CN105758499A - Non-contact type liquid level detection system and method based on ultrasonic pulse echo method - Google Patents
Non-contact type liquid level detection system and method based on ultrasonic pulse echo method Download PDFInfo
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- CN105758499A CN105758499A CN201610239424.2A CN201610239424A CN105758499A CN 105758499 A CN105758499 A CN 105758499A CN 201610239424 A CN201610239424 A CN 201610239424A CN 105758499 A CN105758499 A CN 105758499A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F23/00—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm
- G01F23/22—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water
- G01F23/28—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water by measuring the variations of parameters of electromagnetic or acoustic waves applied directly to the liquid or fluent solid material
- G01F23/296—Acoustic waves
Abstract
The invention discloses a non-contact type liquid level detection system and method based on an ultrasonic pulse echo method. The detection system comprises an ultrasonic transmitting circuit, an ultrasonic receiving circuit, a temperature measuring circuit, a compensating circuit and a single chip control system, wherein the ultrasonic transmitting circuit is used for transmitting an ultrasonic wave with a set frequency; the ultrasonic receiving circuit is used for receiving a first echo generated by an ultrasonic wave on an interface of the inner wall of a container and measured liquid, and a second echo generated by the ultrasonic wave on an interface of the measured liquid and gas above the measured liquid; the temperature measuring circuit is used for measuring a temperature of the measured liquid in real time; the compensating circuit is used for correcting a propagation velocity of the ultrasonic wave in the measured liquid according to the temperature of the measured liquid; the single chip control system is used for calculating time difference between two echoes, and calculating a level of the measured liquid according to the measured time difference and the corrected propagation velocity of the ultrasonic wave in the measured liquid. According to the non-contact type liquid level detection system and method based on the ultrasonic pulse echo method, which are disclosed by the invention, non-contact fixed-point and continuous detection on the closed liquid level can be achieved under the condition of no requirement for protection, compensation is carried out in real time according to changes of a measured environment temperature, and a detection result is more accurate.
Description
Technical field
The present invention relates to ultrasound wave contactless liquid Level Detection field, particularly a kind of non-contact liquid liquid level detection system based on ultrasonic pulse-echo method and method.
Background technology
Accurately measuring of liquid level is to realize important leverage that production process accurately detects and the important means that production process controls in real time.At traditional industry control field, owing to production scale is little, liquid level measurement mainly adopts the Mechanical measurement method such as flanged liquid level transducer and air blowing type and the liquidometer such as microwave type, laser type.But being as production-scale expansion, required storage tank quantity becomes many, then show the drawback of traditional measurement method: flanged liquid level transducer needs insulation, and it is constructed and maintenance workload is bigger；The gas blow pipe of air blowing type needs special order, regularly replace, and air blowing type to consume instrument supply gas, has energy consumption and needs to lay gas source pipe, thus installation and maintenance workload are bigger；And microwave, laser type tank gage can not realize noncontact truly.Gamma ray tank gage can realize tank external pelivimetry liquid level, but affected by environment greatly.Infrared level meter can also realize the requirement of " tank external pelivimetry liquid level ", but requires that measured medium and environment have obvious temperature contrast.
By contrast, ultrasonic liquid level measuring has plurality of advantages: it is capable of fixed point and continuous detecting liquid level, there is wide applicability, and this technology is comparatively safe and price is relatively low, can be selected for multimedium as sound propagating medium, thus outside ultrasound wave, survey tank gage design without to tested container perforate such that it is able to realize real non-cpntact measurement.Ultrasonic continuous measures the method for liquid level to be had a variety of, and such as resonance method, frequency-difference method, ultrasonic attenuation method etc., wherein resonance method detection liquid level is subject to the restriction of some actual conditionses, it is necessary to set up standing wave relation with liquid level, and it belongs to a kind of contact measurement method；Frequency-difference method needs frequency modulator to produce modulating frequency；Damped method need to measure hyperacoustic attenuation.Prior art not yet there is using ultrasound pulse echo method carry out the relevant record of liquid level detection.
Summary of the invention
It is an object of the invention to provide a kind of non-contact liquid liquid level detection system based on ultrasonic pulse-echo method and method.
The technical scheme realizing the object of the invention is: a kind of non-contact liquid liquid level detection system based on ultrasonic pulse-echo method, including:
Ultrasonic emitting circuit, for launching the ultrasound wave of setpoint frequency；
Ultrasound wave receives circuit, for receiving the first echo that ultrasound wave produces at container inner wall and fluid to be measured separating surface, and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface；
Temperature measuring circuit, for the real time measure fluid to be measured temperature；
Compensate circuit, for ultrasound wave spread speed in fluid to be measured being corrected according to fluid to be measured temperature；
Single-chip computer control system, is used for driving ultrasonic emitting circuit transmission ultrasound wave, and calculates the time difference between two echoes, calculates the liquid level of fluid to be measured according to the spread speed after the time difference measured and correction.
The detection method of a kind of non-contact liquid liquid level detection system based on ultrasonic pulse-echo method, comprises the following steps:
Step 1, ultrasonic emitting circuit launch ultrasound wave by ultrasound probe；
Step 2, utilize ultrasound wave to receive circuit to receive the first echo that ultrasound wave produces and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface at container inner wall and fluid to be measured separating surface；
Step 3, the time difference measured between current fluid to be measured temperature and the first echo and the second echo；
Step 4, calculating ultrasound wave spread speed in fluid to be measured, and according to the fluid to be measured temperature recorded in real time, spread speed is corrected；
Step 5, it is that spread speed after time difference and correction determines the liquid level of fluid to be measured according to recording.
Compared with prior art, its remarkable result is the present invention: (1) present invention can realize noncontact fixed point and the closed liquid level of continuous detecting when protecting；(2) the detection system of the present invention and detection method can select gas, liquid or solid as propagation medium, have the bigger suitability；(3) present invention according to the change measuring ambient temperature, can compensate, have higher detection accuracy in real time when measuring liquid level；(4) present invention adopts " Signal separator that time delay receives " technology, effectively inhibits the interference of noise；(5) present invention I&M aspect in actual applications has very big application, more efficient and economical.
Accompanying drawing explanation
Fig. 1 is present invention measuring principle figure in the application.
Fig. 2 is the present invention non-contact liquid liquid level detection system master-plan block diagram based on ultrasonic pulse-echo method.
Fig. 3 is ultrasonic emitting schematic block circuit diagram.
Fig. 4 is that ultrasound wave receives circuit structure block diagram.
Fig. 5 is based on the non-contact liquid liquid level detection system workflow diagram of ultrasound method.
Detailed description of the invention
In conjunction with Fig. 1, Fig. 2, a kind of non-contact liquid liquid level detection system based on ultrasonic pulse-echo method of the present invention, including:
Ultrasonic emitting circuit, for launching the ultrasound wave of setpoint frequency；
Ultrasound wave receives circuit, for receiving the first echo that ultrasound wave produces at container inner wall and fluid to be measured separating surface, and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface；
Temperature measuring circuit, for the real time measure fluid to be measured temperature；
Compensate circuit, for ultrasound wave spread speed in fluid to be measured being corrected according to fluid to be measured temperature；
Single-chip computer control system, is used for driving ultrasonic emitting circuit transmission ultrasound wave, and calculates the time difference between two echoes, calculates the liquid level of fluid to be measured according to the spread speed after the time difference measured and correction.
Further, as it is shown on figure 3, described ultrasonic emitting circuit includes the master oscillator, shaping circuit, controllable silicon, coupling tuner and the transmitting transducer that are sequentially connected with；Master oscillator is used for producing single pulse signal, shaping circuit is to single pulse signal filter shape, single pulse signal after shaping controls silicon controlled and is turned on and off, and coupling tuner is for controlling to launch the concussion time of ultrasonic pulse, and transmitting transducer is used for launching ultrasound wave.
The ultrasonic longitudinal wave that ultrasound wave is 2.5MHZ frequency of described ultrasonic emitting circuit transmission.
Further, as shown in Figure 4, described ultrasound wave reception circuit includes receiving transducer, pre-amplification circuit, voltage comparator circuit, on-off circuit, high-frequency amplifier circuit, suppression circuit and scanning circuit；
Receive transducer by the echo-signal that receives respectively through pre-amplification circuit and voltage comparator circuit, voltage comparator circuit is to echo-signal shaping, filtering noise, controlled the unlatching/closedown of pre-amplification circuit by on-off circuit simultaneously, echo-signal is carried out impedance matching by pre-amplification circuit and power amplification processes, through high-frequency amplifier circuit processing and amplifying, then through suppression circuit, it is suppressed that circuit determines whether it has received echo-signal by the comparison threshold set；Scanning circuit is for controlling whether suppression circuit receives echo-signal.
Above-mentioned transmitting transducer and reception transducer share a ultrasound probe, and described ultrasound probe is piezoelectric ceramics monocrystalline ultrasonic longitudinal wave normal probe.
Further, temperature measuring circuit includes temperature transmission circuit and temperature collection circuit, and temperature speed changing circuit for being converted to the magnitude of voltage of correspondence by temperature of liquid, and temperature collection circuit is for being converted to celsius temperature scale by magnitude of voltage.
Further, liquid level detection system also includes display unit, for showing the liquid level of fluid to be measured.
Further, detection system also includes communication module, is used for and outside real-time Communication for Power.
The present invention also provides for the detection method of a kind of non-contact liquid liquid level detection system based on above-mentioned ultrasonic pulse-echo method, comprises the following steps:
Step 1, ultrasonic emitting circuit launch ultrasound wave by ultrasound probe；
Step 2, utilize ultrasound wave to receive circuit to receive the first echo that ultrasound wave produces and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface at container inner wall and fluid to be measured separating surface；
Step 3, the time difference measured between current fluid to be measured temperature and the first echo and the second echo；
Step 4, calculating ultrasound wave spread speed in fluid to be measured, and according to the fluid to be measured temperature recorded in real time, spread speed is corrected；
Step 5, it is that spread speed after time difference and correction determines the liquid level of fluid to be measured according to recording.
Wherein, the defining method of ultrasonic frequency is:
Area is the transmitting transducer crystal of S, and when launching, with frequency f, the sound wave that wavelength is λ, the gain of its directivity is:
And hyperacoustic absorption value is:
α=c1f+c2f
Wherein, c1For ultrasonic scatterer attenuation quotient；c2For ultrasonic absorption attenuation quotient；
If transmitting transducer TmSending power is PT, receive transducer RmReceiving power is PR, the coverage between two transducers is d, then the equation of sonar transmission information energy has:
By c1'=c1V, c2'=c2v2Substitution above formula obtains:
The maximum condition of sensitivity be when wavelength meet above-listed derivative be 0 time, (-λ2+c1′dλ+2dc′2) zero should be equal to, then obtain optimal wavelength:
Therefore, when absorption value is α, optimal wavelength λ0Tried to achieve by above formula, then optimum frequency can be tried to achieve by following formula:
In formula, α1=c1F, α2=c2f2, takeNapier/rice second/kilohertz,Napier/rice second2/ kilohertz2。
From the foregoing, it will be observed that hyperacoustic optimum frequency is relevant with transmitting transducer and the coverage d received between transducer.
Below in conjunction with specific embodiments and the drawings, the invention will be further described.
Embodiment
First ultrasound probe, ultrasonic propagation form and ultrasonic transducer optimum frequency are selected and determine by the present embodiment.
The selection of ultrasound probe and ultrasonic propagation form: consider engineering practicability, the selection of ultrasonic emitting probe is applied to the needs of special environment, adopts the working method of single internal loopback of popping one's head in.Ultrasound wave mode of propagation in media as well is divided into compressional wave, shear wave and surface wave, the ultrasonic propagation formal character compressional wave of the present embodiment, i.e. ultrasonic longitudinal wave normal probe.
The calculating of ultrasonic transducer optimum frequency: the characteristic according to sound wave, the sound wave directivity that frequency is more low is more poor, but transmission is more remote；Altofrequency directivity is good, but easily decays, therefore by calculating reasonable selection supersonic transducer frequency.According to the specific requirement of experimental subject, container wall thickness is minimum for 9mm, and under room temperature, ultrasound wave spread speed in steel is about 5.85 × 103M/s, the time then receiving the first echo is about 3 μ s, the operation time in conjunction with programmed instruction, the shortest time launching first ultrasonic pulse should be less than 0.5 μ s, in conjunction with above-mentioned ultrasonic transducer frequency approach analysis, launch ultrasonic pulse frequency when should be greater than 2MHz could dead zone-eliminating receive the first echo, the present embodiment selected frequency is 2.5MHZ, wafer diameter is the piezoelectric ceramics monocrystalline ultrasonic longitudinal wave normal probe of 20mm.
Ultrasonic emitting schematic block circuit diagram is as shown in Figure 3.Ultrasonic emitting circuit includes the master oscillator, shaping circuit, controllable silicon, coupling tuner and the transmitting transducer that are sequentially connected with；Master oscillator is used for producing single pulse signal, shaping circuit is to single pulse signal filter shape, single pulse signal after shaping controls silicon controlled and is turned on and off, and coupling tuner is for controlling to launch the concussion time of ultrasonic pulse, and transmitting transducer is used for launching ultrasound wave.
Ultrasound wave receives schematic block circuit diagram as shown in Figure 4.Ultrasound wave receives transducer by the echo-signal that receives respectively through pre-amplification circuit and voltage comparator circuit, and voltage comparator circuit is made up of integrated basic RS filpflop and 4 multilevel comparators, on the one hand to echo-signal shaping, filtering noise；Auto-control switch circuit on the other hand, thus controlling the unlatching/closedown of pre-amplification circuit.Pre-amplification circuit acts primarily as impedance matching and amplifies the effect of input signal power.High-frequency amplifier circuit selects NPN type triode 2N3904, adds buffer stage after 2N3904, it is therefore an objective to reduce interacting and being easy to the coupling of level of front stage circuit.The level of penetrating of rear class amplifying circuit has an adjustable resistor, and the size changing resistance value realizes the AGC control of whole high-frequency amplifier circuit.Suppression circuit is entered back into, it is suppressed that circuit is selected an adjustable resistor set a comparison threshold by the signal of high-frequency amplifier circuit.When the pulse signal received is higher than set thresholding, then it is assumed that had been received by echo-signal；Otherwise, subsequent conditioning circuit is not turned on, not as echo signal processing.Comparison threshold can according to practical situation manual adjustments, to reach optimum reception.Scanning circuit mates work with suppression circuit, the P1.0 pin of Single Chip Microcomputer (SCM) system produce scanning gate level, and this level is used for controlling whether to allow to receive echo-signal.When scanning gate and being high level, it is allowed to receive echo, then decided whether as echo-signal by comparison threshold.Scanning circuit and suppression circuit can effectively suppress noise and improve the signal to noise ratio receiving circuit.Last echo-signal, again through peripheral expansion circuit shaping, level conversion, as the interrupt signal of Single Chip Microcomputer (SCM) system, completes the reception of ultrasonic echo.
The main temperature influence of ultrasound wave spread speed in fluid to be measured, is therefore corrected spread speed, to improve the precision measured.Temperature measuring circuit includes temperature transmission circuit and temperature collection circuit, and the temperature of liquid of 0～60 DEG C is converted to the magnitude of voltage of 0～5V by temperature speed changing circuit, carries out temperature calibration simultaneously.
Single-chip computer control system selects AT89C52 single-chip microcomputer, and its main task is: (1) drives transmitting transducer to send ultrasound wave；(2) control to receive circuit and receive echo, calculate the time difference between two echoes by timing calculator；(3) according to the time measured and the liquid level having related parameter calculating fluid to be measured；(4) display of data is controlled；(5) with host computer communication.
In order to suppress noise, control to receive circuit and receive echo, accurately measure the time difference between two echoes, single-chip computer control system adopts the signal separation techniques that time delay receives, this Technological expression is passing through sweep gate lock and the suppressor pulse of difference pin output respectively, and the unlatching of sweep gate lock is adjusted to and the first echo can be detected.The effect of suppressor pulse is: in the width of suppressor pulse, even if there being echo to arrive, trigger is without upset, it is necessary to wait suppressor pulse could overturn after in the past.So, so that it may the clutter recognition launched near pulse is fallen.The width of suppressor pulse, should be adjusted to and can measure the minimum range that range is determined.
The communication of single-chip computer control system and host computer adopts RS-485 communication mode, and this communication mode adopts balance to send and realizes communicating such that it is able to effectively prevent noise jamming with differential received mode.
As shown in Figure 1, the piezoelectric ceramics monocrystalline ultrasonic longitudinal wave normal probe of frequency to be 2.5MHZ, wafer diameter be 20mm is installed on the underface closing container outer wall, by ultrasonic emitting circuit, time extremely short potential pulse is applied to transmitting transducer, electric pulse can be changed into silent-sound mechanical vibration by transducer, enters liquid with hyperacoustic form through container bottom.Separating surface at container inner wall and fluid to be measured is produced the first echo by ultrasonic propagation process；Propagating after being reflected to liquid upper surface place, the separating surface at fluid to be measured and overhead gas produces the second echo, returns to downwards reception transducer, receives transducer and mechanical vibration are converted to electric oscillation.Meanwhile measuring, by timing circuit, the time t that ultrasound wave is passed by a liquid back and forth, namely the echo time of solid-liquid separating surface and liquid/gas separating surface two echo is poor, and the spread speed that ultrasound wave is in fluid to be measured, then the liquid level of fluid to be measured is:
H=(v t)/2
Wherein, the liquid level of h fluid to be measured；
V ultrasound wave spread speed in fluid to be measured；
Time difference between two echoes of t.
In this kind of detection method, certainty of measurement is limited mainly by the impact of speed v, so needing hyperacoustic spread speed is corrected.Because liquid does not have shearing elasticity, so can only propagate compressional wave in liquid, under linear acoustic condition, liquid medium velocity formula is:
In formula: ksAdiabatic compression coefficient for liquid；For water, when 20 DEG C, ρ0=998kg/m3, ks=45.8*10-11m2/ N, is calculated to obtain c=1480m/s by above formula.
Temperature range 0-60 DEG C of the detected liquid that this method is suitable for, adopts the method compensating circuit to realize velocity correction.For this method level gauging problem, to propagation medium after test in a large number, obtain ultrasonic propagation velocity variation with temperature rule, utilize the output signal of sensing element to carry out speed from dynamic(al) correction.
As it is shown in figure 5, the workflow of the non-contact liquid liquid level detection system of the present invention is: first single-chip computer control system is initialized；Then measure temperature value, then determine ultrasound wave spread speed in a liquid at this temperature；Then launch ultrasound wave, measure the echo time；Calculate the liquid level of fluid to be measured finally according to measurement result and show and communicate.
In sum, the present invention can realize noncontact fixed point and the closed liquid level of continuous detecting when protecting, and the change according to measuring ambient temperature compensates in real time, and testing result is more accurate.
Claims (10)
1. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method, it is characterised in that including:
Ultrasonic emitting circuit, for launching the ultrasound wave of setpoint frequency；
Ultrasound wave receives circuit, for receiving the first echo that ultrasound wave produces at container inner wall and fluid to be measured separating surface, and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface；
Temperature measuring circuit, for the real time measure fluid to be measured temperature；
Compensate circuit, for ultrasound wave spread speed in fluid to be measured being corrected according to fluid to be measured temperature；
Single-chip computer control system, is used for driving ultrasonic emitting circuit transmission ultrasound wave, and calculates the time difference between two echoes, calculates the liquid level of fluid to be measured according to the spread speed after the time difference measured and correction.
2. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1, it is characterised in that ultrasonic emitting circuit includes the master oscillator, shaping circuit, controllable silicon, coupling tuner and the transmitting transducer that are sequentially connected with；Master oscillator is used for producing single pulse signal, shaping circuit is to single pulse signal filter shape, single pulse signal after shaping controls silicon controlled and is turned on and off, and coupling tuner is for controlling to launch the concussion time of ultrasonic pulse, and transmitting transducer is used for launching ultrasound wave.
3. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1 and 2, it is characterised in that the ultrasonic longitudinal wave that ultrasound wave is 2.5MHZ frequency of described ultrasonic emitting circuit transmission.
4. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1, it is characterized in that, ultrasound wave receives circuit and includes receiving transducer, pre-amplification circuit, voltage comparator circuit, on-off circuit, high-frequency amplifier circuit, suppression circuit and scanning circuit；
Receive transducer by the echo-signal that receives respectively through pre-amplification circuit and voltage comparator circuit, voltage comparator circuit is to echo-signal shaping, filtering noise, controlled the unlatching/closedown of pre-amplification circuit by on-off circuit simultaneously, echo-signal is carried out impedance matching by pre-amplification circuit and power amplification processes, through high-frequency amplifier circuit processing and amplifying, then through suppression circuit, it is suppressed that circuit determines whether it has received echo-signal by the comparison threshold set；Scanning circuit is used for controlling whether suppression circuit receives echo-signal.
5. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 4, it is characterized in that, described transmitting transducer and reception transducer share a ultrasound probe, and described ultrasound probe is piezoelectric ceramics monocrystalline ultrasonic longitudinal wave normal probe.
6. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1, it is characterized in that, temperature measuring circuit includes temperature transmission circuit and temperature collection circuit, temperature speed changing circuit for being converted to the magnitude of voltage of correspondence by temperature of liquid, and temperature collection circuit is for being converted to celsius temperature scale by magnitude of voltage.
7. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1, it is characterised in that liquid level detection system also includes display unit, for showing the liquid level of fluid to be measured.
8. the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 1, it is characterised in that detection system also includes communication module, is used for and outside real-time Communication for Power.
9. one kind based on described in claim 1 based on the detection method of the non-contact liquid liquid level detection system of ultrasonic pulse-echo method, it is characterised in that comprise the following steps:
Step 1, ultrasonic emitting circuit launch ultrasound wave by ultrasound probe；
Step 2, utilize ultrasound wave to receive circuit to receive the first echo that ultrasound wave produces and the second echo that ultrasound wave produces at fluid to be measured and overhead gas separating surface at container inner wall and fluid to be measured separating surface；
Step 3, the time difference measured between current fluid to be measured temperature and the first echo and the second echo；
Step 4, calculating ultrasound wave spread speed in fluid to be measured, and according to the fluid to be measured temperature recorded in real time, spread speed is corrected；
Step 5, it is that spread speed after time difference and correction determines the liquid level of fluid to be measured according to recording.
10. the detection method of the non-contact liquid liquid level detection system based on ultrasonic pulse-echo method according to claim 9, it is characterised in that the ultrasonic frequency defining method that described ultrasonic emitting circuit sends is:
Area is the transmitting transducer crystal of S, and when launching, with frequency f, the sound wave that wavelength is λ, the gain of its directivity is:
Hyperacoustic absorption value is:
α=c1f+c2f
Wherein, c1For ultrasonic scatterer attenuation quotient；c2For ultrasonic absorption attenuation quotient.
If transmitting transducer TmSending power is PT, receive transducer RmReceiving power is PR, the coverage between two transducers is d, then the equation of sonar transmission information energy has:
By c1'=c1V, c2'=c2v2Substitution above formula obtains:
The maximum condition of sensitivity be when wavelength meet above-listed derivative be 0 time, (-λ2+c′1dλ+2dc′2) zero should be equal to, then obtain optimal wavelength:
Therefore, when absorption value is α, optimal wavelength λ0Tried to achieve by above formula, then optimum frequency f0For:
In formula, α1=c1F, α2=c2f2。
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