Dead-zone-free atom magnetometer device and method based on pumping-detection information fusion

Abstract

The invention discloses a pumping-detection information fusion-based dead-zone-free atom magnetometer device and method, and relates to the technical field of atom magnetometers. Through optomagnetic double-resonance pulse modulation, atoms can generate free precession signals in all magnetic field directions, output signals of pumping light and detection light are collected and detected in the spin polarization free precession stage, dead zones of the output signals of the two light beams are complementary, and the free precession signals of the two light beams are obtained. And one path of signal with a high signal-to-noise ratio is selected as output through signal processing, so that the dead-zone-free high-sensitivity optical pump atom magnetometer is realized. According to the invention, under the condition that the sensitivity of the magnetometer is not reduced, the omnibearing no dead zone of the magnetometer is realized, and further application of the optical pump atom magnetometer in the fields of space magnetic field measurement and the like in the future is facilitated.

Description

Technical Field

[0001] The invention relates to the technical field of atomic magnetometers, and in particular to a dead-zone-free atomic magnetometer device and method based on pumping-detection information fusion. Background Art

[0002] In the prior art, optically pumped atomic magnetometers, as a quantum precision magnetic field measuring instrument, have gradually become an important development direction for high-sensitivity magnetic field measurement research and application due to the advantages of miniaturization, high sensitivity, and large dynamic range of sensors. The optically pumped atomic magnetometers based on the free precession mechanism have the characteristics of high measurement accuracy, simple circuit structure, and strong robustness, and have made important progress in scientific research and industrialization. There is a dead zone in the optically pumped atomic magnetometer in magnetic field measurement. When the direction of the magnetic field to be measured is within the dead zone, the magnetometer will not have a signal output, resulting in the inability to measure the magnetic field, affecting the use of the optically pumped atomic magnetometer. Therefore, the suppression of the magnetometer dead zone has become an important issue in the research and application of optically pumped atomic magnetometers. Summary of the invention

[0003] The purpose of the present invention is to provide a dead-zone-free atomic magnetometer device and method based on pumping-detection information fusion, which can achieve all-round dead-zone-free magnetometer without reducing the sensitivity of the magnetometer, and is conducive to the further application of optically pumped atomic magnetometers in the fields of space magnetic field measurement in the future.

[0004] To achieve the above-mentioned object, the present invention provides a dead-zone-free atomic magnetometer device based on pumping-detection information fusion, comprising a pumping optical path and a detection optical path; the pumping optical path comprises a pumping laser, an optical intensity modulator, a first polarization-maintaining optical fiber, a first collimator, a first half-wave plate, a first polarizer, a first reflector, a quarter-wave plate, an alkali metal gas chamber, and a first photodetector connected in sequence; the output of the first photodetector is input to the input end of a data acquisition and processing system after passing through a first transimpedance amplifier and a first bandpass filter;

[0005] The detection optical path includes a detection laser, a second polarization-maintaining optical fiber, a second collimator, a second polarizer, the alkali metal gas chamber, a second half-wave plate, a spectrometer module, and a polarization balance differential detection circuit connected in sequence; the output of the polarization balance differential detection circuit is input to the input end of the data acquisition and processing system after passing through a second transimpedance amplifier and a second bandpass filter; the frequency range of the first bandpass filter and the second bandpass filter is centered on the Larmor precession frequency corresponding to the magnetic field to be measured; the output end of the data acquisition and processing system is respectively connected to the first bandpass filter, the second bandpass filter and the signal generator, and the acquired Larmor precession frequency is fed back.

[0006] Preferably, the laser frequency generated by the pumping laser is tuned to the D1 line of the alkali metal atoms; the first half-wave plate in the pumping light path maximizes the optical power of the pumping light after passing through the first polarizer, and the first polarizer, the first reflector, and the quarter-wave plate enable the pumping light to form circularly polarized light and pass through the alkali metal gas chamber.

[0007] Preferably, the input end of the light intensity modulator is connected to the output end of the signal generator.

[0008] Preferably, the laser frequency generated by the detection laser is tuned to a maximum free precession signal; the second polarizer in the detection light path causes the detection light to form linearly polarized light and pass through the alkali metal gas chamber.

[0009] Preferably, the spectroscopic module is composed of a polarization spectroscopic prism and a second reflector, and a second photodetector and a third photodetector are arranged in parallel on the polarization balance differential detection circuit; the second reflector of the spectroscopic module is connected to the second photodetector, and the polarization spectroscopic prism is connected to the third photodetector; the second half-wave plate and the spectroscopic module make the output of the polarization balance differential detection circuit zero when the magnetometer is not working.

[0010] Preferably, an oven, a non-magnetic electric heating coil, a radio frequency coil, and a magnetometer support shell are arranged in sequence around the alkali metal gas chamber from the inside to the outside; the non-magnetic electric heating coil is driven by a high-frequency alternating current far away from the Larmor precession frequency; and the radio frequency coil is connected to the other output end of the signal generator with an axis perpendicular to the direction of the pumping light.

[0011] The present invention also provides a method for controlling a dead zone-free atomic magnetometer device based on pumping-detection information fusion, comprising the following steps:

[0012] S1. Control the signal generator to input a square wave pulse sequence with a period of 1-10ms and a duty cycle of 30%-50% to the light intensity modulator, wherein the duty cycle of the square wave pulse in the sequence is 50% and the pulse repetition frequency is the Larmor precession frequency corresponding to the magnetic field, so that the pumping light performs synchronous optical pumping to prepare atomic spin polarization. After completion, the modulated pulse signal is removed, and a DC signal with a lower amplitude is input to the light intensity modulator to ensure a certain light intensity of the pumping light for subsequent detection;

[0013] S2. At the moment of removing the square wave pulse sequence inputted by the signal generator to the light intensity modulator in each cycle, a radio frequency magnetic field pulse having the same frequency as the square wave pulse frequency of the light intensity modulator is applied to the radio frequency coil perpendicular to the pumping light direction through the signal generator, with a duration of less than 0.05 ms. The spin polarization vector is manipulated to a plane perpendicular to the magnetic field direction by adjusting the amplitude and duration of the radio frequency magnetic field pulse to achieve the maximum amplitude of the free precession signal, and then the radio frequency magnetic field pulse is removed;

[0014] S3, after the input signal from the signal generator to the RF coil is removed in each cycle, the atomic spin polarization undergoes free precession, and the output signals of the pumping light and the detection light are collected by the data acquisition and processing system to realize the collection of the free precession signal;

[0015] S4. The output signals of the pumping light and the detection light are collected and analyzed by the data acquisition and processing system, and the free precession signal with a high signal-to-noise ratio is selected for processing to obtain the magnetic field information to be measured.

[0016] Preferably, in S3, the spin polarization vector performs free precession, and the evolution expression of the spin polarization in the pumping light direction is:

[0017]

[0018] The evolution expression of the spin polarization in the detection light direction is:

[0019]

[0020] Where t is time, R pr is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the z direction, φ is the angle between the magnetic field to be measured and the y direction, P is the spin polarization size participating in the free precession, γ is the gyromagnetic ratio, B0 is the size of the magnetic field to be measured, is the signal phase;

[0021] The first terms of the two formulas are the slowly varying DC terms caused by optical pumping, and the second terms are the free precession expressions of spin polarization.

[0022] Preferably, after the detection light signal passes through the first transimpedance amplifier and the first bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as:

[0023]

[0024] After the detection optical signal passes through the second transimpedance amplifier and the second bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as:

[0025]

[0026] Wherein, V1 and V2 are the voltage signal amplitudes output by the first band-pass filter and the second band-pass filter respectively.

[0027] Therefore, the present invention adopts the above-mentioned dead-zone-free atomic magnetometer device and method based on pumping-detection information fusion based on the dual-beam free precession optical pump atomic magnetometer configuration to achieve dual-light measurement dead-zone complementarity. Without reducing the sensitivity of the magnetometer, the magnetometer is achieved to be dead-zone-free in all directions, and magnetic field measurement problems caused by the dead zone of the magnetometer will not occur, further improving the application flexibility of the optical pump atomic magnetometer.

[0028] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a structural schematic diagram of an embodiment of a dead zone-free atomic magnetometer device based on pump-detection information fusion of the present invention;

[0030] Figure 2 It is a flow chart of a method for controlling a dead-zone-free atomic magnetometer device based on pumping-detection information fusion of the present invention.

[0031] Reference numerals

[0032] 1. Pumping laser; 2. Light intensity modulator; 3. First polarization-maintaining fiber; 4. First collimator; 5. First half-wave plate; 6. First polarizer; 7. First reflector; 8. Quarter-wave plate; 9. Alkali metal gas chamber; 10. First photodetector; 11. First transimpedance amplifier; 12. First bandpass filter; 13. Data acquisition and processing system; 14. Detection laser; 15. Second polarization-maintaining fiber; 16. Second collimator; 17. Second polarizer; 18. Second half-wave plate; 19. Spectral splitter module; 20. Polarization balance differential detection circuit; 201. Second photodetector; 202. Third photodetector; 21. Second transimpedance amplifier; 22. Second bandpass filter; 23. Signal generator; 24. Oven; 25. Non-magnetic electric heating coil; 26. Radio frequency coil; 27. Magnetometer support shell. DETAILED DESCRIPTION

[0033] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0034] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0035] xyz is the three axes (x-axis, y-axis, z-axis) of the Cartesian coordinate system established with the laboratory pumping light direction as the z-axis and the detection light direction as the x-axis.

[0036] Embodiment 1

[0037] like Figure 1 As shown, the present invention provides a dead-zone-free atomic magnetometer device based on pumping-detection information fusion, including a pumping optical path and a detection optical path. The pumping optical path includes a pumping laser 1, an optical intensity modulator 2, a first polarization-maintaining optical fiber 3, a first collimator 4, a first half-wave plate 5, a first polarizer 6, a first reflector 7, a quarter-wave plate 8, an alkali metal gas chamber 9, and a first photodetector 10 connected in sequence. The output of the first photodetector 10 is input to the input end of a data acquisition and processing system 13 after passing through a first transimpedance amplifier 11 and a first bandpass filter 12.

[0038] The detection optical path includes a detection laser 14, a second polarization-maintaining optical fiber 15, a second collimator 16, a second polarizer 17, an alkali metal gas chamber 9, a second half-wave plate 18, a spectrometer module 19, and a polarization balance differential detection circuit 20 connected in sequence. The output of the polarization balance differential detection circuit 20 is input to the input end of the data acquisition and processing system 13 after passing through a second transimpedance amplifier 21 and a second bandpass filter 22.

[0039] The frequency range of the first bandpass filter 12 and the second bandpass filter 22 is centered on the Larmor precession frequency corresponding to the magnetic field to be measured. The output end of the data acquisition and processing system 13 is respectively connected to the first bandpass filter 12, the second bandpass filter 22 and the signal generator 23, and the acquired Larmor precession frequency is fed back for real-time tracking of magnetic field changes.

[0040] Among them, the laser frequency generated by the pump laser 1 is tuned to the alkali metal atom D1 line, the first half wave plate 5 in the pump light path makes the optical power of the pump light maximum after passing through the first polarizer 6, the first polarizer 6 and the first reflector 7 and the quarter wave plate 8 make the pump light form circularly polarized light and pass through the alkali metal gas chamber 9, and the input end of the light intensity modulator 2 is connected to the output end of the signal generator 23.

[0041] The laser frequency generated by the detection laser 14 is tuned to the maximum free precession signal, and the second polarizer 17 in the detection optical path makes the detection light form linear polarized light and pass through the alkali metal gas chamber 9. The light splitting module 19 is composed of a polarization beam splitting prism and a second reflector, and a second photodetector 201 and a third photodetector 202 are arranged in parallel on the polarization balance differential detection circuit 20. The second reflector of the light splitting module 19 is connected to the second photodetector 201, the polarization beam splitting prism is connected to the third photodetector 202, and the second half wave plate 18 and the light splitting module 19 make the output of the polarization balance differential detection circuit 20 zero when the magnetometer is not working.

[0042] An oven 24, a non-magnetic electric heating coil 25, a radio frequency coil 26 and a magnetometer support shell 27 are arranged around the alkali metal gas chamber 9 from the inside to the outside. The non-magnetic electric heating coil 25 is driven by a high-frequency alternating current far away from the Larmor precession frequency. The alkali metal gas chamber 9 is heated by the oven 24 to achieve a high atomic density. The radio frequency coil 26 is connected to the other output end of the signal generator 23 with an axis perpendicular to the direction of the pumping light.

[0043] like Figure 2 As shown, the present invention also provides a method for controlling a dead zone-free atomic magnetometer device based on pumping-detection information fusion, comprising the following steps:

[0044] S1, control signal generator 23 inputs a square wave pulse sequence with a period of 1-10ms and a duty cycle of 30%-50% to the light intensity modulator 2, wherein the duty cycle of the square wave pulse in the sequence is 50%, and the pulse repetition frequency is the Larmor precession frequency corresponding to the magnetic field, so that the pumping light performs synchronous optical pumping to prepare atomic spin polarization. After completion, the modulated pulse signal is removed, and a DC signal with a lower amplitude is input to the light intensity modulator 2 to ensure a certain light intensity of the pumping light for subsequent detection.

[0045] S2. At the moment of each cycle when the square wave pulse sequence input by the signal generator 23 to the light intensity modulator 2 is removed, a radio frequency magnetic field pulse having the same frequency as the square wave pulse frequency of the light intensity modulator 2 is applied to the radio frequency coil 26 perpendicular to the pumping light direction through the signal generator 23, with a duration of less than 0.05 ms. By adjusting the amplitude and duration of the radio frequency magnetic field pulse, the spin polarization vector is manipulated to a plane perpendicular to the magnetic field direction to achieve the maximum amplitude of the free precession signal, and then the radio frequency magnetic field pulse is removed.

[0046] S3. After the input signal from the signal generator 23 to the RF coil 26 is removed in each cycle, the atomic spin polarization undergoes free precession. The output signals of the pumping light and the detection light are collected by the data acquisition and processing system 13 to realize the collection of the free precession signal.

[0047] The spin polarization vector precesses freely, and the evolution expression of the spin polarization in the pumping light direction is:

[0048]

[0049] The evolution expression of the spin polarization in the detection light direction is:

[0050]

[0051] Where t is time, R pr is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the z direction, φ is the angle between the magnetic field to be measured and the y direction, P is the spin polarization size participating in the free precession, γ is the gyromagnetic ratio, B0 is the size of the magnetic field to be measured, is the signal phase;

[0052] The first terms of the two formulas are the slowly varying DC terms caused by optical pumping, and the second terms are the free precession expressions of spin polarization.

[0053] From the free precession expressions of the pumping light and detection light directions, we can see that when the magnetic field to be measured is along the pumping light direction, the pumping light has no free precession signal output, and this direction is the dead zone of the pumping light output. At this time, there is a free precession signal output in the detection light direction. When the magnetic field to be measured is along the detection light direction, the detection light has no free precession signal output, and this direction is the dead zone of the detection light output. At this time, there is a free precession signal output in the pumping light direction.

[0054] After the detection optical signal passes through the first transimpedance amplifier 11 and the first bandpass filter 22, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as:

[0055]

[0056] After the detection optical signal passes through the second transimpedance amplifier 21 and the second bandpass filter 22, the slow-varying DC term is filtered out, and the signal collected by the data acquisition and processing system 13 is expressed as:

[0057]

[0058] Wherein, V1 and V2 are the voltage signal amplitudes output by the first band-pass filter and the second band-pass filter respectively.

[0059] S4. The output signals of the pumping light and the detection light are collected and analyzed by the data collection and processing system 13, and the free precession signal with a high signal-to-noise ratio is selected for processing to obtain the magnetic field information to be measured.

[0060] Selecting a signal with a high signal-to-noise ratio ensures that the sensitivity of the magnetometer will not be lower than the sensitivity of any signal. At the same time, the acquisition of the two signals makes the dead zones complementary. When one signal has a dead zone in the magnetic field direction, the free precession signal of the other signal can be detected. The magnetometer will not be unable to work due to the dead zone of one signal, thus realizing the all-round dead zone-free magnetometer.

[0061] Therefore, the present invention adopts the above-mentioned dead-zone-free atomic magnetometer device and method based on pumping-detection information fusion, firstly prepares atomic spin polarization through synchronous optical pumping, then applies transverse resonant radio frequency magnetic field pulses, and manipulates the spin polarization to a plane perpendicular to the magnetic field to achieve the maximum amplitude of the free precession signal. Optical-magnetic double resonance pulse modulation enables atoms to generate free precession signals in all magnetic field directions, then collects the output signals of the pumping light and the detection light in the spin polarization free precession stage, and selects a signal with a high signal-to-noise ratio as the output, so as to achieve dead-zone complementarity of the output signals of the two optical paths, and then realizes a dead-zone-free high-sensitivity optical pump atomic magnetometer. Without reducing the sensitivity of the magnetometer, the magnetometer is achieved to be free of dead zones in all directions, which is convenient for the further development and application of optical pump atomic magnetometers in the fields of quantum precision magnetic field measurement.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A dead zone-free atomic magnetometer device based on pump-detection information fusion, characterized in that: It includes a pumping optical path and a detection optical path; the pumping optical path includes a pumping laser, a light intensity modulator, a first polarization-maintaining optical fiber, a first collimator, a first half-wave plate, a first polarizer, a first reflector, a quarter-wave plate, an alkali metal gas chamber, and a first photodetector connected in sequence; The output of the first photodetector is input to the input end of the data acquisition and processing system after passing through a first transimpedance amplifier and a first bandpass filter; The detection optical path includes a detection laser, a second polarization-maintaining optical fiber, a second collimator, a second polarizer, the alkali metal gas chamber, a second half-wave plate, a spectrometer module, and a polarization balance differential detection circuit connected in sequence; the output of the polarization balance differential detection circuit is input to the input end of the data acquisition and processing system after passing through a second transimpedance amplifier and a second bandpass filter; the frequency range of the first bandpass filter and the second bandpass filter is centered on the Larmor precession frequency corresponding to the magnetic field to be measured; the output end of the data acquisition and processing system is respectively connected to the first bandpass filter, the second bandpass filter and the signal generator, and the acquired Larmor precession frequency is fed back.

2. The dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 1 is characterized in that: The laser frequency generated by the pumping laser is tuned to the D1 line of the alkali metal atoms; the first half-wave plate in the pumping light path makes the optical power of the pumping light maximum after passing through the first polarizer; the first polarizer, the first reflector and the quarter-wave plate make the pumping light form circularly polarized light and pass through the alkali metal gas chamber.

3. The dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 1 is characterized in that: The input end of the light intensity modulator is connected to the output end of the signal generator.

4. The dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 1, characterized in that: The laser frequency generated by the detection laser is tuned to a maximum free precession signal; the second polarizer in the detection light path causes the detection light to form linearly polarized light and pass through the alkali metal gas chamber.

5. The dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 1, characterized in that: The spectroscopic module is composed of a polarization spectroscopic prism and a second reflector, and a second photodetector and a third photodetector are arranged in parallel on the polarization balance differential detection circuit; the second reflector of the spectroscopic module is connected to the second photodetector, and the polarization spectroscopic prism is connected to the third photodetector; the second half-wave plate and the spectroscopic module make the output of the polarization balance differential detection circuit zero when the magnetometer is not working.

6. The dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 1, characterized in that: An oven, a non-magnetic electric heating coil, a radio frequency coil, and a magnetometer support shell are arranged in sequence around the alkali metal gas chamber from the inside to the outside; the non-magnetic electric heating coil is driven by a high-frequency alternating current far away from the Larmor precession frequency; the radio frequency coil is connected to the other output end of the signal generator at an axis perpendicular to the pumping light direction.

7. A method for controlling a dead-zone-free atomic magnetometer device based on pump-detection information fusion, characterized in that: The following steps are involved: S1. Control the signal generator to input a square wave pulse sequence with a period of 1-10ms and a duty cycle of 30%-50% to the light intensity modulator, wherein the duty cycle of the square wave pulse in the sequence is 50% and the pulse repetition frequency is the Larmor precession frequency corresponding to the magnetic field, so that the pumping light performs synchronous optical pumping to prepare atomic spin polarization. After completion, the modulated pulse signal is removed, and a DC signal with a lower amplitude is input to the light intensity modulator to ensure a certain light intensity of the pumping light for subsequent detection; S2. At the moment of removing the square wave pulse sequence inputted by the signal generator to the light intensity modulator in each cycle, a radio frequency magnetic field pulse having the same frequency as the square wave pulse frequency of the light intensity modulator is applied to the radio frequency coil perpendicular to the pumping light direction through the signal generator, with a duration of less than 0.05 ms. The spin polarization vector is manipulated to a plane perpendicular to the magnetic field direction by adjusting the amplitude and duration of the radio frequency magnetic field pulse to achieve the maximum amplitude of the free precession signal, and then the radio frequency magnetic field pulse is removed; S3, after the input signal from the signal generator to the RF coil is removed in each cycle, the atomic spin polarization undergoes free precession, and the output signals of the pumping light and the detection light are collected by the data acquisition and processing system to realize the collection of the free precession signal; S4. The output signals of the pumping light and the detection light are collected and analyzed by the data acquisition and processing system, and the free precession signal with a high signal-to-noise ratio is selected for processing to obtain the magnetic field information to be measured.

8. The control method of the dead zone-free atomic magnetometer device based on pump-detection information fusion according to claim 7, characterized in that: In S3, the spin polarization vector precesses freely, and the evolution expression of the spin polarization in the pumping light direction is: The evolution expression of the spin polarization in the detection light direction is: Where t is time, is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the z direction, φ is the angle between the magnetic field to be measured and the y direction, P is the spin polarization size participating in the free precession, γ is the gyromagnetic ratio, B0 is the size of the magnetic field to be measured, is the signal phase; The first terms of the two formulas are the slowly varying DC terms caused by optical pumping, and the second terms are the free precession expressions of spin polarization.

9. The control method of the atomic magnetometer device without dead zone based on pump-detection information fusion according to claim 8, characterized in that: After the detection optical signal passes through the first transimpedance amplifier and the first bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as: After the detection optical signal passes through the second transimpedance amplifier and the second bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as: Wherein, V1 and V2 are the voltage signal amplitudes output by the first band-pass filter and the second band-pass filter respectively.

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