Device and method for calibrating microsphere displacement in optical trap by using absolute acceleration of gravity

Abstract

The application discloses a device and method for calibrating microsphere displacement in an optical trap by using absolute gravity acceleration. The device comprises an optical power adjusting module. An optical trap capturing light is emitted by a light source, and after the optical power adjusting, the light is incident on the microsphere and acts on the microsphere, and after the action, the light is emitted to a displacement detection module and is received by the displacement detection module. First, the capturing light is turned off to make the microsphere freely fall, and after falling for a distance, the capturing light is turned on again to capture the microsphere again, so that the microsphere performs under-damped oscillation movement. After a period of time, the microsphere returns to a stable capturing state, and the microsphere oscillation signals of each cycle are repeatedly recorded. The local gravity acceleration is taken as an absolute standard, a theoretical oscillation curve is calculated, and calibration is performed. The application greatly enhances the reliability and traceability of the optical trap detection system, and can calibrate a nonlinear detection system. The device and method avoid setting a complex detection system calibration device, and greatly reduce the complexity and debugging difficulty of the system.

Description

TECHNICAL FIELD

[0001] The application relates to a device and a method for calibrating a detection system, in particular to a device and a method for calibrating displacement of a microsphere in an optical trap by using absolute gravity acceleration. BACKGROUND

[0002] In 1971, Ashkin, an American physicist, first used a lens to weakly focus a vertically upward irradiated laser beam to stably suspend a glass microsphere with a diameter of 20 um by using an optical method. In 1986, he found that a single laser beam can also stably capture a microsphere without relying on gravity after being strongly focused, and this technology is named as optical tweezers. In 2018, Ashkin won the Nobel Prize in Physics for inventing optical tweezers. The principle of optical tweezers is that a strongly focused laser beam produces an action force on a dielectric microsphere, which always points to the focal point, and the size of the force is proportional to the electric field gradient, so it is called gradient force. The force makes the dielectric microsphere be three-dimensionally trapped near the focal point. Optical tweezers provide a non-contact, non-destructive and high spatial and temporal resolution method for controlling and measuring the characteristics of micrometer to sub-micrometer scale objects, and have wide applications and attractive prospects in biology, high-sensitivity sensing and quantum physics.

[0003] Ashkin once predicted when he first realized the suspension of a microsphere in a vacuum: “If the viscous damping (of air) is further reduced, (vacuum optical tweezers) will have the potential to be used to realize inertial sensors such as gyroscopes and accelerometers.” In recent years, it has been found that if the captured dielectric microsphere is placed in a vacuum environment, that is, the influence of external thermodynamic noise is isolated, it will bring a measurement accuracy far exceeding the current conventional means. For example, the David Moorex group of Yale University has realized an acceleration measurement sensitivity of ng level in 2017, which is 3 orders of magnitude higher than the detection sensitivity that can be achieved by the current mechanical sensor at room temperature. Vacuum optical tweezers have shown important application value and broad development prospects in the fields of precise mechanical quantity measurement, high-performance inertial sensors, non-Newtonian gravity exploration and macroscopic quantum state preparation.

[0004] In a sensing and detection system based on an optical trap system, a microsphere captured by a detection optical trap is often used as a sensitive unit, and the size of the to-be-detected physical quantity is calculated by the displacement of the microsphere caused by the to-be-detected physical quantity. Therefore, the calibration of the displacement detection system in the optical trap system, especially the optical trap system that needs to measure the physical quantity absolutely, is very important.

[0005] The common detection system calibration scheme is divided into passive calibration and active calibration. The passive calibration is mainly based on the matching of the power spectrum and the energy equalization theorem of the microsphere in the stable capture state. There are many uncertain factors in the calibration process, and there is no absolute standard, so the reliability is poor. At the same time, these methods cannot calibrate the nonlinearity of the detection system. The active calibration method mainly sets up an electrode plate around the optical trap, and adjusts the microsphere motion through the electric field to calibrate the detection system. These methods lack an absolute standard, have poor traceability, and are affected by factors such as the distance between the electrode plates and the parallelism. At the same time, these methods need to set up a complex calibration device around the optical trap, the system complexity is high, the debugging difficulty is great, and the robustness is poor. SUMMARY

[0006] In many optical trap systems, the microsphere captured by the optical trap is often used as a sensing unit, and the system to be measured physical quantity is solved through the microsphere motion information. Therefore, the calibration of the microsphere displacement detection system in the optical trap is crucial to the detection accuracy of the optical trap system.

[0007] In view of the fact that the calibration method of the detection system in the current optical trap system lacks a calibration method with simple structure, absolute reference, high reliability and the ability to calibrate the nonlinearity of the detection system, the application provides a device and method for calibrating the microsphere displacement in the optical trap by using absolute gravity acceleration. The application has the advantages of simple structure, absolute reference, high reliability and the ability to calibrate the nonlinearity of the detection system, and is of great significance to the sensing accuracy and system complexity of the optical trap system.

[0008] The specific technical scheme adopted by the application is as follows:

[0009] I. A device for calibrating the microsphere displacement in the optical trap by using absolute gravity acceleration:

[0010] The device comprises a vacuum cavity, two lenses, a microsphere, a displacement detection module and a light source. The two lenses and the microsphere are arranged in the vacuum cavity, and the displacement detection module and the light source are arranged outside the vacuum cavity. The light source emits optical trap capture light. The optical trap capture light is incident on one of the lenses in the vacuum cavity, converges on the microsphere and then acts on the microsphere. The optical trap capture light after acting on the microsphere is emitted from the vacuum cavity to the displacement detection module after passing through the other lens in the vacuum cavity, and is received by the displacement detection module.

[0011] The device further comprises a light power adjustment module. The light source emits optical trap capture light. The optical trap capture light is incident on one of the lenses in the vacuum cavity after light power adjustment by the light power adjustment module, converges on the microsphere and then acts on the microsphere. The optical trap capture light after acting on the microsphere is emitted from the vacuum cavity to the displacement detection module after passing through the other lens in the vacuum cavity, and is received by the displacement detection module.

[0012] It also includes a signal processing module, a displacement detection module, and the signal processing module being electrically connected. The displacement detection module receives the light field signal of the light captured by the light trap after interacting with the microsphere and exiting the vacuum cavity.

[0013] In this invention, except for the two lenses and the microspheres which are located inside the vacuum cavity, all other components are located outside the vacuum cavity.

[0014] The lenses include, but are not limited to, spherical lenses, achromatic lenses, and aspherical lenses.

[0015] The optical power adjustment module refers to a module that can adjust the optical power captured by the optical trap, including but not limited to acousto-optic modulators and electro-optic modulators.

[0016] II. A method for calibrating the displacement of microspheres in an optical trap using absolute gravitational acceleration:

[0017] The method includes the following steps:

[0018] Step 1): The microsphere is stably captured by the light trap in the vacuum cavity. In the stable capture state, the displacement detection module receives the light field signal of the light trap captured by the light after interacting with the microsphere and exiting the vacuum cavity, and the signal processing module receives and records it.

[0019] Step 2): Adjust the power of the light captured by the optical trap using the optical power adjustment module until the power of the light captured by the optical trap is zero, i.e., turn off the light capturing by the optical trap. Then, the microsphere falls freely in the vacuum cavity under the influence of gravity, as shown below. Figure 2 As shown;

[0020] Step 3): After the microspheres have been freely falling for a period of time, the optical power adjustment module adjusts the optical trap capture power to reopen the optical trap and capture light. Under the action of the optical trap force generated by the captured light and the damping force of the surrounding gas molecules, the microspheres undergo underdamped oscillating motion, such as... Figure 3 As shown, after undergoing underdamped oscillating motion for a period of time, the energy gained by the microsphere during its fall is completely dissipated by friction with the air in the vacuum chamber, the velocity generated by the falling microsphere returns to zero, and the microsphere returns to the stable capture state in step 1).

[0021] The displacement detection module receives the optical field signal of the light trap captured by the optical trap during the process from the start of the underdamped oscillating motion of the microsphere to its final return to the stable capture state, and the signal processing module receives and records it.

[0022] The falling period is generally in the range of 0.1 microseconds to 1 microsecond.

[0023] Each step 2) and 3) forms a microsphere falling-oscillation cycle.

[0024] Step 4): Repeat the microsphere falling-oscillation cycle process formed in steps 2) and 3). The signal processing module processes the received optical field signal of the optical trap captured light as the displacement detection signal of all microsphere falling-oscillation cycles, eliminates the influence of microsphere Brownian motion and detection noise, and calculates the optical trap parameters of the microsphere displacement detection system composed of optical trap captured light and microsphere.

[0025] Step 5): Based on the local gravitational acceleration and the optical trap parameters calculated in Step 4), process them to obtain the theoretical oscillation displacement curve of the microsphere, and calibrate it one-to-one with the corresponding displacement detection signal to achieve calibration of the microsphere displacement detection system.

[0026] By utilizing the results of the one-to-one calibration of the theoretical oscillation displacement curve and the displacement detection signal, the real-time displacement detection signal is processed under the test condition to obtain the corresponding microsphere displacement, thus realizing the detection of the microsphere displacement under the test condition.

[0027] This invention controls the microsphere to fall freely and undergo underdamped oscillating motion, and performs measurement and calibration during this process. This allows the results to be traced back to the accurate gravitational acceleration, obtaining precise calibration results. This avoids the inaccuracy problem caused by measuring displacement by applying an electric field with a charged object in the prior art (which is due to the difficulty in accurately measuring the electric field and the influence of the microsphere's gravity).

[0028] The vacuum chamber contains rarefied air, which generates frictional force on the microspheres.

[0029] In step 4), the signal processing module performs multi-cycle averaging and filtering on the displacement detection signals of all microspheres during the falling-oscillation cycle, and selects all good signals to eliminate the influence of microsphere Brownian motion and detection noise.

[0030] The optical trap parameters include the resonant frequency of the microsphere displacement detection system and the damping coefficient of the gas molecules surrounding the microsphere.

[0031] In step 4), the signal processing module fits the processed microsphere oscillation signal and calculates the optical trap parameters.

[0032] In step 5), a theoretical oscillation displacement curve model of the microsphere is established by combining the local gravitational acceleration and the optical trap parameters (i.e., the optical trap resonant frequency and the damping coefficient of the surrounding air molecules), so that the displacement detection signal of the microsphere at each moment corresponds one-to-one with the theoretical oscillation displacement curve of the theoretical oscillation displacement curve model, thereby realizing the nonlinear calibration of the microsphere displacement detection system.

[0033] The theoretical oscillation displacement curve is a curve with time on the horizontal axis and displacement of the microsphere on the vertical axis.

[0034] The calibration of the detection system in steps 1) to 4) uses the local gravitational acceleration as the absolute reference. At the same time, all other calibration parameters are accurately obtained by fitting the detection signal in step 3), which makes the calibration of the detection system traceable and highly reliable.

[0035] In steps 1) to 4), the calibration of the detection system in this invention can be achieved outside of a conventional optical trap system by simply setting up an optical power adjustment module, which avoids setting up a complex calibration device, reduces the system size, and lowers the system complexity and debugging difficulty.

[0036] The device and method of the present invention modulate the light captured by the optical trap after the microspheres are stably captured by the optical trap.

[0037] This invention first turns off the trapping light, allowing the microsphere to fall freely. After the microsphere has fallen a certain distance, the trapping light is turned back on, re-tracing the microsphere. The microsphere undergoes underdamped oscillatory motion due to the optical trapping force and the damping force of surrounding air molecules. After a period of time, all the energy gained by the microsphere during its fall is dissipated, and the microsphere returns to a stable trapping state. At this point, the trapping light is turned off again, causing the microsphere to continuously repeat this fall-oscillation cycle. The oscillation signal of the microsphere in each cycle is detected and recorded by the optical trap detection system. The obtained oscillation signal is processed using signal processing techniques to remove the influence of Brownian motion and detection noise. Finally, using the local gravitational acceleration as the absolute standard, a theoretical oscillation curve is calculated. The optical trap detection system is calibrated by comparing the theoretical oscillation curve with the detected oscillation signal.

[0038] This invention is the first to propose a method for calibrating an optical trap detection system using freely falling microspheres. By introducing gravitational acceleration as the absolute reference for calibration, the reliability and traceability of the optical trap detection system are greatly enhanced, and it can also calibrate nonlinear detection systems. Furthermore, this device and method avoid the need for complex calibration devices for the detection system, significantly reducing system complexity and debugging difficulty, and thus possessing practical application value.

[0039] The beneficial effects of this invention are:

[0040] This invention uses gravitational acceleration as an absolute reference to achieve nonlinear calibration of the optical trap detection system, thus ensuring calibration traceability and improving calibration reliability. Furthermore, this device and method eliminate the need for complex calibration equipment, reducing system complexity and debugging difficulty, and enhancing system robustness.

[0041] Therefore, this invention has practical application value, can improve the detection accuracy and feasibility of the detection system in the optical trap, and reduce the complexity of the optical trap system. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the component structure of this device;

[0043] Figure 2 This is a schematic diagram of the component structure in step 2) of Embodiment 1;

[0044] Figure 3 This is a schematic diagram of the component structure in step 3) of Example 1.

[0045] Figures 1-3 In the system, 1. Light trap to capture light, 2. Lens, 3. Lens, 4. Optical power adjustment module, 5. Vacuum cavity, 6. Microsphere, 7. Displacement detection module, 8. Signal processing module, and 9. Light source. Figures 1-3 The dimensions of each component do not represent the actual dimensions of the components. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] like Figure 1 As shown, the specific implementation includes a vacuum cavity 5, two lenses 2 and 3, a microsphere 6, a displacement detection module 7, a light source 9, and a light power adjustment module 4. The two lenses 2 and 3 and the microsphere 6 are arranged inside the vacuum cavity 5, and the displacement detection module 7, the light source 9, and the light power adjustment module 4 are arranged outside the vacuum cavity 5. The light source 9 emits light trapping light 1, which is then regulated by the light power adjustment module 4 and incident on a lens 2 inside the vacuum cavity 5, converging onto the microsphere 6 and acting on it. After acting on the microsphere 6, the light trapping light 1 passes through another lens 3 inside the vacuum cavity 5 and exits from the vacuum cavity 5 to the displacement detection module 7, where it is received.

[0048] The specific implementation also includes a signal processing module 8, a displacement detection module 7, and a signal processing module 8 electrically connected to the displacement detection module 7. The displacement detection module 7 receives the light field signal of the light trap captured by the light 1 after interacting with the microsphere 6 and exiting the vacuum cavity 5. The signal processing module 8 is connected to the displacement detection module 7, receives, records, and processes the signal detected by the displacement detection module 7.

[0049] The light trap 1 captures light including, but not limited to, laser light, and the light source 9 includes, but is not limited to, a laser light source. The optical axis of the light trap 1 is not limited to, the horizontal direction, and the focal point of the light trap 1, which is converged by the first lens 2, is located inside the vacuum cavity 5.

[0050] Lenses 2 and 3 are placed in vacuum chamber 5, including but not limited to spherical lenses, achromatic lenses, and aspherical lenses, and the materials include but are not limited to fused silica glass.

[0051] The optical power adjustment module 4 refers to a module that can adjust the power of the light 1 captured by the optical trap, including but not limited to an acousto-optic modulator and an electro-optic modulator.

[0052] The shape of the microsphere 6 includes, but is not limited to, spherical, rod-shaped and dumbbell-shaped, and the material includes, but is not limited to, fused silica and polyvinyl chloride. The size of the microsphere 6 in the three spatial dimensions is between 100 nanometers and 100 micrometers, and it is captured by the light trap 1.

[0053] Specific embodiments of the present invention are as follows:

[0054] Step 1):

[0055] like Figure 1 As shown, the light captured by the optical trap is focused within the vacuum cavity to form an optical trap, and the microsphere is stably captured within the optical trap. The gas pressure within the vacuum cavity is reduced to decrease the damping effect of gas molecules surrounding the microsphere.

[0056] The captured microspheres are spherical in shape, made of silica microspheres, with a diameter of 10 micrometers, and the air pressure inside the vacuum chamber is 5 millibars.

[0057] Step 2):

[0058] like Figure 2 As shown, adjust the optical power adjustment module to turn off the light trap. At this time, the microsphere falls freely in the vacuum cavity under the action of gravity.

[0059] The damping coefficient of the air molecules surrounding the microsphere is Γ0, the vertical displacement of the microsphere is y, the time elapsed is t, and the acceleration due to gravity is g. Then the equation of motion of the microsphere is:

[0060]

[0061] The initial velocity of the microsphere is v0, and its initial position in the vertical direction is y0. Solve the equation of motion of the microsphere to obtain its displacement y in the vertical direction:

[0062]

[0063] Step 3):

[0064] like Figure 3 As shown, adjust the optical power adjustment module to reopen the optical trap and capture light. The resonant frequency of the microsphere in the optical trap is Ω, and the falling distance of the microsphere is c. fall The velocity acquired by the falling microsphere is v fall At this point, the microsphere undergoes underdamped oscillatory motion, and the equation of motion is:

[0065]

[0066]

[0067]

[0068] Where α represents the damping of the underdamped motion, β represents the angular frequency of the underdamped motion, and A represents the amplitude of the underdamped motion. This indicates the phase of underdamped motion.

[0069] After a period of time, the energy gained by the microsphere during its descent is completely dissipated, and the microsphere returns to the stable capture state in step 1). The underdamped oscillatory displacement information of the microsphere is obtained by the displacement detection module detecting the light field signal of the light captured by the optical trap, which is then received and recorded by the signal processing module.

[0070] Step 4):

[0071] Repeating steps 2) and 3) results in the microsphere continuously falling and oscillating in a cycle.

[0072] The signal processing module records the underdamped oscillation signals of each fall-oscillation cycle of the microsphere and performs multi-cycle averaging on all the good underdamped oscillation signals.

[0073] By using multi-cycle averaging, the effects of microsphere Brownian motion and detection noise are eliminated, resulting in an average signal with less noise.

[0074] As can be seen from formula (3), the vibration frequency β and the attenuation coefficient α of the underdamped oscillation signal are independent of other factors. Therefore, by fitting the obtained average motion signal to formula (3), the values ​​of vibration frequency β and attenuation coefficient α are obtained, and the resonant frequency Ω of the optical trap system and the damping coefficient Γ0 of the air molecules around the microsphere are calculated using the fitting results of the two.

[0075] Step 5):

[0076] The specific detection system implemented is a third-order nonlinear detection system, with third-order coefficients a1 and first-order coefficients a2. The known voltage bias of the detection system is V. 偏置 The detection signal is then represented as:

[0077] V(t) = a1y 3 +a2y+V 偏置 (4)

[0078] Where V(t) is the detection signal;

[0079] Finally, using the known falling and oscillation times of the microspheres in each cycle, the time interval of the signal received by the signal processing module, the resonant frequency Ω of the optical trap and the damping coefficient Γ0 of the air molecules around the microspheres, and the local gravitational acceleration, the theoretical displacement corresponding to each time point of the average signal is calculated according to formulas (2) and (3).

[0080] By combining formula (4), the conversion relationship between the detection signal and the theoretical displacement curve is calibrated. Therefore, it can be seen that the present invention can achieve the calibration of the detection system in the optical trap.

[0081] In summary, this invention proposes a device and method for calibrating the displacement of microspheres in an optical trap using absolute gravitational acceleration. By using gravitational acceleration as an absolute reference, nonlinear calibration of the optical trap detection system is achieved, ensuring traceability and improving the reliability of the calibration. Furthermore, this device and method eliminate the need for complex calibration equipment, reducing system complexity and debugging difficulty, and enhancing system robustness.

[0082] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration, characterized in that: The method employs a device for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration. The device includes a vacuum cavity (5), two lenses (2, 3), a microsphere (6), a displacement detection module (7), and a light source (9). The two lenses (2, 3) and the microsphere (6) are arranged inside the vacuum cavity (5), and the displacement detection module (7) and the light source (9) are arranged outside the vacuum cavity (5). It also includes an optical power adjustment module (4) so ​​that the light source (9) emits optical trap capturing light (1). After the optical power of the optical trap capturing light (1) is adjusted by the optical power adjustment module (4), it is incident on a lens (2) inside the vacuum cavity (5) and converges onto the microsphere (6) to act on the microsphere (6). After acting on the microsphere (6), the optical trap capturing light (1) passes through another lens (3) inside the vacuum cavity (5) and is emitted from the vacuum cavity (5) to the displacement detection module (7), where it is received. The method includes the following steps: Step 1): The microsphere (6) is stably captured by the light trap (1) in the vacuum cavity (5). In the stable capture state, the displacement detection module (7) receives the light field signal of the light trap captured by the light (1) after interacting with the microsphere (6) and exiting the vacuum cavity (5), and the signal processing module (8) receives and records it. Step 2): Adjust the power of the light trap (1) by using the light power adjustment module (4) to make the light power of the light trap (1) zero, and then the microsphere (6) falls freely in the vacuum cavity (5) under the action of gravity; Step 3): After the microsphere (6) falls freely for a period of time, the power of the light trap capturing light (1) is adjusted by the light power adjustment module (4) and the light trap capturing light (1) is turned on again. Under the action of the light trap force generated by the light trap capturing light (1) and the damping force of the surrounding gas molecules, the microsphere (6) undergoes underdamped oscillating motion. After undergoing underdamped oscillating motion for a period of time, the microsphere (6) returns to the stable capture state in step 1). The displacement detection module (7) receives the light field signal of the light trap capture light (1) during the process from the microsphere (6) starting to perform underdamped oscillating motion to finally returning to the stable capture state, and the signal processing module (8) receives and records it. Step 4): Repeat the microsphere falling-oscillation cycle process formed in steps 2) and 3) continuously. The signal processing module (8) processes the light field signal of the received light trap capture light (1) as the displacement detection signal of all microsphere falling-oscillation cycles, eliminates the influence of microsphere Brownian motion and detection noise, and calculates the light trap parameters of the microsphere displacement detection system composed of light trap capture light (1) and microsphere (6). Step 5): Based on the local gravitational acceleration and the optical trap parameters calculated in Step 4), process them to obtain the theoretical oscillation displacement curve of the microsphere (6), and calibrate it one by one with the corresponding displacement detection signal to realize the calibration of the microsphere displacement detection system.

2. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: In step 4), the signal processing module (8) performs multi-cycle averaging and filtering on the displacement detection signals of all microspheres during the falling-oscillation cycle process, and selects all good signals to eliminate the influence of microsphere Brownian motion and detection noise.

3. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: The optical trap parameters include the resonant frequency of the microsphere displacement detection system and the damping coefficient of the gas molecules surrounding the microsphere (6) on the microsphere (6).

4. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: In step 4), the signal processing module (8) fits the processed microsphere oscillation signal and calculates the optical trap parameters.

5. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: In step 5), a theoretical oscillation displacement curve model of the microsphere is established by combining the local gravitational acceleration and the optical trap parameters, so that the displacement detection signal of the microsphere at each moment corresponds one-to-one with the theoretical oscillation displacement curve of the theoretical oscillation displacement curve model, thereby realizing the nonlinear calibration of the microsphere displacement detection system.

6. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: It also includes a signal processing module (8), a displacement detection module (7) and a signal processing module (8) electrically connected. The displacement detection module (7) receives the light field signal of the light trap captured by the light (1) after interacting with the microsphere (6) and exiting the vacuum cavity (5).

7. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: The lenses (2, 3) include, but are not limited to, spherical lenses, achromatic lenses, and aspherical lenses.

8. The method for calibrating the displacement of a microsphere in an optical trap using absolute gravitational acceleration according to claim 1, characterized in that: The optical power adjustment module (4) refers to a module that can adjust the power of the light (1) captured by the optical trap, including but not limited to an acousto-optic modulator and an electro-optic modulator.

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