CN108181007B - The facula mass center calculation method of Hartman wavefront detector weak signal - Google Patents
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Abstract
The invention belongs to adaptive optical imaging technical field, the filtering method of the low problem proposition for causing Wavefront detecting error big of signal-to-noise ratio when being for weak signal.Its basic thought is: each spot intensity distribution should be similar to class Gaussian intensity profile function shown in FIG. 1 on Hartman wavefront detector；If with the class Gaussian intensity profile function on 3 × 3 pixel regions and if 6 × 6 pixel subregion intensity distribution functions carry out relevant calculation, the weight that the weight of spot center strength signal can be protruded, force down subregion edge photon noise forms subregion weight spectral window W；The codomain of W is also on the subregion of 6 × 6 pixels；Weight calculation is done with the intensity distribution I of the subregion again using effective subregion weight spectral window W, can be obtained the intensity distribution for inhibiting the subregion hot spot of noise jamming；Then the mass center of the subregion hot spot is calculated with common centroid algorithm.The present invention can make the Wavefront detecting error of 5.5 magnitudes reduce 20%.
Description
Technical field
The invention belongs to adaptive optical technique fields, are a kind of Wavefront detecting sides based on Hartman wavefront detector
Method.Be related to Hartman wavefront detector noise it is relatively low when facula mass center calculation method so that Hartman wavefront detector
Detection limit magnitude improve.
Background technique
When being observed using telescope to Celestial Objects, due to the random disturbances of atmospheric turbulance, imaging wavefront occurs
Dynamic distortion causes telescope imaging resolution to decline.Adaptive optics system can real-time detection and correction atmospheric turbulance cause
Distorted wavefront, to restore the ideal high-resolution imaging of telescope.Hartman wavefront detector is in current Adaptable System
Widely applied wave front detector.The detector is as shown in Figure 1, by preposition microlens array 1 and positioned at microlens array coke
Back camera 2 in plane forms, and the bore of single lenticule is d, focal length f, and microlens array exports telescope abnormal
Change wavefront division should be particularly noted that in front of each wavelet into the sub- wavefont array of the plane for containing only tilt without containing any high
Rank distortion, only space tilt angle is different, the diameter before wavelet and the atmospheric coherence length r for representing atmospheric turbulence intensity0Phase
Deng corresponding beamlet on back camera 2 by being converged to spot array after microlens array 1 before these wavelets, in camera
The centroid position of each hot spot, the two-dimentional tilt data before can get each wavelet are calculated in the plane coordinate system that pixel is constituted.
Using all two-dimentional tilt datas of sub- wavefont array, the whole distorted wavefront of telescope output can be reconstructed.
Consider that microlens array 1 is the lenticule set of lattice-array arrangement, there is lattice-array row on the panel of back camera 2
The pixel of column.Wavefront detecting light beam is the collimated light beam of normal incidence, and inscribed circle is approximately formed on the panel of back camera 2, circle
Inside it is dispersed with the hot spot that microlens array focuses out.Shown in Fig. 2 is the spot array of a width distorted wavefront, and each hot spot limits
In n × n-pixel subregion, spot intensity is dispersedly distributed over each pixel system.The subregion for having hot spot is to have
Imitate subregion.
Facula mass center coordinate (cx, cy) computation according to [Francois Roddier, Adaptive optics in
Astronomy, Cambridge University Press, 1999, Part two, pp99]:
Rectangular coordinate system x-y is established on effective subregion, is origin, as unit of pixel by the center of subregion, if from
Left-to-right horizontal axis is x-axis, and the longitudinal axis from top to bottom is y-axis, the center-of-mass coordinate of hot spot in subregion are as follows:
Wherein range of summation is all pixels on subregion, and i, j are pixel respectively in horizontal and vertical serial number, i, j
=1,2,3 ... n, xi,jWith yi,jRespectively two coordinate components of (i, j) pixel center point, Ii,jFor the light intensity of (i, j) pixel.
The facula mass center computational accuracy of Hartman wavefront detector determines the precision of wavefront reconstruction.And even if simple consider letter
In number photon noise influence if, near or above 5 apparent magnitudes dark weak signal target in Hartman wavefront detector subregion
Average signal-to-noise ratio is all not above 13 because the intensity of photon noise is the square root of signal strength, so when common mass center
Algorithm it is difficult to ensure that facula mass center computational accuracy.The adaptive optical imaging field of telescope in China, it is considered that 5 TV stars
Etc. the limited detective magnitude for being current Hartman wavefront detector, even the target of 4.5 apparent magnitudes, brightness opposite can be improved
1.6 times, but signal-to-noise ratio opposite can only also improve √ 1.6=1.3 times, i.e. and signal-to-noise ratio is not higher than 16, and centroid algorithm obtains at this time
Facula mass center error is also larger.
If the photon noise of subregion can be inhibited, it can not only guarantee wavefront reconstruction precision, moreover it is possible to accordingly mention
The detectivity of high Hartman wavefront detector, i.e., detectable limiting magnitude.
The calculation method of the target apparent magnitude and the number of photons in Hartman wavefront detector subregion is as follows:
Enable observed object spectral characteristics of radiation identical as solar spectrum.The monochromatic radiation degree of solar radiation can use a temperature
Degree is the black body radiation of 6000K to simulate, and radiometric unit is (W/m2) when reach the earth atmosphere upper bound sun monochrome spoke
Degree of penetrating may be expressed as:
Wherein λ is the optical wavelength that unit takes micron, and R is radius R=6.9599 × 10 of the sun8M, D is the sun to atmosphere
Per day distance D=1.4959787 × 10 in the layer upper bound11m。
Further consider atmosphere transmitance τA, telescopic system transmitance τT, adaptive optics system detection branch penetrate
Rate τSH, for the quantum efficiency η and its received detecting band λ of back camera 21~λ2With sampling time for exposure t, Hart is entered
The photoelectron number of graceful wave front detector subregion can indicate are as follows:
Wherein, h is Planck's constant, and c is the light velocity.Hartmann Wavefront Sensing in usual telescope self adaptive imaging system
The sampling wave band of device is 0.4 μm~0.7 μm visible light wave range, i.e. λ1=0.4 μm, λ2=0.7 μm, sample time for exposure t=
0.6ms, in telescopic system transmitance τT=0.51, detect branch roads system transmitance τSH=0.46, atmospheric coherence length r0=
10cm, choose Andor company Visible Light CCD Camera as shown in Figure 3 photoelectron conversion quantum efficiency as η in the case where,
It can be concluded that Ψsun=1.77 × 1020(e/m2/s)。
Since the absolute magnitude of the sun is -26.74 etc., photoelectron number and magnitude M in subregionvRelationship are as follows:
Therefore the magnitude and the signal-to-noise ratio under the influence of subregion photoelectron number and photon noise that target can be calculated
Corresponding relationship, as shown in table 1.
The magnitude and subregion photoelectron number of 1 target of table and the corresponding relationship of signal-to-noise ratio
| Magnitude | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 |
| Subregion photoelectron number | 265 | 167 | 106 | 67 | 42 | 27 |
| Signal-to-noise ratio | 16 | 13 | 10 | 8 | 6 | 5 |
Summary of the invention
The present invention is directed to the centroid calculation of signal hot spot in subregion when signal-to-noise ratio is lower than 16 in Hartman wavefront detector
The big problem of error proposes a kind of centroid computing method for filtering with weight and being combined, i.e., with close to hot spot scale in subregion
Smaller area on class Gaussian intensity profile function do relevant calculation, generate subregion weight spectral window, then filtered with weight
Window does weighted calculation to the intensity distribution on subregion and generates the spot intensity distribution that noise is greatly reduced, it is therefore an objective to reduce hot spot
The influence of ambient photon noise improves facula mass center computational accuracy, to improve the detection limit star of Hartman wavefront detector
Deng.
For clear expression basic thought of the invention, come by taking an effective subregion on Hartman wavefront detector as an example
Illustrate the present invention.In view of the subregion of the Hartman wavefront detector of general telescope adaptive optics system is 6 × 6 pictures
Pixel number shared by element, hot spot is greater than equal to 2 × 2 and is less than or equal to 4 × 4；It is origin, as unit of pixel by the center of subregion
Rectangular coordinate system x-y is established, if horizontal axis from left to right is x-axis, the longitudinal axis from top to bottom is y-axis, and i, j are effective son respectively
The pixel in region is in horizontal and vertical serial number, i, j=1, and 2,3,4,5,6；xi,jWith yi,jRespectively (i, j) pixel center point
Two coordinate components, Ii,jFor the light intensity of (i, j) pixel.
The basic idea of the invention is that:
It will be approximately class gaussian intensity function not by the intensity distribution function of hot spot in the subregion of noise jamming, define this
A class gaussian intensity function occupies 3 × 3 pixel regions, and intensity distribution is illustrated in Fig. 2, by class Gaussian intensity profile function square
Battle array P is expressed:
Wherein k is weighting parameters, and value is between 0.75~0.95.
Even if there is noise jamming, the spot intensity distribution on Hartman wavefront detector in each effectively subregion should
It is similar to this class Gaussian intensity profile function；If with class Gaussian intensity profile function and 6 × 6 pictures on 3 × 3 pixel regions
If sub-prime field strength distribution function carries out relevant calculation, the weight of spot center strength signal can be protruded, force down subregion
The weight of edge photon noise forms subregion weight spectral window W；The Luminance Distribution value I of 6 × 6 pixels on subregioni,jSquare
Battle array is expressed as I, the mathematical expression of subregion weight spectral window W are as follows:
WhereinIndicate relational operator, the codomain of W is also on the subregion of 6 × 6 pixels；It is filtered using effective subregion weight
Wave window W does weight calculation with the intensity distribution I of the subregion again, can be obtained the subregion hot spot for inhibiting noise jamming
Intensity distribution；Then the mass center of the subregion hot spot is calculated with common centroid algorithm.
In summary, the centroid computing method combined with weight filtering is written as follow expression formula:
Wherein, (Cx)AWCOG(Cy)AWCOGCoordinate value of the facula mass center as of the invention obtained in x-axis and y-axis.
The centroid calculation of other subregion hot spots, repeats the above steps on Hartman wavefront detector.
The specific algorithm of W are as follows: each pixel of subregion is successively directed at the center pixel of P shown in Fig. 2；It is each pair of
As soon as when pixel (i, j) of quasi- subregion, by the respective pixel intensity value of the intensity value of pixel each on P and Chong Die subregion
Product is carried out, sums it up product value between every a pair of of pixel again, the product value i.e. 3 × 3 betweens of pixels of adduction, this product is summed it up
Value is as the intensity value in (i, j) pixel corresponding on W；The center pixel of P is enabled to traverse each pixel of alignment subregion
The intensity Distribution value for acquiring upper 6 × 6 pixel of W is calculated by the product adduction 3 × 3 betweens of pixels each time；When P row pixel or
When column pixel exceeds be aligned subregion, enabling the intensity on the subregion exterior pixel is 0, therefore the intensity of these corresponding pixels
Product is also 0.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of Hartman wavefront detector, wherein 1 is microlens array, the bore of each lenticule
For d, focal length f, 2 be back camera, on the focal plane of microlens array.
Fig. 2 is the spot array schematic diagram of a width distorted wavefront, and what each hot spot was limited to that a dotted line surrounds has n
In the grid of × n-pixel, each grid is the subregion of Hartman wavefront detector, and spot intensity is dispersedly distributed in sub-district
In each pixel in domain.The subregion for having hot spot is effective subregion.
Fig. 3 is that the photoelectron of Andor company Visible Light CCD Camera converts quantum efficiency curve.
Fig. 4 is the class gaussian intensity template schematic diagram on 3 × 3 pixel regions of the invention, wherein the value of weighting parameters k
It is 0.8.
Fig. 5 (a) is 2 meters of the bore obtained on the Atmosphere Turbulence Simulator specification that Lexltek company sells, big gas phase
The grayscale image of the wave front data conversion of dry length 10cm, (b) the distorted wavefront simulation in corresponding (a) calculates 20 × 20 lenticules
Spot array grayscale image on the Hartman wavefront detector of array.
Fig. 6 is intensity distribution grayscale image in the subregion of the 11st column to 15 column of the 11st row of corresponding diagram 5 (b).Wherein (a) is
Grayscale image without photon noise jamming (b) is to have photon noise interference using the Poisson distribution function in Matlab is calculated
Grayscale image, (c) be calculated corresponding weight spectral window, (d) for using present invention inhibits the ashes that photon noise interferes
Degree figure.Normalized has been done to the intensity profile of (a), (b), (c), (d) respectively.
Specific embodiment
Specific simulation process is as follows:
1, Hartman wavefront detector structural parameters are as follows: bore is 5.8mm, lenticule number 20 × 20, and square arrangement is micro-
Lens diameter d takes 288 μm, focal length f=20.1mm, enables light wavelength lambda=550nm；The reading noise of back camera CCD is negligible not
Meter, the pixel number 120 × 120 of CCD, the Pixel Dimensions that subregion pixel number is 6 × 6, CCD are 24 μm of 24 μ m；Lead to before wavelet
An angstrom sharp spot diameter after crossing lenticule is 1.2 λ f/d=1.9 pixels, under the influence of distorted wavefront hot spot can cover about 3 × 3
Pixel.
2, detected target satellite etc. is 5.5, right more than the detection limit magnitude of Hartman wavefront detector before the present invention
The photoelectron number for answering subregion hot spot is 100.
3, the phase mehtod number of distorted wavefront is obtained on the Atmosphere Turbulence Simulator specification that Lexltek company sells
According to grayscale image such as Fig. 5 (a).Diameter of the wavefront in Atmosphere Turbulence Simulator is 5.8mm, atmospheric coherence length is
0.29mm, this pair of of parameter correspond to actual wavefront bore be 2 meters, atmospheric coherence length 10cm, and penetrate atmospheric turbulance mould
The collimated light beam diameter of quasi- device is equal to Hartman wavefront detector bore 5.8mm.
4, there is the Hartman wavefront detector of lenticule number 20 × 20 to carry out to the wavefront of Atmosphere Turbulence Simulator for simulation
Sampling, enables the unified vertical incidence Hartman wavefront detector of collimated light beam for penetrating Atmosphere Turbulence Simulator, and beam diameter exists
120 pixels, 20 lenticules of corresponding Hartman wavefront detector diametrically, each subregion picture are covered on the camera CCD of back
Prime number is 6 × 6；It is origin, as unit of pixel by subregion center, establishes two-dimensional coordinate system, if horizontal axis from left to right is x
Axis, the longitudinal axis from top to bottom are y-axis, and i, j are the serial numbers of pixel in x-axis and y-axis, the i, j=1,2 of effective subregion, 3,4,
5,6；xi,jWith yi,jRespectively two coordinate components of (i, j) pixel center point, Ii,jFor the light intensity of (i, j) pixel；Due to wavelet
Preceding upper only tilt, the angle component being tilted in x-axis and y-axis is respectively φx、φy, and counterclockwise rotation angle be positive,
Angle is rotated clockwise to be negative；The beamlet can be from the center (0.00,0.00) of subregion through the mass center of after lenticule angstroms of sharp spot
Place is moved to (ftg φx, ftg φy)；It is again that 100, mass center is located at (ftg φ by photoelectron numberx, ftg φy) angstrom
The light energy of sharp spot is discrete in each pixel.
Shown in the spot array such as Fig. 5 (b) for calculating noiseless interference.
5, the 11st of the 11st row of Fig. 5 (b) is taken to arrange the subregion to 15 column, and 100 photoelectrons are in 5 sub-regions pixels
Distribution be successively expressed as I1, I2, I3, I4, I5, in which:
I1
I2
I3
I4
I5
Intensity distribution such as Fig. 6 of from left to right 5 continuous arrangement subregions I1, I2, I3, I4, I5 of noiseless interference
(a) shown in.
6, (1) formula is utilized to calculate the facula mass center of 5 continuous arrangement subregions I1, I2, I3, I4, I5 of noiseless interference
Coordinate (cx, cy) value is as follows, wherein unit is pixel, and calculates mean deviation amount of 5 facula mass centers in x-axis and y-axis:
Mean deviation amount of the facula mass center in x-axis in 5 continuous arrangement subregions is 0.306 pixel, on the y axis
Mean deviation amount is 0.327 pixel.
7, the spot intensity under the photon noise interference of Poisson distribution, which is distributed, calculates: being made an uproar using the Poisson in Matlab software
Sound distribution function obtains corresponding diagram 6 successively by I1, I2, I3, I4, I5 input Poisson Noise function in " 5 " step
(a) in 5 continuous arrangement subregions shown in such as Fig. 6 (b) of the intensity distribution containing photon noise, corresponding diagram 6 (b) from left to right 5
Intensity distribution matrix I1 ', I2 ', I3 ', I4 ', I5 ' in a continuous arrangement subregion containing photon noise are as follows:
I1′
I2′
I3′
I4′
I5′
8, corresponding diagram 6 (b) utilizes (1) formula to calculate the facula mass center in 5 continuous arrangement subregions of photon noise interference
(c′x, c 'y), and accordingly calculate error delta x '=c of the mass center caused by noise in x-axis and y-axisx′-cx, Δ y '=c 'y-
cyAnd percentage, that is, relative error of the two errors relatively respective mean deviation amount respectively:
Facula mass center in opposite Fig. 6 (a) in 5 continuous arrangement subregions without photon noise jamming is in x-axis and y-axis
Mean error be respectively 0.063 pixel and 0.097 pixel, average relative error be 21% and 30%.
9, the k in class Gaussian intensity profile Jacobian matrix P takes 0.8；
Utilize (6) formula, obtain corresponding diagram 6 (b) in from left to right weight spectral window W1, W2 of 5 continuous arrangement subregions,
The expression matrix of W3, W4, W5:
W1
W2
W3
W4
W5
Shown in intensity distribution such as Fig. 6 (c) of weight spectral window W1, W2, W3, W4, W5 of 5 continuous arrangement subregions.
10, weight spectral window W1, W2, W3, W4, W5 of acquisition are respectively corresponded hot spot I1 ' under the influence of photon noise,
I2 ', I3 ', I4 ', I5 ' do weight filtering, spot intensity distribution such as Fig. 6 (d) after weight filtering in 5 continuous arrangement subregions
It is shown, it can be seen that Fig. 6 (d) and Fig. 6 (a) that noiseless is interfered are very alike, illustrate weight filtering to light spot image edge noise
With obvious inhibiting effect.5 corresponding intensity distribution matrix I11, I22, I33, I44, I55 after weight filtering are as follows:
I11
I22
I33
I44
I55
11, by weight spectral window W1, W2, W3, W4, W5 of acquisition under the influence of corresponding photon noise hot spot I1 ', I2 ',
I3 ', I4 ', I5 ' successively substitute into (7) formula, calculate the light that the filtered 5 continuous arrangement subregions of weight are carried out to photon noise
Spot center-of-mass coordinate ((cx)AWCOG,(cy)AWCOG) value is as follows, wherein unit is pixel, and accordingly calculates 5 matter after weight filtering
Error delta x of the heart in x-axis and y-axisAWCOG=(cx)AWCOG-cx、ΔyAWCOG=(cy)AWCOG-cyAnd opposite mass center mean deviation
The relative error of amount:
Find out and be suppressed by weight filtered noise, the x-component average relative error of 5 mass centers is 20%, opposite to weigh
Average relative error filter again before reduces by 5%, and y-component average relative error is also 20%, being averaged before relative weighting filtering
Relative error reduces by 33%.
Above-mentioned emulation repeats 500 times, counts average RMS value of the mass center error of weight filtering on x-component and y-component
Relatively traditional centroid algorithm reduces 20%.
Claims (1)
1. the facula mass center calculation method of Hartman wavefront detector weak signal, it is characterized in that noise in Hartman wavefront detector
When than being lower than 16, the facula mass center algorithm in spot array in each subregion is a kind of centroid calculation combined with weight filtering
Method；
The Hartman wavefront detector on telescope is configured, pixel number shared by the hot spot being limited in subregion is greater than
In 2 × 2 and be less than or equal to 4 × 4, subregion have 6 × 6 pixels；It will be not by the intensity of hot spot in the subregion of noise jamming point
Cloth approximation to function is class gaussian intensity function, defines this class gaussian intensity function and occupies 3 × 3 pixel regions, and class Gauss is strong
Degree distribution function is expressed with matrix P:
Wherein k is weighting parameters, and value is between 0.75~0.95；
Even if there is noise jamming, the spot intensity distribution on Hartman wavefront detector in each effectively subregion should be with this
A class Gaussian intensity profile function is similar；If with class Gaussian intensity profile function and 6 × 6 pixels on 3 × 3 pixel regions
If field strength distribution function carries out relevant calculation, the weight of spot center strength signal can be protruded, force down subregion edge
The weight of photon noise forms subregion weight spectral window W；The expression matrix of the intensity distribution value of 6 × 6 pixels is on subregion
I, the mathematical expression of subregion weight spectral window W are as follows:
WhereinIndicate relational operator, the codomain of W is also on the subregion of 6 × 6 pixels；Utilize effective subregion weight spectral window W
Weight calculation is done with the intensity distribution I of the subregion again, can be obtained the intensity for inhibiting the subregion hot spot of noise jamming
Distribution；Then the mass center of the subregion hot spot is calculated with common centroid algorithm.
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| CN101055223A (en) * | 2007-04-26 | 2007-10-17 | 中国科学院光电技术研究所 | Hartman wavefront sensor mass center measurement precision optimization method |
| CN101339004A (en) * | 2008-08-27 | 2009-01-07 | 中国科学院光电技术研究所 | Centroid offset checking method for Hartman wavefront detector based on DFT |
| CN106546326A (en) * | 2016-09-28 | 2017-03-29 | 中国科学院长春光学精密机械与物理研究所 | The wavefront sensing methods of multinomial pattern in Hartman wavefront detector sub-aperture |
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| CN101339004A (en) * | 2008-08-27 | 2009-01-07 | 中国科学院光电技术研究所 | Centroid offset checking method for Hartman wavefront detector based on DFT |
| CN106546326A (en) * | 2016-09-28 | 2017-03-29 | 中国科学院长春光学精密机械与物理研究所 | The wavefront sensing methods of multinomial pattern in Hartman wavefront detector sub-aperture |
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