Estimation method of influence of single-point diamond turning tool mark diffraction on image quality

Abstract

The application relates to the technical field of single-point diamond turning, in particular to a method for estimating the influence of a single-point diamond turning tool mark diffraction on image quality, which comprises the following steps: designing an optical system and modeling a tool mark diffraction surface as a phase diffraction annular grating in the optical system; calculating an amplitude spread function of light rays after the light rays pass through the optical system and reach an image plane; respectively calculating diffraction efficiencies of different diffraction orders under the amplitude spread function of the same wavelength, and superimposing the amplitude spread functions after the amplitude spread functions are normalized to the corresponding diffraction efficiencies; calculating a complex color intensity spread function based on the amplitude spread functions of different wavelengths; and obtaining a modulation transfer function after image quality is reduced based on the complex color intensity spread function, so that a design index can be effectively comprehensively evaluated, processing test cost is reduced, and a production cycle is shortened.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of single-point diamond turning, and particularly relates to a method for estimating the influence of single-point diamond turning tool marks on image quality. BACKGROUND

[0002] Single-point diamond turning is a manufacturing technique for producing infrared material lenses, off-axis parabolic (OAP) mirrors, off-axis elliptical (OAE) mirrors and other precision metal optical elements. A diamond blade is used to scratch a glass or metal surface to remove unwanted material. The diamond blade has a very short step distance per circle, and forms concentric circular ring-shaped tool marks. When light is incident on the metal mirror surface, the tool marks produce diffraction light with a certain direction deviation on the side of the mirror, according to the grating equation. When the diffraction light propagates to the image plane, it may interfere with the imaging quality.

[0003] However, there is currently no quantitative prediction and analysis method for tool mark diffraction. After turning, the surface is treated by blind airbag polishing, which increases the processing cost and may cause secondary damage to the processed surface. Therefore, how to form an evaluation method for the influence of tool mark diffraction on image quality, reduce the processing test cost and improve the processing efficiency has become a problem to be solved. SUMMARY

[0004] An object of one or more embodiments of the present specification is to provide a method for estimating the influence of single-point diamond turning tool mark diffraction on image quality, effectively comprehensively evaluate design indicators, reduce processing test cost and shorten production cycle.

[0005] To solve the above technical problems, one or more embodiments of the present specification are implemented as follows:

[0006] In a first aspect, the application provides a method for estimating the influence of single-point diamond turning tool mark diffraction on image quality, comprising the following steps: designing an optical system and modeling a tool mark diffraction surface as a phase diffraction ring grating in the optical system; calculating an amplitude spread function of light rays reaching an image plane after passing through the optical system; calculating diffraction efficiencies of different diffraction orders under the same wavelength for the amplitude spread function, respectively, and superimposing the amplitude spread functions after normalizing the amplitude spread functions to the corresponding diffraction efficiencies; calculating a complex color intensity spread function based on the amplitude spread functions of different wavelengths; and obtaining a modulation transfer function after image quality degradation based on the complex color intensity spread function.

[0007] The technical solution provided by the one or more embodiments of the present specification can be seen that the single-point diamond turning tool mark diffraction image quality influence estimation method provided by the embodiments of the present application aims at the problem that the tool mark diffraction lacks an image quality analysis method at present, utilizes the characteristics that the tool mark diffraction has the greatest influence possibility in the coaxial field and the phase diffraction annular grating can be approximated as a linear grating in a local part, and based on the scalar diffraction theory, the influence of the tool mark diffraction on the image quality is included in the evaluation method of the modulation transfer function MTF, which is beneficial to the comprehensive evaluation of the design index, reduces the processing test cost, and shortens the production cycle. First, on the basis of the designed optical system, the tool mark diffraction surface is modeled as an annular grating, and the phase coefficient caused by the grating can be given in the form of an absolute value R. Secondly, the amplitude spread function ASF of the light rays passing through the optical system and reaching the image plane is calculated by using the ray tracing program and the three-dimensional grating equation. Then, the amplitude spread functions ASF of the phase diffraction annular grating at different diffraction orders at the same wavelength are calculated according to the Kinoform diffraction efficiency formula, and the diffraction efficiencies are normalized and superimposed. Then, the intensity spread function PSF at the same wavelength is calculated. Finally, the intensity spread functions at different wavelengths are incoherently superimposed, and then the modulation transfer function MTF after the image quality is reduced is obtained. The present application gives the worst estimate of the diffraction effect caused by the tool mark in general single-point diamond turning optical processing based on the scalar diffraction theory, without the strict coupled wave analysis and other electromagnetism solutions that are usually required for grating analysis. Only an approximate and accurate estimate is given from the scalar, and the calculation amount is small. In addition, the present application directly gives the worst estimate of the influence of the tool mark diffraction on the image quality through theoretical analysis and numerical calculation, without the need for multiple processing, testing iteration, and can be used as a link in actual design and manufacturing digital modeling, saving high processing and testing costs. The image quality degradation caused by the tool mark diffraction is included in the image quality index analysis during the design, and the design parameters are inversely indicated, reducing the production and testing cost. BRIEF DESCRIPTION OF DRAWINGS

[0008] In order to more clearly illustrate the technical solutions in the one or more embodiments of the present specification or the prior art, the drawings required in the description of the one or more embodiments or the prior art will be briefly introduced. Obviously, the drawings in the following description are only some embodiments described in the present specification, and other drawings can be obtained by those skilled in the art without creating additional labor.

[0009] Figure 1 is a flowchart of the single-point diamond turning tool mark diffraction image quality influence estimation method provided by the embodiments of the present application;

[0010] Figure 2 is a schematic diagram of an optical system in the single-point diamond turning tool mark diffraction image quality influence estimation method provided by the present application;

[0011] Figure 3 is a modulation transfer function diagram obtained in the estimation method of the influence of single-point diamond turning tool mark diffraction on image quality provided according to the present application. DETAILED DESCRIPTION

[0012] In order for those skilled in the art to better understand the technical solutions in the specification, the technical solutions in the one or more embodiments of the specification will be clearly and completely described below in combination with the drawings in the one or more embodiments of the specification. Apparently, the described one or more embodiments are only a part of the embodiments of the specification, rather than all the embodiments. Based on the one or more embodiments in the specification, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present document.

[0013] The estimation method of the influence of single-point diamond turning tool mark diffraction on image quality provided by the embodiments of the present application effectively comprehensively evaluates design indexes, reduces processing test cost, and shortens production cycle. The estimation method of the influence of single-point diamond turning tool mark diffraction on image quality provided by the specification and each part thereof will be described in detail below.

[0014] Reference Figure 1 As shown in FIG. 1, the estimation method of the influence of single-point diamond turning tool mark diffraction on image quality provided by the embodiments of the present application includes the following steps:

[0015] S10: Design an optical system and model a tool mark diffraction surface as a phase diffraction annular grating in the optical system.

[0016] A single-point diamond blade edge is used to scratch a glass or metal surface to remove unnecessary material. The single-point diamond has a very short step distance per circle, forming annular grooves. When the light field is incident on the metal mirror surface, the annular grooves have a grating-like effect. In view of the problem that there is no image quality analysis method for tool mark diffraction, the present embodiments include tool mark diffraction in the evaluation method of the modulation transfer function MTF, which is beneficial to comprehensively evaluate design indexes, reduce processing test cost, and shorten production cycle, by taking advantage of the characteristics that tool mark diffraction has the greatest influence on the coaxial field and that the phase diffraction annular grating can be approximated as a linear grating in a local area.

[0017] S20: Calculate an amplitude spread function of light rays reaching an image plane after passing through the optical system. The embodiments of the present application use a ray tracing program and a three-dimensional grating equation to calculate an amplitude spread function ASF of light rays reaching an image plane after passing through the optical system.

[0018] In view of the problem that the knife mark diffraction lacks an image quality analysis method at present, the characteristics that the knife mark diffraction has the greatest possibility of affecting the coaxial field and the phase diffraction annular grating can be approximated as a linear grating locally are used, the influence of the knife mark diffraction on the image quality is included in the evaluation method of the modulation transfer function (MTF) based on the scalar diffraction theory, an effective analysis and evaluation method for the surface diffraction phenomenon caused by the machining error is formed, which is beneficial to comprehensively evaluating design indexes such as MTF, RMS and the like, reducing the machining test cost and shortening the production cycle. The above-mentioned utilization of the knife mark diffraction having the greatest possibility of affecting the coaxial field and the phase diffraction annular grating can be approximated as a linear grating locally is the premise of the estimation method provided by the application. In addition, it should be noted that the nature of the light field is electromagnetic wave, which is vector, and therefore there is a vector diffraction calculation theory, including a rigorous coupled wave analysis, a finite difference time domain method, a finite element method and the like numerical methods, but the solving calculation amount is too large to be practically applied to engineering. The light ray tracing, grating equation and the like steps used in the estimation method provided by the application are executed based on the scalar diffraction theory.

[0019] Based on the scalar diffraction theory, the worst estimation of the diffraction effect caused by the general single-point diamond turning optical machining is given, the rigorous coupled wave analysis and the like electromagnetic calculation required by the diffraction grating analysis is not needed, only an approximate and relatively accurate estimation from the scalar is given, and the calculation amount is small. In addition, the worst estimation of the influence of the knife mark diffraction on the image quality is directly given through theoretical analysis and numerical calculation, and it is judged whether the imaging quality based on the worst estimation still meets the requirements. If it meets the requirements, it is indicated that the turning machining parameters will not seriously affect the imaging, the multiple machining and test iteration is avoided, the estimation method can be used as a link in the actual design and manufacturing digital modeling, the high cost of machining and the like is saved, the image quality decline caused by the knife mark diffraction is included in the image quality index analysis in the design, and the design parameters are inversely indicated, and the production test cost is reduced.

[0020] S30: The diffraction efficiency of different diffraction orders is calculated for the amplitude spread function under the same wavelength, and the amplitude spread function is normalized to the corresponding diffraction efficiency and then superimposed. The amplitude spread function (ASF) of the phase diffraction annular grating under the same wavelength is calculated according to the Kinoform diffraction efficiency formula, and the diffraction efficiency is normalized and then superimposed. Based on the scalar diffraction theory, the worst estimation of the diffraction effect caused by the general single-point diamond turning optical machining is given, the rigorous coupled wave analysis and the like electromagnetic calculation required by the grating analysis is not needed, an approximate and relatively accurate estimation from the scalar is given, the calculation amount is small, and the calculation efficiency is high.

[0021] S40: The monochromatic intensity spread function is calculated based on the amplitude spread function under the same wavelength, and then the polychromatic intensity spread function (PSF) under different wavelengths is calculated.

[0022] The design wavelength of the optical system is usually selected as several representative wavelengths in the spectral band as sampling wavelengths. Since the electromagnetic frequencies of different wavelengths are different, interference does not occur, and non-coherent superposition is adopted. The amplitude spread function at each wavelength is repeatedly calculated for the sampling wavelengths of the optical system, and the monochromatic intensity spread function at the corresponding wavelength is calculated by the following formula, and the monochromatic intensity spread functions at all wavelengths are non-coherently superimposed by the following formula to obtain the polychromatic intensity spread function.

[0023] S50: obtaining the modulation transfer function after the image quality is reduced based on the polychromatic intensity spread function.

[0024] The embodiment of the present application directly gives the estimation of the worst influence of the knife mark diffraction on the image quality through theoretical analysis and numerical calculation, does not need multiple processing, testing and iteration, can be used as a link in actual design and manufacturing digital modeling, saves high processing and testing costs, and puts the image quality decline caused by the knife mark diffraction into the image quality index analysis in the design, and reversely indicates the index. The influence of the comprehensive optical design and processing parameters on the image quality can meet the design index. The design index is the optical system design requirement, such as the MTF requirement greater than a certain value.

[0025] Optionally, before the knife mark diffraction surface is modeled as an image plane grating in the optical system, the estimation method of the influence of the single-point diamond turning knife mark diffraction on the image quality provided by the embodiment of the present application further includes: estimating the grating phase polynomial coefficient and the blaze depth caused by the phase diffraction annular grating according to the single-point diamond turning processing parameters. The polynomial coefficient is used to determine the direction of ray tracing, which is embodied in the following formulas (5) and (6); the blaze depth is used to calculate the diffraction efficiency, which is embodied in the following formula (9). The blaze depth is measured along the normal line of the knife mark diffraction surface.

[0026] On the basis of the designed optical system, the knife mark diffraction surface is modeled as a phase diffraction annular grating, and the phase coefficient caused by the grating is given in the form of an absolute value R. The phase coefficient includes the grating phase polynomial and the blaze depth.

[0027] Further, in the estimation method of the influence of the single-point diamond turning knife mark diffraction on the image quality provided by the embodiment of the present application, the grating phase polynomial coefficient and the blaze depth caused by the phase diffraction annular grating are given according to the single-point diamond turning processing parameters, and specifically include:

[0028] The function of the phase diffraction annular grating on the phase is determined based on the tilt phase of the phase diffraction annular grating on the incident light; the grating phase polynomial coefficient is determined based on the function; and the estimated value of the blaze depth is given.

[0029] The estimation method for the worst degree of influence of the single-point diamond turning tool mark diffraction on image quality provided by the embodiment of the application is realized based on the scalar diffraction theory. The grating phase polynomial coefficient and the blazed depth are estimated according to the machining parameters of the single-point diamond turning. The phase diffraction ring grating adds a tilt phase to the incident light field. Therefore, the effect of the phase diffraction ring grating on the incident light can be characterized by the following formula (1).

[0030]

[0031] wherein, f() is the function of the effect of the phase diffraction ring grating on the tilt phase. r is the polar coordinate, and x y is the Cartesian coordinate. Since the phase diffraction ring grating is rotationally symmetric, the polar coordinate is more convenient to use, but the ray tracing program is based on the Cartesian coordinate system, and therefore the coordinate conversion is needed. Generally,

[0032]

[0033] That is, the tilt phase of the phase diffraction ring grating linearly grows with the aperture radius of the tool mark diffraction surface, the grating phase polynomial coefficient C is related to the machining parameters, and represents the tilt slope of the tilt phase between two adjacent tool mark periods:

[0034]

[0035] wherein, a period length is the distance between adjacent tool marks, and θ i and θ m are the incident angle and the diffraction angle of the light field, respectively, and + is taken when the incident light and the diffracted light are on the same side of the normal line of the phase diffraction ring grating; and - is taken when the incident light and the diffracted light are on the opposite sides of the normal line of the phase diffraction ring grating.

[0036] The blazed depth b is a parameter related to the tool tip carving, and the estimated value is given by the following formula,

[0037]

[0038] wherein, r is the integer of the reflection times of the incident light before the tool mark diffraction, m is the tool mark diffraction order, n1 is the front refractive index of the tool mark diffraction surface, and n2 is the rear refractive index of the tool mark diffraction surface. It should be noted that the refractive index of the space where the light is incident on the tool mark diffraction surface is the front refractive index, and the refractive index of the space where the light is incident is the rear refractive index. If the tool mark diffraction surface is refractive, the front refractive index is 1 (air), and the rear refractive index is the refractive index of glass. If the surface is reflective, the front refractive index is 1, and the rear refractive index is -1.

[0039] The phase polynomial coefficient and the density of the tool mark engraving, i.e. the period of the phase diffraction ring grating, are related. The blaze depth and the depth of the tool mark engraving are related, which is the depth measured along the normal of the tool mark diffraction surface. The phase polynomial coefficient of the grating determines the phase expression of the phase diffraction ring grating, and the grating phase coefficient needs to be used in the calculation of the exit direction of the light after passing through the phase diffraction ring grating. The blaze depth and the energy of the exit light are related.

[0040] Optionally, in the estimation method for the influence of the single-point diamond turning tool mark diffraction on image quality provided by the embodiment of the present application, the optical system is designed and the tool mark diffraction surface is modeled as a phase diffraction ring grating in the optical system, and specifically includes: modeling the optical system containing the tool mark diffraction surface; and assigning the tool mark diffraction surface with a grating phase polynomial. The optical system containing the tool mark diffraction surface is modeled, and the tool mark diffraction surface is assigned with a grating phase polynomial. Since the high-order diffraction energy is extremely low, we only need to focus on the diffraction light of the 0, ±1 three diffraction orders, wherein the 0 order is consistent with the normal reflection / refraction light direction, and the ±1 order slightly deviates.

[0041] Optionally, in the estimation method for the influence of the single-point diamond turning tool mark diffraction on image quality provided by the embodiment of the present application, the amplitude spread function of the light reaching the image plane after passing through the optical system is calculated, and specifically includes: performing ray tracing on the optical system to obtain an optical path difference; and obtaining the amplitude spread function of the image plane based on the optical path difference.

[0042] Further, in the estimation method for the influence of the single-point diamond turning tool mark diffraction on image quality provided by the embodiment of the present application, the ray tracing is performed on the optical system to obtain the optical path difference, and specifically includes: calculating the exit direction of the incident light passing through the phase diffraction surface; and recording the optical path difference of each incident light from the entrance pupil to the exit pupil of the optical system at each wavelength.

[0043] The ray tracing is performed on the optical system containing the tool mark diffraction surface, and the direction of the exit light after the light passing through the tool mark diffraction surface is calculated by the following formula.

[0044]

[0045]

[0046] Wherein, l and m are the direction cosine of the incident light, and l' and m' are the direction cosine of the exit light.

[0047] The number of the ray grid traced from the entrance pupil of the optical system is N×N, and the optical path difference of each light from the entrance pupil to the exit pupil of the optical system at each wavelength λ is recorded

[0048]

[0049] where s is the number of surfaces from the first knife mark diffraction surface to the last knife mark diffraction surface, n is the refractive index before the i-th knife mark diffraction surface, OPL i is the optical path from the i-1-th knife mark diffraction surface to the i-th knife mark diffraction surface.

[0050] The amplitude spread function ASF on the image plane is calculated,

[0051]

[0052] where F{} represents Fourier transform, λ w represents the w-th wavelength, represents the optical path difference of the m-th order at the w-th wavelength, represents the amplitude spread function on the image plane of the m-th order at the w-th wavelength.

[0053] Optionally, the single-point diamond turning knife mark diffraction impact on image quality estimation method provided by the embodiment of the present application calculates the diffraction efficiency of different diffraction orders for the amplitude spread function at the same wavelength, and superimposes the amplitude spread function after normalization to the corresponding diffraction order diffraction efficiency, and specifically includes: calculating the diffraction efficiency of different diffraction orders of the grating for the amplitude spread function at the same wavelength; obtaining the normalized amplitude spread function of the corresponding diffraction order by normalizing the diffraction order diffraction efficiency; and coherently superimposing the amplitude spread functions of different diffraction orders at the same wavelength to obtain the superimposed amplitude spread function at the same wavelength.

[0054] The amplitude spread function ASF calculated in formula (8) is not normalized, and cannot represent the energy proportion of the corresponding diffraction order, so the diffraction efficiency of the corresponding diffraction order needs to be calculated to normalize the ASF. First, the diffraction efficiency of the corresponding diffraction order is calculated, and for the Kinoform grating structure, the diffraction efficiency of the m-th diffraction order is given by the following formula:

[0055]

[0056] where, m is the diffraction order, b is the blaze depth, n1 is the front refractive index of the knife mark diffraction surface, n2 is the rear refractive index of the knife mark diffraction surface, λ is the wavelength, θ1 is the incident angle, and θ2 is the diffraction angle.

[0057] The amplitude spread function calculated by formula (9) is normalized by the diffraction efficiency of the corresponding order to obtain the normalized amplitude spread function:

[0058]

[0059] Then different diffraction orders are coherently superimposed, interference can occur between same wavelengths, therefore the amplitude spread functions of different diffraction orders at the same wavelength should be coherently superimposed, and the amplitude spread function at the same wavelength after superimposition is

[0060]

[0061] Optionally, the single-point diamond turning tool mark diffraction estimation method for image quality provided by the embodiment of the present application calculates the complex color intensity spread function based on the amplitude spread function of different wavelengths, and specifically includes: calculating the monochromatic intensity spread function at the same wavelength; non-coherently superimposing the monochromatic intensity spread functions at different wavelengths to obtain the complex color intensity spread function.

[0062] The design wavelength of the optical system is usually selected as several representative wavelengths in the spectral range as sampling wavelengths. Because the electromagnetic frequencies of different wavelengths are different, interference does not occur, and therefore non-coherent superposition is adopted. The amplitude spread function at each wavelength is repeatedly calculated for the sampling wavelengths of the optical system, and the monochromatic intensity spread function at the corresponding wavelength is calculated through the following formula:

[0063]

[0064] The monochromatic intensity spread functions at all wavelengths are non-coherently superimposed through the following formula to obtain the complex color intensity spread function,

[0065] PSF sum =∑ w PSF w (13)

[0066] Optionally, the single-point diamond turning tool mark diffraction estimation method for image quality provided by the embodiment of the present application obtains the modulation transfer function after the image quality is degraded based on the complex color intensity spread function, and specifically includes: obtaining the estimated value of the worst influence of the tool mark diffraction on the intensity spread function and the modulation transfer function of the optical system under the set machining parameters based on the complex color intensity spread function; and judging whether the optical design parameters and the machining parameters are reasonable based on the estimated value. The modulation transfer function of the optical system is calculated through the following formula,

[0067] MTF=|F{PSF sum}| (14)

[0068] Through the above steps, the estimated value of the worst influence of the tool mark diffraction on the intensity spread function and the modulation transfer function of the optical system under the set optical design parameters and machining parameters is calculated, so that whether the optical design parameters and the machining parameters are reasonable can be judged, and the scheme is further optimized.

[0069] Embodiment

[0070] The embodiment of the present application provides an estimation method for the influence of single-point diamond turning tool mark diffraction on image quality, taking a Ritchey-Chrétien coaxial reflective optical system as an example, and the optical system layout is shown in the figure Figure 2 to solve the problem that the influence of tool mark diffraction on image quality cannot be quantitatively analyzed in related engineering problems, Figure 2 The reduced scale is shown in the figure.

[0071] The estimation method for the influence of single-point diamond turning tool mark diffraction on image quality is realized based on scalar diffraction theory, and includes the following steps:

[0072] Step 1: Estimate the phase diffraction ring grating phase polynomial coefficient and the blazed depth according to the machining parameters. The phase diffraction ring grating adds a tilt phase to the incident light field. Therefore, the effect of the phase diffraction ring grating on the incident light can be characterized by the following formula.

[0073]

[0074] wherein, f() is the function of the phase diffraction ring grating on the tilt phase. Generally,

[0075]

[0076] That is, the tilt phase increases linearly with the radius, the grating phase polynomial coefficient C is related to the machining parameters, and represents the tilt slope of the tilt phase between two adjacent periods:

[0077]

[0078] wherein, θ i and θ m are the incident angle and the diffraction angle of the light field, respectively, and + is taken when the incident light and the diffracted light are on the same side of the normal line of the phase diffraction ring grating; and - is taken when the incident light and the diffracted light are on the opposite sides of the normal line of the phase diffraction ring grating.

[0079] Preferably, in the embodiment of the present application, C=1E-5 is set.

[0080] The blazed depth is measured along the surface normal, and the blazed depth b is a parameter related to the tool tip scratching, and the estimated value is given by the following formula,

[0081]

[0082] wherein r is an integer representing the number of reflections of the incident light before diffraction, m is the tool mark diffraction order, n1 is the front refractive index of the tool mark diffraction surface, and n2 is the rear refractive index of the tool mark diffraction surface. Preferably, in the embodiment of the present application, the wavelength is the central wavelength 587nm, the mirror, n1=1, n2=-1, r=0, and the approximate value is calculated and taken to obtain b=3E-4.

[0083] Step 2: Modeling the optical system and performing initial data calculation

[0084] In this embodiment, the 0 field of view on the optical axis is analyzed, and three wavelengths λ = 656 nm, 587 nm, and 486 nm in the visible light band are set, with a weight ratio of 1:1:1.

[0085] Step 2.1: Modeling the optical system containing a knife mark diffractive surface

[0086] The knife mark diffractive surface is given a diffractive attribute, which is given by superimposing a phase (a layer of diffractive attribute can be superimposed on the designed surface of the optical system by modeling software). Since the high-order diffractive energy is very low, we only need to focus on the diffracted light of 0, ±1 three diffraction orders.

[0087] Step 2.2: Ray tracing of the optical system containing the knife mark diffractive surface

[0088] Through ray tracing, the angle and optical path of the light after passing through the knife mark diffractive surface are calculated. For the knife mark diffractive surface, the direction of the outgoing light after passing through the knife mark diffractive surface is calculated by the following formula,

[0089]

[0090]

[0091] where l and m are the direction cosines of the incident light, and l' and m' are the direction cosines of the outgoing light.

[0092] Step 2.3: Calculate the amplitude spread function

[0093] Trace the N x N ray grid from the entrance pupil of the optical system, and record the optical path difference of each ray from the entrance pupil to the exit pupil surface

[0094]

[0095] In the embodiment of the present application, N is preferably 64. The amplitude spread function ASF on the image plane can be calculated,

[0096]

[0097] where F{} represents the Fourier transform, λ w represents the wth wavelength, represents the mth order optical path difference at the wth wavelength, represents the amplitude spread function on the image plane at the wth wavelength.

[0098] Step 3: Repeat the calculation for the target diffraction order and normalize

[0099] The amplitude spread function obtained in step 2.3 is not normalized and cannot represent the proportion of energy under the corresponding diffraction order, so the diffraction efficiency under the corresponding diffraction order needs to be calculated to normalize the ASF.

[0100] Step 3.1: Calculate the diffraction efficiency of different diffraction orders

[0101] For a kinoform grating structure, the diffraction efficiency of the mth diffraction order is given by the following formula:

[0102]

[0103] wherein, m is the diffraction order, b is the blazed depth, n1 is the refractive index in front of the knife mark diffraction surface, n2 is the refractive index behind the knife mark diffraction surface, λ is the wavelength, θ1 is the incident angle, and θ2 is the diffraction angle.

[0104] Step 3.2: Normalize the amplitude spread function according to the diffraction efficiency

[0105] The amplitude spread function obtained in step 2.3 is normalized by the diffraction efficiency of the corresponding diffraction order to obtain the normalized amplitude spread function,

[0106]

[0107] Step 3.3: Coherent superposition of amplitude spread functions of different diffraction orders

[0108] The amplitude spread function after superposition under the same wavelength is:

[0109]

[0110] Step 4: Calculate the complex color intensity spread function

[0111] The complex color intensity spread function represents the response of the optical system to different wavelengths of light, and the calculation of the complex color intensity spread function is realized by the superposition of the monochromatic intensity spread functions.

[0112] Step 4.1: Calculate the monochromatic intensity spread function

[0113] Repeat steps 2-3 to calculate the amplitude spread function under each wavelength for the sampled wavelengths of the optical system, and calculate the corresponding monochromatic intensity spread function by the following formula,

[0114]

[0115] The monochromatic intensity spread functions are incoherently superimposed by the following formula to obtain the complex color intensity spread function,

[0116] ​PSF sum =∑ w PSF w (27)

[0117] Step 5: Calculate the modulation transfer function of the optical system.

[0118] The modulation transfer function of the optical system is calculated by the following formula,

[0119] MTF = |F{PSF sum}| (28)

[0120] Through the above steps, the estimated value of the worst influence of the knife mark diffraction on the intensity spread function and the modulation transfer function of the optical system under the set optical design parameters and processing parameters is calculated, and the MTF curve is as shown in Figure 3 The MTF after considering the knife mark diffraction has a certain decline compared with the MTF without considering the knife mark diffraction. From the degree of decline of the MTF curve caused by the knife mark diffraction, it can be judged whether the optical design and processing parameters are reasonable, and further optimization of the design is guided.

[0121] It can be seen from the above analysis that the single-point diamond turning tool mark diffraction image quality influence estimation method provided by the embodiment of the application is aimed at the problem that there is no image quality analysis method for tool mark diffraction at present, utilizes the characteristics that tool mark diffraction has the greatest influence possibility in the coaxial field and the tool mark grating can be approximately linear grating in the local, and based on the scalar diffraction theory, the influence of tool mark diffraction on image quality is contained in the evaluation method of the modulation transfer function MTF, which is beneficial to comprehensive evaluation of design indexes, reduces the processing test cost, and shortens the production cycle. Firstly, on the basis of the designed optical system, the tool mark diffraction surface is modeled as an annular grating, and the phase coefficient caused by the grating can be given in the form of an absolute value R. Secondly, the amplitude spread function ASF of the light rays after passing through the optical system and reaching the image plane is calculated by using the ray tracing program and the three-dimensional grating equation. Then, the diffraction efficiency of the amplitude spread function ASF of the phase diffraction annular grating at different diffraction orders at the same wavelength is calculated according to the Kinoform diffraction efficiency formula, and the diffraction efficiencies are normalized and superimposed, and then the intensity spread function PSF at the same wavelength is calculated. Finally, the intensity spread functions at different wavelengths are incoherently superimposed, and then the modulation transfer function MTF after the image quality is reduced is obtained. The present application gives the worst estimate of the diffraction effect caused by the tool mark in general single-point diamond turning optical processing based on the scalar diffraction theory, without the strict coupled wave analysis and other electromagnetism solutions that are usually required for grating analysis, and only gives an approximate and accurate estimate from the scalar, with smaller calculation amount. In addition, the present application directly gives the worst estimate of the influence of tool mark diffraction on image quality through theoretical analysis and numerical calculation, without the need for multiple processing, testing iteration, and can be used as a link in actual design and manufacturing digital modeling, saving high processing and testing costs, and reducing the production and testing costs by taking the image quality decline caused by tool mark diffraction into the image quality index analysis and inversely indicating the design parameters.

[0122] In summary, the above only describes preferred embodiments of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0123] The system, device, module or unit illustrated by one or more embodiments described above can be specifically implemented by a computer chip or entity, or by a product with certain functions. A typical implementation device is a computer. Specifically, the computer may, for example, be a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an electronic mail device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0124] It is also to be noted that the terms "comprising", "including", and any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises a... " does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the recited element.

[0125] Each of the embodiments in the present specification is described in a progressive manner, and the same or similar parts between the embodiments can be mutually referred to, and each of the embodiments focuses on the difference from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the description of the method embodiments.

[0126] The above describes specific embodiments of the present specification. Other embodiments are within the scope of the appended claims. In some cases, the acts or steps recited in the claims can be performed in a different order than the order in which the acts or steps are recited in the embodiments and still achieve desirable results. In addition, the processes depicted in the figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous.

Claims

1. A method of estimating the effect of a single point diamond turning tool mark diffraction on the quality of an object, characterized by, The method comprises the following steps: According to the single-point diamond turning processing parameter, the phase diffraction annular grating causes the polynomial coefficient of the grating phase and the blaze depth; Specifically, it comprises: determining the action function of the phase diffraction annular grating on the phase based on the inclination phase of the phase diffraction annular grating to the incident light; determining the polynomial coefficient of the grating phase based on the action function; and giving an estimated value of the blaze depth; Designing an optical system and modeling the knife mark diffraction surface as a phase diffraction annular grating in the optical system; Calculating the amplitude spread function of the light reaching the image plane after passing through the optical system; Calculating the diffraction efficiency of different diffraction orders under the same wavelength for the amplitude spread function respectively, and superimposing the amplitude spread function after normalization to the corresponding order diffraction efficiency; Specifically, it comprises: calculating the diffraction efficiency of the amplitude spread function of different diffraction orders under the same wavelength respectively; obtaining the normalized amplitude spread function of the corresponding diffraction order by normalizing the amplitude spread function of different diffraction orders to the diffraction efficiency of the corresponding order; and coherently superimposing the amplitude spread functions of different diffraction orders under the same wavelength to obtain the superimposed amplitude spread function under the same wavelength. Based on the amplitude spread functions of different wavelengths, the complex color intensity spread function is calculated. Based on the complex color intensity spread function, the modulation transfer function after the image quality is reduced is obtained.

2. The method of claim 1, wherein the method further comprises: Designing an optical system and modeling the knife mark diffraction surface as a phase diffraction annular grating in the optical system, specifically comprising: Modeling the optical system containing the knife mark diffraction surface; Imparting the grating phase polynomial to the knife mark diffraction surface.

3. The method of estimating the effect of a single-point diamond turning tool mark diffraction pattern on the quality of an image according to claim 1 or 2, characterized in that, Calculating the amplitude spread function of the light reaching the image plane after passing through the optical system, specifically comprising: Carrying out ray tracing on the optical system to obtain the optical path difference; Based on the optical path difference, the amplitude spread function of the image plane is obtained.

4. The method of claim 3, wherein the method further comprises: Carrying out ray tracing on the optical system to obtain the optical path difference, specifically comprising: Calculating the direction of the outgoing light of the incident light passing through the phase diffraction surface; Recording the optical path difference of each incident light from the entrance pupil to the exit pupil of the optical system under each wavelength.

5. The method of claim 1, wherein the method further comprises: Based on the amplitude spread functions of different wavelengths, the complex color intensity spread function is calculated, specifically comprising: Calculating the monochromatic intensity spread function under the same wavelength; Incoherently superimposing the monochromatic intensity spread functions under different wavelengths to obtain the complex color intensity spread function.

6. The method of claim 5, wherein the method further comprises: Based on the complex color intensity spread function, the modulation transfer function after the image quality is reduced is obtained, specifically comprising: Based on the complex color intensity spread function, the estimated value of the worst influence of the knife mark diffraction on the intensity spread function and the modulation transfer function of the optical system under the set processing parameter is obtained; Based on the estimated value, it is judged whether the optical design parameter and the processing parameter are reasonable.

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