CN102778300A - Method for stably measuring atmospheric coherence length - Google Patents

Abstract

The invention belongs to the field of optical technology, and particularly relates to a method for stably measuring atmospheric coherence length r0. According to space-time probability consistency characteristic of atmospheric turbulence, multiple pairs of sub-apertures which are in regular polygon symmetrical distribution on a Hartman wave front detector are selected, so as to increase the space statistic probability and simultaneously reduce the sampling time; In order to continue to calculate r0 by use of a formula (1), the method of selecting the multiple pairs of sub-apertures is as follows: the distance between centers of each pair of sub-apertures is strictly the same and simultaneously meets the principle of selecting one pair of sub-apertures, the regular polygon symmetrical distribution of the multiple pairs of sub-apertures is simplified as square distribution under the structure restriction of the Hartman wave front detector; and by utilizing hundreds of light spot array signals of a turbulence wave surface collected within one second, the difference movement of multiple pairs of image points which are in square symmetrical distribution on each light spot array signal is substituted into the formula (1) so as to be subjected to identical statistic average, so that an accurate atmospheric coherence length r0 value with an instant characteristic can be obtained.

Description

A Stable Measurement Method of Atmospheric Coherence Length

technical field

The invention belongs to the field of adaptive optics, and relates to an evaluation parameter of an adaptive correction effect of an atmospheric channel, in particular to a stable measurement method of an atmospheric turbulence intensity parameter, that is, an atmospheric coherent length.

Background technique

There is an atmosphere of 10-20 kilometers in the vertical direction on the earth's surface. Due to the uneven temperature change, the local density of the air is different, which leads to the uneven refractive index of the atmosphere, thus forming the dynamic disturbance phenomenon of atmospheric turbulence on the light wavefront. When astronomical telescopes are used to observe and image space targets, the target light waves received by the astronomical telescopes are subject to dynamic disturbances of atmospheric turbulence, resulting in varying degrees of wavefront distortion, which seriously affects the imaging quality. Therefore, the adaptive wavefront correction system has become a necessary facility for telescopes with apertures above the meter level. In order to evaluate the ability of adaptive wavefront correction system to cope with atmospheric turbulence, the measurement of atmospheric turbulence intensity has always been an important topic in the field of adaptive optics.

The value of the atmospheric coherence length r ₀ can express the spatial coherence of the light beam propagating in the atmospheric turbulence and the comprehensive strength of the dynamic disturbance of the atmospheric turbulence. The smaller the value of the atmospheric coherence length r ₀ , the more severe the dynamic disturbance representing atmospheric turbulence, and the value range is generally between a few centimeters and tens of centimeters. The value of r ₀ is defined as: the RMS value of the phase fluctuation of the optical wavefront in a circle with the diameter of the atmospheric coherence length r ₀ is 1 rad. When the diameter of the optical wavefront exceeds the scale of the atmospheric coherence length _r0 , the distortion of the optical wavefront will reduce the imaging resolution of the optical receiving system.

Two methods are usually used to measure the atmospheric coherence length r ₀ : one is to obtain the atmospheric coherence length r ₀ by measuring the structural constant of the refractive index of the atmospheric turbulence, and it takes long-term observations to obtain the statistical law of the structural constant of the refractive index; the other is The atmospheric coherence length r ₀ is obtained by measuring the phase information of the distorted wavefront, which is the so-called differential satellite image motion method (DIMM), which has been widely used.

The differential star point image motion method (DIMM) was proposed by Stock and Keller in 1960. Its measurement principle is: a baffle is placed at the entrance pupil of the astronomical telescope, and there are two sub-apertures on the baffle, and the gap between the two sub-apertures is The distance is much larger than the sub-aperture diameter. The point target beam from the other end of the atmospheric channel will be divided into two independent star point images after reaching the observation CCD camera through two sub-apertures. In a certain period of time, the value of the atmospheric coherence length _r0 can be calculated by recording the change of the relative distance between two image points caused by the dynamic disturbance of atmospheric turbulence in real time. F.Roddie deduced the basic formula for calculating the atmospheric coherence length r ₀ on the basis of Fried's theoretical research [F.Roddier, The effects of atmospheric turbulence inoptical astronomy, [J].Prog.Optics,1981,19:281~376 】:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="r"\; filenames="HDA00001941412100021.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 0.358</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 0.242</span>}\mathrm{<span\; class="notranslate">\; Z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="Z\; q"\; filenames="HDA00001941412100011.png"\; state="\{\{state\}\}">Z</figure-callout></span><figure-callout\; id="2"\; label="Z\; q"\; filenames="HDA00001941412100011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">q</span>}}<span\; class="notranslate">\; ></span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ></span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 5</span>}}$

Among them, f is the focal length of the measurement system, λ is the central wavelength of the received light, D is the diameter of the sub-aperture, Z is the center distance between the two sub-apertures, and Z>>r ₀ , Z _q is the centroid of the imaging point of the two sub-apertures The interval, <> is the time statistical average symbol. The calculation method of the centroid coordinates (c _x , c _y ) of the image point is based on [Francois Roddier, Adaptive optics in astronomy, Cambridge University Press, 1999, Part two, pp99]:

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Where i, j are the serial numbers of pixels on the Cartesian coordinate system composed of CCD camera pixels, x _{i, j} and y _{i, j} are the two coordinate components of (i, j) pixels respectively, and I _{i, j} is (i, j ) pixel light intensity.

In fact, r ₀ can be measured by the DIMM method using the Shack-Hartmann wavefront detector [Rao Changhui, Jiang Wenhan, Ling Ning. Measuring atmospheric turbulence parameters using the Hartmann-Shack wavefront sensor[J]. Acta Optics Sinica, 2000, 20(9):1201~1207]. Using a Shack-Hartmann wavefront detector with a sampling frequency of about kilohertz, select two sub-apertures with a sufficient distance on it, and usually the positions of these two sub-apertures are centrally symmetrical on the receiving wave surface. During the measurement, about 10,000 light point arrays on the atmospheric channel are continuously collected for 10s, and then only the centroid distances of the star point images of the two selected sub-apertures are considered in each frame, and r ₀ is statistically calculated according to formula (1).

However, the r ₀ value of atmospheric coherence length measured at a certain moment by using the DIMM method often suddenly jumps by two or three centimeters after a few seconds, and sometimes it can jump by nearly ten centimeters. This phenomenon does not match the velocity characteristics of atmospheric turbulence. Analyzing the reason, it should be caused by insufficient statistics, because the intensity of wavefront fluctuations is different in all directions, and the DIMM method only counts the movement of the center of mass of the two sub-aperture image points at fixed positions. In order to make comprehensive statistics, it is necessary take a long time. If it is difficult to guarantee the accuracy of r ₀ measurement after counting 10,000 times, it means that the statistics of 10,000 times are not enough; but if the statistics are increased, it may also cause the sampling time to be too long, exceeding the time when r ₀ remains constant, and the average loss of r ₀ changes. Therefore, the traditional DIMM method of measuring the atmospheric coherence length r ₀ is flawed.

In 2000, Rao Ruizhong adopted the differential motion method of three holes, that is, three pairs of star point images [Rao Ruizhong, Wang Shipeng, Liu Xiaochun, et al. Experimental study of laser beam drift in turbulent atmosphere[J]. China Laser, 2000, 27(11): 1011-1015. ], trying to make up for the incompleteness of a pair of star-like motion statistics. In 2007, Rao Ruizhong’s research group also reported the method of differential motion using two pairs of holes (four holes) that are perpendicular to each other, that is, six pairs of star point images [Huang Honghua, Yao Yongbang, Rao Ruizhong, Research on the method of four-hole differential image motion to measure atmospheric coherence length[ J]. Intense Laser and Particle Beam, 2007,19 (3): 357-360.], and in the article in 2010 [Ni Zhibo, Huang Honghua, Huang Yinbo, Zhu Wenyue, Rao Ruizhong [J]. Dome effect on four holes Influence of Atmospheric Coherence Length Meter System Performance, Intense Laser and Particle Beam, 2010, 22(11): 2551-2555.] The difference results of 6 pairs of star images × 200 images were counted, and the measured r ₀ change speed was greatly Slow down, about 0.6～0.7cm/min, but it is still impossible to confirm whether this statistic is sufficient, that is, whether the change of r ₀ is real, and whether there is an influence of wave front local anisotropy changing with time; The center spacing of the apertures is not the same, so the statistical calculation method of formula (1) must be modified to increase the amount of calculation.

Contents of the invention

In order to overcome the defect of atmospheric coherence length r ₀ statistical method, the present invention proposes to select multiple pairs of sub-apertures with symmetrical distribution of regular polygons on the spot array measured by the Shack-Hartmann wavefront detector, greatly increasing the probability of ensemble statistics, while maintaining the formula The statistical calculation method in (1) is effective, and the purpose is to provide an accurate and simple stable measurement method of the atmospheric coherence length _r0 .

The present invention is described in detail below. The Shack-Hartmann wavefront detector is optically connected to an astronomical telescope, so that the light beam of any star received by the telescope can be detected with full aperture and the same receiving aperture as the Shack-Hartmann wavefront detector, and parallel incident Shack-Hartmann wavefront detection device. According to the uniform characteristics of temporal and spatial probability of atmospheric turbulence, multiple pairs of sub-apertures with regular polygonal symmetrical distribution are selected on the spot array measured by the Shack-Hartmann wavefront detector to increase the spatial statistical probability and reduce the sampling time. In order to continue to use formula (1) to calculate r ₀ , the method of selecting multiple pairs of sub-apertures is to keep the Z value in formula (1) unchanged, that is, the distance between the centers of each pair of sub-apertures is strictly the same, and is much larger than r ₀ . In this way, under the restriction of the Shack-Hartmann wavefront detector structure, the multiple pairs of sub-apertures distributed symmetrically in a regular polygon can only be simplified to a square or hexagonal distribution as shown in Figure 1, and 10 to 14 pairs of sub-apertures are selected on it. The sampling frequency of the Shack-Hartmann wavefront detector shall not be less than 500Hz, and continuously collect 300-500 spot array signals of the turbulent wavefront. Substituting the centroid spacing Z _q of each pair of image points on the 300-500 arrays into the formula (1) for statistical average, the atmospheric coherence length r ₀ value with an error of less than 3% and real-time characteristics is obtained.

Description of drawings

Fig. 1 is a schematic diagram of an indoor experimental optical path for measuring the atmospheric coherence length r ₀ by using an atmospheric turbulence simulator in the present invention. Among them, 1 is a halogen lamp point light source, 2 is a monochromatic filter with a wavelength of 785nm, 3 is the first lens, which collimates the light of the point light source into parallel light with a suitable diameter, and 4 is the rotating phase plate of the atmospheric turbulence simulator, 5 is the aperture stop, 6 is the second lens, 7 is the third lens, the two form a narrowing lens group, 8 is the Shack-Hartmann wavefront detector, which receives the beam disturbed by the atmospheric turbulence simulator at full aperture, and 9 is The computer connected to the Shack-Hartmann wavefront detector 8 reads out and stores the collected light spot array image data.

Fig. 2 is the selection method of 12 pairs of points on the Shack-Hartmann spot array diagram in the present invention. In the two vertical directions of the spot array, select 6 pairs of spots with a spacing of 12 spots, that is, 12 times r ₀ , to form a star point image of 12 pairs of sub-apertures in a square distribution, and mark the paired spots with letters: a and a′, b with b', c with c', d with d', e with e', f with f', g with g', h with h', i with i', j with j', k with k', l and l'.

Fig. 3 selects 1 pair of points and 12 pairs of points respectively on the light spot array figure of Shack-Hartmann in the specific embodiment of the present invention, and the r obtained varies with the curve of statistics, wherein curve _A is the result of 1 pair of points, curve B is the result of 12 pairs of points.

Detailed ways

1) Set up the experimental optical path for measuring r ₀ according to Figure 1. Among them, the spherical light wave emitted by the halogen lamp point light source 1 has a wavelength of 785nm, becomes monochromatic light through the monochromatic filter 2, and then collimates into parallel light through the first lens 3, and then enters the rotating phase plate 4 of the atmospheric turbulence simulator. Above, the aperture stop 5 is set close to the aperture of the rotating phase plate of the atmospheric turbulence simulator. The lens 7 shrinks the beam by 2.5 times to become a parallel light beam with a 4mm diameter and enters the inscribed circle of the light transmission window of the Shack-Hartmann wavefront detector 8. The computer 9 is connected with the Shack-Hartmann wavefront detector 8, and the readout and storage are collected. The spot array image data.

2) The atmospheric turbulence simulator described in step 1) is a product of Lexltek Company. The atmospheric coherence length r ₀ is determined by controlling the aperture of the phase plate, and the turbulence frequency, namely the Greenwood frequency, is determined by controlling the rotation speed of the phase plate: First set the center wavelength of turbulence to 785nm, then set the aperture of the telescope to 500mm, and set the atmospheric coherence length _r0 to 5.0cm. Find the spot diameter on the corresponding phase plate as 10mm in the user manual of the product, and select the turbulence frequency That is, the Greenwood frequency is 31Hz, and the corresponding phase plate speed is found to be 20 rpm in the user manual of the product.

3) The aperture of the aperture diaphragm 5 can be continuously adjusted within the range of 1 mm to 15 mm, which can control the diameter of the beam incident on the rotating phase plate 4 of the atmospheric turbulence simulator.

4) The Shack-Hartmann wavefront detector 8 has a frame rate of 1020Hz, and the photosensitive element is a MicroVista-NIR back-illuminated CMOS camera from Intevac Photonics. The number of pixels of this camera reaches 1280×1024, and the number of microlenses is 20×20 , Arranged in a grid array, each microlens corresponds to 7×7 pixels, the total number of pixels used in the CMOS camera is 140×140, and the corresponding window is 4mm×4mm.

5) The first lens 3, the second lens 6, and the third lens 7 are all achromatic doublet lenses, in which the diameter of the first lens 3 is 40mm, and the focal length is 270mm, so that the diameter of the light spot reaching the phase plate is 10mm, with Simulate a wavefront with a caliber of 500mm; the calibers of the second lens 6 and the third lens 7 are 40mm and 25mm respectively, and the focal lengths are 250mm and 100mm respectively, so that the beam is shrunk by 2.5 times, and its caliber is the same as that of a Shack-Hartmann wavefront detector 8 have the same aperture.

6) After turning on the point light source 1, the spot array obtained by the Shack-Hartmann wavefront detector 8 is shown in Figure 2. In the two vertical directions of the spot array, select 6 pairs of spots with a distance of 12 spots, that is, 12 times r ₀ , to form a square The star point images of the distributed 12 pairs of sub-apertures are shown as the paired light points marked with letters in Figure 2.

7) After turning on the rotating phase plate 4 of the atmospheric turbulence simulator, continuously collect 10,000 pieces of spot array data, select 1 pair of points and 12 pairs of points on the spot array map, and calculate the centroid distance Z _q of each pair of star point images and substitute them into the formula In (1), the variation curve of r ₀ obtained with statistics is shown in Figure 3, where curve A is the result of 12 pairs of points, and curve B is the result of 1 pair of points. It can be seen that the data of 300 spot arrays in curve A The calculated r ₀ has converged, which is 5.1cm, which is only 2% error compared with the r ₀ set value of 5.0cm, while the curve B does not converge until after 6500 pieces, and converges to 5.5cm, which is the same as the r ₀ set value There is a 10% error compared to 5.0cm.

Claims (3)

1. The stable measurement method of the atmospheric coherence length r ₀ is characterized in that the Shack-Hartmann wavefront detector is optically connected with an astronomical telescope, so that the light beam of any star received by the telescope can be full-aperture and compatible with the Shack-Hartmann wave The front detector receives the same aperture and parallel incident Shack-Hartmann wavefront detector; 10-14 pairs of sub-apertures with square symmetrical distribution are selected on the spot array measured by the Shack-Hartmann wavefront detector to increase the probability of spatial statistics. Reduce sample time; utilize formula $r_0={\left[\frac{{2f}^2{l}^2({0.358\mathrm{D.}}^{-1/3}-{0.242Z}^{-1/3})}{<Z_q^2>-{<Z_q>}^2}\right]}^{3/5}$ To calculate r ₀ , f in the formula is the focal length of the measurement system, λ is the central wavelength of the received light, D is the diameter of the sub-aperture, Z is the center distance of each pair of sub-apertures, and Z>3r ₀ , Z _q is two The centroid spacing of the imaging points of the sub-apertures, <> is the time statistical average symbol; the method of selecting multiple pairs of sub-apertures is to keep the Z value in the formula unchanged, that is, the center spacing of each pair of sub-apertures is strictly the same; the Shack-Hartmann wave The sampling frequency of the front detector shall not be less than 500Hz, and continuously collect 300-500 spot array signals of turbulent wave fronts; Substituting the centroid distance Z _q of each pair of image points on the 300-500 arrays into the formula for statistical average, it is obtained Stable atmospheric coherence length r ₀ values with instantaneous features. 2. the stable measuring method of atmospheric coherence length r ₀ according to claim 1 is characterized in that: the Shack-Hartmann wavefront detector frame frequency is 1020Hz. 3. the stable measuring method of atmospheric coherence length r according to claim ₂ is characterized in that: the spot array figure that obtains on the Shack-Hartmann wavefront detector, selects spacing 12 spots respectively on its two perpendicular directions That is, 6 pairs of light spots with 12 times r ₀ form star point images of 12 pairs of sub-apertures in a square distribution, continuously collect 300 pieces of light spot array data, and substitute the centroid distance Z _q of each pair of star point images into the formula described in claim 1 , statistically calculated r ₀ .

Images