SENSORS RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application

No.62/427521, filed on November 29, 2016, the content of which is hereby incorporated by reference in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] The present invention was made with United States government support under Grant No. HR0011-11-C-0073, awarded by the Defense Advanced Research Projects Agency (DARPA), and under Grant No. W911NF-15-1-0548, awarded by the Army Research Office (ARO). The United States government has certain rights in this invention. TECHNICAL FIELD

[0003] The present application relates to noise cancellation for measurement systems. More particularly, the present application relates to all-digital noise cancellation for solid state spin sensor systems used to measure physical quantities. BACKGROUND OF THE INVENTION

[0004] Solid state spin sensors may be used to measure physical quantities. For example, magnetometers based on nitrogen-vacancy (NV) diamond technology may operate by encoding magnetic field information in the intensity of fluorescence light emitted by the NV color centers in a diamond, which are one example of many fluorescent point defects in solid- state materials. This fluorescence may be generated by illuminating a diamond with an optical signal from an optical illumination source, such as a laser. Changes in the optical intensity illuminating the diamond may result in equal fractional changes in the intensity of fluorescence emitted by the NVs of the diamond. For example, if the diamond is illuminated with green light, the diamond may emit red light in proportion to a magnetic field (e.g., the physical quantity being measured). Additionally, changes in the optical illumination spectral profile can also correspond to changes in the emiitted flurescence. . [0005] Because the magnetic field signal may be encoded via the intensity of the fluorescence signal emitted from the diamond, amplitude and frequency noise of the optical illumination source, if unaccounted for, may result in spurious (and possibly false) measurement signals. Therefore, a challenge for solid state spin sensors, such as NV diamond magnetometers, is to correct for amplitude and frequency noise from the optical illumination source. This noise can be large enough that, if left uncorrected, it may reduce measurement sensitivity by a factor on the order of ten to one hundred.

[0006] In some examples, because the time required to measure small physical quantities (such as small magnetic signals) with a given signal-to-noise ratio (SNR) scales as the square of sensor sensitivity, uncorrected amplitude and frequency noise of an optical illumination source can increase measurement times to reach a given SNR by a factor on the order of one hundred to ten thousand.

[0007] Therefore, to achieve improved sensitivity in measurements of physical quantities, and to minimize the time to perform a measurement requiring a predetermined signal to noise ratio (SNR), it is desirable to correct the amplitude and frequency noise of the optical illumination source. BRIEF SUMMARY OF THE INVENTION

[0008] Embodiments of the present disclosure include a digital scheme to reduce amplitude and frequency noise of an optical illumination source in measurement systems. The digital scheme can provide flexibility and/or avoid non-linearities inherent to alternative analog approaches. The same principles of this system can also be adapted to cancel other sources of noise such as microwave amplitude noise.

[0009] In some embodiments, an optical illumination source noise cancellation system for a solid state spin sensor includes an analog to digital converter that converts a reference waveform into at least one digitized reference waveform, and converts a signal waveform into at least one digitized signal waveform; and a processor that receives the at least one digitized reference waveform and the at least one digitized signal waveform, wherein the processor calculates a corrected signal waveform using the at least one digitized reference waveform and the at least one digitized signal waveform, and derives a measurement of a physical quantity from the corrected signal waveform. [0010] In some embodiments, the measurement of the physical quantity is a measurement of a magnetic field, an electric field, temperature, pressure, a molecular species, a biological species, pH, voltage, or any combination thereof.

[0011] In some embodiments, the optical illumination source noise cancellation system further includes: a light source that generates a first light; a reference photodetector that detects a first portion of the first light and outputs the reference waveform; a solid state spin sensor that receives a second portion of the first light and emits a second light, the solid state spin sensor including one or more fluorescent point defects; and a signal photodetector that detects the second light and outputs the signal waveform.

[0012] In some embodiments, the second light includes fluorescence generated from the fluorescent point defects of the solid state spin sensor.

[0013] In some embodiments, the one or more fluorescent point defects include a color center defect.

[0014] In some embodiments, the reference waveform is AC-coupled prior to

digitization or during digitization; and the signal waveform is AC-coupled prior to digitization or during digitization.

[0015] In some embodiments, the processor calculates the corrected signal waveform by: generating a first reference scaling factor from a correlation of a variation in the AC-coupled digitized reference waveform and the AC-coupled digitized signal waveform; generating a first scaled AC-coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the first reference scaling factor; and subtracting the first scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform.

[0016] In some embodiments, the at least one digitized reference waveform includes a

DC-coupled digitized reference waveform and an AC-coupled digitized reference waveform, and the at least one digitized signal waveform includes a DC-coupled digitized signal waveform and an AC-coupled digitized signal waveform.

[0017] In some embodiments, the processor calculates the corrected signal waveform by: generating a second reference scaling factor by calculating a ratio between the DC-coupled digitized signal waveform and the DC-coupled digitized reference waveform; generating a second scaled AC-coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the second reference scaling factor; and subtracting the second scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform. [0018] In some embodiments, the at least one digitized reference waveform includes a DC-coupled digitized reference waveform, and the at least one digitized signal waveform includes an AC-coupled digitized signal waveform.

[0019] In some embodiments, the processor calculates the corrected signal waveform by: filtering the DC-coupled digitized reference waveform to generate a filtered DC-coupled digitized reference waveform; calculating a ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform; and multiplying the calculated ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform by a scaling constant.

[0020] In some embodiments, the scaling constant is a time-averaged value of the filtered DC-coupled digitized reference waveform.

[0021] In some embodiments, the optical illumination source noise cancellation system includes a light source that generates a first light; a first solid state spin sensor that receives a first portion of the first light and emits a second light, the first solid state spin sensor including fluorescent point defects; a reference photodetector that detects the second light and outputs the reference waveform; a second solid state spin sensor that receives a second portion of the first light and emits a third light, the second solid state spin sensor including fluorescent point defects; and a signal photodetector that detects the third light and outputs the signal waveform.

[0022] In some embodiments, the fluorescent point defects are color center defects.

[0023] In some embodiments, the first solid state spin sensor produces a first spectral response and the second solid state spin sensor produces a second spectral response, and the first spectral response and the second spectral response are matched.

[0024] In some embodiments, the first solid state spin sensor is a first NV diamond, and the second solid state spin sensor is a second NV diamond.

[0025] In some embodiments, an optical illumination source noise cancellation method for a solid state spin sensor includes converting a reference waveform into at least one digitized reference waveform; converting a signal waveform into at least one digitized signal waveform; receiving the at least one digitized reference waveform and the at least one digitized signal waveform; calculating a corrected signal waveform using the at least one digitized reference waveform and the at least one digitized signal waveform; and deriving a measurement of a physical quantity from the corrected signal waveform. [0026] In some embodiments, the measurement of the physical quantity is a measurement of a magnetic field, an electric field, temperature, pressure, a molecular species, a biological species, pH, voltage, or any combination thereof.

[0027] In some embodiments, the optical illumination source noise cancellation method further includes generating a first light; detecting a first portion of the first light; outputting the reference waveform based on the detected first portion of the first light; receiving, by a solid state spin sensor, a second portion of the first light; emitting, by the solid state spin sensor, a second light, wherein the solid state spin sensor includes fluorescent point defects; detecting the second light; and outputting the signal waveform based on the detected second light.

[0028] In some embodiments, the second light includes fluorescence generated from the fluorescent point defects of the solid state spin sensor.

[0029] In some embodiments, the one or more fluorescent point defects include a color center defect.

[0030] In some embodiments, the at least one reference waveform is AC-coupled prior to digitization or during digitization; and the at least one signal waveform is AC-coupled prior to digitization or during digitization.

[0031] In some embodiments, the corrected signal waveform is calculated by generating a first reference scaling factor from a correlation of a variation in the AC-coupled digitized reference waveform and the AC-coupled digitized signal waveform; generating a first scaled AC-coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the first reference scaling factor; and subtracting the first scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform.

[0032] In some embodiments, the at least one digitized reference waveform includes a

DC-coupled digitized reference waveform and an AC-coupled digitized reference waveform , and the at least one digitized signal waveform includes a DC-coupled digitized signal waveform and an AC-coupled digitized signal waveform.

[0033] In some embodiments, the corrected signal waveform is calculated by: generating a second reference scaling factor by calculating a ratio between the DC-coupled digitized signal waveform and the DC-coupled digitized reference waveform; generating a second scaled AC- coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the second reference scaling factor; and subtracting the second scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform. [0034] In some embodiments, the at least one digitized reference waveform includes a DC-coupled digitized reference waveform, and the at least one digitized signal waveform includes an AC-coupled digitized signal waveform.

[0035] In some embodiments, the corrected signal waveform is calculated by: filtering the DC-coupled digitized reference waveform to generate a filtered DC-coupled digitized reference waveform; calculating a ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform; and multiplying the calculated ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform by a scaling constant.

[0036] In some embodiments, the scaling constant is a time-averaged value of the filtered DC-coupled digitized reference waveform.

[0037] In some embodiments, the optical illumination source noise cancellation method includes generating a first light; receiving, by a first solid state spin sensor, a first portion of the first light; emitting, by the first solid state spin sensor, a second light, wherein the first solid state spin sensor includes fluorescent point defects; detecting the second light; outputting the reference waveform based on the detected second light; receiving, by a second solid state spin sensor, a second portion of the first light; emitting, by the second solid state spin sensor, a third light, wherein the second solid state spin sensor includes fluorescent point defects; detecting the third light; and outputting the signal waveform based on the detected third light.

[0038] In some embodiments, the fluorescent point defects are color center defects.

[0039] In some embodiments, the first solid state spin sensor produces a first spectral response and the second solid state spin sensor produces a second spectral response, and the first spectral response and the second spectral response are matched.

[0040] In some embodiments, the first solid state spin sensor is a first NV diamond, and the second solid state spin sensor is a second NV diamond.

[0041] In some embodiments, a noise cancellation system for a solid state spin sensor includes an analog to digital converter that converts a reference waveform into at least one digitized reference waveform, and converts a signal waveform into at least one digitized signal waveform; and a processor that receives the at least one digitized reference waveform and the at least one digitized signal waveform, wherein the processor calculates a corrected signal waveform using the at least one digitized reference waveform and the at least one digitized signal waveform, and derives a measurement of a physical quantity from the corrected signal waveform.

[0042] In some embodiments, the measurement of the physical quantity is a

measurement of a magnetic field, an electric field, temperature, pressure, a molecular species, a biological species, pH, voltage, or any combination thereof.

[0043] In some embodiments, the noise cancellation system further includes a microwave source that generates a microwave radiation; a reference microwave power meter that measures a first portion of the microwave radiation and outputs the reference waveform; a solid state spin sensor that receives a second portion of the microwave radiation and emits a fluorescence light, the solid state spin sensor including one or more fluorescent point defects; and a signal photodetector that measures the emitted fluorescent light and outputs the signal waveform.

[0044] In some embodiments, the noise cancellation system further includes a power splitter configured to divide the microwave radiation into the first portion and the second portion.

[0045] In some embodiments, the reference waveform is AC-coupled prior to

digitization or during digitization; and the signal waveform is AC-coupled prior to digitization or during digitization.

[0046] In some embodiments, the processor calculates the corrected signal waveform by: generating a first reference scaling factor from a correlation of a variation in the AC-coupled digitized reference waveform and the AC-coupled digitized signal waveform; generating a first scaled AC-coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the first reference scaling factor; and subtracting the first scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform.

[0047] In some embodiments, the at least one digitized reference waveform includes a

DC-coupled digitized reference waveform and an AC-coupled digitized reference waveform, and the at least one digitized signal waveform includes a DC-coupled digitized signal waveform and an AC-coupled digitized signal waveform.

[0048] In some embodiments, the processor calculates the corrected signal waveform by: generating a second reference scaling factor by calculating a ratio between the DC-coupled digitized signal waveform and the DC-coupled digitized reference waveform; generating a second scaled AC-coupled digitized reference waveform by scaling the AC-coupled digitized reference waveform using the second reference scaling factor; and subtracting the second scaled AC-coupled digitized reference waveform from the AC-coupled digitized signal waveform.

[0049] In some embodiments, the at least one digitized reference waveform includes a DC-coupled digitized reference waveform and the at least one digitized signal waveform includes an AC-coupled digitized signal waveform.

[0050] In some embodiments, the processor calculates the corrected signal waveform by: filtering the DC-coupled digitized reference waveform to generate a filtered DC-coupled digitized reference waveform; calculating a ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform; and multiplying the calculated ratio between the AC-coupled digitized signal waveform and the filtered DC-coupled digitized reference waveform by a scaling constant. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The objects and advantages of the present disclosure will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which:

[0052] FIG.1A is a schematic illustration of an optical setup according to some embodiments;

[0053] FIG.1B is a schematic illustration of a setup according to some embodiments;

[0054] FIG.2A is a block diagram of a measurement system according to some embodiments;

[0055] FIG.2B is an exemplary diagram of a noise cancellation technique for a solid state spin sensor, according to some embodiments;

[0056] FIG.3 is a graphical illustration of the degree of correlation between

experimental recordings of ) and

[0057] FIG.4 is a graphical illustration of timewise-paired values of experimental ^{recordings of and} _,

[0058] FIG.5 is a graphical illustration showing experimental values of the reference ^{scaling factor ^and the exponentially time-averaged reference scaling factor ^} over time.

[0059] FIG.6 is a graphical illustration showing experimental recordings of

compared to experimental recordings of

[0060] FIG.7 is a graphical illustration showing root-mean-squared (RMS) voltage noise versus frequency (e.g., a spectral profile) for the processed waveform ^ _{ୡ୭୰୰,^େ} (^) ;

[0061] FIG.8 is a graphical illustration showing average noise density plotted versus time for a magnetometer with a signal photocurrent of 8.15 mA and a reference photocurrent of 30.77 mA;

[0062] FIG.9 is a graphical illustration showing how fluorescence from NVs in a diamond depends on the excitation wavelength; and

[0063] FIG.10 is another schematic illustration of an optical setup according to some embodiments. DETAILED DESCRIPTION

[0064] Embodiments of the present disclosure are explained with reference to solid state spin sensors that use nitrogen vacancy (NV) color centers in diamond (“NV diamond”). NV diamond can be used to sense magnetic fields (e.g., as a magnetometer). However, NV diamond may also be used to detect other quantities, such as temperature, electric field, and pressure, among others. Therefore, while embodiments of the present disclosure are explained with reference to using NV diamond for magnetic field sensing, embodiments of the present disclosure apply to a wide variety of solid state spin sensor systems (such as, for example, silicon-vacancies in diamond, nickel-vacancies in diamond, and silicon-vacancies in silicon carbide, among others) used to make measurements of various physical quantities, including electric fields, temperature, pressure, orientation, a molecular species, a biological species, pH, voltage, or any combination thereof, for example. Moreover, the described noise cancellation of the present disclosure is explained with reference to optical noise, but may be applied to numerous other kinds of noise for solid state spin sensors, including microwave noise, for example.

[0065] Embodiments of the present disclosure provide for a digital scheme to reduce noise resulting from intensity fluctuations of an optical illumination source. For example, intensity noise and spectral fluctuations (e.g., amplitude and frequency fluctuations respectively) from a laser can cause amplitude fluctuations in the NV diamond fluorescence, which can affect the overall device sensitivity. In order to account for such fluctuations, the techniques described herein measure the laser intensity noise and use the measured noise to digitally remove its effects from the recorded NV fluorescence. Once such noise is reduced, a measured quantity may be derived from a resulting signal with a higher degree of accuracy.

[0066] FIG.1A is a schematic illustration of an optical setup 100 according to one or more embodiments. Optical setup 100 includes an optical illumination source 102 (e.g., a laser). The optical setup 100 includes a beamsplitter 104, which directs light generated by optical illumination source 102 in a first direction to the reference photodetector 110, and a second direction to the mirror 116, thereby splitting the light into a first light portion 106 and a second light portion 108. The first light portion 106 may be homogenized and/or collected by optional optical elements 112 prior to its impingement on the reference photodetector 110.

[0067] The mirror 116 directs the second light portion 108 toward a diamond with NVs (signal diamond 114). Microwave radiation can optionally be applied to the signal diamond 114 by a microwave source 118. The second light portion 108 illuminates the one or more NVs in the signal diamond 114 and causes the one or more NVs to emit NV fluorescence light 120. The NV fluorescence light 120 is directed toward signal photodetector 122. Before reception of NV fluorescence light 120 by signal photodetector 122, NV fluorescence light 120 may be collected by light collection element 124. The light output from light collection element 124 may be spectrally filtered to remove excitation light by filter 126. The NV fluorescence light 120 may also be collected by another light collection element 128 before illuminating signal photodetector 122.

[0068] Referring to the optical illumination source 102, the optical illumination source 102 may be, for example, a laser, a light emitting diode (LED), a laser diode, a spectrally filtered lamp, or another kind of light source that provides optical illumination. The optical illumination may include wavelengths ranging from 200 nm to 2000 nm. For example, the optical illumination may include wavelengths in the visible spectrum range from about 390-700 nm. As another example, the optical illumination can include wavelengths in the green part of the visible wavelength range from about 495-570 nm.

[0069] While FIG.1A only shows one optical illumination source 102, multiple illumination sources may be included in optical setup 100. Each optical illumination source may provide optical illumination of the same wavelength and/or different wavelengths compared to the other optical illumination source(s). When a plurality of optical illumination sources 102 are used, optical setup 100 may cancel noise from one, some, or all of the plurality of optical illumination source 102 [0070] Referring to the beamsplitter 104, the beamsplitter 104 may be a laser beam sampler, a laser beam pick-off, a half-silvered mirror, a laser beam splitting cube, and/or any other light sampling device. In some embodiments, beamsplitter 104 may partition light generated by optical illumination source 102 into more than two portions.

[0071] Referring to the reference photodetector 110, the reference photodetector 110 may be an optical detector such as a photodiode, photomultiplier tube, bolometer, CCD camera, CMOS camera, and/or the like.

[0072] Referring to the optical elements 112, optional optical elements 112 may include one or more spectral filters and/or light homogenizers. A light homogenizer may be used to improve spatial uniformity of light, and may be a fluorescent sheet such as polyoxymethylene (Delrin), an optical diffuser, a hexagonal or other shaped light homogenizer, or a reference diamond with one or more NV centers. For example, the reference diamond may include a large number of NV centers, such as 10 ¹² NV centers. Homogenized light may be collected by a light collection element before illuminating reference photodetector 110. For example, optional optical elements 112 may include one or more light collection element such as a lens, a parabolic concentrator, an elliptical concentrator, an objective, and/or a light pipe. If light homogenization is not desired, first light portion 106 can impinge on reference photodetector 110 directly without homogenization and with or without collection by a light collection element of optional optical elements 112.

[0073] Referring to the mirror 116, the mirror 116 may be any kind of structure used to steer second light portion 108, such as a metal mirror, dielectric mirror, deformable mirror, concave mirror, prism, and/or the like.

[0074] Referring to the microwave source 118, the microwave source 118 may be a microwave-frequency signal generator or any other source that provides microwave radiation at specified frequencies. For example, microwave source 118 may apply microwave radiation to signal diamond 114 that includes frequencies that drive transitions between the magnetic sublevels of quantum states in NV centers of signal diamond 114. Microwave radiation from microwave source 118 may be used in conjunction with optical illumination to determine the energy levels of NV centers. For example, the energy levels can be changed by the strength and direction of a quantity such as a magnetic field. The specific energy level of a given magnetic sublevel can be determined by noting the microwave radiation frequency that causes a decrease in the NV fluorescence. In some embodiments, microwave source 118 is not applied to signal diamond 114, and not included in optical setup 100.

[0075] For example, as discussed above, when microwave source 118 is included in optical setup 100, microwave source 118 may apply microwave radiation to signal diamond 114 to drive transitions between the magnetic sublevels of quantum states in NV centers of signal diamond 114. The applied microwave radiation can cause a fraction of the NVs in signal diamond 114 to change from their initial magnetic sublevel (for example, m=0) to a different magnetic sublevel (for example, m=l). The change in magnetic sublevel may cause the NVs to emit less fluorescence relative to when the NVs are in the initial magnetic sublevel. An optimal microwave frequency that causes this change in magnetic sublevel depends on the magnetic field (or other physical quantity being measured) that signal diamond 114 is subject to. Thus, the amplitude of fluorescence emitted by the NVs may be monitored while varying the microwave frequency of microwave radiation applied to signal diamond 114, and the magnetic field may be determined by observing which microwave frequency results in the largest decrease in fluorescent light emitted by the NV centers of signal diamond 114. Alternatively, for measurements of magnetic fields on the order of 1 gauss or less, the microwave radiation can be held at a fixed frequency near the optimal frequency to cause the change in magnetic sublevel, and the magnetic field may be inferred from the amplitude of the NV fluorescence.

[0076] When microwave source 118 is included in optical setup 100, the microwave radiation that it applies to signal diamond 114 may exhibit amplitude noise (for example, variations in the amplitude of the microwave radiation applied to the diamond). In certain embodiments, amplitude noise of the microwave radiation may result in amplitude noise of the NV fluorescence. The amplitude noise of the microwave radiation may be corrected by a configuration similar to optical setup 100, but adapted to cancel microwave amplitude noise. The microwave noise may be corrected in addition to noise from optical illumination source 102, and may be corrected in the same manner as will be described in the following noise

cancellation schemes discussed below.

[0077] For example, as shown in FIG. IB, microwave radiation 132 produced by a microwave source 130 may be sampled by a microwave element 134, such as a directional coupler or a power splitter, to divide the microwave radiation 132 into two or more split microwave radiations 136 and 140. A first microwave radiation 136 may be measured by a reference microwave power meter 138, such as a crystal detector, for example. The reference microwave power meter may then output a measured reference microwave radiation signal based on the measured reference microwave radiation. A second microwave radiation 140 may be applied to signal diamond 114. Signal diamond 114 may then emit NV fluorescence 142, which is recorded by signal photodetector 122. Signal photodetector 122 may then output an NV fluorescence signal waveform. Noise cancellation in accordance with the following noise cancellation schemes discussed below may then be performed using the measured reference microwave radiation signal and the NV fluorescence signal waveform.

[0078] Referring back to FIG.1A and to the NV fluorescence light 120, the amount of NV fluorescence light 120 emitted by signal diamond 114 may change in relation to the intensity and spectral content of the illumination light, and in relation to the physical quantity being measurement. NV fluorescence light 120 may be in a red part of the visible wavelength range, which may include light with a predominant wavelength of 600 to 850 nm. The emitted red light may be proportional to, for example, a physical quantity such as a magnetic field, and can therefore be used to measure the magnetic field at the signal diamond 114. In some

embodiments, NV fluorescence light 120 may be in the ultraviolet wavelength range, the visible wavelength range, the near infrared wavelength range, the infrared wavelength range, or any other wavelength range.

[0079] Referring to the signal photodetector 122, the signal photodetector 122 is sensitive to the wavelength range of NV fluorescence light 120. Signal photodetector 122 may be an optical detector such as a photodiode, photomultiplier tube, bolometer, CCD camera, CMOS camera, and/or the like. If a plurality of optical illumination sources 102 are used, light may be sampled from each optical illumination source and directed to a respective number of reference photodetectors 110 and/or signal photodetector 122.

[0080] Referring to the light collection element 124, light collection element 124 may be one or more of a light collection element such as a lens, a parabolic concentrator, an elliptical concentrator, an objective, or a light pipe.

[0081] Referring to the filter 126, the excitation light removed by filter 126 may be, for example, light in the green part of the visible wavelength range. Filter 126 may be one or more of an interference filter, colored glass, a prism, a diffraction grating or other spectral filter. Filter 126 may be appropriately tuned depending on the wavelength of light from optical illumination source 102 and/or NV fluorescence light 120 so that excitation light can be removed from the light output from light collection element 124 [0082] Referring to the light collection element 128, the light collection element 128 may be one or more of a light collection element such as a lens, a parabolic concentrator, an elliptical concentrator, an objective, or a light pipe, as described above in regard to light collection element 124. In some embodiments, one or more of light collection element 124, filter 126, and light collection element 128 may not be included in optical setup 100.

[0083] Referring to the reference photodetector 110 and the signal photodetector 122, these photodetectors can be configured to process the light into various signals. For example, the reference photodetector 110 and signal photodetector 122 can be configured to each convert the respective optical signals they detect to a voltage. For example, if one or both of reference photodetector 110 and signal photodetector 122 include photodiodes, photocurrent from the photodiodes can be converted into a voltage using a resistor, a transimpedance amplifier, an external current-to-voltage amplifier, or other amplifier. The respective voltages output by reference photodetector 110 and signal photodetector 122 may be voltage waveforms. As another example, the reference photodetector 110 and signal photodetector 122 can be configured to each provide a current. For example, the current can be measured directly rather than being converted to a voltage. In some embodiments, the current can be amplified.

[0084] As noted above, optical illumination source 102 may be a laser diode. In some embodiments, a photodetector (e.g., a photodiode, phototransistor, avalanche photodiode, and/or the like), such as a built-in photodetector, may be provided with the laser diode of optical illumination source 102. The photodetector may detect an optical signal emitted by the laser diode, and convert it to a voltage. For example, if the photodetector is a photodiode, photocurrent from the photodiode can be converted into a voltage using a resistor, a

transimpedance amplifier, an external current-to-voltage amplifier, or another amplifier. The voltage output by the photodetector may include a voltage waveform. The voltage waveform may be digitized by analog to digital converter (ADC) 206 as will be discussed below in regard to reference photodetector 110. The voltage supplied from the photodetector provided with the laser diode of optical illumination source 102 may reflect the same information as that supplied by the voltage output by reference photodetector 110. Thus, when optical illumination source 102 is a laser diode that is provided with a built-in photodetector, reference photodetector 110, as well as optional optical elements 112 and beamsplitter 104 may be removed from optical setup 100. [0085] FIG.2A is a block diagram of measurement system 200, according to some embodiments. Measurement system 200 includes the same elements as discussed in regard to optical setup 100 in conjunction with FIG.1A, including the optical illumination source 102, beamsplitter 104, reference photodetector 110, optional optical elements 112, signal diamond 114, and signal photodetector 122. Moreover, light collection assembly 202 may include light collection element 124, filter 126, and light collection element 128, as also described in regard to optical setup 100 in FIG.1A. In addition to the components discussed in conjunction with FIG. 1A, FIG.2A includes an analog to digital converter (ADC) 204, ADC 206, and computer 208.

[0086] As noted above, intensity fluctuations from the optical illumination source 102 (e.g., laser) cause amplitude fluctuations in the NV fluorescence from the signal diamond 114, which affect the device sensitivity. As described further herein, the computer 208 can be configured to account for this optical illumination source intensity variation by measuring the optical illumination source intensity noise and, with that information, digitally removing its effects from the recorded NV fluorescence.

[0087] FIG.2B shows an exemplary technique for noise cancellation for a solid state spin sensor, according to some embodiments. At step 250, a signal waveform is received (e.g., by the computer 208) that is associated with a signal channel. At step 252, a reference waveform is received that is associated with a reference channel. Step 250 and step 252 occur

simultaneously; that is, the signal waveform and the reference waveform are received simultaneously. At step 254, a corrected signal waveform is calculated using the reference waveform and the signal waveform. At step 256, a measurement of a physical quantity from the corrected signal waveform is derived. The measurement of the physical quantity can be, for example, a measurement of a magnetic field, an electric field, temperature, pressure, and/or the like.

[0088] Reference photodetector 110 and signal photodetector 122 each convert the respective optical signals they detect to signals that are further processed as described herein. For example, the reference photodetector 110 and signal photodetector 122 each convert the respective optical signals to voltages to generate voltage waveforms. As mentioned above, in some embodiments the photocurrent is amplified to a larger current and/or digitized (as described below) as a current, as known to a person of skill in the art. For ease of explanation, FIG.2A is described below assuming that the photodetectors output voltage waveforms. [0089] Referring to steps 252 and 254 of FIG.2B, to provide for flexibility with the noise cancellation techniques, the system can be configured to record both AC-coupled and DC- coupled waveforms from both the signal and reference channel. As shown in FIG.2A, the voltage waveform from signal photodetector 122 is digitized by ADC 204. In some

embodiments, ADC 204 may include two ADCs: an AC-coupled ADC and a DC-coupled ADC. The voltage waveform from signal photodetector 122 may be converted by both the AC-coupled ADC and a DC-coupled ADC simultaneously, and/or one after the other in serial fashion. The AC-coupled ADC digitized waveform from signal photodetector 122 is denoted herein as and the DC-coupled ADC digitized waveform from signal photodetector 122 is d ^{enoted herein as} _. ^{The waveforms can be AC- or DC-coupled prior to digitization} and/or during digitization.

[0090] Similarly, the voltage waveform from reference photodetector 110 is digitized by ADC 206. Like with ADC 204, in some embodiments ADC 206 may include two ADCs: an AC-coupled ADC and a DC-coupled ADC. The voltage waveform from reference photodetector 110 may be converted by both an AC-coupled ADC and a DC-coupled ADC simultaneously, or one after the other in serial fashion. The AC-coupled ADC digitized waveform from reference photodetector 110 is denoted as _, and the DC-coupled ADC digitized waveform from r ^{eference photodetector 110 is denoted as ADC 204 and ADC 206 may be separate} ADCs, or may be a single ADC.

[0091] As shown in FIG.2A, the outputs of the ADCs 204, 206 are input into computer 208. F ^{or example, if each of ADCs 204, 206 include two ADCs as discussed above, then ^} _୰ୟ^,^େ ^{(^)} _{, are input into computer 208 for processing. Computer 208} may include one or more processors and one or more memory devices. The processor can e _xecute ^{instructions and one or more memory devices can store instructions and/or data. The} memory device can be a non-transitory computer readable medium, such as a dynamic random access memory (DRAM), a static random access memory (SRAM), flash memory, a magnetic disk drive, an optical drive, a programmable read-only memory (PROM), a read-only memory (ROM), or any other memory or combination of memories. The memory device can be used to temporarily store data. The memory device can also be used for long-term data storage. The processor and the memory device can be supplemented by and/or incorporated into special purpo l i i i [0092] For each of the signal and reference voltage waveforms, these noise cancellation techniques may simultaneously record both a DC-coupled voltage waveform (with the DC- coupled ADC set to have large dynamic range) and an AC-coupled voltage waveform (with the AC-coupled ADC set to have very small dynamic range). For a given voltage waveform, combining the information from both the AC-coupled ADC and the DC-coupled ADC can effectively provide for very accurate digitation of a signal with a large DC offset (e.g. more accurate than is possible with a single ADC alone).

[0093] For example, by removing the DC voltage offset, AC-coupling of voltage waveforms may reduce the dynamic range requirement of the ADCs 204 and 206. Reducing the dynamic range requirement can allow for the discrete digitization levels associated with ADC 204 and ADC 206 to lie closer together, and can result in a more precise digitization of the voltage waveforms. This reduction in required dynamic range can be beneficial for NV diamond magnetometers that generate a large photocurrent with only a small fractional change in the photocurrent corresponding to a magnetic signal. The reduction of the dynamic range associated with AC-coupling is beneficial because in the absence of AC-coupling, the larger dynamic range of the ADC (required to accommodate the large DC offset of a DC-coupled signal) will lead to increased digitization noise (since the digitized levels of the ADC will lie farther apart as required to span the larger dynamic range). If the digitization noise is larger than or comparable to shot noise, the SNR of the measurement of the physical quantity will be worse than when digitization noise is negligible.

[0094] FIG.3 is a graphical illustration 300 of the degree of correlation between

experimental recordings of As shown in graphical illustration 300,

experimental recordings of the voltage waveforms illustrate a high

degree of temporal correlation. This correlation occurs because, during the experimental recordings, the fractional changes of the overall optical illumination signal (as a function of time) result in equal fraction changes in optical illumination of both the signal and reference photodetectors.

[0095] FIG.4 is a graphical illustration 400 of timewise-paired values of experimental ^{recordings . Graphical illustration 400 shows that a variation in the} values of can be explained nearly completely by variation in the values of ^ _୰ୟ^,^େ ⁽ ^ ⁾ . The variation shown results almost entirely from random temporal fluctuations of the overall optical illumination source in time, which may be amplitude noise of the optical illumination source intensity in time.

[0096] With the AC signal waveform, DC signal waveform, AC reference waveform, and DC reference waveform (or a subset of these waveforms), various techniques for noise cancellation can be used, as described further herein. The noise cancellation techniques can be selected based on, for example, which signals are available, and/or considerations depending on the physical quantity to be measured. Three exemplary noise cancellation schemes are discussed below, including when particular noise cancellation techniques may be suitable over other techniques. While these examples describe cancelling noise from optical sources, this is for illustrative purposes only and not intended to be limiting. For example, these techniques can be used to cancel noise from other sources, such as microwave sources.

[0097] Exemplary noise cancellation scheme 1

[ ^{0098] A reference scaling factor, denoted M} _, ^{and an offset, denoted B, between} a _{nd is calculated by linear regression using the equation}

This calculation is performed every k seconds to determine a value of the reference scaling f ^{actor. M, and k may be a small fraction of a second, such as 0.05 seconds, for example. The} value of k may be different based on the application, and may be a value from less than 0.001 seconds, for example, to more than 1000 seconds, for example. Moreover, the choice of k may depend on a time scale of the magnetic signal that is sought for detection. If k is too short, then t ^{here may not be enough data gathered during time period ^ to determine the value of M} accurately. On the other hand, if k is too long, then the calculation of M may fail to correct for effects, such as thermal drift, that cause M to vary on shorter time scales than the set value of k. Thus, k may be selected such that there is enough data for the linear regression to achieve an a ^{ccurate fit between timewise-paired values of experimental recordings} _, ^and

s ^{uch as the timewise-paired values of experimental recordings and}

_{shown in FIG. 4, for example.}

[0099] B is a compensation value that is included to compensate for non-idealities that are experienced by optical setup 100 and induce offsets in the detector voltages. Such non-idealities may be, for example, light from an optical source other than optical illumination source 102, such as ambient light or sunlight, for example, that is detected by reference photodetector 110 and/or signal photodetector 122. In an ideal system where there are no non-idealities, B is equal to zero. The value B may be determined such that the linear regression achieves an accurate fit b ^{etween timewise-paired values of experimental recordings ( ) such as the timewise-paired values of experimental recordings ) shown in FIG.}

4, for example.

[00100] An exponential time-averaged reference scaling factor, denoted (e.g., where discrete time is parameterized in units of K), is calculated after every ^ seconds based on _, ^{the value of α} _, ^{and the present value of ^} _, ^{using the formula ^}

_, ^{where α may be adjusted. The value ^ is a time constant in units k. FIG.} 5 is a graphical illustration showing experimental values of ^ and over time. In FIG.5, the values indicate that is approximately equal to 0.556.

[00101] The intensity-noise-corrected signal voltage waveform, denoted S (t is then c _{alculated using the equation From}

the magnetic signal (or other physical quantity being measured) can then be derived by computer 2 ^{08. The quantity α times α indicates the value of the exponential moving average time} c _{onstant used to calculate If a ratio of and changes on a timescale}

l ^{onger than the quantity of k times α, noise will be efficiently removed from S} _raw,AC ^{(^t to} produce Moreover, in view of is approximately equal to

minus 0.556 times

[00102] FIG.6 is a graphical illustration showing experimental recordings of S _, using noise cancellation scheme 1 compared to experimental recordings of . The

values of FIG.6 use the M and M values of FIG.5. Using the experimental recordings shown in FIG.6, the waveform shows a reduced noise compared to , where

the root-mean squared (RMS) variation of is reduced by a factor of approximately 56 compared to the RMS variation of S (a person of skill in the art will understand that while the factor of noise reduction in this example was approximately 56, the factor of noise r _{eduction is not related to the value of M The recordings of fluctuate over a}

range of approximately 5500 µV, while the recordings of fluctuates over a range of

1 ^{00 µV.} [00103] Noise in the waveform can be limited by statistical fluctuations in the

number of detected photoelectrons. The scheme described in noise cancellation scheme 1 ^{removes correlated fluctuations between and ^} _, ^{which may occur at}

f ^{requencies above approximatel} _. ^{If the amplitude-modulated fluorescence containing}

the magnetic signal (or other physical quantity) is near or below this frequency, this scheme may remove or attenuate that fluorescence signal as well, resulting in loss of the magnetic signal. The amplitude modulation of the signal photodetector voltage waveform (associated with the magnetic signal) should therefore occur at a frequency substantially higher than _, so that the magnetic signal can be recovered. For example, the lowest component of spectral frequency profile associated with the magnetic signal may be ten or one hundred times higher than _{for example.}

[00104] The quantity kα determines the time scale of noise cancellation. Correlated noise _{between that occurs faster than the quantity kα are not detected, while}

variations in a ratio of that are slower than the quantity kα may change the reference scaling factor Thus, the quantity kα may be set larger than the time scale of the magnetic signal that is being measured.

[00105] Exemplary digital noise cancellation scheme 2

[00106] In some embodiments, the calculation of M can be performed slightly differently compared to digital noise cancellation scheme 1. In particular, every seconds the reference ^{scaling factor ^ can be determined by calculating M}

^{With the given value of the values of and are calculated as before in digital noise}

cancellation scheme 1. Digital noise cancellation scheme 2 may perform similarly to digital noise cancellation scheme 1 in noise-cancellation performance. However, digital noise cancellation scheme 2 may be beneficial in situations where broadband magnetic noise or large magnetic signals are encountered during magnetometer operation. Digital noise cancellation scheme 2 may also be beneficial for NV measurement schemes that employ amplitude, phase or frequency modulation of the microwave radiation applied to the signal diamond. Broadband magnetic noise, large magnetic signals, or certain microwave modulation schemes may add _{additional variation to , which is not common-mode to , , and may therefore} interfere with the calculation of M in digital noise cancellation scheme 1. Both digital noise cancellation schemes 1 and 2 can allow for shot-noise-limited performance, where the remaining noise on is bounded by statistical limits that depend only on the number of

photons collected.

[00107] Exemplary digital noise cancellation scheme 3

[00108] In some embodiments, the optical illumination source noise cancellation is performed ^{using a third scheme, which utilizes division. is passed through a digital low-pass}

f ^{ilter to produce The intensity-noise-corrected signal voltage waveform is then}

c ^{alculated using the formula}

_, ^{where ^ is a static (non-} changing) scaling constant. In some embodiments, A may be defined as approximately equal to a ^{time-averaged value} of _. ^{Defining A in this manner can} result in minimal scaling difference between _{, ,} because ) is

multiplied by a value (A) that is approximately equal to , which provides that the noise correction exhibits approximately unity gain. The roll-off frequency of the low-pass filter that produces should be low enough that the amplitude modulation of the fluorescence corresponding to a magnetic signal experiences little to no attenuation.

[00109] Physical quantity measurement

[00110] After noise cancellation is performed using one or more of the discussed noise cancellation schemes, the physical quantity being measured may be recovered from the intensity-noise-corrected signal voltage waveform discussed above, denoted For example, Scorr, AC(t) may be multiplied by a conversion constant C to obtain a measurement of the physical quantity in time. The value of C may be determined via calibration that determines, for example, how is related to the desired physical quantity. The value of C may alternatively be calculated from first principles or from known properties of NV centers. The desired physical quantity may be a magnetic field, electric field, temperature, pressure, or orientation, for example.

[00111] Noise cancellation performance

[00112] In some embodiments, sensors that employ one of the aforementioned optical illumination source noise cancellation schemes may reach the shot noise limit (e.g., the SNR limit imposed by the statistical fluctuations on the number of detected photons alone). FIG.7 is a graphical illustration 700 showing root-mean-squared (RMS) voltage noise versus frequency (a spectral profile) for an experimental recording of for digital noise cancellation scheme 1. The spectral profile illustrates near-shot-noise-limited operation of the sensor over the vast majority of the 2 kHz to 90 kHz frequency range. Because the statistical origins of shot noise result in noise that is evenly distributed across all frequencies, a flat spectral noise profile is a necessary but not sufficient condition to demonstrate a sensor measurement is shot-noise- limited. In FIG.7 the shot noise limit corresponds to approximately

[00113] In some embodiments, the practical limit to sensor performance (e.g., magnetometer performance) may be described by shot noise on the signal photocurrent alone (e.g., the current produced by the signal photodetector 122).

[00114] To correct for intensity noise of optical illumination source 102, the above schemes employ reference photodetector 110. The use of the reference photodetector 110 imposes a ^{fundamental noise penalty on the SNR of optical system 100, given by}

, where in this example and are termination resistors for the signal photodetector 122 and

the reference photodetector 110 respectively, so that correspond

to the signal photocurrent and reference photocurrent respectively. If the signal and reference ^{photocurrents are equal then the measurement noise will be a} factor of higher than in the case of a noiseless optical illumination source and no reference photodetector. The value of can be reduced by increasing the amount of light incident on the reference photodetector 110, which will increase the value of ^

[00115] FIG.8 is a graphical illustration 800 showing the recorded average noise density (nV/Hz ^1/2 ) plotted versus time in seconds for measurement system 200 with a signal

photocurrent of 8.15 milliamps (mA) and a reference photocurrent of 30.77 mA. FIG.8 illustrates that embodiments of the present disclosure are suitable to reduce the value of from√2 (with equal values of the signal and reference photodetector currents) to 1.12 (or lower), which therefore shows improved noise cancellation performance. FIG.8 further illustrates that embodiments of the present disclosure may achieve performance (even with photocurrents up to 8.15 mA) with total noise level only approximately 20% higher than an ideal case in which all fluctuations are due to shot noise on the signal photocurrent alone. Item 1 of FIG.8 shows the theoretically-calculated noise level assuming the only noise source is shot noise on the signal photodetector photocurrent alone. This noise level may be the best possible performance for sensors that do not employ any quantum entanglement to circumvent the shot noise limit. Item 2 of FIG. 8 shows the theoretically-calculated noise level of Item 1 when shot noise of the reference photodetector is taken into account as well, which corresponds to the H _rei being equal to 1.12, and the noise level of item 2 therefore being 1.12 times the noise level shown by item 1. Item 3 of FIG. 8 shows the theoretically-calculated noise level of Item 2 when ADC read noise is included as well. Item 4 of FIG. 8 shows the actual experimental

performance realized in the measurement. Item 5 of FIG. 8 shows the theoretical shot noise for equal signal and reference photodetector photocurrents of 8.15 mA each, which is substantially higher than Items 1, 2, 3, and 4. Item 5 therefore illustrates the benefits gained by using a reference photocurrent substantially higher than the signal photocurrent. As shown by item 5, when a reference photocurrent equal to the signal photocurrent is used, the noise level is higher than the noise levels of items 1, 2, 3, and 4. As shown in FIG. 8, the noise level of item 5 is V2 times the noise level shown by item 1. In FIG. 8, the noise is the average value from 10kHz to 40kHz, and the lower the noise level shown by each of items 1, 2, 3, 4, and 5, the better the noise cancellation performance.

[00116] The all-digital implementation outlined above offers additional advantages over analog implementations. For example, inadvertent phase delays between the signal

photodetector 122 and reference photodetector 110 can be corrected for digitally. These unwanted phase delays may be introduced by different path lengths (relative to the point at which the light is split) of the respective light portions hitting the signal photodetector and hitting the reference photodetector.

[00117] Correcting optical illumination source frequency noise

[00118] In some embodiments, the aforementioned methods can correct for amplitude noise/modulation of optical illumination source 102 down to statistical fluctuations (for example, to the shot noise limit). For example, for single-frequency lasers with frequency held fixed, the aforementioned methods can remove all non- statistical noise sources associated with the optical illumination. However, if the spectral illumination profile (for example, the amount of optical power at different wavelengths) varies in time, this variation may produce an additional source of noise that must be corrected.

[00119] The fluorescence from NVs in diamond depends on the wavelength of the excitation light. FIG. 9 is an example graphical illustration 900 depicting how fluorescence from NVs in a diamond depends on the excitation wavelength. For example, the data show that for the given experimental conditions with a single NV center and 1 microwatt of excitation light, the fluorescence rate with illumination at 550 nm is roughly 65% higher than the fluorescence rate with illumination at 540 nm. Although these experimental conditions may differ from the conditions employed in high-sensitivity NV diamond-based sensors (where there may exist a large number of NV's and a higher optical illumination source intensity), the conclusion that the NV fluorescence is wavelength-dependent still holds.

[00120] A consequence of this wavelength dependence is that variations in the illumination wavelength can couple to amplitude changes in the diamond fluorescence, thereby mimicking a magnetic signal or other physical quantity being measured. For example, for high-cost single- frequency ring lasers based on diode-pumped solid state (DPSS) laser technology, which are common in lab environments and may emit at only a single wavelength, this noise source can often be experimentally negligible. However, for deployable systems (where space, weight, power, and possibly cost are at a premium), the optical illumination source may be a multimode (multiple-frequency) laser diode. These multimode laser diodes may emit multiple wavelengths, and the intensity of each wavelength may vary rapidly in time. Because the amount of NV fluorescence is wavelength-dependent, the rapidly varying spectral profile of the multimode laser diode may result in amplitude variations of the NV fluorescence which are not related to the value of the physical quantity being measured. This unwanted amplitude noise of the NV fluorescence may not be negligible and may skew measurements. Therefore, it is advantageous for noise cancellation schemes to cancel amplitude noise of the NV fluorescence caused by the varying spectral profile of the illumination source, so that deployable multimode laser diodes can be used instead of larger, more expensive and more complex lasers or other optical illumination sources. The noise cancellation schemes of the present disclosure are applicable to noise that may occur from variations in the illumination spectral profile, such as variations in the intensity of the different wavelengths emitted from multimode (multiple-frequency) laser diodes.

[00121] FIG. 10 is a schematic illustration of an optical setup for noise cancellation applicable to multimode laser diodes, according to some embodiments. Numerals 104, 106, 108, 110, 114, 116, 118, 122, 124, 126, and 128, are as described previously with reference to FIG. 1A.

[00122] Optical illumination source 1002 is a multimode (multiple-frequency) laser diode light source, which may include one or more laser diodes. To enable frequency noise

cancellation, the spectral response of the light incident on reference detector 110 is matched to the spectral response of signal diamond 114. This is achieved by illuminating diamond 1004, which has the same NV characteristics as signal diamond 114, with first light portion 106.

Diamond 1004 may homogenize reference light 106 so that frequency noise of the optical illumination source will produce the same fractional amplitude change in the light collected by reference photodetector 110 and signal photodetector 122. First light portion 106 may illuminate diamond 1004 and cause diamond 1004 to emit NV fluorescence light 1006.

Diamond 1004 may have a lower number, the same number, or a higher number of NVs compared to signal diamond 114. However, if diamond 1004 has a lower number of NVs compared to signal diamond 114, optical illumination source 1002 may need to apply more illumination to diamond 1004. If diamond 1004 has a higher NV density relative to signal diamond 114, more red light will be emitted from diamond 1004 for detection by reference photodetector 110 when both diamonds are illuminated with the same optical illumination power and intensity

[00123] NV fluorescence light 1006 is caused by the one or more NV centers in diamond 1004. NV fluorescence light 1006 may include light that is in the red part of the visible wavelength range. NV fluorescence light 1006 is directed to reference photodetector 110 for detection. Thereafter, signals are converted via ADCs 204 and 206 as previously described, and computer 208 processes the signals in accordance with the correction schemes previously described. If the overall spectral profile of the optical illumination source 1002 changes, this change produces the same fractional change in photocurrent for the signal photodetector 122 and the reference photodetector 110. A similar effect of achieving the same fluorescence

dependence upon the light’s spectral profile may be achieved by filtering the reference light with an appropriately matched spectral filter, colored glass, absorptive filter, or interference filter, or by filtering the light with another crystal with fluorescent point defects, one example being color center defects, and/or by using other materials to filter the light.

[00124] Upon review of the description and embodiments provided herein, those skilled in the art will understand that modifications and equivalent substitutions may be performed in carrying out the invention without departing from the essence of the invention. Thus, the invention is not meant to be limiting by the embodiments described explicitly above.