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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 3 — Mar. 1, 2014
  • pp: 876–881
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Optical multichannel room temperature magnetic field imaging system for clinical application

G. Lembke, S. N. Erné, H. Nowak, B. Menhorn, A. Pasquarelli, and G. Bison  »View Author Affiliations


Biomedical Optics Express, Vol. 5, Issue 3, pp. 876-881 (2014)
http://dx.doi.org/10.1364/BOE.5.000876


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Abstract

Optically pumped magnetometers (OPM) are a very promising alternative to the superconducting quantum interference devices (SQUIDs) used nowadays for Magnetic Field Imaging (MFI), a new method of diagnosis based on the measurement of the magnetic field of the human heart. We present a first measurement combining a multichannel OPM-sensor with an existing MFI-system resulting in a fully functional room temperature MFI-system.

© 2014 Optical Society of America

1. Introduction

The magnetic field of the human heart contains information, which cannot be inferred with the measurement of its electric field outside the body [1–3

1. B. J. Roth and J. P. Wikswo Jr., “Electrically silent magnetic fields,” Biophys. J. 50(4), 739–745 (1986). [CrossRef] [PubMed]

]. The magnetic sensor can detect current loops for which the ECG is blind [1,4,5

1. B. J. Roth and J. P. Wikswo Jr., “Electrically silent magnetic fields,” Biophys. J. 50(4), 739–745 (1986). [CrossRef] [PubMed]

]. The visualization of the magnetic field in the form of a map above the chest as it is performed in magnetic field imaging (MFI) [6

6. BMDSys Production GmbH, http://www.bmdsys.com

] can be very helpful in heart diagnosis, e.g. to infer the risk of sudden cardiac death [7

7. T. Toennis, “Magnetic field imaging for risk stratification of sudden cardiac death in patients with primary preventive ICD-indication,” BIOMAG 2012 Book of Abstracts, 41 (2012)

].

The existing MFI-systems are based on Superconducting QUantum Interference Devices (SQUIDs) [8

8. J. Vrba, J. Nenonen, and L. Trahms, “The SQUID Handbook Vol. II,” J. Clarke, A. I. Braginski, ed. (Wiley-VCH, Weinheim, 2006)

], working at 4 K requiring weekly liquid helium (lHe) refilling. This leads to complicated handling and it causes heavy running cost for lHe and maintenance.

Possible candidates to replace SQUID-sensors in MFI-systems are optically pumped magnetometers (OPM) working at room temperature, which were already shown to be able to measure the magnetic field of the human heart in the 1970s [9

9. M. N. Livanov, A. N. Kozlov, A. V. Korinevskiĭ, V. P. Markin, and S. E. Sinel’nikova, “[Recording of human magnetic fields],” Dokl. Akad. Nauk SSSR 238(1), 253–256 (1978). [PubMed]

]. However, the bandwidth of those measurements was very limited, which made the systems unfeasible for heart diagnosis.

In the last years research on optical magnetometers lead to enormous improvements, reaching sensitivities similar to SQUIDs [10,11

10. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007). [CrossRef]

]. The most sensitive optical magnetometers are even able to measure the weak signals of the human brain [12

12. T. H. Sander, J. Preusser, R. Mhaskar, J. Kitching, L. Trahms, and S. Knappe, “Magnetoencephalography with a chip-scale atomic magnetometer,” Biomed. Opt. Express 3(5Issue 5), 981–990 (2012). [CrossRef] [PubMed]

] and heart signals of an unborn child [13,14

13. R. Wyllie, M. Kauer, G. S. Smetana, R. T. Wakai, and T. G. Walker, “Magnetocardiography with a modular spin-exchange relaxation-free atomic magnetometer array,” Phys. Med. Biol. 57(9), 2619–2632 (2012). [CrossRef] [PubMed]

]. However, these magnetometers work in the spin-exchange relaxation-free (SERF) regime. This means, that they are heated to temperatures higher than 100°C and they only operate in very low magnetic fields, needing heavily shielded environments.

In the last years Bison et al. showed in [15

15. G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, M. Kasprzak, H. Saudan, and A. Weis, “A room temperature 19-channel magnetic field mapping device for cardiac signals,” Appl. Phys. Lett. 95(17), 173701 (2009). [CrossRef]

] that even with less effort (weak shielding and room temperature), optically pumped magnetometers are able to measure the weak signals of the human heart. To prove the feasibility of a clinical system based on optical sensors, a system with 57 sensing channels was designed at the University of Jena [16

16. G. Lembke, M. Stumpf, S. N. Erné, and G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]

]. This system was modified to be integrated into an available clinical system designed for MFI-measurements with SQUIDs. This MFI-system now consists of an optical sensor head and special electronics designed for the readout of the optical system. The acquisition software provides real time preprocessing with power line filtering, anti-aliasing, band pass filtering, and software noise compensation. Also provided is an offline data analysis with blind source separation, trigger point selection, segmentation, editing and averaging of the measured signal. Finally, the fragmentation index is calculated, which is used to indicate an increased risk of sudden cardiac death [7

7. T. Toennis, “Magnetic field imaging for risk stratification of sudden cardiac death in patients with primary preventive ICD-indication,” BIOMAG 2012 Book of Abstracts, 41 (2012)

]. We present the results of the first measurement with the system, performed in the aluminum shielding room described in [16

16. G. Lembke, M. Stumpf, S. N. Erné, and G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]

].

2. Methods

In our setup, we utilize the dependence of light absorption in Cesium (Cs) vapor from the magnitude of an outer magnetic field. The spin of the Cs-atoms is oriented by optical pumping with circularly polarized laser light with the wavelength of the D1-transition (894 nm). In an outer magnetic field B0 the incurred macroscopic magnetization precesses around the field direction with the Larmor frequencyωL=γB0, and the gyromagnetic ratioγ=2π3.5Hz/nT. A weak magnetic field Brf oscillating with the frequency ωrf perpendicular to B0 drives the precession and leads to a modulation of the transmitted laser light with ωrf. When ωrf = ωL, the signal shows resonant behavior with maximum amplitude. Thus, an optical double resonance in the so-called Mx-configuration [17

17. S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx-magnetomter,” Eur. Phys. J. D 38(2), 239–247 (2006). [CrossRef]

] is realized.

The phase shift of the recorded modulation with respect to Brf shows an arctan-behavior:

θ=θ0arctan[ωrfωL/Γ].
(1)

Here, θ0 describes the phase offset mainly given by technical phase shifts in the detection system and Γ is the relaxation rate of the spin system [18

18. N. Castagna, G. Bison, G. Di Domenico, A. Hofer, P. Knowles, C. Macchione, H. Saudan, and A. Weis, “A large sample study of spin relaxation and magnetometric sensitivity of paraffin coated Cs vapor cells,” Appl. Phys. B 96(4), 763–772 (2009). [CrossRef]

]. The phase shift shows a steep linear zero crossing at resonance, linking small changes in the outer magnetic field to a linear phase shift. By feedback coils around the Cs-cell, driven by proportional and integral controllers (PI-controllers) locked to the zero crossing of the phase curve, the resonance condition is stabilized. Small changes in the outer magnetic field lead to a compensating current in the feedback coils, which contains the information about the magnetic field to be recorded.

The basic module layout of a single sensor was investigated inside a small magnetic shield (3 layers) [16

16. G. Lembke, M. Stumpf, S. N. Erné, and G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]

]. A photo of a single module including Cs-glass-cell (Cs-cell) and photodiode (PD) is shown in Fig. 1
Fig. 1 Left: Photo of a single module. OM: Optical module containing a lens for collimating the light, two linear polarizers for intensity adjustment and a λ/4-plate for circularly polarizing the light, PD: Photodiode, Cs-Cell: cesium-cell. FB: Indicated position of the feedback coils. Right: Photo of the lowest sensor plane.
, left. The Cs-cells were manufactured at the University of Fribourg [18

18. N. Castagna, G. Bison, G. Di Domenico, A. Hofer, P. Knowles, C. Macchione, H. Saudan, and A. Weis, “A large sample study of spin relaxation and magnetometric sensitivity of paraffin coated Cs vapor cells,” Appl. Phys. B 96(4), 763–772 (2009). [CrossRef]

], have a diameter of about 27 mm and contain no buffer gas. The cell walls are paraffin coated to prevent the atoms from depolarizing during wall collisions. The laser light is applied to the module via an optical fiber. The position of the feedback-coils (FB) is also shown. Figure 1, right, shows a photo of the lowest level with inserted optical modules.

The individual modules are mounted on a quadratic grid with 32 mm sensor separation. The complete sensor head consists of three parallel levels, the bottom one (measuring level: planar sensor array parallel to the chest of the test person) containing 57 sensor modules, the middle and upper one with 13 modules each (Fig. 2
Fig. 2 Layout of the sensor array. Left: 3D-display of all three levels with a spacing of 70 mm. Right: Top view on lowest sensor plane. At the positions marked with + the reference sensors in the second and third level are located.
), all together 83 single modules.

A commercially available laser (Toptica DL pro) provides the laser light. Its output is divided into a main beam for the optical modules and a secondary one used in a saturation spectroscopy setup [19

19. D. W. Preston, “Doppler-free saturated absorption: Laser spectroscopy,” Am. J. Phys. 64(11), 1432 (1996). [CrossRef]

] for frequency adjustment. The main beam is focused on a microlens array to create a homogeneously illuminated square of 4.5 x 4.5 mm2, which holds a fiber bundle in such way, that all fibers yield the required light intensity for each respective optical sensor module. The aluminum shielding room (pure aluminum, 12 mm thick) containing the system reduces noise at 50 Hz by a factor of approximately 90, being sufficient for cardiac measurements in a quiet environment [16

16. G. Lembke, M. Stumpf, S. N. Erné, and G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]

].

To provide the necessary magnetic fields B0 and Brf, inside the walls of the shielded room a number of coils were integrated: First, a set of coils for the compensation of constant magnetic fields in each room direction (Bx, By and Bz), two coils per room direction. Second, coil sets made of 4 adapted coils each for compensating the field gradients dBz/dx, dBz/dy, dBz/dz, dBx/dx, dBy/dy. Additional coils for active noise compensation were installed parallel to the coils for Bz and driven by an additional optical sensor in the middle plane.

The signals from the photodiodes are amplified and fed to specially designed printed circuit boards (PCBs) based on field programmable gate arrays (FPGA), providing the phase sensitive detection. First, the signals are converted from analog to digital by ADC-converters. The signals are multiplied with the reference signal ωrf itself and the 90° phase shifted reference signal, then filtered by low-pass-filters (lock-in technique). The phase of the signals is extracted with the CORDIC-algorithm [20

20. J. E. Volder, “The CORDIC Trigonometric Computing Technique,” IRE Trans. Electron. Comput. 8(3), 330–334 (1959). [CrossRef]

] (COordinate Rotation DIgital Computer) and used as input value for the PI-controllers. The controllers generate feedback currents so that the phase signals are locked to zero. The current signal is converted from digital to analog by DA-converters and fed into the feedback coils around each individual Cs-cell. This current is proportional to outer changes of the magnetic field caused for example by the human heart. A schematic of the data processing is shown in Fig. 3
Fig. 3 Schematics of the data processing. PD: photodiode, PA: preamplifier, ADC: Analog-Digital-Converter, x: Multiplier, LPF: Low-pass-filter, PI: Proportional-integral controller, DAC: Digital-Analog-Converter, FB: Feedback-coils, PC: workstation for data recording.
.

Eight FPGA-boards are used, one of them as master providing the rf-signal and collecting the data from the other boards for transfer to the workstation (PC). Each slave board processes 16 channels, measuring the photodiodes’ signals and controlling the feedback currents for 16 modules. All boards communicate via one backplane.

The measured data are sent as UDP-packets (User Datagram Protocol) to a special workstation designed for data acquisition and evaluation, which is modified from the one used in a clinical MFI-Systems based on SQUID-sensors. This protocol allows a real-time data transfer enabling the measured signal to be displayed in real-time on the screen. Like in the clinical setup, a simultaneously recorded 4-lead electrocardiogram (at ankles and wrists) was used as trigger for data averaging.

3. Results

The active compensation reduces the noise between 0.1 Hz and 10 Hz by a factor of about 10 compared to the uncompensated case (see Fig. 4
Fig. 4 Root noise density of one single channel with (green) and without (red) active compensation. A square-wave signal with amplitude of 6 nT and a frequency of 1 Hz was used as test signal.
). We measured a square-wave test signal applied via a coil at the lower measuring level with amplitude of 6 nT and a frequency of 1 Hz. The peaks are the odd harmonics of the square-wave signal. The regions between the peaks show the noise improvement achieved.

The position plot of the MFI-Recordings (Fig. 5
Fig. 5 First MFI-measurement of a healthy test person performed with the optical sensor head. The data was recorded for 10 minutes and averaged. The arrow indicates the position of the test person’s head.
) shows 55 channels. The current version of the real time preprocess software considers the use of 9 reference channels to perform noise compensation. Linear combinations of reference signals are subtracted from the data of each measuring channel (first order software gradiometer). The coefficients for the reference signals are calculated performing minimization of the environmental noise before the actual measurement.

We calculated the crosstalk matrix numerically for our geometry and built the inverse matrix. The maximum value for the crosstalk (between nearest neighbors) was about 15%. During the real-time data processing, the inverse matrix is used to eliminate the crosstalk. The heart signal was measurable in a room only being eddy current shielded. Figure 5 shows the measurement of a healthy test person, with 10 minutes of data recording and averaging after preprocessing.

As expected, the heart signals are different in amplitude and shape in each channel, corresponding to the placement of the sensor.

With the analysis console, the data can be processed further and the diagnostically relevant information can be extracted (see Fig. 6
Fig. 6 Evaluation of the first optical MFI-measurement of a healthy test person. Upper part: Three channels with the averaged heart signal and magnetic field map. Upper left: Signal with maximum amplitude. Upper right: “Butterfly plot” of all relevant channels. Middle left: Channel with highest fragmentation. Middle right: Magnetic field map. Lower part: As result, the fragmentation index is displayed in comparison to the normal range of healthy test persons.
) like in a clinical SQUID-based MFI-system. The averaged heart signal is shown in three diagrams. In the upper left one the signal with maximum amplitude is shown, in the upper right one a “butterfly plot” of all relevant channels is displayed and finally in the middle left diagram the channel with the highest fragmentation is shown. Finally, the fragmentation index of the QRS-complex is displayed compared to the range of the values of healthy subjects.

4. Conclusion

Acknowledgments

This work was supported by the German Federal Ministry for Education and Research (Project numbers 0315024B and 0316069B).

References and links

1.

B. J. Roth and J. P. Wikswo Jr., “Electrically silent magnetic fields,” Biophys. J. 50(4), 739–745 (1986). [CrossRef] [PubMed]

2.

K. Tolstrup, B. E. Madsen, J. A. Ruiz, S. D. Greenwood, J. Camacho, R. J. Siegel, H. C. Gertzen, J.-W. Park, and P. A. Smars, “Non-invasive resting magnetocardiographic imaging for the rapid detection of ischemia in subjects presenting with chest pain,” Cardiology 106, 270–276 (2006).

3.

P. Korhonen, T. Husa, I. Tierala, H. Väänänen, M. Mäkijärvi, T. Katila, and L. Toivonen, “Increased Intra-QRS fragmentation in magnetocardiography as a predictor of arrhythmic events and mortality in patients with cardiac dysfunction after myocardial infarction,” J. Cardiovasc. Electrophysiol. 17(4), 396–401 (2006). [CrossRef] [PubMed]

4.

S. Dutz, M. E. Bellemann, U. Leder, and J. Haueisen, “Passive vortex currents in magneto- and electrocardiography: comparison of magnetic and electric signal strengths,” Phys. Med. Biol. 51(1), 145–151 (2006). [CrossRef] [PubMed]

5.

M. Liehr, J. Haueisen, M. Goernig, P. Seidel, J. Nenonen, and T. Katila, “Vortex Shaped Current Sources in a Physical Torso Phantom,” Ann. Biomed. Eng. 33(2), 240–247 (2005). [CrossRef] [PubMed]

6.

BMDSys Production GmbH, http://www.bmdsys.com

7.

T. Toennis, “Magnetic field imaging for risk stratification of sudden cardiac death in patients with primary preventive ICD-indication,” BIOMAG 2012 Book of Abstracts, 41 (2012)

8.

J. Vrba, J. Nenonen, and L. Trahms, “The SQUID Handbook Vol. II,” J. Clarke, A. I. Braginski, ed. (Wiley-VCH, Weinheim, 2006)

9.

M. N. Livanov, A. N. Kozlov, A. V. Korinevskiĭ, V. P. Markin, and S. E. Sinel’nikova, “[Recording of human magnetic fields],” Dokl. Akad. Nauk SSSR 238(1), 253–256 (1978). [PubMed]

10.

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007). [CrossRef]

11.

D. Sheng, S. Li, N. Dural, and M. V. Romalis, “Subfemtotesla scalar atomic magnetometry using multipass cells,” Phys. Rev. Lett. 110(16), 160802 (2013). [CrossRef] [PubMed]

12.

T. H. Sander, J. Preusser, R. Mhaskar, J. Kitching, L. Trahms, and S. Knappe, “Magnetoencephalography with a chip-scale atomic magnetometer,” Biomed. Opt. Express 3(5Issue 5), 981–990 (2012). [CrossRef] [PubMed]

13.

R. Wyllie, M. Kauer, G. S. Smetana, R. T. Wakai, and T. G. Walker, “Magnetocardiography with a modular spin-exchange relaxation-free atomic magnetometer array,” Phys. Med. Biol. 57(9), 2619–2632 (2012). [CrossRef] [PubMed]

14.

R. Wyllie, M. Kauer, R. T. Wakai, and T. G. Walker, “Optical magnetometer array for fetal magnetocardiography,” Opt. Lett. 37(12), 2247–2249 (2012). [CrossRef] [PubMed]

15.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, M. Kasprzak, H. Saudan, and A. Weis, “A room temperature 19-channel magnetic field mapping device for cardiac signals,” Appl. Phys. Lett. 95(17), 173701 (2009). [CrossRef]

16.

G. Lembke, M. Stumpf, S. N. Erné, and G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]

17.

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx-magnetomter,” Eur. Phys. J. D 38(2), 239–247 (2006). [CrossRef]

18.

N. Castagna, G. Bison, G. Di Domenico, A. Hofer, P. Knowles, C. Macchione, H. Saudan, and A. Weis, “A large sample study of spin relaxation and magnetometric sensitivity of paraffin coated Cs vapor cells,” Appl. Phys. B 96(4), 763–772 (2009). [CrossRef]

19.

D. W. Preston, “Doppler-free saturated absorption: Laser spectroscopy,” Am. J. Phys. 64(11), 1432 (1996). [CrossRef]

20.

J. E. Volder, “The CORDIC Trigonometric Computing Technique,” IRE Trans. Electron. Comput. 8(3), 330–334 (1959). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(230.0230) Optical devices : Optical devices

ToC Category:
Clinical Instrumentation

History
Original Manuscript: January 1, 2014
Revised Manuscript: January 17, 2014
Manuscript Accepted: January 22, 2014
Published: February 25, 2014

Virtual Issues
April 10, 2014 Spotlight on Optics

Citation
G. Lembke, S. N. Erné, H. Nowak, B. Menhorn, A. Pasquarelli, and G. Bison, "Optical multichannel room temperature magnetic field imaging system for clinical application," Biomed. Opt. Express 5, 876-881 (2014)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-5-3-876


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References

  1. B. J. Roth, J. P. Wikswo., “Electrically silent magnetic fields,” Biophys. J. 50(4), 739–745 (1986). [CrossRef] [PubMed]
  2. K. Tolstrup, B. E. Madsen, J. A. Ruiz, S. D. Greenwood, J. Camacho, R. J. Siegel, H. C. Gertzen, J.-W. Park, P. A. Smars, “Non-invasive resting magnetocardiographic imaging for the rapid detection of ischemia in subjects presenting with chest pain,” Cardiology 106, 270–276 (2006).
  3. P. Korhonen, T. Husa, I. Tierala, H. Väänänen, M. Mäkijärvi, T. Katila, L. Toivonen, “Increased Intra-QRS fragmentation in magnetocardiography as a predictor of arrhythmic events and mortality in patients with cardiac dysfunction after myocardial infarction,” J. Cardiovasc. Electrophysiol. 17(4), 396–401 (2006). [CrossRef] [PubMed]
  4. S. Dutz, M. E. Bellemann, U. Leder, J. Haueisen, “Passive vortex currents in magneto- and electrocardiography: comparison of magnetic and electric signal strengths,” Phys. Med. Biol. 51(1), 145–151 (2006). [CrossRef] [PubMed]
  5. M. Liehr, J. Haueisen, M. Goernig, P. Seidel, J. Nenonen, T. Katila, “Vortex Shaped Current Sources in a Physical Torso Phantom,” Ann. Biomed. Eng. 33(2), 240–247 (2005). [CrossRef] [PubMed]
  6. BMDSys Production GmbH, http://www.bmdsys.com
  7. T. Toennis, “Magnetic field imaging for risk stratification of sudden cardiac death in patients with primary preventive ICD-indication,” BIOMAG 2012 Book of Abstracts, 41 (2012)
  8. J. Vrba, J. Nenonen, and L. Trahms, “The SQUID Handbook Vol. II,” J. Clarke, A. I. Braginski, ed. (Wiley-VCH, Weinheim, 2006)
  9. M. N. Livanov, A. N. Kozlov, A. V. Korinevskiĭ, V. P. Markin, S. E. Sinel’nikova, “[Recording of human magnetic fields],” Dokl. Akad. Nauk SSSR 238(1), 253–256 (1978). [PubMed]
  10. D. Budker, M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007). [CrossRef]
  11. D. Sheng, S. Li, N. Dural, M. V. Romalis, “Subfemtotesla scalar atomic magnetometry using multipass cells,” Phys. Rev. Lett. 110(16), 160802 (2013). [CrossRef] [PubMed]
  12. T. H. Sander, J. Preusser, R. Mhaskar, J. Kitching, L. Trahms, S. Knappe, “Magnetoencephalography with a chip-scale atomic magnetometer,” Biomed. Opt. Express 3(5Issue 5), 981–990 (2012). [CrossRef] [PubMed]
  13. R. Wyllie, M. Kauer, G. S. Smetana, R. T. Wakai, T. G. Walker, “Magnetocardiography with a modular spin-exchange relaxation-free atomic magnetometer array,” Phys. Med. Biol. 57(9), 2619–2632 (2012). [CrossRef] [PubMed]
  14. R. Wyllie, M. Kauer, R. T. Wakai, T. G. Walker, “Optical magnetometer array for fetal magnetocardiography,” Opt. Lett. 37(12), 2247–2249 (2012). [CrossRef] [PubMed]
  15. G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, M. Kasprzak, H. Saudan, A. Weis, “A room temperature 19-channel magnetic field mapping device for cardiac signals,” Appl. Phys. Lett. 95(17), 173701 (2009). [CrossRef]
  16. G. Lembke, M. Stumpf, S. N. Erné, G. Bison, “Towards clinical MCG with room-temperature sensors,” IFMBE Proc. 28, 62–65 (2010). [CrossRef]
  17. S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, A. Weis, “A high-sensitivity laser-pumped Mx-magnetomter,” Eur. Phys. J. D 38(2), 239–247 (2006). [CrossRef]
  18. N. Castagna, G. Bison, G. Di Domenico, A. Hofer, P. Knowles, C. Macchione, H. Saudan, A. Weis, “A large sample study of spin relaxation and magnetometric sensitivity of paraffin coated Cs vapor cells,” Appl. Phys. B 96(4), 763–772 (2009). [CrossRef]
  19. D. W. Preston, “Doppler-free saturated absorption: Laser spectroscopy,” Am. J. Phys. 64(11), 1432 (1996). [CrossRef]
  20. J. E. Volder, “The CORDIC Trigonometric Computing Technique,” IRE Trans. Electron. Comput. 8(3), 330–334 (1959). [CrossRef]

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