CN113358222B - High-precision locking ring-down device and measuring method - Google Patents
High-precision locking ring-down device and measuring method Download PDFInfo
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- 239000000919 ceramic Substances 0.000 claims abstract description 47
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- 230000003287 optical effect Effects 0.000 claims description 10
- 230000008878 coupling Effects 0.000 claims description 8
- 238000010168 coupling process Methods 0.000 claims description 8
- 238000005859 coupling reaction Methods 0.000 claims description 8
- 229910001374 Invar Inorganic materials 0.000 claims description 7
- 239000013307 optical fiber Substances 0.000 claims description 6
- 238000000605 extraction Methods 0.000 claims description 5
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- 230000009471 action Effects 0.000 claims description 3
- 229910045601 alloy Inorganic materials 0.000 claims description 3
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- 239000013078 crystal Substances 0.000 claims description 3
- 230000005684 electric field Effects 0.000 claims description 3
- 238000000691 measurement method Methods 0.000 claims description 3
- 239000010935 stainless steel Substances 0.000 claims description 3
- 229910001220 stainless steel Inorganic materials 0.000 claims description 3
- 230000000694 effects Effects 0.000 description 7
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- ZCYVEMRRCGMTRW-UHFFFAOYSA-N 7553-56-2 Chemical compound [I] ZCYVEMRRCGMTRW-UHFFFAOYSA-N 0.000 description 2
- 238000000180 cavity ring-down spectroscopy Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000004069 differentiation Effects 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- CPBQJMYROZQQJC-UHFFFAOYSA-N helium neon Chemical compound [He].[Ne] CPBQJMYROZQQJC-UHFFFAOYSA-N 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/02—Details
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/12—Generating the spectrum; Monochromators
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
Abstract
The invention relates to a high-precision locked ring-down device, comprising: the microwave phase-locked laser device comprises a frequency-stabilized laser, an electro-optic modulator, a mode matching light path and a ring-down cavity, wherein the electro-optic modulator is positioned between the frequency-stabilized laser and the mode matching light path, a microwave signal source provides a modulation signal to the electro-optic modulator, and phase-modulated laser is coupled into the ring-down cavity through the mode matching light path; the ring-down cavity comprises a first end and a second end, and light transmission ports are formed in the first end and the second end; a reflector is arranged at a position with a preset distance outside the first end, PZT piezoelectric ceramics are arranged on the second end, and the distance between the first end and the second end is changed by the PZT piezoelectric ceramics; and obtaining an error signal from the comparison of the reference frequencies of the light intensity signals after the light intensity signals of the ring-down cavity exit the cavity, and connecting the error signal to a PID controller, wherein the PID controller controls a driver of the PZT piezoelectric ceramics, and the driver controls the PZT piezoelectric ceramics to adjust the cavity length.
Description
Technical Field
The invention belongs to the field of measurement, and particularly relates to a high-precision locking ring-down device and a measurement method.
Background
The cavity ring-down spectroscopy technology has higher sensitivity and accuracy in the aspect of measuring the concentration of trace gas, but the high-performance measurement of the cavity ring-down spectroscopy technology is closely related to the stability of the cavity length of the ring-down cavity, and the cavity length cannot be changed for a long time in an ideal state.
At present, most of optical cavity ring-down uses the same lock cavity principle, but has the problems of complex device, difficult operation and the like, and the locking effect of some devices is lower than the frequency stability of a laser by several orders of magnitude, which has relatively great inaccuracy on the measurement of trace gas.
Disclosure of Invention
In order to overcome the defects of the prior art and achieve the purpose, the invention provides a high-precision locking ring-down cavity device and a high-precision locking ring-down cavity method, which can automatically recover a locking state under certain external interference, can realize automatic long-time cavity length locking, simplifies the prior locking device, and ensures that the uncertainty of the locking effect is basically consistent with the uncertainty of a laser.
Furthermore, parameters such as the modulation signal of the EOM and the gain of the PID private server system are changed by finely adjusting the modulation depth of the microwave signal source, so that the amplitude of the locked modulation signal is minimum, and the locking effect is optimal.
The invention provides a high-precision locked ring-down device, which comprises: the device comprises a frequency stabilized laser, an electro-optic modulator, a mode matching light path and a ring-down cavity, wherein the electro-optic modulator is positioned between the frequency stabilized laser and the mode matching light path, a microwave signal source provides a modulation signal to the electro-optic modulator, and laser after phase modulation is coupled into the ring-down cavity through the mode matching light path; the ring-down cavity comprises a first end and a second end, and light transmission ports are formed in the first end and the second end; a reflector is arranged at a preset distance outside the first end, PZT piezoelectric ceramics are arranged on the second end, and the distance between the first end and the second end is changed by the PZT piezoelectric ceramics; and obtaining an error signal from the comparison of the reference frequencies of the light intensity signals after the light intensity signals of the ring-down cavity exit the cavity, and connecting the error signal to a PID controller, wherein the PID controller controls a driver of the PZT piezoelectric ceramics, and the driver controls the PZT piezoelectric ceramics to adjust the cavity length.
The mode matching optical path comprises a collimator, a coupling lens, an isolator, a first lens, a second lens, a first reflecting mirror and a second reflecting mirror.
The ring-down cavity comprises a two-side plano-concave high reflecting mirror and an adjusting mechanism, wherein the two-side plano-concave high reflecting mirror is arranged on the adjusting mechanism capable of finely adjusting the angle.
The adjusting mechanism is fixed on a right-angle plate of invar steel, the adjusting mechanism and the right-angle plate are fixed through four invar alloy rods with the same length, and the middle cavity is a stainless steel pipe.
The light emitted from the ring-down passes through a half-wave plate and a polarization beam splitter prism, and after passing through the polarization beam splitter prism, one beam of light enters the CCD, and the other beam of light enters the error extraction module through a detector.
Wherein further comprising a function generator connected to the PZT piezoelectric ceramic.
A measurement method employing the high-precision locked ring-down apparatus as described above, comprising:
the method comprises the following steps: the electro-optical modulator is connected to a light path, and a sine modulation signal is set to the electro-optical modulator through a microwave signal source;
step two: finely adjusting the angle of the reflector and the position of the coupling mirror, and eliminating other redundant peaks to maximize the amplitude of the carrier wave and the sideband;
step three: the positive modulation sideband of frequency is taken as a locked transmission peak, a function generator is used for generating a triangular wave signal, the signal drives the fast moving cavity length of the piezoelectric ceramics, and a piezoelectric ceramic voltage driver is adjusted, so that two TEM00 modes are contained in one scanning period;
step four: an error signal output by the phase-locked amplifier is sent to a PID servo controller, a feedback signal is output to a piezoelectric ceramic driver by adjusting PID related gain parameters, an adjusting voltage is output, the position of the piezoelectric ceramic is quickly adjusted, and the cavity length is preliminarily locked;
step five: the modulation depth is obtained by fine tuning the microwave signal source to change the modulation signal of the electro-optical modulator and fine tuning parameters such as the gain of the PID controller, so that the amplitude of the locked modulation signal is minimum.
Compared with the prior art, the invention has the following beneficial effects: the invention simplifies the prior experimental device of the locking ring-down cavity, utilizes the electro-optical modulator to modulate the laser before the laser is called as free space light, reduces the additional use of devices, utilizes the laser modulation sideband instead of directly using the original laser frequency, and enhances the accuracy and the reliability of locking.
The invention can quickly restore the cavity length to the state matched with the modulation sideband frequency when the system receives external non-strong interference, and the uncertainty of locking and the uncertainty of laser frequency are in the same order of magnitude.
Description of the drawings:
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic diagram of the optical path pattern matching of the present invention;
FIG. 3 is a modulated laser produced edge band diagram of the present invention;
FIG. 4 is a graph of error signals during scanning according to the present invention
FIG. 5 is a graph of the slope of the error signal of the present invention;
FIG. 6 is a graph of the error signal deviation after locking of the present invention;
FIG. 7 is a graph of the deviation of the driving adjustment voltage signal of the piezoelectric ceramic of the present invention.
Detailed Description
To facilitate an understanding of the present invention, embodiments of the present invention will be described below with reference to the accompanying drawings, and it will be understood by those skilled in the art that the following descriptions are provided only for the purpose of illustrating the present invention and are not intended to specifically limit the scope thereof.
The apparatus of the present invention comprises: the optical path part mainly comprises a frequency stabilized laser 1, an electro-optical modulator (EOM), a mode matching optical path, a ring-down cavity and the like; the power supply comprises an electrical part, a power supply part and a control part, wherein the electrical part mainly comprises a microwave signal source, a function generator, a detector, a PID (proportion integration differentiation) controller, a phase-locked amplifier and piezoelectric ceramic PZT (piezoelectric ceramic); the device is not limited to these two parts, and the division of the two parts is only for the convenience of simple and general understanding of the device, and is not intended as a specific limitation on the structure. The structure of the device is further described below
The frequency stabilized laser 1 has stable laser frequency, preferably, the frequency stabilized laser 1 is an iodine frequency stabilized helium-neon laser, laser emitted by the frequency stabilized laser 1 is incident into an optical fiber, and the laser is transmitted in the optical fiber; the electro-optical modulator 2 is connected to the middle of the optical fiber, and sets parameters Freq, Mod Rate and Mod Deep through a microwave signal source 13 to modulate signals for the electro-optical modulator; under the action of an external electric field provided by a microwave signal source 13, the electro-optic crystal in the electro-optic modulator 2 changes the refractive index distribution in all directions, and positive and negative first-order modulation sidebands are generated on two sides of a carrier.
The laser light emitted from the electro-optical modulator 2 is incident on a mode matching optical path including a collimator 3, a coupling lens 4, an isolator 5, a first lens L1, a second lens L2, a first mirror 6, and a second mirror 7. The light emitted from the collimator 3 enters the coupling lens 4, the isolator 5, the first lens L1, the second lens L2, the first mirror 6, and the second mirror 7 in this order, and the laser light reflected by the second mirror 7 enters the ring-down cavity 8. The angles of the first reflector 6 and the second reflector 7 and the position of the coupling lens 4 are finely adjusted in the mode matching light path, other redundant peaks are eliminated, the amplitude of the carrier and the amplitude of the sideband are maximized, one modulation sideband is used as a locked transmission peak, the mode matching light path mainly couples more light energy into the cavity, and if the mode matching efficiency is not high, a high-order mode appears to influence the accuracy of the device.
The ring-down cavity 8 is preferably an F-P cavity, which may preferably be formed using a vacuum tube and two-sided plano-concave mirrors: four 70cm long invar steel bars (coefficient of thermal expansion) for vacuum tube<1×10 7 V deg.C) to reduce the effect of thermal expansion on the length of the cavity, with the concave surface of the planoconvex mirror facing inwards, the radius of curvature of 1m, and the reflectivity of 95%. The ring-down cavity 8 includes a first end and a second end, and both the first end and the second end are provided with a light transmission port. The ring-down cavity 8 is connected to a pressure gauge 14, and the pressure in the ring-down cavity 14 is measured by the pressure gauge 14. A third mirror is disposed at a predetermined distance outside the first end, a PZT piezoelectric ceramic 9 is disposed on the second end,and two ends of the ring-down cavity are provided with concave reflectors. Preferably, the ring down cavity comprises a two-sided plano-concave high reflecting mirror and an adjusting mechanism, wherein the two-sided plano-concave high reflecting mirror is arranged on the adjusting mechanism capable of finely adjusting the angle. The adjusting mechanism is fixed on a right-angle plate of invar steel, the adjusting mechanism and the right-angle plate are fixed through four invar alloy rods with the same length, and the middle cavity is a stainless steel pipe.
The cavity length of the ring-down optical cavity 8 is locked by comparing the frequency of a stable reference frequency source with a resonant frequency of an F-P cavity, emergent light from a second end of the ring-down optical cavity 8 is reflected to a half wave plate through a third reflector, and after passing through a polarization prism 10, one beam of light enters a CCD (charge coupled device), the other beam of light enters an error extraction module through a detector 11, preferably, the error extraction module is a phase-locked amplifier 12, an error signal with frequency deviation is obtained through extraction of the phase-locked amplifier 12, then the error signal is input to a PID (proportion integration differentiation) controller 16, an adjusting signal is output to drive the piezoelectric ceramic to move, the distance between the first end and the second end can be changed by the PZT piezoelectric ceramic, and the cavity length is returned to the cavity length corresponding to the reference frequency, so that the purpose of locking the cavity length is achieved.
The function generator 15 is connected to the PZT piezoelectric ceramics 9, preferably, the function generator 15 generates a triangular wave signal with constant frequency and amplitude, the signal is amplified by a high-voltage amplifier HV on a piezoelectric ceramic driver 17 and then applied to the PZT piezoelectric ceramics 9, and the position of the PZT piezoelectric ceramics 9 is quickly adjusted, so that two TEM00 modes are included in one scanning period, and the requirement of primary locking cavity length is met.
The phase-locked amplifier 12 compares the detected and referenced frequency signals, adjusts the phase of the obtained error signal through the phase-locked amplifier, turns the error signal over 90 degrees, then finely adjusts the phase of the error signal to form an approximate straight line, and turns the error signal back 90 degrees, so that the error signal can be output from the X axis or the Y axis; the PID controller 16 is used for receiving an error signal output by the phase-locked amplifier, adjusting PID related gain parameters, and outputting a feedback signal to the piezoelectric ceramic driver 17, wherein the piezoelectric ceramic driver 17 is connected with a digital service meter 18, and the piezoelectric ceramic driver 17 outputs an adjustment voltage to preliminarily lock the cavity length of the ring-down cavity.
The working process of the device comprises the following steps:
the method comprises the following steps: an iodine frequency-stabilized helium-neon reference laser is used as a reference light source, a light beam in a free space is obtained through a collimator 3, and the intensity distribution of the cross section of the light beam is a Gaussian curve and is called as a Gaussian light beam.
Step two: the width of the gaussian beam varies as the beam propagates along the axis and can therefore shrink to a minimum spot at the phase front. In order to inject the beam into a given ring down cavity, mode matching is required. According to a pattern matching formula:
b 1 ＝2πw 1 2 /λ
b 2 ＝2πw 2 2 /λ
in the formula b 1 And b 2 As a confocal parameter f 1 And f 2 Focal length of lens selected for mode matching, 2w 1 Measuring the Beam waist diameter of the Gaussian Beam by a Beam Profiler, determining the Beam waist diameter and the Beam waist position, and then selecting a lens with a proper focal length by calculation to be placed at a distance d from the Beam waist 1 Location.
Step three: the ring-down cavity is fixed, a proper light path propagation path is designed, perfect mode matching is achieved as far as possible, more energy is coupled into the cavity, and the mode matching is shown in detail in fig. 2.
Step four: the electro-optical modulator 2 is connected to an optical path, sinusoidal modulation signals with Freq being 35MHz, Mod Rate being 25kHz and Mod Dep being 5MHz are set to the electro-optical modulator 2 through a microwave signal source, and under the action of an external electric field, the electro-optical crystal in the electro-optical modulator 2 changes the distribution of the refractive index in each direction, and positive and negative first-order modulation sidebands are generated on two sides of a carrier.
Step five: the angle of the mirror and the position of the coupling mirror are finely adjusted to eliminate other unwanted peaks and maximize the amplitude of the carrier and sideband, and the waveform observed from the oscilloscope is shown in fig. 3.
Step six: the positive modulation sideband of frequency is taken as a locked transmission peak, a function generator is used for generating a triangular wave signal with the frequency of 3Hz and the amplitude of 0.3V, the signal is amplified by a high-voltage amplifier HV on a piezoelectric ceramic driver and then is applied to piezoelectric ceramic PZT to drive the fast moving cavity length of the piezoelectric ceramic, the piezoelectric ceramic voltage driver is adjusted, two TEM00 modes are included in one scanning period, and an error signal is obtained as shown in figure 4.
Step seven: analysis of the error signal equation reveals that the offset of the error signal from the cavity length is non-linear and the absolute value of the error signal slope at zero is the maximum, from which the slope D of the error signal is found to be 109.36mV/nm, as shown in detail in fig. 5.
Step eight: and adjusting the phase of the obtained error signal through the phase of a phase-locked amplifier to turn the error signal by 90 degrees, then finely adjusting the phase of the error signal to form an approximate straight line, turning the approximate straight line by 90 degrees, and ensuring that the error signal is simply output from an X axis or a Y axis.
Step nine: and an error signal output by the phase-locked amplifier is sent to a PID servo controller, a feedback signal is output to a piezoelectric ceramic driver by adjusting PID related gain parameters, an adjusting voltage is output, the position of the piezoelectric ceramic is quickly adjusted, and the effect of primarily locking the cavity length is achieved. It should be noted that, because the error signal contains high-frequency noise, in order to prevent the high-frequency noise from damaging the piezoelectric ceramic, a 100Hz low-pass filter is added in the feedback loop to perform low-pass filtering, so as to eliminate the high-frequency noise.
Step ten: the modulation depth is obtained by fine tuning the microwave signal source to change the modulation signal of the EOM and fine tuning parameters such as the gain of the PID controller, so that the amplitude of the locked modulation signal is minimum, and the locking effect is optimal. The error signal output by the lock-in amplifier after locking is shown in fig. 6.
Standard deviation of error signal is sigma error 1.7454mV, obtained from the equation for stability of lumen length and the equation for stability of relative deviation (L is the lumen length, here 730 mm):
step eleven: in order to verify the reliability of the locking result of the ring-down cavity, the output correction voltage signal of the piezoelectric ceramic driver is connected to a digital multimeter, and the locking effect is judged by measuring the output voltage signal of the piezoelectric ceramic driver. Collecting voltage data by Labview software, setting the NPCL of the digital multimeter to be 0.1, collecting time to be 5s, analyzing and processing the obtained voltage data to obtain a deviation value of a voltage signal as shown in figure 7, and calculating to obtain a standard deviation value sigma V 1.8139 mV. The stability formula of the relative deviation brought by the locking cavity length control ring can be used for obtaining the following stability formula:
the above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications based on the principles and design concepts disclosed herein are intended to be included within the scope of the present invention.
It is to be understood that while the present invention has been described in conjunction with the preferred embodiments thereof, it is not intended to limit the invention to those embodiments. It will be apparent to those skilled in the art from this disclosure that many changes and modifications can be made, or equivalents modified, in the embodiments of the invention without departing from the scope of the invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.
Claims (6)
1. A high precision locked ring down device, comprising: frequency stabilized laser, electro-optical modulator, mode matching light path and ring down chamber, its characterized in that: laser emitted by the frequency stabilized laser is incident into an optical fiber, and the laser is transmitted in the optical fiber; the electro-optical modulator is connected to the middle of the optical fiber, and parameters are set through a microwave signal source; under the action of an external electric field provided by a microwave signal source, the refractive index distribution of an electro-optic crystal in the electro-optic modulator changes in all directions, and positive and negative first-order modulation sidebands are generated on two sides of a carrier; the electro-optic modulator is positioned between the frequency stabilized laser and the mode matching light path, the microwave signal source provides a modulation signal to the electro-optic modulator, and the laser after phase modulation is coupled into the ring-down cavity through the mode matching light path; the ring-down cavity comprises a first end and a second end, and light transmission ports are formed in the first end and the second end; a reflector is arranged at a position with a preset distance outside the first end, PZT piezoelectric ceramics are arranged on the second end, and the distance between the first end and the second end is changed by the PZT piezoelectric ceramics; obtaining an error signal from comparison of reference frequencies of light intensity signals after the light intensity signals of the ring-down cavity exit, and connecting the error signal to a PID controller, wherein the PID controller controls a driver of the PZT piezoelectric ceramics, and the driver controls the PZT piezoelectric ceramics to adjust the cavity length; the function generator is connected to the PZT piezoelectric ceramics, generates a triangular wave signal with constant frequency and amplitude, amplifies the signal by a high-voltage amplifier HV on a piezoelectric ceramic driver and then applies the amplified signal to the PZT piezoelectric ceramics, and quickly adjusts the position of the PZT piezoelectric ceramics, so that two TEM00 modes are contained in one scanning period, and the length of a locked cavity is achieved.
2. The high precision locked ring down device of claim 1, wherein: the mode matching optical path comprises a collimator, a coupling lens, an isolator, a first lens, a second lens, a first reflecting mirror and a second reflecting mirror.
3. The high accuracy locked ring down device of claim 1, wherein: the ring-down cavity comprises a two-sided plano-concave high reflecting mirror and an adjusting mechanism, wherein the two-sided plano-concave high reflecting mirror is arranged on the adjusting mechanism capable of finely adjusting the angle.
4. The high precision locked ring down device of claim 3, wherein: the adjusting mechanism is fixed on a right-angle plate of invar steel, the adjusting mechanism and the right-angle plate are fixed through four invar alloy rods with the same length, and the middle cavity is a stainless steel pipe.
5. The high precision locked ring down device of claim 1, wherein: the light emitted from the ring-down passes through a half-wave plate and a polarization beam splitter prism, and after passing through the polarization beam splitter prism, one beam of light enters the CCD, and the other beam of light enters the error extraction module through a detector.
6. A measurement method using the high-precision lock-ring down apparatus as set forth in any one of claims 1 to 5, characterized in that:
the method comprises the following steps: the electro-optical modulator is connected to a light path, and a sine modulation signal is set to the electro-optical modulator through a microwave signal source;
step two: finely adjusting the angle of the reflector and the position of the coupling mirror, and eliminating other redundant peaks to maximize the amplitude of the carrier wave and the sideband;
step three: the positive frequency modulation sideband is used as a locked transmission peak, a function generator is used for generating a triangular wave signal which drives the fast moving cavity length of the piezoelectric ceramic, and a piezoelectric ceramic voltage driver is adjusted, so that two TEM00 modes are contained in one scanning period;
step four: an error signal output by the phase-locked amplifier is sent to a PID servo controller, a feedback signal is output to a piezoelectric ceramic driver by adjusting PID related gain parameters, an adjusting voltage is output, the position of the piezoelectric ceramic is quickly adjusted, and the cavity length is preliminarily locked;
step five: the modulation depth is obtained by fine tuning the microwave signal source to change the modulation signal of the electro-optical modulator and fine tuning parameters such as the gain of the PID controller, so that the amplitude of the locked modulation signal is minimum.
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