CN114425732B - Automatic optimization method, system and medium for sub-caliber processing technology - Google Patents
Automatic optimization method, system and medium for sub-caliber processing technology Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
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Abstract
The invention is suitable for the technical field of optical processing, and provides an automatic optimization method, a system and a medium for a sub-caliber processing technology, wherein the automatic optimization method for the sub-caliber processing technology comprises the following steps: obtaining effective removal rate spectrums of different removal functions, wherein the effective removal rate spectrums are convergence rates of correction of error volumes of all spatial frequencies by the removal functions; acquiring a volume spectral density function of the optical element, wherein the volume spectral density function is the density of the volume of residual error material contained in the surface shape error of the optical element at each frequency; and obtaining the optimal processing technology through the effective removal rate spectrum and the volume spectral density function. The automatic optimization method, system and medium for the sub-caliber processing technology provided by the invention have the advantages of high processing efficiency and low production cost.
Description
Technical Field
The invention relates to the technical field of optical processing, in particular to an automatic optimization method, system and medium for a sub-caliber processing technology.
Background
The sub-aperture polishing technology is proposed by U.S. R.A. Jones in 60 s, and the basic principle is that a tool far smaller than the aperture of a processing element is adopted, the residence time is controlled by a numerical control technology to remove local materials, the error convergence is realized by combining high-precision surface shape detection iterative processing, and the surface shape error RMS of the large-aperture optical element, which is better than 0.01 μm, can be obtained. Due to the advantages of high precision and high certainty, the sub-aperture polishing technology is widely applied to the final precise shaping stage of ultra-precision machining, and is the most feasible means for realizing high-precision machining of large-aperture optical elements at present. Advanced optical manufacturing technologies such as small tool numerical control, air bags, atmospheric plasma, magnetorheological, jet flow, ion beams and the like all belong to sub-aperture polishing technologies, the processing precision and efficiency of optical elements are greatly improved, but the ultra-precision processing cost of the existing large-aperture optical elements is still very high, and tens of thousands and millions of times are used.
In the sub-aperture polishing digital automatic control model, the surface shape error represents the distribution of the spatial frequency band error of the function to be removed of the element to be processed, the removal function represents the capability of a processing tool for correcting the spatial frequency band error, and the removal function can represent the removal rate distribution of the tool in a fixed-point processing influence range by using a two-dimensional matrix.
Although the sub-aperture polishing technologies such as magnetorheological, ion beam and small tool numerical control are adopted, the processing of the large-aperture optical element with the RMS value less than 0.1 μm can be realized, and as the surface shape error distribution has the characteristics of randomness and diversity of removal functions, in order to obtain the final precision, the low removal rate and small-size removal function which are conservative as much as possible are generally adopted, so that the processing working hours are greatly increased.
The method for representing the correction capability of the removal function mainly comprises two methods, namely, the convergence capability of the removal function on the error distribution of a processed element is indirectly reflected according to a processing experiment result, a large number of experiment results are required to be used as a premise, and an experimenter can have a certain degree of real operability only by having a certain experience accumulation; and secondly, the Fourier transform of the removal function is directly carried out, and the correction capability of removing the spatial frequency band error can be qualitatively represented. The two methods can only evaluate the correction capability of the removal function through experience or qualitative characterization among a plurality of removal functions, and the targeted process optimization cannot be made according to different conditions and different surface shape error distributions of the optical element.
In summary, none of the automatic optimization methods for the sub-aperture processing techniques in the prior art solves the problem that the most suitable process parameters (removal functions) for the current element cannot be obtained by combining the surface shape error distribution of the current element in actual processing, and the comprehensive efficiency of sub-aperture polishing is seriously reduced.
Disclosure of Invention
The invention aims to provide an automatic optimization method, system and medium for a sub-caliber machining process, which have high machining efficiency and low production cost.
The invention provides an automatic optimization method of a sub-caliber processing technology in a first aspect, which comprises the following steps:
step S10: obtaining effective removal rate spectrums of different removal functions, wherein the effective removal rate spectrums are convergence rates of correction of error volumes of all spatial frequencies by the removal functions;
step S20: acquiring a volume spectral density function of the optical element, wherein the volume spectral density function is the density of the volume of residual error material contained in the surface shape error of the optical element at each frequency;
step S30: and obtaining the optimal processing technology through the effective removal rate spectrum and the volume spectral density function.
Further, step S10 further includes: and obtaining an effective removal rate spectrum according to the ratio of the volume variation of the surface shape error to the processing time.
Further, a preferred processing technique is obtained by the effective removal rate spectrum and the volume spectral density function.
Further, step S20 further includes calculating a time spectral density function according to the effective removal rate spectrum and the volume spectral density function, and integrating the time spectral density function to obtain the processing time of the removal function; the removal function is a preferred machining process when the machining time of the removal function is minimal.
Further, in step S20, the temporal spectral density function is a volume spectral density function divided by the effective removal rate spectrum.
Further, step S20 further includes: and integrating the volume spectral density function at a preset space frequency band to obtain the surface shape error volume of the optical element under the preset space frequency band, calculating the surface shape error volume outside the cut-off frequency of the removal function, and selecting the removal function with the minimum volume difference value as the optimal processing technology.
Further, the volume spectral density function is a two-dimensional volume spectral density function or a one-dimensional volume spectral density function.
The invention provides a preferred system of a sub-caliber processing technology, which comprises an effective removal rate spectrum acquisition module, a volume spectrum density function acquisition module and a preferred processing technology acquisition module; the effective removal rate spectrum acquisition module is used for acquiring effective removal rate spectrums of different removal functions; the volume spectral density function acquisition module is used for acquiring a volume spectral density function of the optical element; the optimal processing technology obtaining module is used for obtaining an optimal processing technology through the effective removal rate spectrum and the volume spectrum density function.
A third aspect of the invention provides a readable storage medium for storing a program which, when executed, implements the automated preferred method of sub-aperture machining process.
In summary, the present invention has at least the following technical effects:
1. according to the invention, the quantitative characterization and the frequency-band division characterization of the surface shape error volume of the optical element on a frequency domain are realized through the volume spectrum density function of the optical element, the surface shape error volume quantity of the optical element on different frequency bands can be obtained, and accurate data reference is provided for the processing of the optical element;
2. according to the invention, the optimized processing technology is obtained by effectively removing the rate spectrum and the volume spectrum density function, so that the volume data of the removed function and the surface shape error volume data of the optical element can be matched with each other, thereby effectively solving the problem that the removed function in the prior art cannot be combined with the surface shape error distribution of the optical element to obtain the most suitable technological parameters of the optical element, effectively improving the comprehensive efficiency of sub-aperture polishing, reducing the production cost and bringing huge economic benefits;
3. according to the method, the effective removal rate spectrum is obtained through the ratio of the surface shape error volume variation to the processing time, the concept of the effective removal rate spectrum directly related to the form, the size and the like of the removal function is provided, the capability of the removal function for correcting the spatial frequency error can be quantitatively represented by utilizing the effective removal rate spectrum, and the quantitative representation of the removal function is realized;
4. according to the method, the optimized processing technology is obtained through the effective removal rate spectrum and the volume spectrum density function, the effective removal rate of the removal function is combined with the surface shape error distribution to be removed of the optical element, and the combination of the removal functions can be used for improving the processing rate or the processing precision of the optical element, so that experimenters can perform optimization according to actual conditions;
5. according to the invention, the processing time of the removal function is obtained by integrating the time spectrum density function, so that the removal function with the minimum processing time is selected as an optimal processing technology, the processing speed of the optical element is effectively increased, the comprehensive efficiency of sub-aperture polishing is improved, and the method has great economic benefits and practical production application value;
6. according to the invention, the volume spectral density function is integrated in a preset spatial frequency band to obtain the surface shape error volume, the volume difference value between the residual error material volume and the surface shape error volume is calculated, and then the removal function with the minimum volume difference value is selected as the optimal processing technology.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention or in the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of an automatically preferred method and system for the sub-caliber manufacturing process of the present invention;
FIG. 2 is a plot of the areal error 1 volume spectral density function of the present invention;
FIG. 3 is a graph of the effective removal rate spectrum for removal function 1 in accordance with the present invention;
FIG. 4 is a first schematic diagram of an automatically preferred method of the sub-caliber manufacturing process of the present invention;
FIG. 5 is a graph of time spectral density in the present invention;
FIG. 6 is a graph of the error distribution and values of profile 1 in the present invention;
FIG. 7 is a graph of the error distribution and values for profile 2 of the present invention;
FIG. 8 is a graph of the morphological distribution and parameters of the removal function 1 of the present invention;
FIG. 9 is a graph of the morphological distribution and parameters of the removal function 2 of the present invention;
FIG. 10 is a second schematic diagram of an automatically preferred method of the sub-caliber manufacturing process of the present invention;
fig. 11 is a schematic diagram of the rand rotation transformation function of the present invention.
Detailed Description
The following description provides many different embodiments, or examples, for implementing different features of the invention. The particular examples set forth below are intended as a brief description of the invention and are not intended as limiting the scope of the invention.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present invention, the terms "first", "second", and the like are used only for distinguishing the description, and are not construed as indicating or implying relative importance.
The first embodiment is as follows:
as shown in fig. 1, a first embodiment of the present invention provides an automatic optimization method for a sub-caliber processing technology, including the following steps:
step S10: obtaining effective removal rate spectrums of different removal functions, wherein the effective removal rate spectrums are convergence rates of correction of error volumes of all spatial frequencies by the removal functions;
step S20: acquiring a volume spectral density function of the optical element, wherein the volume spectral density function is the density of the volume of residual error material contained in the surface shape error of the optical element at each frequency;
step S30: and obtaining the optimal processing technology through the effective removal rate spectrum and the volume spectral density function.
The embodiment of the automatic optimization method for the neutron caliber processing technology enables quantitative representation of matching of the removal function and the surface shape error, solves the problem that in the prior art, in the machining process of the neutron caliber, the requirement of the surface shape error of an element to be processed needs to be met, reasonable technological parameters can be selected for machining, automatic optimization of the technological parameters can be achieved, the removal function which is most matched with the spatial distribution of the surface shape error of the current element to be processed is obtained, high-efficiency machining is achieved, and production cost is reduced.
Volume spectral density functionVSD(ω)The quantitative characterization mathematical model of the error volume content of the surface shape error in each spatial frequency band can be characterized, and the frequency domain quantitative characterization of the error volume content of the surface shape is obtained, as shown in fig. 2.
The quantitative characterization and the frequency-division characterization of the surface shape error volume of the optical element on the frequency domain are realized through the volume spectral density function of the optical element, the quantity of the surface shape error volumes of the optical element on different frequency bands can be obtained, and accurate data reference is provided for the processing of the optical element.
The optimal processing technology is obtained by effectively removing the rate spectrum and the volume spectrum density function, so that the volume data of the removed function and the surface shape error volume data of the optical element can be matched with each other, the matching degree of the removed function and the surface shape error of the element to be processed is realized, and an effective and reliable technical approach is provided for automatic intelligent optimal selection of the ultra-precision processing technology parameters of the optical element, thereby effectively solving the problem that the removed function in the prior art cannot be combined with the surface shape error distribution of the optical element to obtain the most suitable technological parameters of the optical element, effectively improving the comprehensive efficiency of sub-aperture polishing, reducing the production cost and bringing huge economic benefits;
further, step S10 further includes: and obtaining an effective removal rate spectrum through the ratio of the volume change of the surface shape error to the processing time.
The effective removal rate spectrum is calculated based on airspace simulation to obtain an effective removal rate spectrum of the error of each space frequency band trimmed by the removal function, and quantitative representation of the error correction capability of each space frequency band by the removal function is obtained.
The surface shape error volume variation is the volume variation of the surface shape error before and after processing under the preset spatial frequency, and the effective removal rate spectrum is obtained according to the ratio of the surface shape error volume variation to the processing timeRE(ω)As shown in fig. 3, the quantitative characterization of the removal function of all sub-aperture polishing such as small tool numerical control polishing, air bag polishing, jet polishing, atmospheric plasma polishing, magnetorheological polishing, ion beam polishing, etc. can be realized, the concept of the effective removal rate spectrum directly related to the form, size, etc. of the removal function is provided, the capability of the removal function to correct the spatial frequency error can be quantitatively characterized by using the effective removal rate spectrum, and the quantitative characterization of the removal function is realized.
Further, a preferred processing technique is obtained by the effective removal rate spectrum and the volume spectral density function.
The optimal processing technology is obtained through the effective removal rate spectrum and the volume spectrum density function, the effective removal rate of the removal function is combined with the surface shape error distribution to be removed of the optical element, the combination of the removal functions can be used for improving the processing rate or the processing precision of the optical element, and experimenters can perform optimization according to actual conditions conveniently.
Further, as shown in fig. 4, step S20 further includes calculating a time spectral density function according to the effective removal rate spectrum and the volume spectral density function, and integrating the time spectral density function to obtain a processing time of the removal function; the removal function is a preferred machining process when the machining time of the removal function is minimal
By efficient removal rate spectroscopyRE(ω)And characterizing the correction capability of the removal function, and quantitatively characterizing the effective removal rate spectrum of the removal function for correcting the error of each frequency band. By volume spectral density functionVSD(ω)Quantitatively characterizing the volume content of each frequency band.
After the correction capability of the removal function and the representation of the surface shape error on the frequency domain are respectively obtained, the information is combined to quantitatively represent the matching degree of the removal function and the surface shape error, namely a time spectral density functionT(ω). And the time spectrum density function is used for representing the removal function and the sub-band matching representation of the surface shape error.
As shown in fig. 5, the function of the volume spectral density can be knownVSD(ω)And effective removal Rate SpectrumRE(ω)Curve obtaining time density spectrum functionT(ω)The time spectrum density curve is integrated, so that the theoretical total time for removing the function correction surface shape error can be obtained, and the theoretical time for removing the function correction surface shape error of each spatial frequency band of the element to be processed, namely the processing time, is obtained.
For the error distribution of the element to be processed, the error distribution of all the removing functions to be selected can be calculated quicklyT i (ω)Correcting the processing time corresponding to the target frequency band error by comparisont i ，iIn order to remove the serial number of the function, a simple sorting is performed, that is, the removal function with the highest processing efficiency can be selected preferably, so as to improve the processing efficiency, as shown in fig. 4.
In order to verify whether the obtained time spectrum density is in accordance with the real machining process, verification is performed by comparing whether the time of the time spectrum density is in accordance with the actual simulation machining. Orthogonal tests are performed through two groups of surface shape errors (surface shape 1 shown in figure 6 and surface shape 2 shown in figure 7) and two groups of removal functions (removal function 1 shown in figure 8 and removal function 2 shown in figure 9), four groups of time spectrum densities are obtained through calculation and simulation processing, detailed information and feature description of specific parameters are shown in table 1, and removal functions with different sizes and surface shape error data with obvious difference in error frequency domain distribution are selected as cross validation parameters.
Table 1 simulation process input parameter conditions
The cross validation results are shown in table 2, which indicates that the total processing time obtained by calculation by using the time spectrum density curve is basically consistent with the time of simulation processing, the deviation is less than 1%, and the correctness of the model is fully proved.
TABLE 2 simulation verification results
In the first embodiment, the processing time of the removal function is obtained by integrating the time spectrum density function, so that the removal function with the minimum processing time is selected as the optimal processing technology, the processing speed of the optical element is effectively increased, the comprehensive efficiency of sub-aperture polishing is improved, and the method has great economic benefits and practical production and application values.
Further, in step S20, the temporal spectral density function is a volume spectral density function divided by the effective removal rate spectrum.
Volume spectral density functionVSD(ω)And effective removal rate spectrumRE(ω)The division can obtain the time spectrum density functionT(ω)The physical meaning of which is to be modified by a removal functionThe surface shape error corresponds to the time consumed by the unit frequency volume on the frequency band, and the obtained full-band curve is the time spectral density curve.
Further, as shown in fig. 10, step S20 further includes: and integrating the volume spectral density function at a preset space frequency band to obtain the surface shape error volume of the optical element under the preset space frequency band, calculating the surface shape error volume outside the cut-off frequency of the removal function, and selecting the removal function with the minimum volume difference value as the optimal processing technology.
And integrating the volume spectral density function at a preset spatial frequency band to obtain a surface shape error volume, calculating the volume difference value between the volume of the residual error material and the surface shape error volume, and selecting the removal function with the minimum volume difference value as the optimal processing technology. The volume spectral density function is integrated in a preset spatial frequency band to obtain a surface shape error volume, the volume difference value between the volume of the residual error material and the surface shape error volume is calculated, and then the removal function with the minimum volume difference value is selected as an optimal processing technology.
It should be noted that, when a person skilled in the art selects the removal function, the general rule is: the smaller the size of the machining tool, the better the machining accuracy. However, this rule also has a certain limitation, and in practical application, the machining precision of the large-size machining tool is better than that of the small-size machining tool, because the fundamental reason for determining the machining precision is the distribution form of the removal function, not the size of the machining tool. Therefore, the embodiment can effectively avoid errors caused by the fact that a person skilled in the art only selects the size of the machining tool, and improves the polishing efficiency.
Further, the volume spectral density function is a two-dimensional volume spectral density function or a one-dimensional volume spectral density function.
The two-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),Sthe area of the element is defined as the area of the element,ΔLin order to be the sampling interval of the sample,xin a first direction, the first direction is,yin the second direction, the first direction is the first direction,Nis the number of sampling points in the first direction,Mis the number of sample points in the second direction,
is a fourier transform of the arithmetic square root of the surface error,
is the frequency domain spatial coordinate of the first direction,
is the frequency domain spatial coordinate of the second direction.
Fourier transform of arithmetic square root of surface shape error
The calculation formula of (c) is:
wherein, in the step (A),
is a two-dimensional matrix of surface-shaped error amplitude values, i is an imaginary number unit,jis the serial number of the sampling point in the second direction,kis the number of the first direction sampling points,j、kis a positive integer.
The surface shape error amplitude two-dimensional matrixz(j,k) The optical element can be detected by a detection instrument such as a three-coordinate measuring machine and an interferometer.
The one-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the process,
for the rotational transformation of a two-dimensional volumetric spectral density function,θin order to be the angle of rotation,
is the sample length of the first direction after the rotation transformation.
The rotational transformation two-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),randis a rotational transformation function.
randThe rotation transformation is as shown in FIG. 11 whenθ=0, obtainXThe calculation formula of the one-dimensional volume spectral density of the direction is as follows:
wherein, in the step (A),L y a second direction sample length in cartesian coordinates. When in useθ=(ii) 90 °, obtainYThe calculation formula of the one-dimensional volume spectral density of the direction is as follows:
wherein, in the step (A),L x the first direction sample length in cartesian coordinates.
The one-dimensional volume spectral density function
A certain frequency band of
Is integrated as the error volume in that frequency band
I.e. by
Wherein, in the step (A),
the lower form error amplitude of the spatial frequency band is preset.
The two-dimensional volume spectral density function
Or one-dimensional volume spectral density function
The predetermined spatial frequency band integral of (a) is equal to the surface shape error volume of the optical element, i.e.
Wherein, in the step (A),
is the average height of the surface-shaped errors,Vis the surface error volume.
Example two:
as shown in fig. 1, a second embodiment of the present invention provides a preferred system for a sub-aperture processing technology, including an effective removal rate spectrum obtaining module, a volume spectrum density function obtaining module, and a preferred processing technology obtaining module; the effective removal rate spectrum acquisition module is used for acquiring effective removal rate spectrums of different removal functions; the volume spectral density function acquisition module is used for acquiring a volume spectral density function of the optical element; the optimal processing technology obtaining module is used for obtaining an optimal processing technology through the effective removal rate spectrum and the volume spectrum density function.
Example three:
the third embodiment of the invention provides a readable storage medium for storing a program, and the program is used for realizing the automatic optimization method of the sub-aperture machining process when being executed.
Example four:
an embodiment of the present invention provides an electronic device, including: one or more processors; a memory having one or more programs stored thereon; the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the automated preferred method of sub-aperture machining.
The automatic optimization method, the system and the medium for the sub-caliber processing technology can realize the quantitative characterization of the surface shape error and the removal function matching degree in the sub-caliber polishing processing process, can be suitable for processing any surface shape error distribution by all sub-caliber polishing technologies, and have the advantages of simple and rapid realization process and good stability. Meanwhile, by quantitative representation of the matching degree of the removal function and the surface shape error, the removal function with the optimal matching degree of the surface shape error of the element to be processed can be automatically optimized, the uncertain influence of human factors on the production process is avoided, the processing efficiency of the large-caliber optical element is greatly improved, the production cost is reduced, and great economic benefit can be brought.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (8)
1. An automatic optimization method for a sub-caliber processing technology is characterized by comprising the following steps:
step S10: obtaining effective removal rate spectrums of different removal functions, wherein the effective removal rate spectrums are convergence rates of correction of error volumes of all spatial frequencies by the removal functions;
step S20: acquiring a volume spectral density function of the optical element, wherein the volume spectral density function is the density of the volume of residual error material contained in the surface shape error of the optical element at each frequency;
step S30: obtaining a preferred processing technology through the effective removal rate spectrum and the volume spectrum density function;
step S10 further includes: obtaining an effective removal rate spectrum according to the ratio of the surface shape error volume variation to the processing time;
the volume spectral density function is a two-dimensional volume spectral density function or a one-dimensional volume spectral density function;
the two-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),Sthe area of the element is defined as the area of the element,ΔLin order to be the sampling interval of the sample,xin a first direction, the first direction is,yin the second direction, the first direction is the first direction,Nis the number of sampling points in the first direction,Mis the number of sample points in the second direction,
is a fourier transform of the arithmetic square root of the surface error,
is the frequency domain spatial coordinate of the first direction,
is the frequency domain space coordinate of the second direction;
the one-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),
for the rotational transformation of a two-dimensional volumetric spectral density function,θin order to be the angle of rotation,
is the sample length of the first direction after the rotation transformation.
2. An automatic optimization method for sub-caliber manufacture process as claimed in claim 1, wherein said fourier transform of the square root of the arithmetic error of profile shape
The calculation formula of (2) is as follows:
wherein, in the step (A),
is a two-dimensional matrix of surface-shaped error amplitude values, i is an imaginary number unit,jis the serial number of the sampling point in the second direction,kis the number of the first direction sampling points,j、kis a positive integer.
3. An automatic optimization method for sub-caliber manufacture process as claimed in claim 1, wherein said rotation transform two-dimensional volume spectrum density function
Is calculated by the formula
Wherein, in the step (A),randis a rotational transformation function.
4. The automatic optimization method of sub-caliber machining process according to claim 1, wherein the step S20 further comprises calculating a time spectrum density function by the effective removal rate spectrum and the volume spectrum density function, and integrating the time spectrum density function to obtain the machining time of the removal function; the removal function is a preferred machining process when the machining time of the removal function is minimal.
5. The method of claim 4, wherein in step S20, the time spectrum density function is divided by the effective removal rate spectrum.
6. The method of claim 1, wherein step S20 further comprises: and integrating the volume spectral density function at a preset space frequency band to obtain the surface shape error volume of the optical element under the preset space frequency band, calculating the surface shape error volume outside the cut-off frequency of the removal function, and selecting the removal function with the minimum volume difference value as the optimal processing technology.
7. A preferred system of a sub-caliber processing technology is characterized by comprising an effective removal rate spectrum acquisition module, a volume spectrum density function acquisition module and a preferred processing technology acquisition module; the effective removal rate spectrum acquisition module is used for acquiring effective removal rate spectra of different removal functions and obtaining the effective removal rate spectra according to the ratio of the surface shape error volume variation to the processing time; the volume spectral density function acquisition module is used for acquiring a volume spectral density function of the optical element, wherein the volume spectral density function is a two-dimensional volume spectral density function or a one-dimensional volume spectral density function; the optimal processing technology acquisition module is used for acquiring an optimal processing technology through the effective removal rate spectrum and the volume spectrum density function;
the two-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),Sthe area of the element is defined as the area of the element,ΔLin order to be the sampling interval of the sample,xin a first direction of the second direction,yin the second direction, the first direction is the first direction,Nis the number of sampling points in the first direction,Mis the number of sample points in the second direction,
is a fourier transform of the arithmetic square root of the surface error,
is the frequency domain spatial coordinate of the first direction,
is the frequency domain space coordinate of the second direction;
the one-dimensional volume spectral density function
Is calculated by the formula
Wherein, in the step (A),
for the rotational transformation of a two-dimensional volumetric spectral density function,θin order to be the angle of rotation,
is the sample length of the first direction after the rotation transformation.
8. A readable storage medium for storing a program which, when executed, implements an automated preferred method of sub-aperture machining process according to any one of claims 1 to 6.
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