CN111427147B - Method for selecting wavefront corrector according to wavefront Zernike mode - Google Patents
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Abstract
The invention discloses a method for selecting a wavefront corrector according to a wavefront Zernike mode, which is implemented according to the following steps: step 1, a signal laser is used for emitting collimated light beams, the collimated light beams are transmitted through free space atmosphere, a distorted wavefront is detected by a wavefront sensor of a self-adaptive optical system, and a distorted wavefront phase is generated; step 2, expanding the wave front phase according to a Zernike coefficient to obtain a piston term, an inclined component and a high-order component; the Zernike coefficients of the piston terms are 0 and are ignored; solving the independent distortion generated by the inclined component and the high-order component; step 3, judging the influence of the independent distortion of the inclined component and the high-order component on the performance of the optical fiber type mixing coherent detection system to obtain the error rate of the heterodyne detection system; and 4, selecting a proper wavefront corrector according to the error rate.
Description
Technical Field
The invention belongs to the technical field of wireless laser communication, and relates to a method for selecting a wavefront corrector according to a wavefront Zernike mode.
Background
The wireless laser communication is a communication mode that laser is used as a carrier and is transmitted through the atmosphere, after long-distance transmission, the power of signal light received on a photosensitive surface of a photoelectric detector of a receiving end is very weak, and coherent detection can recover information carried by the signal under the condition that the received signal is weak. The optical fiber type frequency mixing coherent detection is limited by the bottleneck of optical fiber coupling, and the coupling efficiency and the frequency mixing efficiency are reduced due to the wave front distortion phase caused by the atmospheric turbulence, so that the performance of the wireless optical communication system is influenced.
For wavefront aberrated phases, Adaptive Optics (AO) techniques are typically used for correction. The active device in the self-adaptive optical system is a wave-front corrector, and it can change the optical path length of every point on the beam cross-section to attain the goal of correcting wave-front distortion phase.
The stroke resolution and the stroke quantity of the wavefront corrector directly determine the wavefront distortion phase correction precision and the wavefront distortion phase correction range. When the correction range of a single wavefront corrector is exceeded, the correction capability of the single wavefront corrector cannot meet the problem of phase distortion of large-amplitude wavefront of light waves under the conditions of strong turbulence, high-power output, large-aperture receiving and the like, and the service life of the wavefront corrector is shortened under the working state of being close to a full stroke for a long time.
Disclosure of Invention
The invention aims to provide a method for selecting a wavefront corrector according to a wavefront Zernike mode, which correctly selects the wavefront corrector through the Zernike mode and corrects an atmospheric distorted wavefront in real time by using the selected wavefront corrector.
The technical scheme adopted by the invention is that the method for selecting the wavefront corrector according to the wavefront Zernike mode is characterized by comprising the following steps:
and 4, selecting a proper wavefront corrector according to the error rate.
The invention is also characterized in that:
the step 1 is implemented according to the following steps:
step 1.1, focusing incident waves on a photosensitive surface of a CCD by a micro-lens array of a wavefront sensor to form a light spot array image;
step 1.2, calculating the offset of the centroid of the light spot according to the difference between the collected light spot array image and the target light spot image of the wavefront sensor; obtaining the offset delta x and delta y of the actual detection point and the target point in the x direction and the y direction;
step 1.3, offset quantity delta x and delta measured according to wave-front sensory is through gx(y)Calculating the wavefront slope by 2 pi delta x (delta y)/lambda f, wherein lambda is the wavelength of the light wave, and f is the focal length of the coupling lens;
step 1.4, converting the wavefront Slope into a wavefront Zernike coefficient through a wavefront reconstruction matrix, wherein the Zernike is Slope and Slope2Zernike, the Zernike is a Zernike coefficient, the Slope is a Slope matrix, and the Slope2Zernike is a conversion matrix generated by the wavefront sensor;
step 1.5, calculating the wavefront Phase according to the wavefront Zernike coefficient, namely
Phase-Zernike 2Phase, where Zernike2Phase is a wavefront reconstruction matrix corresponding to a polynomial of Zernike coefficients.
The step 2 is implemented according to the following steps:
step 2.1, any wavefront phase affected by Kolmogorov atmospheric turbulence can be decomposed into the form of Zernike polynomials, so the wavefront aberration phase can be expressed as
Wherein a isiIs the coefficient of the i-th Zernike polynomial, ZiThe i term Zernike polynomial, phi (x, y) is the wavefront phase;
step 2.2, the proportion of the skew component in the wavefront aberration phase can be expressed as
The proportion of the higher order components can be expressed as
Wherein a isjCoefficients of Zernike polynomials of the j-th term;
step 2.3, the independent distortion produced by the tilt component in the wavefront distortion phase, in terms of orthogonality of the Zernike polynomials, can be expressed as
The independent distortion caused by the higher order components can be expressed as
step 3.1, the complex amplitude of the light field affected by the distorted wavefront phase can be expressed as u0(r,θ)＝A·ejφ(r,θ)Wherein A is the amplitude of the light field, phi (r, theta) is the phase of the distorted wavefront, r represents the radial spatial frequency of the light field, and theta is the angular frequency of the light field;
after the light field passes through the coupling lens, the complex amplitude on the single-mode fiber focal plane is diffracted through the near-field Fraunhofer to obtain the light field of the end face of the single-mode fiber:
wherein
The method is called Fourier Bessel transformation, k is 2 pi/lambda is the spatial angular frequency (wave vector) of light waves, z is the focal length of a coupling lens, and r is the distance from any point in the radial direction of the lens surface to the center of the lens;
step 3.2, solving the light field distribution of the end face of the single-mode fiber:
wherein WmIs the mode field radius of a single mode fiber; the wavefront distortion phase has an effect on the coupling efficiency of the single-mode fiber, which can be expressed as
Wherein denotes a conjugate operation;
3.3, solving the light field value of the signal light through the light field and the coupling efficiency of the end face of the single-mode fiber:
and 3.4, solving the frequency mixing efficiency through the light field value of the signal light and the light field of the local oscillator light:
wherein
ALAmplitude, ω, of the local oscillator lightLIs the central angular frequency of the local oscillator light,
the phase of the local oscillation light; s is the effective area of the detector;
and 3.5, obtaining the power of the I path (or Q path) intermediate frequency current output by the balanced detector by using the frequency mixing efficiency, wherein the power of the intermediate frequency current can be expressed as:
step 3.6, solving the signal-to-noise ratio output by the balance detector
step 3.7, obtaining the bit error rate of the BPSK heterodyne detection system according to the signal-to-noise ratio
Where erfc (·) is a complementary error function.
step 4.1, the independent distortions generated by the different turbulence condition oblique components and the higher order components are different. When D/r0When the Zernike coefficient is 2, the weak turbulence condition is met, and 10000 groups of data generated by the Zernike coefficient are processed by adopting a Monte Carlo methodStatistical averaging, for the slope component, first order example, the statistical average is about 0.96 μm and the bit error rate is about 10-10(ii) a For the higher order components, taking the fifth order astigmatism as an example, the statistical mean value is about 0.22 μm, and the bit error rate is about 10-12(ii) a When D/r0When the average turbulence condition is 10, the statistical average value of the first-order inclined component is about 3.67 μm and the error rate is about 10 by adopting the same method-2(ii) a The statistical average value of the fifth order astigmatism of the higher order components is about 0.83 μm, and the error rate is about 10-10(ii) a When D/r0When the maximum turbulence condition is satisfied at 20, the statistical average value of the first-order inclined component is about 6.44 μm and the error rate is about 10 by the same method-2(ii) a The statistical average of the amounts of astigmatism of the fifth order is about 1.46 μm, and the error rate is about 10-8；
Step 4.2, error rate is 10-9The correction is a critical value as a communication judgment standard, and only the correction is higher than 10-9The amount of distortion of (2): under weak turbulence conditions, neither the tilt component (first order tilt component) nor the higher order component (fifth order astigmatism) need to be corrected; under medium turbulence conditions, the tilt component (first order tilt component) needs to be corrected, while the higher order component (fifth order astigmatism amount) does not need to be corrected, so the deflection mirror is selected for correction; under the condition of strong turbulence, the inclined component (first-order inclined component) and the high-order component (fifth-order astigmatism) need to be corrected, so that the deflection mirror and the deformable mirror are selected to be corrected together.
The invention has the beneficial effects that:
when the free space optical communication system based on the Zernike mode completes wavefront correction, the influence of wavefront distortion phase on the system performance is analyzed according to the Zernike mode, so that a proper wavefront corrector is selected;
when the influence of the inclined component of the wavefront distortion phase on the system error rate is large and the influence of the high-order component on the system error rate is small and negligible, selecting a deflection mirror to correct; and when the inclined component and the high-order component have large influence on the error rate of the system, selecting the deflection mirror and the deformable mirror for common correction. The power of the deformable mirror driver is effectively relieved compared with the power of a single closed loop, the wavefront distortion is weakened, the wavefront corrector is prevented from being in a full-load state for a long time, and the service life of the wavefront corrector is prolonged.
Drawings
FIG. 1 is an atmospheric coherence length r for a method of selecting a wavefront corrector according to a wavefront Zernike mode of the present invention0A relation simulation diagram with a wave front Peak-Valley value (Peak to Valley, PV) and a Root Mean Square value (RMS);
FIG. 2 is an atmospheric coherence length r for a method of selecting a wavefront corrector according to a wavefront Zernike mode of the present invention0A relationship simulation graph proportional to the tilt component;
FIG. 3 is a schematic diagram of a free-space optical communication system for a method of selecting a wavefront corrector in accordance with a wavefront Zernike mode of the present invention;
FIG. 4 is a simulation diagram showing the relationship between wavefront distortion and error rate according to the method for selecting a wavefront corrector according to a wavefront Zernike mode of the present invention;
FIG. 5 is a table of measured wavefront values at different distances for the method of selecting a wavefront corrector according to the wavefront Zernike model of the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a method for selecting a wavefront corrector according to a wavefront Zernike mode, which is implemented according to the following steps:
step 1.1, detecting a distorted wavefront by a wavefront sensor; the method comprises the following steps that a micro-lens array of a wavefront sensor focuses incident waves on a photosensitive surface of a CCD to form a light spot array image;
step 1.2, calculating the offset of the centroid of the light spot according to the difference between the collected light spot array image and the target light spot image of the wavefront sensor; and obtaining the offset deltax and deltay of the actual detection point and the target point in the x direction and the y direction.
Step 1.3, passing g according to the offsets Deltax and Deltay measured by the wavefront sensorx(y)The wavefront slope is calculated as 2 pi Δ x (Δ y)/λ f, where λ is the wavelength of the light and f is the coupling lens focal length.
And step 1.4, converting the wavefront Slope into a wavefront Zernike coefficient through a wavefront reconstruction matrix, wherein the Zernike is Slope and Slope2Zernike, the Zernike is Zernike coefficient, the Slope is Slope matrix, and the Slope2Zernike is a conversion matrix generated by the wavefront sensor.
And step 1.5, calculating a wavefront Phase from the wavefront Zernike coefficients, namely Phase is Zernike and Zernike2Phase, wherein the Zernike2Phase is a wavefront reconstruction matrix and is equivalent to a polynomial corresponding to the Zernike coefficients.
step 2.1, any wavefront phase affected by Kolmogorov atmospheric turbulence can be decomposed into the form of Zernike polynomials, so the wavefront aberration phase can be expressed as
Wherein a isiIs the coefficient of the i-th Zernike polynomial, ZiThe i term Zernike polynomial, phi (x, y) is the wavefront phase;
step 2.2, the proportion of the skew component in the wavefront aberration phase can be expressed as
The proportion of the higher order components can be expressed as
Wherein a isjCoefficients of Zernike polynomials of the j-th term; diagram of the ratio of the atmospheric turbulence to the wavefront distortion phase and the tilt component1. In 2, it can be seen that the coherence length r follows the atmospheric coherence length r0The turbulence intensity is increased, and the wave front peak-valley value and the root mean square value are respectively and gradually increased, which shows that the wave front distortion degree is more serious. But the proportion of the inclined component is still maintained at 70-80%, and the proportion of the high-order component is also kept unchanged; FIG. 5 shows the actual measured tilt component ratios at different distances, i.e., from indoor, 1km, 5km, and 10km, and it can be seen from FIG. 5 that the tilt component ratio is maintained at 70% to 80%, which corresponds to the simulation result of FIG. 2;
step 2.3, the independent distortion produced by the tilt component in the wavefront distortion phase, in terms of orthogonality of the Zernike polynomials, can be expressed as
The independent distortion caused by the higher order components can be expressed as
and 3.1, calculating the influence of the inclined component and the high-order component of the wavefront distortion on the coupling efficiency. The complex amplitude of the light field affected by the distorted wavefront phase can be expressed as u0(r,θ)＝A·ejφ(r,θ)Where A is the amplitude of the light field, φ (r, θ) is the phase of the distorted wavefront, r represents the radial spatial frequency of the light field, and θ is the angular frequency of the light field. After the light field passes through the coupling lens, the complex amplitude on the single-mode fiber focal plane is diffracted through the near-field Fraunhofer to obtain the light field of the end face of the single-mode fiber:
wherein
Called the Fourier Bessel transform, k 2 π/λ is the spatial angular frequency (wavevector) of the light wave, and z isCoupling the focal length of the lens, wherein r is the distance from any radial point on the surface of the lens to the center of the lens;
step 3.2, the optical field distribution of the end face of the single-mode optical fiber is
Wherein WmIs the mode field radius of a single mode fiber; the wavefront distortion phase has an effect on the coupling efficiency of the single-mode fiber, which can be expressed as
Wherein denotes a conjugate operation; in the optical fiber type frequency mixing coherent detection system, the coupled signal light and the local oscillator light are subjected to coherent frequency mixing, so that the independent distortion generated by the inclined component and the independent distortion generated by the high-order component cause the difference of signal light fields in optical heterodyne detection;
3.3, solving the light field value of the signal light through the light field and the coupling efficiency of the end face of the single-mode fiber:
step 3.4, the influence of the tilted component and the higher-order component of the wavefront distortion on the mixing efficiency can be calculated through the formula of the mixing efficiency
To obtain wherein ELIs the optical field of the local oscillation light:
ALamplitude, ω, of the local oscillator lightLIs the central angular frequency of the local oscillator light,
the phase of the local oscillation light; and S is the effective area of the detector. Since the signal light in the coherent detection is influenced by the coupling efficiency, the coupling efficiency caused by the wavefront distortion influences the mixing efficiency;
step 3.5,Since the mixing efficiency is affected by the phase of the wavefront distortion, and thus the power of the I-path (or Q-path) intermediate frequency current output by the balanced detector is affected, the power of the intermediate frequency current can be expressed as
Wherein R is the responsivity of the balanced detector, Z0Is a free space impedance;
step 3.6, on the basis that the wavefront distortion phase influences the power of the intermediate frequency current, the signal-to-noise ratio output by the balance detector can be expressed as
Wherein
Shot noise, Δ f, caused by local oscillator lightIFFor effective noise bandwidth, ε is the quantum efficiency, h is the Planckian constant, and v is the carrier frequency;
step 3.7, in the actual heterodyne detection system, the bit error rate of the heterodyne detection system with the modulation method of BPSK may be expressed as
Where erfc (·) is a complementary error function. The influence of the inclined component and the high-order component of the wavefront distortion phase on the performance of the free space optical communication system is analyzed through the influence of the wavefront distortion phase on the error rate.
step 4.1, the independent distortions generated by the different turbulence condition oblique components and the higher order components are different. According to the relationship simulation diagram of wavefront distortion and error rate in FIG. 4, when D/r is0When the value is 2, the weak turbulence condition is met, 10000 groups of data generated by Zernike coefficients are subjected to statistical averaging by adopting a Monte Carlo method, and for the inclined component, taking the first order as an example, the statistical averaging value is about 0.96 mu m, and the error rate is about 10-10(ii) a For higher order components, toFor example, the fifth order astigmatism has a statistical mean of about 0.22 μm and a bit error rate of about 10-12(ii) a When D/r0When the average turbulence condition is 10, the statistical average value of the first-order inclined component is about 3.67 μm and the error rate is about 10 by adopting the same method-2(ii) a The statistical average value of the fifth order astigmatism of the higher order components is about 0.83 μm, and the error rate is about 10-10(ii) a When D/r0When the maximum turbulence condition is satisfied at 20, the statistical average value of the first-order inclined component is about 6.44 μm and the error rate is about 10 by the same method-2(ii) a The statistical average of the amounts of astigmatism of the fifth order is about 1.46 μm, and the error rate is about 10-8；
Step 4.2, error rate is 10-9The correction is a critical value as a communication judgment standard, and only the correction is higher than 10-9The amount of distortion of (2): under weak turbulence conditions, neither the tilt component (first order tilt component) nor the higher order component (fifth order astigmatism) need to be corrected; under medium turbulence conditions, the tilt component (first order tilt component) needs to be corrected, while the higher order component (fifth order astigmatism amount) does not need to be corrected, so the deflection mirror is selected for correction; under the condition of strong turbulence, the inclined component (first-order inclined component) and the high-order component (fifth-order astigmatism) need to be corrected, so that the deflection mirror and the deformable mirror are selected to be corrected together.
The invention adopts a wave front Zernike mode to analyze the inclined component and the high-order component of the wave front distortion phase, and selects the wave front corrector according to the influence of the inclined component and the high-order component on the system error rate, so as to improve the correction precision and efficiency.
As can be seen from fig. 1: with atmospheric coherence length r0Increased, less turbulent, reduced PV and RMS, and reduced wavefront distortion, indicating that the greater the turbulent, the greater the distortion.
As can be seen in fig. 2: with atmospheric coherence length r0The ratio of the tilt component is kept stable at 70% -80%, which shows that the ratio of the tilt component and the high-order component is hardly affected by the atmospheric turbulence.
As can be seen in fig. 3: the method comprises the steps of using a narrow-linewidth laser as signal light and local oscillator light respectively, using an electro-optic phase modulator to load information source information onto the signal light and access a transmitting optical system to send out the information, transmitting the information to a receiving end through an atmospheric turbulence random channel, and completing recovery of an electric signal by adopting an AO technology, a coherent detection technology and a high-speed digital signal processing technology, wherein the coherent detection is optical fiber type frequency mixing coherent detection.
As can be seen in fig. 4: as the amount of distortion increases, the error rate also increases gradually. The first order tilt component is represented by the boxed line and the fifth order astigmatism component is represented by the triangular line. Under the condition that the distortion is less than 5 mu m, the influence of the first-order inclined component on the error rate is greater than the influence of the fifth-order astigmatism on the error rate; when the distortion is larger than 5 mu m, the influence of the first-order inclined component on the error rate is smaller than the influence of the fifth-order astigmatism on the error rate; when the amount of distortion is equal to 5 μm, the influence of the first order tilt component on the bit error rate is equal to the influence of the fifth order astigmatism component on the bit error rate.
From fig. 5 it can be seen that: in the measured wave front analysis under different distances, the inclination component proportion is basically maintained at 70-80%, which shows that the inclination component proportion is irrelevant to the communication distance of free space optical communication.
Claims (3)
1. A method of selecting a wavefront corrector in accordance with a wavefront Zernike mode, the method comprising the steps of:
step 1, a signal laser is used for emitting collimated light beams, the collimated light beams are transmitted through free space atmosphere, a distorted wavefront is detected by a wavefront sensor of a self-adaptive optical system, and a distorted wavefront phase is generated;
step 1.1, focusing incident waves on a photosensitive surface of a CCD by a micro-lens array of a wavefront sensor to form a light spot array image;
step 1.2, calculating the offset of the centroid of the light spot according to the difference between the collected light spot array image and the target light spot image of the wavefront sensor; obtaining the offset delta x and delta y of the actual detection point and the target point in the x direction and the y direction;
step 1.3, pass g according to offsets Deltax and Deltay measured by wavefront sensorx(y)Calculating the wavefront slope as 2 pi delta x (delta y)/lambda f, wherein lambda is the wavelength of the light wave and f is the focal length of the coupling lens；
Step 1.4, converting the wavefront Slope into a wavefront Zernike coefficient through a conversion matrix generated by the wavefront sensor, wherein the Zernike is Slope and Slope2Zernike, the Zernike is Zernike coefficient, the Slope is Slope matrix, and the Slope2Zernike is the conversion matrix generated by the wavefront sensor;
step 1.5, calculating to obtain a distorted wavefront Phase according to the wavefront Zernike coefficient, namely
Phase ═ Zernike · Zernike2Phase, where Zernike2Phase is the wavefront reconstruction matrix, corresponding to the polynomial corresponding to the Zernike coefficients;
step 2, expanding the distorted wavefront phase according to a Zernike coefficient to obtain a piston term, an inclined component and a high-order component; the Zernike coefficients of the piston terms are 0 and are ignored; solving the independent distortion generated by the inclined component and the high-order component;
step 3, judging the influence of the independent distortion of the inclined component and the high-order component on the performance of the optical fiber type mixing coherent detection system to obtain the error rate of the heterodyne detection system;
step 3.1, the complex amplitude of the light field affected by the distorted wavefront phase can be expressed as u0(r,θ)＝A·ejφ(r,θ)Wherein A is the amplitude of the light field, phi (r, theta) is the phase of the distorted wavefront, r represents the radial spatial frequency of the light field, and theta is the angular frequency of the light field;
after the light field passes through the coupling lens, the complex amplitude on the single-mode fiber focal plane is diffracted through the near-field Fraunhofer to obtain the light field of the end face of the single-mode fiber:
wherein
Called fourier bessel transform, k 2 pi/λ is the spatial angular frequency of the light wave, z is the coupling lens focal length, r is the radial spatial frequency of the optical field;
step 3.2, solving the light field distribution of the end face of the single-mode fiber:
wherein WmIs the mode field radius of a single mode fiber; the distorted wavefront phase affects the coupling efficiency of a single-mode fiber, which can be expressed as
Where denotes the conjugate operation, r is the radial spatial frequency of the light field;
3.3, solving the light field value of the signal light through the light field and the coupling efficiency of the end face of the single-mode fiber:
r is the radial spatial frequency of the light field;
and 3.4, solving the frequency mixing efficiency through the light field value of the signal light and the light field of the local oscillator light:
wherein
ALAmplitude, ω, of the local oscillator lightLIs the central angular frequency of the local oscillator light,
the phase of the local oscillation light; s is the effective area of the detector;
and 3.5, obtaining the power of the intermediate frequency current of the I path or the Q path output by the balanced detector by using the frequency mixing efficiency, wherein the power of the intermediate frequency current can be expressed as:
step 3.6, solving the signal-to-noise ratio output by the balance detector
Wherein
Is shot noise, Δ f, caused by local oscillation lightIFFor effective noise bandwidth, ε is the quantum efficiency, h is the Planckian constant, and v is the carrier frequency;
step 3.7, obtaining the bit error rate of the BPSK heterodyne detection system according to the signal-to-noise ratio
Where erfc (·) is a complementary error function;
and 4, selecting a proper wavefront corrector according to the error rate.
2. A method of selecting a wavefront corrector depending on a wavefront Zernike mode as claimed in claim 1, characterized in that said step 2 is carried out in particular according to the following steps:
step 2.1, any distorted wavefront phase affected by Kolmogorov atmospheric turbulence can be decomposed into the form of Zernike polynomials, so the distorted wavefront phase can be expressed as
Wherein a isiIs the coefficient of the i-th Zernike polynomial, ZiThe i term Zernike polynomial, phi (x, y) is the wavefront phase;
step 2.2, the proportion of the skew component in the distorted wavefront phase can be expressed as
The proportion of the higher order components can be expressed as
Wherein a isiCoefficients of Zernike polynomials of the i-th term;
step 2.3, according to ZerniOrthogonality of the ke polynomials, independent distortion due to the skew component in the phase of the distorted wavefront can be expressed as
The independent distortion caused by the higher order components can be expressed as
3. A method of selecting a wavefront corrector depending on a wavefront Zernike mode as claimed in claim 1, characterized in that said step 4 is carried out in particular according to the following steps:
step 4.1, independent distortion generated by different turbulence condition inclined components and high-order components is different when D/r0When the value is 2, the weak turbulence condition is met, 10000 groups of data generated by Zernike coefficients are subjected to statistical averaging by adopting a Monte Carlo method, and for the inclined component, taking the first order as an example, the statistical averaging value is about 0.96 mu m, and the error rate is about 10-10(ii) a For the higher order components, taking the fifth order astigmatism as an example, the statistical mean value is about 0.22 μm, and the bit error rate is about 10-12(ii) a When D/r0When the average turbulence condition is 10, the statistical average value of the first-order inclined component is about 3.67 μm and the error rate is about 10 by adopting the same method-2(ii) a The statistical average value of the fifth order astigmatism of the higher order components is about 0.83 μm, and the error rate is about 10-10(ii) a When D/r0When the maximum turbulence condition is satisfied at 20, the statistical average value of the first-order inclined component is about 6.44 μm and the error rate is about 10 by the same method-2(ii) a The statistical average of the amounts of astigmatism of the fifth order is about 1.46 μm, and the error rate is about 10-8(ii) a Wherein r is0Representing the atmospheric coherence length, D/r0Indicating the strength of the atmospheric turbulence;
step 4.2, error rate is 10-9The correction is a critical value as a communication judgment standard, and only the correction is higher than 10-9The amount of distortion of (2): under weak turbulence conditions, both the dip component and the higher order components need not be corrected; in medium turbulence conditions, the tilt component needs to be corrected, while highThe order component does not need to be corrected, so that the deflection mirror is selected for correction; under the condition of strong turbulence, the inclined component and the high-order component need to be corrected, so that the deflection mirror and the deformable mirror are selected to be corrected together.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102288305A (en) * | 2011-07-18 | 2011-12-21 | 中国科学院光电技术研究所 | Adaptive optical system wavefront sensor and detection method thereof |
| CN103293663A (en) * | 2013-06-12 | 2013-09-11 | 中国科学院光电技术研究所 | Self-adaptive optical system for controlling multiple wavefront correctors based on voltage decoupling |
| CN104618017A (en) * | 2015-01-21 | 2015-05-13 | 中国科学院上海光学精密机械研究所 | Device and method for improving wavefront quality of atmosphere laser communication link |
| CN106324828A (en) * | 2016-09-28 | 2017-01-11 | 中国科学院长春光学精密机械与物理研究所 | Liquid crystal-distorting lens' hybrid self-adaptive optical system designing method |
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-
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- 2020-04-30 CN CN202010362988.1A patent/CN111427147B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102288305A (en) * | 2011-07-18 | 2011-12-21 | 中国科学院光电技术研究所 | Adaptive optical system wavefront sensor and detection method thereof |
| CN103293663A (en) * | 2013-06-12 | 2013-09-11 | 中国科学院光电技术研究所 | Self-adaptive optical system for controlling multiple wavefront correctors based on voltage decoupling |
| CN104618017A (en) * | 2015-01-21 | 2015-05-13 | 中国科学院上海光学精密机械研究所 | Device and method for improving wavefront quality of atmosphere laser communication link |
| CN106324828A (en) * | 2016-09-28 | 2017-01-11 | 中国科学院长春光学精密机械与物理研究所 | Liquid crystal-distorting lens' hybrid self-adaptive optical system designing method |
Non-Patent Citations (2)
| Title |
|---|
| 外差探测系统波前校正实验研究;谭振坤 等;《仪器仪表学报》;20181231;第39卷(第12期);121-127 * |
| 自适应光学波前处理器的软件测试研究;王亮 等;《电子测量与仪器学报》;20160229;第30卷(第2期);193-199 * |
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