CN107145667A - A kind of quick calculation method of wavefront structure function - Google Patents
A kind of quick calculation method of wavefront structure function Download PDFInfo
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Abstract
A kind of quick calculation method of wavefront structure function, is related to beam quality and evaluates field, solves the problem of being unable to Efficient Characterization large aperture telescope main mirror face full range characteristic of field of existing computational methods presence.This method includes：Step 1: calculating the structure function of two orthogonal directions of the original face shape of large aperture telescope primary mirror；Step 2: original face shape is rotated；Step 3: being regular grid by postrotational original face shape interpolation, repeat step two terminates after original face shape is rotated repeatedly；Step 4: obtaining final structure function by the method for square mean.The present invention carries out frequency domain presentation using mirror surface structure function, is calculated with reference to power spectrum, can greatly improve computational efficiency.
Description
Technical field
The present invention relates to beam quality assessment technique field, and in particular to a kind of quick calculating side of wavefront structure function
Method.
Background technology
With the development of large aperture telescope, it is that can not effectively characterize the spy of its full frequency-domain to only rely on wavefront rms
Levy.Power spectrum is the abbreviation of power spectral density function, is defined as the signal power in per unit band, represents signal power with frequency
The distribution situation of the situation of change of rate, i.e. signal power in frequency domain.Power spectrum evaluation method is that the end of last century NIF is proposed
, there is more ripe standard (ISO 10110).But, power spectrum evaluation method can only evaluate the ripple of a direction
Before (when ripple is propagated in media as well, certain moment has just started the face that the particle of displacement is constituted, referred to as wavefront, and it represents certain moment ripple
The locus that energy is reached, it is moving) rise and fall, for super-smooth surface, some direction can be taken as commenting
The standard of valency.But for large aperture telescope, due to cost limitation and the influence of air, its face shape is not necessarily to reach
To Subnano-class, under this yardstick, anisotropic of the face shape in large scale just becomes apparent upon.Afterwards for power spectrum
Research introduce two-dimensional power spectrum, finally collapsing to one-dimensional carries out face shape evaluation.But Fourier transformation must be directed to
Orthogonal data are handled, and the statistics feature for the face shape in other angles can not just be evaluated.On the other hand, low
The part of frequency, power spectrum evaluation method reduces noise due to lacking averagely, therefore its effect evaluated also can be impacted.
Structure function is that D.L.Fried is put forward in nineteen sixty-five, to describe the atmospheric turbulance under different scale.From
Primarily, what structure function was represented is the different second-order centrals calculated on yardsticks away from the institute of wavefront is a little in different slide rulers
It is required for participating in calculating when on degree.With continuing to develop for large aperture telescope, its bore is also increasing therewith, in order to ensure
Resolution ratio, generally ensures the resolution of large aperture telescope using the method such as sub-aperture stitching technology or increase CCD unit numbers
Rate.By taking the large aperture telescope primary mirror of 4 meters of bores as an example, the more CCD of the interferometer institute band of advanced configuration is 1k × 1k at present,
Therefore the minute surface size corresponding to each pixel is 0.4mm, it is assumed that its F=1.5#, its focal length is 3 meters, corresponding angle is 26 ", and
Diffraction limit is 25 ".If detected with this resolution ratio, can not just be distinguished when actual use minute surface fluctuating or
The fluctuating of actual wavefront.In this case, in order to preferably analyze mirror shape, the data obtained by minute surface detection will Cheng Ping
Square gauge rule increase.But if calculated using the original definition of structure function, it will cause calculating cost to increase substantially.
On the other hand, the requirement that the detection of modern large aperture telescope is debug for real-time is also being improved.
Therefore, just seem very necessary in the urgent need to designing a kind of fast algorithm for wavefront structure function.
The content of the invention
Efficient Characterization large aperture telescope main mirror face full range characteristic of field is unable in order to solve that existing computational methods are present
The problem of, the present invention provides a kind of quick calculation method of wavefront structure function.
The present invention is as follows to solve the technical scheme that technical problem is used：
A kind of quick calculation method of wavefront structure function of the present invention, comprises the following steps：
Step 1: calculating the structure function of two orthogonal directions of the original face shape of large aperture telescope primary mirror；
Step 2: original face shape is rotated；
Step 3: being regular grid by postrotational original face shape interpolation, repeat step two rotates until by original face shape
Terminate after repeatedly；
Step 4: obtaining final structure function by the method for square mean.
Further, the detailed process of step one is as follows：
According to wavefront structure function DwavefrontDefinition calculate the original face shape of large aperture telescope primary mirror two orthogonal sides
To structure function；Wavefront structure function DwavefrontDefinition such as formula (1) shown in：
In formula (1)：Φ represents the wavefront for being detected and being obtained using wave front detector, is a two-dimensional matrix,WithIt is
Position vector on wavefront,<·>Represent being averaged on wavefront.
Further, the detailed process of step 2 is as follows：
1. the number of times M of original face shape rotation is determined；
2. the space coordinate of point in original face shape is set as (xi,yi,zi), the space coordinate after rotation θ angles is changed into (xb,
yb,zb), as shown in Equation 2：
3. formula (2) is calculated using the definition of expectation computing, obtained shown in its convolution form such as formula (3)：
In formula (3), window functionW* represents window function w conjugation, and Φ * represent wavefront Φ conjugation, and r is
Position vector on wavefrontMould；
4. Fast Fourier Transform (FFT)
It is equal to the product of Fast Fourier Transform (FFT) by the Fast Fourier Transform (FFT) of convolution, fast Fourier is carried out to formula (3)
Conversion：
Further, determine that the number of times M of original face shape rotation detailed process is as follows：
Fast Fourier Transform (FFT) once rotates to be 8- neighborhoods, revolved twice equivalent to the calculating carried out for 4- neighborhoods
Turn equivalent to 12 points are circumferentially calculated, by that analogy；The average power spectra obtained with rotating different number of times is surrounded with transverse axis
Area be token state, after the number of times of increase rotation, this token state institute increments is less than 10%, you can determine that original face shape is needed
The number of revolutions M wanted.
Further, the detailed process of step 3 is as follows：
Using interpolation arithmetic by postrotational wavefront interpolation be regular grid, be allowed to rotate before grid it is corresponding, wherein
The interpolation error of generation difference of the RMS value of wavefront before and after rotation is indicated, and rotates θ and the wavefront of interpolation is changed into againθ is the angle that original face shape rotates,Angle before being rotated for original face shape, meanwhile, according to power spectrum PSD's
Definition obtains formula (5)：
In formula (5),For spatial frequency vector.
Further, the detailed process of step 4 is as follows：
1. carry out inverse fast fourier transform using formula (3), formula (4) and formula (5) and obtain formula (6)：
In formula (6), θiRepresent the angle of original face shape ith rotation；
2. bring formula (6) into formula (1) calculate obtaining final wavefront structure function, as shown in formula (7)：
The beneficial effects of the invention are as follows：
For the calculating of wavefront structure function, it is possible to data all in some radius are evaluated, practical operation
When, because the discreteness of data is, it is necessary to think over specific embodiment.The present invention basic ideas be：It will treat first point
The wavefront of analysis is rotated, and calculates its power spectrum, and finally obtained some power spectrum are averaged.
1st, power spectrum is used as the method for evaluation system face shape, for essence, power spectrumanalysis before contrasting
The frequency information along certain dimension, as its improved two-dimensional power spectrum, research be two orthogonal dimensions information.And
Described by structure function is the information at certain interval under any direction, performance it is more comprehensive.The present invention utilizes mirror surface structure letter
Number carries out frequency domain presentation, is calculated with reference to power spectrum, can greatly improve computational efficiency.
2nd, compared with power spectrum, structure function can preferably be contacted with optical transfer function.For actual heavy caliber
The optical system of telescope, can be according to the concrete condition of each optical element, to obtain structure function curve, finally by simple
Addition can synthesize last error curve.For machinery with tracking brought error, optical transfer function can be passed through
To carry out unified consideration to it and carry out error distribution.
3rd, by the present invention, system engineer can be controlled for the intermediate frequency error of system, and reasonable distribution is limited
Precision index, while the optical information transfer performance of real system can also be predicted；Meanwhile, system can be more fully appreciated by
The not same-action that different frequency components is played in error, can also allow limited resource more fully to be utilized.
Brief description of the drawings
Fig. 1 is a kind of principle schematic of the quick calculation method of wavefront structure function of the present invention.
Embodiment
The present invention is described in further detail below in conjunction with accompanying drawing.
The present invention proposes a kind of method that utilization Fourier transformation and power spectrum quickly calculate wavefront structure function, its
Basic ideas are that the rotation of original matrix is realized using spin matrix；After rotation, using interpolation arithmetic by new data with it is original
Data are alignd, and finally obtain final wavefront structure function using the method for square mean.
As shown in figure 1, a kind of quick calculation method of wavefront structure function of the present invention, it is comprised the following steps that：
1st, first according to wavefront structure function DwavefrontBasic definition calculate large aperture telescope primary mirror original face shape
The structure function of two orthogonal directions.Wavefront structure function DwavefrontBasic definition such as formula (1) shown in：
In formula (1)：Φ represents the wavefront for being detected and being obtained using wave front detector, is a two-dimensional matrix,WithIt is
Position vector on wavefront,<·>Being averaged on wavefront is represented, the content in ＜ ＞ is represented, similarly hereinafter, for example：In formula (1),RepresentBeing averaged on wavefront.
2nd, determine that original face shape needs the number of times M rotated
As shown in figure 1, a Fast Fourier Transform (FFT) is equivalent to the calculating carried out for 4- neighborhoods, 8- is once rotated to be adjacent
Domain, twice rotation is equivalent to circumferentially calculate 12 points, by that analogy.To rotate the average power spectra that different number of times are obtained
It is token state with the area that transverse axis is surrounded, after the number of times of increase rotation, this token state institute increments is less than 10%, you can it is determined that
The number of revolutions M that original face shape needs, also rule of thumb can directly choose appropriate average number of revolutions.
3rd, the rotation of original face shape
If the space coordinate of the point in original face shape is (xi,yi,zi), the space coordinate after the θ that rotates to an angle is changed into
(xb,yb,zb), i.e., the relative rotation at θ angles is carried out between the two, and formula (2) is calculated using the basic definition of expectation computing,
It can obtain that its form is very similar with convolution, shown in the convolution form such as formula (3) of acquisition：
In formula (3), window function (W* is represented：Window function w conjugation, Φ * are represented：Wavefront Φ conjugation,For the position vector on wavefront, r is the position vector on wavefrontMould.
4th, Fast Fourier Transform (FFT) (FFT)
It is equal to the product of Fast Fourier Transform (FFT) by the Fast Fourier Transform (FFT) of convolution, fast Fourier is carried out to formula (3)
Conversion can be obtained：
5th, it is necessary to data progress interpolation arithmetic, be inserted postrotational wavefront using interpolation arithmetic after original face shape rotation
It is worth for regular grid, is allowed to corresponding with the grid before rotation, wherein the interpolation error produced, by the RMS value of the front and rear wavefront of rotation
Difference be indicated, rotate the θ and wavefront of interpolation is changed into againθ is the angle that original face shape needs to rotate,
Angle before being rotated for original face shape, meanwhile, it can be obtained according to the basic definition of power spectrum (PSD)：
In formula (5),For spatial frequency vector (circle/rad).
6th, repeat step 3 is to step 5, until original face shape is rotated into M end.
7th, final wavefront structure function is obtained by the method for square mean, as shown in formula (7).Particularly：First
Carrying out inverse fast fourier transform (IFFT) using formula (3), formula (4) and formula (5) can obtain：
In formula (6), θiRepresent：The angle of original face shape ith rotation.
Then bring formula (6) into formula (1) calculate obtaining final wavefront structure function, as shown in formula (7)：
It should be noted that：In a kind of quick calculation method of above-mentioned wavefront structure function, it is related to same in all formula
One letter represents to be meant that identical.
For the evaluation meanses of power spectrum, the expression formula of two-dimensional power spectrum can be drawn according to the basic definition of power spectrum.
By the calculating process of comparison structure function and power spectrum, can obtain main difference is that：1st, structure function calculates yardstick first
Less error, and power spectrum is started with the sign of low frequency aberration；2nd, structure function needs to calculate a certain yardstick each side
To error, and power spectrum only calculates the error of two orthogonal directions.As seen from the above comparison, wavefront structure letter of the invention
Number computational accuracy and efficiency are increased substantially.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of quick calculation method of wavefront structure function, it is characterised in that comprise the following steps：
Step 1: calculating the structure function of two orthogonal directions of the original face shape of large aperture telescope primary mirror；
Step 2: original face shape is rotated；
Step 3: being regular grid by postrotational original face shape interpolation, repeat step two is multiple until original face shape is rotated
After terminate；
Step 4: obtaining final structure function by the method for square mean.
2. a kind of quick calculation method of wavefront structure function according to claim 1, it is characterised in that the tool of step one
Body process is as follows：
According to wavefront structure function DwavefrontDefinition calculate two orthogonal directions of large aperture telescope primary mirror original face shape
Structure function；Wavefront structure function DwavefrontDefinition such as formula (1) shown in：
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In formula (1)：Φ represents the wavefront for being detected and being obtained using wave front detector, is a two-dimensional matrix,WithIt is wavefront
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3. a kind of quick calculation method of wavefront structure function according to claim 2, it is characterised in that the tool of step 2
Body process is as follows：
1. the number of times M of original face shape rotation is determined；
2. the space coordinate of point in original face shape is set as (xi,yi,zi), the space coordinate after rotation θ angles is changed into (xb,yb,
zb), as shown in Equation 2：
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4. Fast Fourier Transform (FFT)
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4. the quick calculation method of a kind of wavefront structure function according to claim 3, it is characterised in that determine original face
The number of times M of shape rotation detailed process is as follows：
Fast Fourier Transform (FFT) once rotates to be 8- neighborhoods, phase is rotated twice equivalent to the calculating carried out for 4- neighborhoods
When in circumferentially calculate 12 points, by that analogy；The face that the average power spectra obtained with rotating different number of times is surrounded with transverse axis
Product is token state, and after the number of times of increase rotation, this token state institute increments is less than 10%, you can determine what original face shape needed
Number of revolutions M.
5. a kind of quick calculation method of wavefront structure function according to claim 3, it is characterised in that the tool of step 3
Body process is as follows：
Using interpolation arithmetic by postrotational wavefront interpolation be regular grid, be allowed to rotate before grid it is corresponding, wherein producing
Interpolation error before and after rotation the difference of RMS value of wavefront be indicated, rotate θ and the wavefront of interpolation be changed into againθ is the angle that original face shape rotates,Angle before being rotated for original face shape, meanwhile, according to power spectrum PSD's
Definition obtains formula (5)：
In formula (5),For spatial frequency vector.
6. a kind of quick calculation method of wavefront structure function according to claim 5, it is characterised in that the tool of step 4
Body process is as follows：
1. carry out inverse fast fourier transform using formula (3), formula (4) and formula (5) and obtain formula (6)：
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2. bring formula (6) into formula (1) calculate obtaining final wavefront structure function, as shown in formula (7)：
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