
It is well-known that the electromagnetic solutions for a TEM mode consist of the electrostatic solution with the magnetic solution derivable from the electrostatic field (specifically in Jackson, 18 Sec. 8.2, Problem 6.5). 19 Consequently, we can use an analytic electrostatic solution for the capacitance per unit length of the two-conductor transmission line. The capacitance per unit length can be approximated by modeling the line as two thin parallel conductors facing each other. An exact two-dimensional electrostatic solution derived from conformal mapping techniques is given by Smythe 20 in Problem 59, Chap. IV, where 0 represents the electric permittivity of free space, the dimensions w and t are defined in Table I and the dimensionless function h, which is a function of the ratio w/t, is given by Here, K represents the complete elliptic integral of the first kind, and the parameter κ in the arguments of the elliptic integral is a real number between zero and one determined by solving the equation, In this equation, E of single argument represents the complete elliptic integral of the second kind while E of double argument represents the elliptic integral of the second kind. Also, F represents the elliptic integral of the first kind. Equation (3) was solved numerically and Eq. (2) evaluated using Mathematica. This method was also used to determine the capacitance of a loop-gap resonator (LGR) gap at high frequencies. 21 Because of the TEM transmission line mode, the product of the capacitance per unit length and the inductance per unit length along the line are 0 μ 0 . 18,19 Therefore, the inductance per unit length must also be corrected by the same dimensionless function, This technique has been used to determine the impedance of a long coupling iris at high frequencies. 22 From these results, the impedance of a length of the transmission line can be expressed as where the characteristic impedance of the line is and the wavenumber where the free space wavelength λ = c/f. Since k < π/4, Z l is inductive. The natural resonance frequency of the surface resonator is determined by the equation where ω is the radian frequency and C b is the total capacitance formed by the bridge connections on the PC board and the stray capacitance at the end of the line. The bridge capacitance can be expressed as the sum of capacitances due to six distinct structures, C n , which are described below. Because adjacent transmission lines alternate, rf currents reside primarily on the conductor surfaces that face nearby conductors. Consequently, in order to calculate the capacitance, the conductors should be divided in half along a line parallel to the transmission line length. By symmetry, the bridge structure should also be divided in half at the crossing. The divided metallic structures feeding a single two-element transmission line are shown in Fig. 4(b). The first capacitance structure is a triangle formed by the part of the bridge conductors on the two surfaces of the PC board that overlap each other. A modified form of the capacitance formula of Eqs. (1)-(3) is used, In this equation, r is the unitless relative dielectric constant of the PC board (in this case PTFE), d is the overlapping triangle dimension defined by and the other dimensions are defined in Table I and Fig. 4. The relative dielectric constant is brought into the function h because the dielectric is between and does not surround the conductors. The second capacitance structure is formed by the PC board elements that run from the opposing sides of the two-conductor transmission line and run toward the capacitor C 1 . As an approximation, we use another capacitance formula derived by conformal mapping techniques given by Smythe 20 in Problem 58, Chap. IV. The capacitance per unit length of two thin conducting strips each of dimension b − a and lying in a plane a distance 2a apart is given by where the dimensionless function g is a function of the complete elliptic integrals, In order to handle the diagonal approach of the conductors on the PC board, the capacitance is integrated over the geometry, where The capacitance is divided in half because only the surfaces that face the PC board dielectric contribute significantly to the capacitance. The third capacitance structure is formed by the remaining triangle between C 2 and C 1 , where The integrals were performed numerically using Mathematica. The fourth capacitance is formed by the plated-throughholes, or via, in the PC board and is approximated by the formula for the capacitance per unit length of two round parallel wires, 19 The factor 0.8 is used because only half the conductor contributes capacitance. The outer sides contribute capacitance to the adjacent transmission line. The fifth capacitance is formed by the PC board conductor surfaces that face each other in air and that make up the conducting pad and trace at the end of each through-hole, The capacitance is multiplied by two because there is one on each side of the PC board. The sixth capacitance is formed by the conducting pads at the top and bottom of the PC board via, Other capacitances due to the interface between the metal pad and the PTFE were omitted in the model. Since comparison to the finite-element simulations shows close agreement, the approximation is justified. Two resonators were designed and fabricated. The first is the seven-element SRA described in Table I. The natural resonance frequency of a seven-element SRA was found by solving Eq. (8) for the frequency. The predicted frequency for the seven-element surface resonator dimensions given in Table I by the circuit theory is 9.78 GHz. The corresponding system was modeled and analyzed with HFSS using the eigenmode solution method, which predicted 9.66 GHz, a 1% difference. The second is an 11-element SRA with conductor center-to-center spacing, s, of 1.0544 mm and conductor spacing, t, of 0.3044 mm. The 11-element SRA is designed to have the same sample cross-section as the seven-element but with a further limited depth sensitivity due to the 40% reduction of spacing between elements.

IV. DESIGN
Using the transmission model in Mathematica, the frequency of a seven-element SRA was calculated and the structure designed in Ansys HFSS. Both an eigenmode calculation, to find the resonance, and a driven mode calculation, to determine coupling feasibility, have been performed for this structure. With the finger phantom in place, the Q 0 -value of the simulated resonator is approximately 200.
A PC board micro-strip line coupling circuit was used to make impedance transformations to present a balanced differential voltage at the SRA and a 50 characteristic impedance at the input. The PC board coupling circuit is illustrated in Fig. 5.
Following from Fig. 5, the 50 characteristic impedance micro-strip line input was connected to a 85 quarter-wave transformer. The characteristic impedance of the quarter-wave transformer was chosen to obtain a voltage split that will reduce reflections between the unbalanced source and balanced load of the SRA. 23 A compensated 3 dB micro-strip in-line power divider was used for power division with equal phase characteristics at each of the output ports, illustrated by plane A.
To limit internal reflections in the transmission lines while maintaining shorter line lengths, double hyperboliccosine tapered lines are used for power division. The tapered lines provide consistent impedance transformation while maintaining low amplitude ripple (approximately 0.3 dB peak-to-peak) in the transmission coefficient and acceptable return loss (>30 dB) in the frequency band of interest. 24 The 85 micro-strip line gradually tapers to plane A, illustrated in Fig. 5, into two branches of equal magnitude and phase with a characteristic impedance of 50 . The 50 line attached at plane A and the SRA input was chosen arbitrarily. It provides a base impedance for a second micro-strip line impedance transfer of 95 . The characteristic impedance of the 95 transformation was chosen by simulation to obtain the desired coupling characteristics. Simulating the structure with the full-finger model, the transformation impedance was increased, which lowered the coupling coefficient and reduced an over-coupled system. An impedance of 95 was chosen to be adequately over-coupled (approximately 15 dB) to account for loss variability in samples during experimental testing.
A balanced differential transmission line is required at the input of the SRA, illustrated by planes B and B in Fig. 5. Fundamentally, two modes exist in a strip-line transmission model: differential mode, where the current flow is equal in magnitude and 180 • out of phase, and common mode, where the current flow is equal in magnitude and phase. [25][26][27] In the common mode, the return path is through the ground plane. Common mode currents can arise due to discontinuities in the transmission lines, such as tapers, bends, finite ground planes, and external noise. The common mode is undesired and will give rise to unwanted resonant modes, which may reduce the incident power to the SRA and decrease the circuit Q-value.
Suppression of the common mode is essential for proper system performance. A number of methods have been combined to suppress the common mode by greater than 30 dB. The first method is to provide a quarter wave transformer to alter the characteristic impedance of the micro-strip feed line at the splitter. The transformer provides an "open" to the common mode, while providing a low transmission coefficient to the differential mode. The second method is use of a double hyperbolic-cosine power splitter, which provides a smooth impedance transformation as well as shorter transformation length compared to a linear taper. The third method to suppress common mode coupling is adjustment of the lengths of the feed lines to provide 180 • phase differential at the input to maximize the coupling coefficient to the SRA. An additional transmission line length, corresponding to a half-wave PC Board wavelength at the eigenmode frequency of the SRA, is added.
As shown by simulation in Fig. 6, the common mode has been suppressed by greater than 30 dB while maintaining the expected differential mode insertion loss of approximately 3 dB. In Fig. 6, both modes are compared to the 50 input. A comparison was made for the PC Board circuit with and without the directional coupler to access perturbations made by the coupling structure. Minimal shifts in the common mode and differential mode profiles were found. Minimal shifts are required to reduce frequency pulling during SRA matching as well as to maintain surface current distributions. The addition of the coupling system to the SRA geometry lowers the op-FIG. 6. Simulation of the common and differential modes with (solid) and without (dashed) the directional coupler. The seven-element SRA operating frequency is marked at 9.352 GHz. erating frequency from 9.66 GHz to 9.352 GHz due to stray impedance in the circuit.
In order to account for manufacture and sample variability, a mechanical coupling has been designed into the PC Board. Two methods are available: a coarse stub tuner and a fine-matching directional coupler. The placement of the parallel coarse stub tuner was designed to provide maximum under-coupling when all micro-strip stubs are connected. The coarse coupling adjustment is accomplished by soldering the stubs while the resonator is connected to a network analyzer before final assembly. An equivalent sample is placed on the SRA during this adjustment. The fine tuning adjustment employs a variable transmission line coupled to the circuit with a directional coupler. The adjustable transmission line is an open coax where the dielectric depth is varied by a fine PTFE screw on the side of the copper shield and the inner coaxial wire is soldered to the fine coupler adjustment via on the circuit board, illustrated in Fig. 5. The change in coaxial dielectric depth changes the characteristic impedance associated with the transmission line which provide a variable match.
A PC board substrate thickness of 0.254 mm was chosen to ensure that there are no spurious modes excited in the dielectric substrate. The dielectric substrate thickness limits the coupling bandwidth of the directional coupler. However, the directional coupler can be adjusted by placing low-loss high frequency capacitors across the coupler and the 85 transmission line to overcome coupling limits after fabrication.
The SRA surface, where a sample is placed, is shown in Fig. 7(a). Finally, field modulation coil holders are attached to the structure that provide two main functions: (i) support   FIG. 7. (a) Assembled seven-element SRA with PTFE protection which is placed in (b) the saddle shaped modulation coils. of the saddle-shaped coil and (ii) support of the sample itself. A saddle-shaped modulation coil, illustrated in Fig. 7(b), provides a surface to hold the sample. Vibration dampening material is placed on the sides and bottom of the sample to hold it in place. Finally, the resonator is mounted on a bracket that affixes it between the magnet poles. Table II. Experimental EPR values were acquired with a time constant of 5.12 ms and sampling time of 20.48 s over 300 G. The amplitude of the 100 kHz field modulation was 5 G and was chosen for maximum EPR signal intensity. Experiments were performed using the SRA and the Bruker Super High-Q cavity at two incident powers chosen on the basis of the power saturation characteristics of the alanine-polystyrene standard model and the resonator under test, shown in Fig. 8. Both powers were chosen based on stability, noise, and peak P 1/2 signal for each resonator. The direct comparison of the point of saturation is complicated by the microwave field profiles of the resonators. The Bruker cavity is relatively uniform in the volume of the sample, while the microwave field of the SRA is uniform in a plane and diminishes exponentially. Here, power saturation characteristics of the SRA are used as a fingerprint to compare the EPR signal intensities at either constant power or relative constant microwave field. Optimal power for the Bruker Super High-Q cavity was 1 mW, while the optimal power for the SRA was 37 mW.

Comparison of resonators in both simulation and experiment is shown in
Simulated and measured results for saturable samples, where the signal is compared at relative P 1/2 values, and unsaturable samples, where the signal is compared at constant microwave power, are shown in Table II. 28 Here, the ratio of the simulated calculations can be directly compared to the ratio of the measured results. Good agreement is shown. Calculated resonator efficiency, , provides a general metric of losses associated with the sample, where P 1/2 results give an average resonator efficiency over the sample region. Close agreement between the ratios of ave and P 1/2 is shown. Measured and simulated experiments testing the depth sensitivity were performed on two fabricated SRAs. The data of Fig. 9 were collected using a known EPR background in Rogers 5880 PC board material. The PC board sample was 0.2 mm thick and placed at varying depths of 0.083 mm spacing on a polyacrylamide gel finger model. Experiments were FIG. 9. SRA depth sensitivity curve showing good agreement of measured data from a seven-element (circle) and 11-element (triangle) geometry with an overlay of Ansys HFSS simulated data from a seven-element (solid line) and 11-element (dashed line) geometry.
repeated five times. The data are normalized to average peak intensity at 0.1 mm and compared to simulated Ansys HFSS EPR sensitivity at varying depths. The curves show that 90% of the EPR signal is obtained in the first 0.75 mm and 0.5 mm, with the seven-and 11-element SRA, respectively, of the nail sample as predicted by simulation and theory. Signals below the depth of 0.6 mm were unobtainable using the 11-element SRA.
The seven-and 11-element SRA signal intensities shown in Fig. 9 illustrate the ability to design the resonator to maximize signal intensity at a surface. Reduction in the losses of the polyacrylamide increase the efficiency of the 11-element SRA to 1.58 G/W (1/2) . By making the depth sensitivity smaller than the thickness of the sample, the EPR signal is less sensitive to variations in sample thickness. Additionally, it may be advantageous to test a sample at both resonator depths to distinguish signals at different layers.
The alanine-polystyrene sample was irradiated at seven different doses. From the same alanine-polystyrene batch, two samples were prepared: the first for the Bruker Super High-Q resonator to compare against irradiated finger nails, and the second to be placed on the finger model and tested on the SRA. Figure 10 shows the results of these experiments. The Bruker Super High-Q data, shown in Fig. 10(a), compare the dose-dependent increase in the intensities of the radiationinduced signal in the fingernail sample (dashed line; triangle) and the alanine-polystyrene (solid line; circle). The signals are normalized to a fixed Bruker reference standard (g-value of 1.98) that is outside of the measured alanine and fingernail signals. Both sets of data are baseline corrected at 0 Gy and mass normalized. There is a 65% greater dose-response for the ionizing radiation signal in the alanine-polystyrene as compared to the finger-nail clipping. Both show a linear dose response. The signal-to-noise at 5 Gy for the alanine radiation-induced signal is 183 compared to 96 for the nail clipping in the Bruker High-Q resonator, whereas the signalto-noise at 5 Gy for the alanine radiation-induced signal with a full-finger model using the seven-element SRA is 12.
The irradiated full-finger model was placed on the sevenelement SRA and the dose curve of Fig. 10(b) was obtained. The alanine signal was again normalized to the reference Bruker standard. Good dose resolution is shown in the experimental data. These estimates for the radiation-induced signal in a finger nail model establishes that an X-band EPR dosimetry method based on a SRA resonator is capable of achieving the detection sensitivity required to derive dose estimates of 2 Gy or less based on the radiation-induced signal in finger (or toe) nails in humans exposed to ionizing radiation. The 2 Gy dose is considered to be the threshold dose for triage of victims in an accidental or intentional radiation or nuclear event who will need medical care to treat the acute effects of radiation. 29,30 Additional refinements in the SRA to further limit depth penetration of the B 1 field into the nail plate and accommodate the curvature of the plate are expected to improve the detection sensitivity for the radiation-induced signal in nails.
A second experiment was performed to exhibit the use of an SRA for surface chemistry experiments where the sample cannot be removed from a surface, or the sample of interest is formed by bonding to the surface. Such experiments are of interest in surface spectroscopy and coating science. Here, a CaO sample with 50 mM concentration of Mg 2 + was dissolved in chloroform and polystyrene to a final concentration of 1.44 μM of Mg 2 + . The overall thickness of the polystyrene sample was 1.1 mm and, when dried, bonded to an aluminum surface that was 2.5 mm thick. The sample was placed on the 11-element SRA within the modulation coils and a spectrum was recorded. Shown in Fig. 11 is the spectrum obtained at 32 mW with a 100 kHz modulation amplitude of 5 G, 40.96 s sweep over 600 G, 25 averages and a time constant of 5.12 ms. The 11-element SRA frequency shifted up by 50 MHz, indicating a small interaction with the aluminum surface.

VI. DISCUSSION
This paper is concerned with limiting depth sensitivity by tailoring the geometry for acquisition of EPR signals from surfaces with a known region of interest. The SRA geometry has been shown to function satisfactorily in experiments where the surface is surrounded by lossy material that does not contribute to the EPR signal, such as in vivo tissue in dosimetry of irradiated fingernails, or experiments where material beneath the region of interest yield an unwanted EPR signal. The adjustability of the depth sensitivity during design is a strength of the SRA structure and is expected to be generally useful for EPR surface spectroscopy where the sample cannot be placed inside a traditional cavity. Good EPR signal intensities and resonator efficiency with samples surrounded by lossy material are shown in simulation and experimental results. Finally, experimental results with metal objects close to the resonator show that the metal does not perturb the limited near field. There may be applications in coating or material science, where, for example, qualitative or quantitative analysis of unpaired spin centers is required to understand the properties or reactivity of various surfaces.
Design of the surface resonator at X-band uses a unique combination of lumped-circuit and distributed electromagnetic approaches coupled with numerical analysis to understand the modes of interest. Intuition from analytical analysis is used to match the SRA geometry to a 50 coaxial line. Structures such as the SRA are not readily matched by irises typically used at X-band, and must be treated like near-field surface antenna. Care must go into the design of the PC board matching circuit in order to minimize spurious modes while maintaining an acceptable bandwidth for frequency deviation caused by variable sample losses.