NMR magnetometry with single-chip RF transceivers. Giovanni Boero Ecole Polytechnique Federale de Lausanne (EPFL) Lausanne Switzerland

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1 NMR magnetometry with single-chip RF transceivers Giovanni Boero Ecole Polytechnique Federale de Lausanne (EPFL) Lausanne Switzerland Giovanni Boero IMMW

2 Magnetic Resonance Domain NMR Nuclear Magnetic Resonance ESR Electron Spin Resonance FMR Ferromagnetic Resonance Weakly coupled nuclear spins Weakly coupled electron spins Strongly coupled electron spins Introduction Giovanni Boero IMMW

3 NMR: Resonance frequency Many nuclei have a non-zero magnetic moment. Nucleus Spin I Natural Abundance Magnetic Moment (µ/µ Ν ) Gyromagnetic Ratio γ (10 7 rad/s T) Resonance Frequency (MHz/T) 1 H 1/ H C 1/ O 5/ F 1/ P 1/ e 27 Nuclear Magneton µ N = 5 10 J/T 2m p e 24 Electron Magneton µ B = 9 10 J/T 2m e Giovanni Boero IMMW

4 NMR: simple experiment ω γ B 0 1 ω = γ B Giovanni Boero IMMW

NMR: signal and noise (inductive detection)

ω t e t/ T * 2 SNR = MVB ω 0 S u 0 4kTR f V

5 NMR: signal and noise (inductive detection) V Signal (t=0): V = 0 0 S u 0 Noise: MVBω noise, rms 4 = ktr f Signal-to-noise ratio: B u (r s ) V 0 M(r s,t) V(t) V cos ( ) 0 0 ω t e t/ T * 2 SNR = MVB ω 0 S u 0 4kTR f V noise Giovanni Boero IMMW

6 NMR: main applications Molecular Structure Determination 3D Imaging Introduction Giovanni Boero IMMW

7 NMR of SMALL molecules Ethanol CH 3 -CH 2 -OH 1 H 13 C CH 3 -CH 2 -OH 1 H: 43 MHz/T 13 C: 11 MHz/T Introduction Giovanni Boero IMMW

8 NMR of LARGE molecules (up to 500 kda) Ubiquitin protein (8.5 kda) Introduction Giovanni Boero IMMW

9 NMR magnetometry L. Bottura, CERN Giovanni Boero IMMW

10 NMR magnetometry key-features Typical Best. Field range 10 mt to 30 T 1 µt to 100 T Accuracy 10 ppm 10 ppb Resolution 100 ppb/hz 1/ ppb/hz 1/2 Temperature range 280 K to 310 K sub-k to 1000 K Giovanni Boero IMMW

11 NMR magnetometry: Applications Application When By whom Magnetic resonance imaging (MRI) magnets Particles accelerator magnets Ordinary electromagnets and permanent magnets During fabrication During installation in hospitals After quenching in hospitals After room changes in hospitals During fabrication During operation Calibration Hall sensors Physics experiments. General Electrics Philips Toshiba. CERN Fermilab DESY KEK Argonne PSI/SLS. Hall sensors companies University labs. Giovanni Boero IMMW

12 Metrolab NMR magnetometer (Array) 16 probes 40 probes Giovanni Boero IMMW

13 Metrolab NMR magnetometer (modified) Giovanni Boero IMMW

14 Metrolab probes with single-chip transceiver 10 mm 1 mm Single chip CMOS transceiver Giovanni Boero IMMW

15 Why a single chip integrated transceiver? Single-chip Integrated Transceiver VS Discrete Components Transceiver (for NMR magnetometry) No search of many non-magnetic components. Broadband operation with marginal compromise in noise figure. Much smaller size. Better or equal SNR and magnetic field resolution. Giovanni Boero IMMW

16 Single-chip transceivers 1 mm Chips area: about 1 mm 2 Single chip I-only transceiver Single chip I-only transceiver (with integrated coil) 300 μm 1 mm Microcoil Single chip IQ transceiver 50 μm Giovanni Boero IMMW

17 Single-chip IQ transceiver (with external resonator) Single-chip IQ transceiver External resonator Giovanni Boero IMMW

18 Single-chip IQ transceiver: details RF f = f 0 TX RF Input: -3 dbm TX RF Output: ~10 mw TX Bandwidth: MHz AF RF AF f = Δ f = 2( f 0 +Δ ) f = Δ TX/RX recovery time: ~ 1 µs RX Bandwidth: MHz RX Input noise: 1.1 nv/hz 1/2 RX Gain: 54 db IQ error: 3 at 3 MHz 0.1 at 1 GHz Power cons. ~20 mw Giovanni Boero IMMW

19 Field range SNR = MVB ω 0 S u 0 4kTR f To measure a small B 0 : - Large sample volume - Dynamic nuclear polarization - Polarization at an higher field (flowing sample) - Non-inductive detection methods Giovanni Boero IMMW

Accuracy: accurate «calibrations» Free proton : γ f0 = B0 2π γ = ( 42.577 478 92 ± 0.

20 Accuracy: accurate «calibrations» Free proton : γ f0 = B0 2π γ = ( ± ) MHz/T 2π ± 7 ppb Proton in a spherical sample of pure water at 25 C : γ γ f0 = (1 σ) B0= B0 σ = ± π 2π γ = ( ± ) MHz/T 2π ±13 ppb 6 ( ) Accurate "calibrations" 0.01 ppm CODATA 2014 Giovanni Boero IMMW

21 Accuracy: chemical shift HO 2 + Free CuSO4 Proton (sat. sol) HO 2 TMS ppm Giovanni Boero IMMW

22 Accuracy: Temperature dependence Shielding (ppm) Temperature dependence: 0.1 ppm for T=10 C at 25 C in water T ( C) B.W. Petley et al., Metrologia 20, 81 (1984) Yu I Nerenov et al., Metrologia 51, 54 (2014) Giovanni Boero IMMW

Accuracy: Susceptibility effects Material χ (10-6 ) Material χ (10-6 ) Air +0.

5 Silver -24 FR4-5 Gold -34 SU8-9.75 Silicon -4.

23 Accuracy: Susceptibility effects Material χ (10-6 ) Material χ (10-6 ) Air Platinum +290 Water Aluminum Quartz Copper -9.6 Teflon Silver -24 FR4-5 Gold -34 SU Silicon ω0( χ) ω0( χ = 0) α = χ ω ( χ = 0) Susceptibility and Shape of: - Objects in proximity to the sample - Sample itself Susceptibility effects: up to 10 ppm 0 Giovanni Boero IMMW

24 Accuracy: summary Accurate "calibrations" (in given material, temperature, sample shape,...) 0.01 ppm Temperature dependence: 0.1 ppm for T=10 C at 25 C in water Susceptibility effects: up to 10 ppm Giovanni Boero IMMW

25 Resolution: Basics Cramer - Rao Lower Bound (CRLB) : Standard deviation on the frequency measurement ( f ) : min f 3/2 2x 1 8(1 e ) TACQ min [Hz] = *, x * T x x 2 ( s0 / N) 2 π (1 e ) 4 x e T2 s 0 : signal amplitude in time domain [V] 1/2 N : noise voltage spectral density [V/Hz ] T * 2 : effective exponential decay time of the signal [s] f ( f ) 2 1 [Hz] = (for x ) T s N s N FWHM min * π 2 0 / 0 / 3/2 Nikiel A., et al. "Ultrasensitive 3 He magnetometer for measurements of high magnetic fields." Eur. Phys. J. D (2014) Gemmel C., et al. "Ultra-sensitive magnetometry based on free precession of nuclear spins." Eur. Phys. J. D (2010) Gross S., et al. "Dynamic nuclear magnetic resonance field sensing with part-per-trillion resolution." Nat. Comm. (2016) Giovanni Boero IMMW

26 Resolution: Signal processing It (), Qt () 0 { It Qt} FFT ( ), ( ) { } Peak - finder. vi on FFT I( t), Q( t) (or Lorentz fit. vi) f «FFT» It (), Qt () 0 ( It Qt) ϕ=arctg ( ) / ( ) " Unwrap phase. vi" on and " Linear fit. vi" of ϕ f «PHASE» ϕ Giovanni Boero IMMW

27 Resolution: Results Probe A B C D Frequency [MHz] Field [T] 7.05 (SC) 7.05 (SC) 7.05 (SC) 1.4 (EM) Sample NR Natural Rubber MQ Silicone Rubber H 2 O Water NR Natural Rubber Sample vol. [μl] T 2 [ms] T 2 * [ms] T 1 [ms] Chem. shift [ppm] 5.1/2.1/ /2.1/1.7 Pulse length [μs] Repetition time [ms] Averages Averaging time [s] Measurements Measuring time [s] s 0 [V] N [μv/hz 1/2 ] Standard dev. [Hz] [nt] [ppb] CRLB [Hz] [nt] [ppb] Exp. standard deviation >> CRLB!! Reason: Magnetic field fluctuations (electronic noise and frequency stability of the source are negligible) Giovanni Boero IMMW

Two channels probe (to cancel field fluctuations) Two coils, two resonators, two single-chip IQ transceivers Copper wires Acrylic-embedded probe head acrylic 1 cm PMMA

28 Two channels probe (to cancel field fluctuations) Two coils, two resonators, two single-chip IQ transceivers Copper wires Acrylic-embedded probe head acrylic 1 cm PMMA capillary PDMS mold Sample material: Water Sample volume: 500 nl Cramer-Rao Lower Bound: 0.02 ppb/hz 1/2 Exp. Measured: 0.06 ppb/hz 1/2 Giovanni Boero IMMW

29 NMR magnetometry for surgical interventions Spatial resolution: 100 µm Time resolution: 100 ms J. Anders et al., Magn. Reson. Medicine 67, 290 (2012) Our research Giovanni Boero IMMW

30 NMR spectroscopy of single sub-nanoliter eggs 1.5 pig Richtersius coronifer 50 μm whale Ovum volume [nl] lancelet human guineapig Heligmosomoides polygyrus bakeri 50 μm 300 μm 0 sea urchin rat roundworm Microcoil 50 μm M. Grisi et al., Scientific Reports 7,44670 (2017) Giovanni Boero IMMW

31 Multi-nuclei excitation/detection Sample NaBF 4 +H2O Na + +BF 4- +H2O Giovanni Boero IMMW

32 Sponsors and people Marco Grisi Enrica Montinaro Alessandro Matheoud Gabriele Gualco Giovanni Boero IMMW

Introduction to MRI. Spin & Magnetic Moments. Relaxation (T1, T2) Spin Echoes. 2DFT Imaging. K-space & Spatial Resolution.

Introduction to MRI. Spin & Magnetic Moments. Relaxation (T1, T2) Spin Echoes. 2DFT Imaging. K-space & Spatial Resolution. Introduction to MRI Spin & Magnetic Moments Relaxation (T1, T2) Spin Echoes 2DFT Imaging Selective excitation, phase & frequency encoding K-space & Spatial Resolution Contrast (T1, T2) Acknowledgement: