Out-of-focus holographic measurement method of radio telescope based on planetary zooming

Abstract

According to the out-of-focus holographic measurement method of the radio telescope based on planetary zooming, a planet is used as a source for out-of-focus observation, a beam pattern of an actually observed planet is obtained through deconvolution, a theoretical far-field model of the planet is established, and the theoretical far-field model of the planet is compared with the actually observed beam pattern to calculate a redundancy value. And continuously updating the coefficient of the Zernike polynomial by minimizing the redundancy value and iterating until the optimal phase model is determined, and determining the phase error on the aperture plane according to the phase model. According to the out-of-focus holographic measurement method, the planet is introduced to serve as a radio source, the measurement precision and stability are improved, the real-time measurement effect and the multi-frequency calibration capability are enhanced, the calibration accuracy and the overall performance of the Tianmar radio telescope are remarkably improved, many limitations of a traditional surface type measurement method are solved, and the measurement precision and the measurement stability are improved. For example, the measurement speed is slow, additional hardware equipment is needed, the influence of weather is large, and the application range is limited.

Description

Technical Field

[0001] The invention belongs to the field of radio astronomy, and in particular relates to a defocus holographic measurement method of a radio telescope based on planetary zoom. Background Art

[0002] The core indicators of large radio telescopes include sensitivity and resolution, both of which have a decisive impact on the quality and depth of astronomical research.

[0003] The sensitivity of a telescope is related to its effective receiving area. Specifically, the larger the antenna aperture, the smaller the minimum detectable flux and the higher the sensitivity. This relationship shows that as the receiving area increases, the point source sensitivity of the telescope increases significantly, and more electromagnetic waves can be collected, thereby more effectively detecting weak celestial signals.

[0004] The resolution of a telescope is closely related to the beam width, aperture and operating wavelength of the antenna. Specifically, the relationship between the resolution θ of a telescope and its primary mirror diameter D and the operating wavelength λ is: This shows that the larger the aperture and the shorter the operating wavelength, the higher the imaging resolution of the telescope.

[0005] Therefore, sensitivity mainly measures the ability of an antenna to receive weak signals, while resolution reflects the ability of an antenna to detect target details. In order to improve the sensitivity and resolution of antennas, scientists have put forward increasing requirements for the caliber, operating frequency and working efficiency of antennas. This demand has promoted the research and development of antenna structure design, surface measurement methods and active surface systems.

[0006] However, large telescopes are often limited by their size, which is mainly reflected in the gravity deformation when the telescope changes its altitude, the thermal deformation caused by different heating or cooling of the telescope structure, and the inaccuracy of the panel setting on the surface. When the radio telescope is working, errors caused by dynamic loads such as gravity, temperature, and wind load cannot be avoided. Among these loads, gravity has the greatest impact on the structure of the radio telescope and the surface accuracy of the main reflector, and gravity deformation is long-term, followed by temperature, and finally wind load.

[0007] Based on this, in the design and use of large radio telescopes, the surface measurement of the main reflector of the antenna is particularly important. Accurate surface measurement and adjustment can significantly improve the antenna's receiving efficiency and observation accuracy.

[0008] Out-of-Focus holography (OOF) is an effective surface measurement technology. Existing radio telescopes such as the Tianma telescope usually use radio sources as sources for out-of-focus holography. Out-of-focus holography uses a linear combination of a set of basis functions (Zernik eThe aperture plane phase error is represented by a polynomial (a), and the defocus pattern is introduced to effectively solve the inverse problem of finding the surface error from the beam pattern. The theoretical far-field model is compared with the actual observation results to obtain the deformation information of the antenna surface. The main reflector system is adjusted accordingly to compensate for the deformation of the main reflector surface, thereby improving the antenna working efficiency. It can help astronomers understand the performance limitations, errors and impacts of the actual telescope system.

[0009] The measurement principle of traditional defocus holographic measurement technology is as follows:

[0010] Traditional phase holographic measurement technology measures the amplitude and phase of the far-field beam pattern by equipping an auxiliary phase reference antenna. After a simple Fourier inversion, the aperture function C(i,j) can be obtained, thereby knowing the deformation of the telescope. OOF (out-of-focus holographic measurement) technology uses a well-known relationship in antenna theory: the far-field pattern of a reflective antenna is the Fourier transform of the field distribution on the antenna aperture plane, which is applicable to a small angle range of the far-field pattern. The aperture plane is the effective receiving area of ​​the telescope. The far-field pattern of the reflective antenna and the aperture field distribution function E a This relationship of (x,y) can be expressed as:

[0011]

[0012] Where P(u, v) is the far-field beam of the reflecting antenna in the direction cosine coordinate system; E a (x, y) is the aperture field distribution function of the reflective antenna in the aperture plane coordinate system, and its unit is w; λ is the observation wavelength.

[0013] In the defocus holographic measurement technology, according to the aperture model, the aperture field distribution function E a The relationship between (x,y) and aperture phase distribution is:

[0014] E a =D(x,y)·I(x,y)exp{-i[φ(x,y)+δ(x,y,dz)]} (2)

[0015] Where D(x, y) is the obstruction distribution (such as truncation or occlusion distribution) on the aperture plane, the unit is m, I(x, y) is the illumination, δ(x, y, dz) is the additional term of the phase, that is, the additional phase caused by defocusing (corresponding to the optical path difference), Ф(x, y) represents the aperture phase distribution, dz is the axial offset, and the positive value of dz corresponds to the movement of the sub-reflector away from the main reflector.

[0016] Unfortunately, defocus holography cannot directly measure the aperture phase distribution, only the power pattern, which means the problem is degenerate. Defocus holography aims to break this degeneracy by utilizing a series of beam patterns, one of which is in focus and the other two are defocused, the latter being achieved by adding an axial offset to the telescope's sub-reflector. This axial offset dz is known in advance.

[0017] In order to solve these problems, a convenient and efficient method is to use Zernike polynomials to parameterize the aperture phase distribution:

[0018]

[0019] φ(x, y) is the aperture phase distribution, a n，l is the coefficient to be determined, n is the radial order, l is the angular order, n=1~max determines the total number of coefficients to be found by fitting [(n+1)(n+2) / 2]. Zernike polynomials are orthogonal on the unit circle. This strict orthogonality fails when applied to the Tianma Telescope (TMRT). Due to the edge taper and central occlusion, the illumination is not uniform across the aperture, thus destroying the orthogonality, but it is still approximately orthogonal and some low-order Zernike polynomials are very similar to the aberrations that may exist in the optical system. In addition, low-order polynomials represent large-scale aberrations on the aperture plane.

[0020] Combining all the above situations, according to the theoretical far-field model, the far-field beam P(u,v) of the reflector antenna can be expressed as:

[0021]

[0022] Where D(x, y) is the cutoff or occlusion distribution on the aperture plane, I(x, y) is the illumination, δ(x, y, dz) is the additional term of the phase, that is, the additional phase caused by defocus (corresponding to the optical path difference), Ф(x, y) represents the aperture phase distribution, and the unit of the far-field beam P(u, v) of the reflector antenna is w (watt).

[0023] For a standard Cassegrain telescope, the optical path difference δ(x, ydz) is:

[0024]

[0025] Among them, a and b are intermediate parameters, a=r / 2f, b=r / 2F, r is the cross-sectional radius of the telescope that changes with altitude, The unit is m; f is the focal length of the main reflector; F is the effective total focal length of the telescope at the Cassegrain focus; dz is the axial offset, and a positive value of dz corresponds to the movement of the sub-reflector away from the main reflector, and the unit is mm.

[0026] The amplitude model is a formula for calculating the amplitude of the illumination to be fitted. The amplitude model is:

[0027]

[0028] Where R is the radius of the main reflector; (x 0 ,y 0 ) defines the illumination center on the main reflector; σ r is the illumination cone, I 0 is the amplitude of the illumination to be fitted, and I(x,y) is the illumination.

[0029] The optical path difference δ(x,y,dz) and the illumination I(x,y) are both needed to calculate the aperture model.

[0030] However, due to the shape of the Tianma Telescope (TMRT), formulas (5) and (6) cannot be used to calculate the additional phase and illumination. Otherwise, the final result will have a large error, so Dong Jian et al. proposed a new calculation method to calculate these two terms, which is defined by high-density points.

[0031] The design of the double-reflection optical system is based on the equal light distance condition, so this shape of telescope can be regarded as a set of standard Cassegrain telescopes, and the focus of all Cassegrain telescopes is restricted to the optical axis. The following formula can calculate the additional phase caused by defocusing:

[0032]

[0033] Where δ(r, dz) represents the additional phase caused by defocusing; θ r It represents the angle between the optical axis and the light from the focus to the sub-reflector; represents the angle between the optical axis and the light from the sub-reflector to the main reflector, r is the cross-sectional radius of the telescope that varies with altitude, The unit is m, dz is the axial offset, a positive value of dz corresponds to the movement of the sub-reflector away from the main reflector, the unit is mm; λ is the wavelength, the unit is mm.

[0034] The receiver feed pattern follows a Gaussian distribution, and the amplitude model is then:

[0035]

[0036] Where, I(r) is the illumination; I 0 is the amplitude of the illumination to be fitted, in m; θ r It represents the angle between the optical axis and the light from the focus to the sub-reflector, in rad. is θ r The maximum value of σ r is the lighting cone.

[0037] Therefore, according to existing research, defocus holographic measurement has been used on radio telescopes such as the Tianma Telescope. However, there are currently few radio sources that can be used. For example, 3C84 observations are easily affected by weather, making it impossible to measure all-weather, the measurement accuracy is not high enough, and the real-time measurement effect is poor. Summary of the invention

[0038] The object of the present invention is to provide a defocus holographic measurement method for a radio telescope based on planetary zoom, so as to improve the calibration accuracy of the Tianma radio telescope.

[0039] In order to achieve the above object, the present invention provides a defocus holographic measurement method of a radio telescope based on planetary zoom.

[0040] Step S0: setting a resolution grid [xy] to achieve aperture discretization, setting an iteration count value i=0, and establishing an aperture model, an amplitude model, and a phase model;

[0041] Step S1: Taking the planet as the source, the sub-reflector is moved to perform defocus observation to obtain an observed power data set, and the observed power data set, wavelength and axial offset after deconvolution are used as input data of the model;

[0042] Step S2: According to the calculation formula and amplitude model of the additional phase generated by defocus, corresponding to the coordinates of each sampling point of the power data set, an additional phase matrix and an illumination matrix are interpolated;

[0043] Step S3: Initialize model parameters;

[0044] Step S4: Establishing a theoretical far-field model of the planet; determining the spectrum map of the planet according to the given planet map data, and performing frequency domain convolution based on FFT transformation to determine the beam output value of the theoretical far-field model of the planet;

[0045] Step S5: comparing the observed power data set with the beam output value of the theoretical far-field model to calculate the redundancy value;

[0046] Step S6: Determine whether the coefficients of the current Zernike polynomial are the optimal solution by using the current redundancy value and the least square method. If so, proceed to step S9; otherwise, minimize the redundancy value to update the coefficients of the Zernike polynomial, and then proceed to step S7;

[0047] Step S7: If the current radial order n of the Zernike polynomial is less than the maximum radial order M, the radial order n and the iteration count value i are both incremented by 1, and step S8 is executed; otherwise, step S9 is entered;

[0048] Step S8: Obtain an updated phase model according to the coefficients of the Zernike polynomial, and then update the theoretical far-field model of the planet, and interpolate to obtain its beam output value; return to step S5;

[0049] Step S9: Determine the best phase model according to the coefficients of the Zernike polynomial, and determine the phase error on the aperture plane according to the phase model.

[0050] Preferably, in step S1, the observed power data set is obtained by performing flight scanning by moving the sub-reflecting surface and undergoing preprocessing, and the preprocessing of the power data set includes:

[0051] Calculate the average value and center frequency of DIBAS data, obtain the original Tcal data, calculate the average Tcal data, average gain, system temperature and cal value to process the power data;

[0052] Process antenna data by interpolating azimuth, elevation, and time;

[0053] Fit the processed power data and antenna data and perform baseline processing;

[0054] A deconvolution process is performed to obtain a deconvolution-processed observed power data set.

[0055] Preferably, the step of deconvolution processing comprises:

[0056] Step B1: Establish a convolution model of the observed image;

[0057] Step B2: Perform Fourier transform on the observed image and the point spread function of the telescope to obtain the spectrum values ​​of the observed image and the point spread function, and obtain the relationship between the two according to the convolution model of the observed image;

[0058] Step B3: according to the spectrum values ​​of the observed image and the point spread function and the relationship between the two, inverse filtering is used to estimate the spectrum of the original image;

[0059] Step B4: performing inverse Fourier transform on the estimated spectrum of the original image to obtain a deconvolved image; or

[0060] The deconvolution algorithm used in the deconvolution process is Wiener filtering, Lucy-Richardson deconvolution or maximum entropy method.

[0061] Preferably, in step S0, the amplitude model is:

[0062]

[0063] Where, I(r) is the illumination; I 0 is the amplitude of the illumination to be fitted, in m; θr It represents the angle between the optical axis and the light from the focus to the sub-reflector, in rad. is θ r The maximum value of σ r is the lighting cone;

[0064] The phase model is:

[0065]

[0066] The caliber model is:

[0067] E a =D(x,y)·I(x,y)exp{-i[φ(x,y)+δ(x,y,dz)]},

[0068] E a (x, y) is the aperture field distribution function, the unit is w, x, y are the coordinates of the point on the aperture plane, D(x, y) is the blocking distribution on the aperture plane, the unit is m, I(x, y) is the illumination, φ(x, y) is the aperture phase distribution, the unit is rad, δ(x, y, dz) represents the additional phase caused by defocusing, dz is the axial offset, the unit is mm; λ is the wavelength, the unit is mm, r is the cross-sectional radius of the telescope that varies with altitude, the unit is m;

[0069] In step S2, the calculation formula of the additional phase generated by defocusing is:

[0070] Where r is the cross-sectional radius of the telescope that varies with altitude, in meters; dz is the axial offset, in millimeters; λ is the wavelength, in millimeters, and θ r is the angle between the secondarily reflected telescope incident beam and the telescope principal axis, It is the angle between the incident beam of the telescope after one reflection and the main axis of the telescope.

[0071] Preferably, in step S4, the spectrum map of the planet includes a first spectrum map and a second spectrum map; the first spectrum map and the second spectrum map are obtained through actual experience of scanning the planet, such as the code planetFF in the virtual machine.

[0072] Frequency domain convolution includes:

[0073] Step A1: First, check whether the dimensions of the first spectrum map and the second spectrum map are the same. If the dimensions are not the same, end the process;

[0074] Step A2: extracting amplitude distribution and phase distribution from the first spectrum map and the second spectrum map respectively, and then initializing the amplitude and phase to zero;

[0075] Step A3: transforming the amplitude distribution and the phase distribution using inverse Fourier transform;

[0076] Step A4: multiplying the transformed amplitude distribution and phase distribution to obtain a product result;

[0077] Step A5: using forward Fourier transform to inversely transform the product result to obtain an inverse transform result;

[0078] Step A6: Divide the inverse transformation result by the size of the spectrum map and multiply it by the cosine value of the phase to obtain the spectrum map of the convolution result, where the spectrum map of the convolution result is the beam output value of the far-field theoretical model.

[0079] Preferably, the step S3 specifically includes: setting the Zernike polynomial Z n,l (x, y) parameters, x, y are the coordinates of the point on the aperture plane, n is the radial order, l is the angular order; the amplitude I of the illumination to be fitted in the amplitude model 0 The initial value of is set to 0; the preset threshold of the least squares algorithm is set to the default value;

[0080] Set the Zernike polynomial Z n,l The parameters of (x,y) specifically include: Setting the Zernike polynomial Z n,l (x,y) the maximum radial order M; all the coefficients of the Zernike polynomial {a n,l} is set to 0; the current radial order n is initially set to 1.

[0081] Preferably, in step S6, the current redundancy value is input into a least squares algorithm to determine whether a preset threshold of the least squares algorithm is satisfied, thereby determining whether the coefficients of the current Zernike polynomial are an optimal solution.

[0082] Preferably, in step S8, the theoretical far-field model of the planet is updated, specifically comprising: interpolating the phase model to obtain three sets of aperture phase matrices; using the aperture model to combine the aperture phase matrix with an additional phase matrix δc(i,j,dz) and an illumination matrix Ic(i,j) to generate three sets of aperture field distribution functions, and then, respectively updating three theoretical far-field models according to the three sets of aperture field distribution functions.

[0083] Compared with the existing defocus holographic measurement technology, the defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention not only improves the measurement accuracy and stability, but also enhances the real-time measurement effect and multi-frequency calibration capability by introducing planets as radio sources, significantly improving the calibration accuracy and overall performance of the Tianma radio telescope, and solving many limitations of traditional surface measurement methods, such as slow measurement speed, the need for additional hardware equipment, great influence of weather, and limited scope of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flow chart of a defocus holographic measurement method of a radio telescope based on planetary zoom according to an embodiment of the present invention.

[0085] Figure 2 This is a structural diagram of a telescope involved in the defocus holographic measurement method of a radio telescope based on planetary zoom.

[0086] Figure 3 It is the function relationship diagram of the OOF preprocessor module.

[0087] Figure 4 It is a workflow diagram of the OOF pre-processor module and the OOF post-processor module. DETAILED DESCRIPTION

[0088] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings and described in detail.

[0089] The defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention is used to receive the beam pattern and obtain the measurement of the antenna surface deformation through Fourier transformation. Figure 1 As shown, the defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention determines the aperture phase error of the telescope through the defocus observation data, and comprises the following steps:

[0090] Step S0: setting a resolution grid [xy] to achieve aperture discretization, setting an iteration count value i=0, and establishing an aperture model, an amplitude model, and a phase model;

[0091] In the resolution grid [xy], [xy] represents the point coordinates on the aperture plane, and A is the grid size of the resolution grid.

[0092] In this embodiment, the amplitude model is determined by the receiver of the telescope. Due to the particularity of the geometric shape of the Tianma telescope, the amplitude model is:

[0093]

[0094] Where, I(r) is the illumination; I 0is the amplitude of the illumination to be fitted, in m; θ r It represents the angle between the optical axis and the light from the focus to the sub-reflector, in rad. is θ r The maximum value of σ r is the lighting cone.

[0095] The phase model is:

[0096]

[0097] The aperture model consists of a phase model and an amplitude model, which is:

[0098] E a =D(x,y)·I(x,y)exp{-i[φ(x,y)+δ(x,y,dz)]},

[0099] E a (x, y) is the aperture field distribution function, the unit is w, x, y are the coordinates of the point on the aperture plane, D(x, y) is the blockage distribution on the aperture plane, the unit is m, I(x, y) is the illumination, φ(x, y) is the aperture phase distribution, the unit is rad, δ(x, y, dz) represents the additional phase caused by defocus, the calculation formula of the additional phase caused by defocus is It is expressed in the form of , where dz is the axial offset in mm, λ is the wavelength in mm, and r is the cross-sectional radius of the telescope that varies with height in m.

[0100] According to the geometric shape of the Tianma telescope, the present invention uses an improved amplitude model I(r) to replace the traditional amplitude model I(x,y), so the measurement result will be more accurate. In the present invention, the phase model and the aperture model are given an initial value, and then finally obtained through formula iteration.

[0101] Step S1: Taking the planet as the source, moving the sub-reflector to perform defocus observation to obtain an observed power data set, and using the observed power data set, wavelength and axial offset after deconvolution as input data of the model;

[0102] Existing technologies all use radio sources as sources for defocused holographic measurements. The far-field image based on the reflective antenna is the Fourier transform of the field distribution on the antenna aperture plane. Using planets as sources enables all-weather measurements with stronger flux.

[0103] The observed power data set is obtained by moving the sub-reflector for flight scanning and preprocessing. In fact, the power data set without preprocessing is a fits file, which includes power (W), integration time (s), etc. After preprocessing, the power data set includes the power of the far-field beam and the coordinates of the sampling points on the aperture plane (including x-axis offset and y-axis offset), which is represented as a power matrix.

[0104] In the present invention, the preprocessing of the power data set is implemented by an OOF preprocessing program module. The input data of the OOF preprocessing program module is a raw data fits file including uncalibrated power, integration time and other information, and the output data is a fits file including x-axis offset, y-axis offset, power, time, that is, the required observed power data set.

[0105] like Figure 3 As shown in the figure, the specific workflow of the OOF preprocessor module is as follows: Get the raw data fits file from DIBAS, including the power, time, azimuth, pitch, displacement and other information in the focus and defocus data. Use the rawBkDataReader.py of the OOF preprocessor module to preprocess the raw data, define some empty lists pData and integ, use the pyfits.open function to open the specified FITS data file, and get the data header information and the data itself. Print the TDIM keyword in the data header information and output the value of TDIM3. Then, process the data line by line, extract the timestamp and data, perform a series of calculations and processing, store the results in the corresponding list, and print out part of the integ list. Then, preprocess the DIBAS data obtained from DIBAS, which includes: calculating the average value and center frequency of the DIBAS data, obtaining the original Tcal data, calculating the average Tcal data, the average gain, the system temperature and the cal value (i.e. the calibration value) for power processing. Next, use rawTelDataReader.py to interpolate the azimuth, pitch and time to process the antenna data. Then, the processed power data and antenna data are fitted through mergeData.py, baseline processing is performed through oof_bk.py, and finally, planetary deconvolution is performed through deconvolve.py, and three fits files are finally obtained, including x-axis offset, y-axis offset, power and time, which serve as the observed power data set in the defocus holographic measurement method of the present invention and the input file of the OOF post-processing program module.

[0106] Different from the existing preprocessing process of power data of radio sources, since a planetary source is used in the present invention, the preprocessing includes the step of performing planetary deconvolution on the observed power data set.

[0107] Planetary deconvolution: In radio astronomy, planets are extended sources with large angular diameters, so their signals are affected by the main beam of the radio telescope, causing the observed data to contain the blurring effect of the device response function. In order to restore the true signal distribution of the planet, deconvolution must be performed. Radio sources are usually point sources with an angular diameter much smaller than the main beam of the telescope. The observed signal can be approximated as the direct output of the device response function, so there is no need for a complex deconvolution process.

[0108] Planetary deconvolution is an important method to recover the original signal from the observed image, mainly for the following reasons:

[0109] 1. Improve image resolution: During observation, images are usually blurred by the point spread function (PSF) of the instrument. Deconvolution technology can reduce this blur, improve image resolution, and make the details of the planetary surface clearer.

[0110] 2. Reduce noise and artifacts: Deconvolution can effectively reduce noise and artifacts in the image, making the observed data more accurate and reliable. This is very important for subsequent analysis and research.

[0111] 3. Enhanced details and contrast: Deconvolution can enhance the details and contrast in images, making the features of the planet's surface more obvious and helping to identify and analyze subtle geological and atmospheric phenomena.

[0112] 4. Correct the influence of the optical system: The optical characteristics of the telescope will affect the image quality. Deconvolution technology can correct these influences and restore the true information of the image.

[0113] 5. Improve measurement accuracy: Accurate measurement is crucial for scientific research. Deconvolution can improve the measurement accuracy of planetary surface features and atmospheric phenomena, thereby providing more accurate scientific data.

[0114] The steps of deconvolution are as follows:

[0115] Step B1: Establish a convolution model of the observed image;

[0116] According to the convolution model, the observation image I obs is the original image I true Convolution with the telescope's point spread function PSF, plus noise N.

[0117] I obs =I ture *PSF+N

[0118] Among them, represents the convolution operation.

[0119] Step B2: Observe image I obs The Fourier transform of the telescope's point spread function PSF is performed to obtain the spectrum F(I obs ) and the value of the frequency spectrum F (PSF) of the telescope's point spread function, and obtain the relationship between the two based on the convolution model of the observed image;

[0120] Fourier transform: Convolution is more difficult to handle in the spatial domain, but it becomes a simple multiplication in the frequency domain. Therefore, the observed image I can be obs The Fourier transform of the telescope's point spread function PSF is performed to obtain the spectrum F(I obs ) and the frequency spectrum of the telescope's point spread function F (PSF). The relationship between the two is:

[0121] F(I obs )=F(I ture )×F(PSF)+F(N)

[0122] Step B3: According to the spectrum of the observed image and the spectrum of the telescope's point spread function and the relationship between the two, inverse filtering is used to estimate the spectrum F(I ture ).

[0123] Inverse filtering: In the frequency domain, the spectrum F(I ture ).

[0124] The estimated spectrum of the original image F(I ture )for:

[0125] F(I ture )≈F(I obs ) / F(PSF)

[0126] It should be noted that direct inverse filtering tends to amplify noise, so regularization methods are usually used to suppress the influence of noise.

[0127] Regularization method: In step B3, in order to reduce the influence of noise, a regularization method such as Tikhonov regularization or constrained least squares method can be introduced.

[0128] After the regularization method is introduced, the estimated spectrum of the original image is:

[0129] F(I ture )=F(I obs )×F(PSF)* / [|F(PSF)| 2 +α]

[0130] where F(PSF)* is the complex conjugate of the PSF and α is the regularization parameter.

[0131] Step B4: Estimating the spectrum F(I ture ) to perform inverse Fourier transform to obtain the deconvolved image (i.e. the original image I true ).

[0132] In this embodiment, the point spread function PSF of the telescope is known.

[0133] In other embodiments, the point spread function PSF of the telescope may be unknown, and accordingly, the deconvolution algorithm used in the deconvolution process may be a deconvolution algorithm commonly used in radio astronomy, such as Wiener filtering, Lucy-Richardson deconvolution, and maximum entropy method. Wiener filtering uses the signal-to-noise ratio in the frequency domain for deconvolution, which has high computational efficiency and is suitable for images with known noise characteristics, but it relies heavily on the noise model and has limited processing capabilities. Lucy-Richardson deconvolution is based on maximum likelihood estimation and can well restore the details of low signal-to-noise ratio data, but it has high computational complexity, may produce artifacts, and is sensitive to parameter selection. The maximum method restores the image by maximizing the image entropy, which is suitable for sparse or incomplete data, can enhance details and contrast, but it is computationally complex, relies on prior information, and may have unstable convergence. The selection of a suitable algorithm depends on the specific data characteristics and application scenarios.

[0134] Since the present invention is a defocus holographic measurement method, the number of power data sets is 3 groups and they are obtained by moving the sub-reflecting surface for defocus observation. The 3 groups of power data sets are obtained by moving the sub-reflecting surface, including two groups of positive defocus aperture planes moving facing the main reflecting surface and negative defocus aperture planes moving away from the main reflecting surface, and one group located on the focusing aperture plane of the main reflecting surface.

[0135] In this embodiment, the sampling interval of the aperture plane sampling is a=DA×3, where D is the diameter of the Tianma telescope and A is the grid size (equal to 192). Therefore, the sampling point coordinates are (i, j), and the aperture plane sampling obtains a 192×192 power matrix A(i, j).

[0136] The wavelength is determined by selecting a specific wavelength band.

[0137] The axial offset is the defocus distance, which is freely assignable and the physical quantity is the length in cm.

[0138] Step S2: Calculation formula of the additional phase generated by defocusing and amplitude model Corresponding to the coordinates (i, j) of each sampling point of the power data set, the additional phase δc(r, dz) and illumination Ic(r) generated by defocus are interpolated to the aperture plane by linear interpolation method to interpolate the additional phase matrix δc(i, j, dz) and illumination matrix Ic(i, j);

[0139] Subsequent calculation of the aperture field distribution function requires the coefficients a of the Zernike polynomials n,l , additional phase matrix δc(i,j,dz) and illumination matrix Ic(i,j), therefore, it is necessary to obtain the additional phase matrix δc(i,j,dz) and illumination matrix Ic(i,j). The units of the additional phase δc(r,dz) and illumination Ic(r) are rad and W / m respectively. 2 .

[0140] The calculation formula for the additional phase caused by defocus is:

[0141] Where r is the cross-sectional radius of the telescope that varies with altitude, in meters; dz is the axial offset, in millimeters; λ is the wavelength, in millimeters, and θ r is the angle between the secondarily reflected telescope incident beam and the telescope principal axis, φ r is the angle between the incident beam of the telescope after one reflection and the main axis of the telescope. The specific positions of the two are as follows: Figure 2 shown.

[0142] Step S3: Initialize the model parameters, including: setting the Zernike polynomial Z n,l (x, y) parameters; the amplitude of the illumination to be fitted in the amplitude model I 0 The initial value of is set to 0; the preset threshold of the least squares algorithm is set to the default value;

[0143] Among them, for the phase model formula, the Zernike polynomial Z n,l (x, y) represents a polynomial, x, y are the coordinates of the point on the aperture plane, n is the radial order, l is the angular order, a n,l is the coefficient of the Zernike polynomial, which is the key part to be solved. n,l will change.

[0144] Set the Zernike polynomial Z n,l The parameters of (x,y) specifically include: Setting the Zernike polynomial Z n,l (x,y) the maximum radial order M; all the coefficients of the Zernike polynomial {a n,l} is set to 0; the current radial order n is initially set to 1.

[0145] The maximum radial order M is the maximum value of the radial order n. In this embodiment, the maximum radial order M of the Zernike polynomial is usually 5 or 6, depending on the signal-to-noise ratio.

[0146] The threshold of the least squares algorithm is used in subsequent steps.

[0147] Step S4: start the first round of iteration; wherein, a theoretical far-field model of the planet is established, a spectrum map of the planet is constructed according to given planet map data, and a frequency domain convolution based on FFT transformation is performed on the spectrum map to determine the beam output value of the theoretical far-field model of the planet;

[0148] In the present invention, the first and second spectrum maps of the planet are constructed according to given planet map data (including the radius and wavelength of the planet), and finally the beam output value of the far-field theoretical model is obtained through a frequency domain convolution operation based on FFT transformation.

[0149] In this embodiment, by initializing the properties of the planet, the first spectrum map m1 and the second spectrum map m2 are directly created using the mkModel function according to the properties of the planet, and the power of the planet is extracted using the Power function. The first spectrum map m1 and the second spectrum map m2 are both amplitude spectra and phase spectra.

[0150] Among them, the input parameters of the frequency domain convolution operation include the first spectrum map m1 and the second spectrum map m2, and the output of the frequency domain convolution operation is the spectrum map mres of the convolution result. The specific process of frequency domain convolution is as follows:

[0151] Step A1: First, check whether the dimensions of the first spectrum map m1 and the second spectrum map m2 are the same. If the dimensions are not the same, throw a std::runtime_error exception to end the process;

[0152] Step A2: extracting the amplitude distribution and the phase distribution of the first spectrum map m1 and the second spectrum map m2 respectively, and then initializing the amplitude and the phase to zero;

[0153] After extraction, it is initialized to zero to facilitate subsequent data processing. The original amplitude and phase characteristics are not lost, but are initialized to zero here for subsequent operations.

[0154] Step A3: Use inverse Fourier transform (such as InverseFF function) to transform the amplitude distribution and phase distribution.

[0155] Step A4: Multiply the transformed amplitude distribution and phase distribution to obtain a product result, wherein the amplitudes of the two are multiplied and the phases are added.

[0156] Step A5: Use forward Fourier transform (such as ForwardFF function) to inversely transform the product result to obtain an inverse transform result.

[0157] Step A6: Divide the inverse transformation result by the size of the spectrum map and multiply it by the cosine value of the phase to obtain the spectrum map mres of the convolution result, where the spectrum map mres of the convolution result is the beam output value of the far-field theoretical model.

[0158] For the second overloaded function FFTConvolve, a pointer to the spectrum map mres of the convolution result is returned, so the OFF preprocessing module can process it.

[0159] This code implements frequency domain convolution based on Fast Fourier Transform (FFT), which performs convolution operations through multiplication and phase adjustment between spectrum maps.

[0160] The theoretical far-field model obtained is:

[0161]

[0162] P(u,v) is the far-field beam of the reflecting antenna in the direction cosine coordinate system, E a (x, y) is the aperture field distribution function of the reflector antenna in the aperture plane coordinate system, with the unit of w; λ is the observation wavelength; u, v are the coordinates in the direction cosine coordinate system, x, y are the point coordinates on the aperture plane, with the unit of m; D(x, y) is the blocking distribution on the aperture plane, with the unit of m, I(x, y) is the illumination, δ(x, y, dz) is the additional phase caused by defocusing, Ф(x, y) represents the aperture phase distribution, dz is the axial offset, and the positive value of dz corresponds to the movement of the sub-reflector away from the main reflector.

[0163] Step S5: Compare the observed power data set with the beam output values ​​of the theoretical far-field model of the planet to calculate the redundancy value.

[0164] The redundancy value is the value of the actual observation data at the same coordinate position on the aperture plane minus the beam output value of the theoretical far-field model.

[0165] Step S6: Determine whether the coefficients of the current Zernike polynomial are the optimal solution through the current redundancy value and the least squares method. If so, proceed to step S9 (the coefficients of the Zernike polynomial output at this time can represent the phase model); otherwise, use the least squares method to minimize the redundancy value to update the coefficients of the Zernike polynomial, and then execute step S7 to continue iteration.

[0166] Among them, by inputting the current redundancy value into the least squares algorithm to determine whether it is less than the preset threshold of the least squares method, and then determining whether the coefficient of the current Zernike polynomial is the optimal solution (if it is less than the preset threshold, the coefficient of the current Zernike polynomial is the optimal solution). If the preset threshold of the least squares method is met, step S9 is entered.

[0167] In this embodiment, the least square method adopted is the Levenberg-Marquardt (LM) algorithm.

[0168] Step S7: If the current radial order n is less than the maximum radial order M, the radial order n and the iteration count value i are both incremented by 1 (i=i+1 means n=n+1), and step S8 is executed to continue iteration; otherwise, step S9 is entered;

[0169] Step S8: Based on the coefficients of all Zernike polynomials {a n,l} Obtain an updated phase model, then update the theoretical far-field model of the planet, and interpolate the beam output value of the theoretical far-field model; then return to step S5.

[0170] The theoretical far-field model of the planet is updated, specifically including: interpolating the phase model to obtain three sets of aperture phase matrices; using the aperture model to combine the aperture phase matrix with the additional phase matrix δc(i,j,dz) and the illumination matrix Ic(i,j) to generate three sets of aperture field distribution functions, and then, respectively updating the three theoretical far-field models according to the three sets of aperture field distribution functions. Among them, the aperture phase matrix corresponds to the aperture phase distribution Ф(x,y) in the aperture model, the additional phase matrix δc(i,j,dz) corresponds to the additional phase δ(x,y,dz) generated by defocus in the aperture model, and the illumination matrix Ic(i,j) corresponds to the illumination I(x,y) in the aperture model.

[0171] When three theoretical far-field model beam output values ​​are interpolated, these beam output values ​​are interpolated to the positions of the sampling points of each power data set by Gaussian function interpolation.

[0172] In this embodiment, each set of aperture phase matrices obtained by interpolation is a 192×192 matrix. The interpolation here means first flattening the aperture into a 192×192 matrix corresponding to the sampling points of the observed power data set on the aperture plane, and then interpolating the additional phase matrix and illumination matrix to correspond to the sampling points on the aperture plane.

[0173] The present invention only performs the calculation on the coefficients {a n ,l} is updated without changing the remaining additional phase matrix δc(i,j,dz) and illumination matrix Ic(i,j).

[0174] Therefore, the present invention can obtain the theoretical far-field model of the planet (i.e., the first spectrum map and the second spectrum map) based on actual experience, and thus infer the aperture field distribution function. Among them, the aperture model and the theoretical far-field model are determined at the beginning, and the theoretical far-field model is obtained through actual experience of planetary scanning, such as the code planetFF in the virtual machine. When the redundancy value obtained by subtracting the beam output value of the theoretical far-field model from the observed power data reaches the threshold, the zernik e The polynomial can represent the aperture phase; when the redundancy value is large, the zernik e The coefficients of the polynomial, the aperture model and the theoretical far-field model of the planet are changed accordingly until the redundancy value reaches a threshold.

[0175] Step S9: Based on the coefficients {a n ,l} determine the optimal phase model, determine the phase error on the aperture plane based on the phase model, and then determine the gravity deformation of the main reflector.

[0176] When the radial order n is greater than or equal to 2, the final Zernike polynomial coefficients {a n ,l} calculate the phase error on the aperture plane. Finally, the gravity deformation of the main reflector is calculated through these phase errors.

[0177] According to the prior art, the calculation formula of the phase error is:

[0178]

[0179] Among them, λ is the wavelength, x, y are the coordinates of the point on the aperture plane, F is the focal length of the main reflection surface, Z n,l (x,y) is a Zernike polynomial, a n,l are the coefficients of the Zernike polynomial, n is the radial order, l is the angular order, and phase{} represents the phase function, which returns the phase angle (angle) of a complex number, that is, the argument (arg) of the complex number. Phase is an angle that represents the direction of the complex number relative to the real axis on the complex plane.

[0180] The calculation formula for the gravity deformation of the main reflector is:

[0181] a n，l (E)=a sin(E)+b cos(E)+k×E+c

[0182] Among them, a n,l (E) represents Zerneike polynomial, a, b, k are coefficients, and E represents the independent variable of Zerneike polynomial.

[0183] Through the above steps, the planetary OOF algorithm can accurately calculate the phase error of the telescope aperture, providing an important basis for further optimizing the performance of the telescope. This method achieves accurate measurement and correction of the telescope surface error by improving the signal-to-noise ratio and optimizing the calculation process.

[0184] Experimental results:

[0185] The defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention is implemented based on a computer. In this experiment, the software system of the computer is composed of two program modules, namely, an OOF pre-processing program module and an OOF post-processing program module. Figure 4 As shown, by inputting the original DIBAS data (fits file) and preprocessing it through the OOF preprocessing program module, three fits files are obtained, and the phase error map on the aperture plane is obtained through post-processing.

[0186] Among them, the input data of the OOF preprocessing program module is a raw data fits file including uncalibrated power, integration time and other information, and the output data is a fits file including x-axis offset, y-axis offset, power, time, that is, the required observed power data set.

[0187] As described above, the specific workflow of the OOF preprocessor module is as follows: Get the raw data fits file from DIBAS, including power, time, azimuth, pitch, displacement and other information in the focus and defocus data. Use the rawBkDataReader.py of the OOF preprocessor module to preprocess the raw data, define some empty lists pData and integ, use the pyfits.open function to open the specified FITS data file, and get the data header information and the data itself. Print the TDIM keyword in the data header information and output the value of TDIM3. Then, process the data line by line, extract the timestamp and data, perform a series of calculations and processing, store the results in the corresponding list, and print out part of the integ list. Then, preprocess the DIBAS data obtained from DIBAS, which includes: calculating the average value and center frequency of the DIBAS data, obtaining the original Tcal data, calculating the average Tcal data, average gain, system temperature and cal value (i.e. calibration value) for power processing. Next, use rawTelDataReader.py to interpolate the azimuth, pitch and time to process the antenna data. Then, the processed power data and antenna data are fitted by mergeData.py, baseline processing is performed by oof_bk.py, and finally, planet deconvolution is performed by deconvolve.py, and finally three fits files are obtained, including x-axis offset, y-axis offset, power and time, which are used as the observed power data set in the defocus holographic measurement method of the present invention and the input file of the OOF post-processing program module. The specific workflow of the OOF post-processing program module is as follows:

[0188] Step 2: Use the preprocessed FITS file as the input file, and create a data set mapres (pyoof.MapToResidualDS) through the MkMapResDS function based on the telescope information, skymapsample, and interpolation parameters in the observation file; output ps (pyoof.ObsDefocus) through the MkPhaseScreen function based on the telescope information and aperture sampling in the observation file; add mapres and ps to oc (the object for comparison of the observation and far-field response model) through the LoadOCData function; based on the information of the telescope and chopthorw in the observation file and the information of the electric field distribution in the telescope aperture plane, output FF (far-field object) (pyoof.PlanetFF) according to the name of the telescope, the type of the receiver, and the selection of the observation source through the MkFF function; based on the observation file, image resolution, the maximum Zernike order to be fitted, and oversampling The sampling factor, fwhm, and extent are used to generate the aperture distribution function (aperture) through the MkObsCompare function according to the type of receiver and the number of observations; the MkFF function is called to create and calculate the far-field antenna response object (ff), and oc is output based on aperture and ff (used to compare observations and models) (pyoof.ObsCompare); the function (pybnmin1.LMMin) is called to fit the oc object using the least squares method LM, and the fitting results are saved in fitspars.txt. The functions (pyoof.WriteAperture, pyoof.WriteBeams, pyoof.WriteAperture,) are called to write the aperture information (aperture), beam information (fitbeam.fits), and untilted aperture information (aperture-notilt.fits) in the oc object into the fits file and save them.

[0189] Finally, pass the oc object to Lmm, write the oc object containing the perfect beam information into the (perfectbeams.fit) file through (pyoof.WriteBeams), and output fitpars.txt (a file of fitting parameters); traverse the zernike order through the Red function, and use the highest order for fitting output.

[0190] The final output document of the program: This program finally gets the oofout file, each opened as a file from z1 to z6 (because the maximum Zernike order to be processed is 6). Each opened has (aperture.fits (aperture distribution), aperturenotilt.fits (aperture distribution of the telescope without tilt), fitsbeams.fits (beam information), fitpars.txt (file of fitting parameters), OOF phase error distribution.

[0191] The defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention obtains the beam pattern of the actual observed planet by deconvolution, uses the planet as the source to perform defocus holographic measurement, establishes a theoretical model, compares the theoretical far-field model of the planet with the beam pattern of the actual observation to obtain the surface error of the telescope, and uses the calibration accuracy of the Tianma radio telescope. The planet is an individual source with strong enough flux and high signal-to-noise ratio, which can improve the accuracy of calibration. In addition, the position of the planetary source is accurate and can support calibration in multiple frequency ranges, which is crucial to the performance improvement of the telescope.

[0192] In addition, because the prior art does not have a data processing flow with planets as sources, it encounters the difficulty of establishing a theoretical far-field model using planets as sources in software for defocused holographic measurement, as well as the difficulty of convolving the data observed with planets as sources. The present invention establishes a theoretical model using planets as sources by optimizing the code of software for defocused holographic measurement.

[0193] Compared with the prior art, the present invention has the following advantages:

[0194] 1) Higher measurement accuracy: Planets are used as radio sources. Planets have high flux and high signal-to-noise ratio, which significantly improves the measurement accuracy, makes the measurement faster, improves the efficiency and accuracy of astronomical observations, and provides more reliable data support for astronomical research.

[0195] 2) All-weather measurement capability: Planetary observations are not easily affected by weather, and all-weather measurements are achieved, which improves the stability and reliability of measurements. Traditional methods often cannot provide high-precision and high-reliability measurement results under complex environmental conditions, which has an adverse impact on the efficiency and accuracy of astronomical observations.

[0196] 3) Calibration support for multiple frequency ranges: The precise location of the planetary source can support calibration in multiple frequency ranges, further improving the applicability and flexibility of the telescope in different observation tasks.

[0197] 4) Improved real-time measurement results: Using planets as radio sources improves real-time measurement results, allowing high-quality data to be obtained even under dynamic conditions.

[0198] 5) Reduce equipment dependence: This technical solution does not require additional hardware equipment, which reduces equipment costs and maintenance difficulties, allowing more scientific research institutions to adopt this method. It improves the calibration accuracy and stability of the telescope, extends the service life of the equipment, and further reduces long-term operating costs.

[0199] To sum up, compared with the existing defocus holographic measurement technology, the defocus holographic measurement method of the radio telescope based on planetary zoom of the present invention not only improves the measurement accuracy and stability, but also enhances the real-time measurement effect and multi-frequency calibration capability by introducing planets as radio sources, significantly improving the calibration accuracy and overall performance of the Tianma radio telescope, and solving many limitations of traditional surface measurement methods, such as slow measurement speed, the need for additional hardware equipment, great influence by weather, and limited scope of application.

[0200] The above is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. The above embodiments of the present invention can also be modified in various ways. All simple, equivalent changes and modifications made according to the claims and the description of the present invention fall within the scope of protection of the claims of the present invention. The contents not described in detail in the present invention are all conventional technical contents.

Claims

1. A defocus holographic measurement method for a radio telescope based on planetary zoom, characterized in that: include: Step S0: setting a resolution grid [xy] to achieve aperture discretization, setting an iteration count value i=0, and establishing an aperture model, an amplitude model, and a phase model; Step S1: Taking the planet as the source, the sub-reflector is moved to perform defocus observation to obtain an observed power data set, and the observed power data set, wavelength and axial offset after deconvolution are used as input data of the model; Step S2: According to the calculation formula and amplitude model of the additional phase generated by defocus, corresponding to the coordinates of each sampling point of the power data set, an additional phase matrix and an illumination matrix are interpolated; Step S3: Initialize model parameters; Step S4: Establishing a theoretical far-field model of the planet; determining the spectrum map of the planet according to the given planet map data, and performing frequency domain convolution based on FFT transformation to determine the beam output value of the theoretical far-field model of the planet; Step S5: comparing the observed power data set with the beam output value of the theoretical far-field model to calculate the redundancy value; Step S6: Determine whether the coefficients of the current Zernike polynomial are the optimal solution by using the current redundancy value and the least square method. If so, proceed to step S9; Otherwise, minimize the redundancy value to update the coefficients of the Zernike polynomial, and then execute step S7; Step S7: If the current radial order n of the Zernike polynomial is less than the maximum radial order M, the radial order n and the iteration count value i are both incremented by 1, and step S8 is executed; otherwise, step S9 is entered; Step S8: obtaining an updated phase model according to the coefficients of the Zernike polynomial, and then updating the theoretical far-field model of the planet, and interpolating its beam output value; Return to step S5; Step S9: Determine the best phase model according to the coefficients of the Zernike polynomial, and determine the phase error on the aperture plane according to the phase model.

2. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 1, characterized in that: In step S1, the observed power data set is obtained by performing flight scanning by moving the sub-reflector and undergoing preprocessing. The preprocessing of the power data set includes: Calculate the average value and center frequency of DIBAS data, obtain the original Tcal data, calculate the average Tcal data, average gain, system temperature and cal value to process the power data; Process antenna data by interpolating azimuth, elevation, and time; Fit the processed power data and antenna data and perform baseline processing; A deconvolution process is performed to obtain a deconvolution-processed observed power data set.

3. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 2, characterized in that: The steps of deconvolution processing include: Step B1: Establish a convolution model of the observed image; Step B2: Perform Fourier transform on the observed image and the point spread function of the telescope to obtain the spectrum values ​​of the observed image and the point spread function, and obtain the relationship between the two according to the convolution model of the observed image; Step B3: according to the spectrum values ​​of the observed image and the point spread function and the relationship between the two, inverse filtering is used to estimate the spectrum of the original image; Step B4: performing inverse Fourier transform on the estimated spectrum of the original image to obtain a deconvolved image; or The deconvolution algorithm used in the deconvolution process is Wiener filtering, Lucy-Richardson deconvolution or maximum entropy method.

4. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 1, It is characterized in that, in the step S0, the amplitude model is: Where I(r) is the illumination; I0 is the amplitude of the illumination to be fitted, in m; θ represents the angle between the optical axis and the light from the focus to the sub-reflector, the unit is rad, is θ r The maximum value of σ r is the lighting cone; The phase model is: The caliber model is: E a =D(x,y)·I(x,y)exp{-i[φ(x,y)+δ(x,y,dz)]}, E a (x, y) is the aperture field distribution function, the unit is w, x, y are the coordinates of the point on the aperture plane, D(x, y) is the blockage distribution on the aperture plane, the unit is m, I(x, y) is the illumination, φ(x, y) is the aperture phase distribution, the unit is rad, δ(x, y, dz) represents the additional phase caused by defocusing, dz is the axial offset, the unit is mm; λ is the wavelength, the unit is mm, r is the cross-sectional radius of the telescope that varies with altitude, the unit is m; In step S2, the calculation formula of the additional phase generated by defocusing is: Where r is the cross-sectional radius of the telescope that varies with altitude, in meters; dz is the axial offset, in millimeters; λ is the wavelength, in millimeters, and θ r is the angle between the secondarily reflected telescope incident beam and the telescope principal axis, It is the angle between the incident beam of the telescope after one reflection and the main axis of the telescope.

5. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 1, characterized in that: In step S4, the spectrum map of the planet includes a first spectrum map and a second spectrum map; Frequency domain convolution includes: Step A1: First, check whether the dimensions of the first spectrum map and the second spectrum map are the same. If the dimensions are not the same, end the process; Step A2: extracting amplitude distribution and phase distribution from the first spectrum map and the second spectrum map respectively, and then initializing the amplitude and phase to zero; Step A3: transform the amplitude distribution and the phase distribution using inverse Fourier transform; Step A4: multiplying the transformed amplitude distribution and phase distribution to obtain a product result; Step A5: using forward Fourier transform to inversely transform the product result to obtain an inverse transform result; Step A6: Divide the inverse transformation result by the size of the spectrum map and multiply it by the cosine value of the phase to obtain the spectrum map of the convolution result, where the spectrum map of the convolution result is the beam output value of the far-field theoretical model.

6. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 1, characterized in that: The step S3 specifically includes: setting the Zernike polynomial Z n,l (x, y) parameters, x, y are the coordinates of the point on the aperture plane, n is the radial order, l is the angular order; the initial value of the amplitude I0 of the illumination to be fitted in the amplitude model is set to 0; the preset threshold of the least squares algorithm is set to the default value; Set the Zernike polynomial Z n,l The parameters of (x,y) specifically include: Setting the Zernike polynomial Z n,l (x,y) the maximum radial order M; all the coefficients of the Zernike polynomial {a n,l } is set to 0; the current radial order n is initially set to 1.

7. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 6, characterized in that: In step S6, the current redundancy value is input into the least squares algorithm to determine whether a preset threshold of the least squares algorithm is satisfied, thereby determining whether the coefficients of the current Zernike polynomial are the optimal solution.

8. The defocus holographic measurement method of a radio telescope based on planetary zoom according to claim 1, characterized in that: In the step S8, the theoretical far-field model of the planet is updated, specifically including: interpolating the phase model to obtain three groups of aperture phase matrices; using the aperture model to combine the aperture phase matrix with the additional phase matrix δc(i,j,dz) and the illumination matrix Ic(i,j) to generate three groups of aperture field distribution functions, and then, respectively updating the three theoretical far-field models according to the three groups of aperture field distribution functions.

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