CN102848287A - Combination machining method for removing high-frequency errors in optical elements - Google Patents

Abstract

The invention discloses a combination machining method for removing high-frequency errors in optical elements. The combination machining method includes measuring surface shape errors of an optical element to be machined by an interferometer, carrying out PSD (power spectral density) analysis, and determining distribution characteristics of the medium and high-frequency errors on the basis of a DSD curve; acquiring an optimized removal function model according to predetermined machining time and machining precision, and acquiring an amplitude spectral line of a removal function; acquiring cut-off frequency of the removal function according to the amplitude spectral line; machining by a magneto-rheological finishing process if correctable medium and high-frequency errors with the frequency lower than the cut-off frequency exist according to the frequency distribution of the medium and high-frequency errors; and machining by a computer controlled optical surfacing process if uncorrectable medium and high-frequency errors with the frequency higher than the cut-off frequency exist according to the frequency distribution of the medium and high-frequency errors. By the combination machining method, technical advantages of MRF (magneto-rheological finishing) and technical advantages of CCOS (computer controlled optical surfacing) can be sufficiently combined, efficient uniform convergence of all-band errors of the optical element can be realized, and performance of the optical element is effectively improved.

Description

The combined type processing method of optical element medium-high frequency error

Technical field

The present invention relates to a kind of processing method of optical element, relate in particular to a kind of control process of optical element medium-high frequency error.

Background technology

In traditional optics manufacturing process, machining tool is conducive to the successional generation of face shape error with there being large-area space geometry contact form between the optics element, and error shows as macro-scale, i.e. the low frequency form error; And micro-nano magnitude polishing abrasive material is with the mechanochemistry comprehensive function between the optics element material, and major embodiment is that the error of micro-scale develops, i.e. the high frequency roughness error.Therefore, substantially do not comprise serious medium-high frequency error form in the resulting surface of the work error of traditional manufacturing process (such as allusion polishing, ring throwing etc.), can guarantee the favorable optical performance of optical element.

The development of modern advanced optical fabrication methods trends towards adopting the computer control small tool that optical surface is carried out the certainty controllable material and removes, and belongs to the category of footpath, computer control rim of the mouth polishing technology.Because the small tool size that adopts generally all is far smaller than workpiece size, therefore in the process that realizes the definite convergence of low frequency face shape error, more and more tend to form periodic small scale foozle feature in the medium-high frequency section.What people were popular is classified as the medium-high frequency error to this class small scale foozle feature, and the medium-high frequency error has become the notable feature of footpath, computer control rim of the mouth class processing method.

The material of MRF (MRF) is removed, and mainly the shear action by magnetic flow liquid under the high strength gradient magnetic realizes.Magnetic flow liquid is under the effect of high-intensity magnetic field, although have certain hardness, it still belongs to the category of beformable body, and namely MRF belongs to a kind of flexible polishing mode.This flexible removing method has determined that it is adding man-hour to the optical surface error, and magnetic flow liquid can keep good contact condition with the optics surface.When the magnetic flow liquid under the high strength gradient magnetic carried out the material removal to surface of the work, the flexible polishing mould that magnetic flow liquid forms was with machining area generation comprehensive engagement, and the polish abrasive of magnetic flow liquid is all had an effect with the surface of the work error.Because material is removed the impact that active shearing force is not subjected to the face shape error micro Distribution substantially, no matter be protruding peak or the groove of optical element surface therefore, the flexible polishing mould is basically identical to its removal efficient.In other words, evenly remove if utilize MRF that optical element surface is carried out material, the medium-high frequency error character of optical surface remains unchanged substantially so.Yet, the removal Function feature of MRF and the frequency domain distribution of face shape error have determined that its centering high frequency error has certain capability for correcting, namely by distributing residence time can realize certain medium-high frequency error correction, thereby provide means for the control of medium-high frequency error.

Computer controlled optical surfacing shaping (CCOS) realizes that the theoretical foundation that material is removed is the Preston equation, and it is that a kind of normal pressure that relies on realizes the effectively processing method of removal of material.Typical CCOS structure is to cover pitch at metal sheet, and this structure is also referred to as " rigid tool " usually.The pitch dish is removed and can be understood from two aspects the material of surface of the work: in the polishing disk size range, the removal amount macro manifestations is shaped as the class Gaussian usually for removing function.And for the medium-high frequency error of wavelength less than the polishing disk size, material is removed and is followed " the preferential principle of removing of high point ".Namely when pitch dish processing work, the pitch dish at first comes in contact with the high point of surface of the work zone, and then the pitch hair updo is given birth to necessarily to be out of shape to adapt to the surface of the work micro-shape and changed.Because in the height point zone of surface of the work, the pitch dish will produce larger pressure, therefore can cause larger material removal amount, this and Preston equation coincide.The removal mechanisms at work of CCOS has determined that it has certain fairing effect to the error that the error frequency range is higher than the polishing disk size.Obviously, pitch dish rigidity is larger, and the fairing ability of centering high frequency error is stronger; And flexibility is larger, and is more weak to the fairing ability of medium-high frequency.

Yet, generally all adopt single removal mechanisms at work that the medium-high frequency error of optical element is controlled in the prior art, and single removal mechanisms at work is difficult to realize effective control of medium-high frequency error, and usually residual with the directly related machining feature of removal mechanisms at work, single removal mechanisms at work also has to be hoisted to the processing effect of optical element medium-high frequency error.

Summary of the invention

The technical problem to be solved in the present invention is to overcome the deficiencies in the prior art, provide a kind of can be fully in conjunction with MRF and CCOS separately technical advantage and realize the efficient uniform convergence of optical element full frequency band error, the effective combined type processing method of the optical element medium-high frequency error of improving optical part performance.

For solving the problems of the technologies described above, the technical scheme that the present invention proposes is a kind of combined type processing method of optical element medium-high frequency error, described combined type processing method is to treat first the processing optical part to carry out the assessment of medium-high frequency error machinability, then selectively carry out following operation (a) or operation (b) according to assessment result, wherein:

Described medium-high frequency error machinability assessment may further comprise the steps: the face shape error that at first utilizes interferometer measurement optical element to be processed, then the face shape error that obtains being carried out PSD (wavefront power spectral density) analyzes, obtain the PSD curve of face shape error, the purpose that obtains the PSD curve is exactly in order to observe face shape error at the distribution character of frequency domain, distribution character according to it just can carry out suitable judgement by the centering high frequency error, and definite medium-high frequency error frequency distribution characteristics; According to predetermined process time and machining accuracy (according to different optical elements to be processed, after considering, draft in advance process time and machining accuracy) the removal function of MRF instrument is optimized, (remove function optimization mainly is reflected on the shape and efficient of optimizing the removal function removal function model after being optimized, can change process time and machining accuracy by feature that change to remove function, thereby can realize removing the combined optimization of function according to process time and machining accuracy); Removal function model after optimizing is carried out spectrum analysis, obtain removing the amplitude spectral line of function; Remove again the cut-off frequency of function according to this amplitude spectral line acquisition, and this cut-off frequency is compared with the aforementioned medium-high frequency error frequency distribution that needs control; If there is the medium-high frequency the revised error that is lower than cut-off frequency during the medium-high frequency error frequency distributes, then forwards following step (2) to and can revise the medium-high frequency error to this and process; Exist during if the medium-high frequency error frequency distributes be higher than cut-off frequency can not revise the medium-high frequency error, then forward following step (3) to and can not revise the medium-high frequency error to this and process;

Described operation (a) refers to: employing MRF processes is described revises the medium-high frequency error, until satisfy the surface figure accuracy requirement, stops processing;

Described operation (b) refers to: the processing of employing computer controlled optical surfacing forming technology is described can not revise the medium-high frequency error, until satisfy the surface figure accuracy requirement, stops processing.

In the technique scheme, described medium-high frequency error machinability assessment mainly is based on following principle:

The process of MRF is to remove function in the two-dimensional convolution process of surface of the work with residence time in essence, removing control by computer realization certainty material then is the inverse process of said process, input face shape error and removal function before the processing, utilize Mathematical Modeling output residence time, and realize the material removal by the continuous variation of speed on the machining path; The two-dimensional convolution model of reflection process is launched at frequency domain, can obtain following formula:

D(w _x，w _y)＝R(w _x，w _y)·T(w _x，w _y)+E(w _x，w _y) (1)

In the formula (1), D (w _x, w _y), R (w _x, w _y), T (w _x, w _y) and E (w _x, w _y) represent respectively face shape error d (x, y), remove the two-dimensional fourier transform form of function r (x, y), residence time t (x, y) and residual error e (x, y); For simplification, we represent respectively D (w with D, R, T and E _x, w _y), R (w _x, w _y), T (w _x, w _y) and E (w _x, w _y), formula (1) is carried out can obtaining following formula (2) after the conversion:

$T=\frac{D}{R}-\frac{E}{R}---\left(2\right)$

From the angle of signal, remove function serves as wave filter in process effect, as shown in Figure 1.Signal T obtains " pure " signal D ' by system's R filtering, signal D ' is polluted by E and obtains actual signal D, H represents that (finding the solution of residence time is the process of signal being carried out liftering in the liftering system, specifically with the optical element face shape error with remove function as input, obtain residence time output, output realizes to residence time by lathe, thereby realizes effective convergence of optical element face shape error); The characteristic of removing function has determined that its centering high-frequency signal has Truncation, and namely it is typical low pass filter; The characteristic that the removal function blocks the medium-high frequency signal is reflected as the cut-off frequency of removing function.Assess the machinability of the medium-high frequency error of optical element face shape error, needs define the modification capability (namely removing the ability of function correction optical surface error) of MRF removal function first; Estimate the modification capability of removing function, generally start with from the frequency spectrum of removing function, present certain bandwidth characteristic owing to removing function at frequency domain, this characteristic is determining to remove the modification capability of function; Consider that removing function has low-pass filter characteristic, the cut-off frequency size of removing function has determined in fact to remove the modification capability of function; When error frequency during greater than cut-off frequency, remove function it is carried out signal cutout, namely remove function to being higher than the error forfeiture modification capability of cut-off frequency.

The combined type processing method of above-mentioned optical element medium-high frequency error, in the described medium-high frequency error machinability evaluation process, described cut-off frequency is preferably the frequency that the amplitude spectral line of removing function drops to peak value 5% place.

The combined type processing method of above-mentioned optical element medium-high frequency error, in the described operation (a), the described concrete steps of revising the medium-high frequency error of MRF processes preferably include: the face shape error of measuring gained in the first centering high frequency error machinability evaluation process carries out discrete processes, then the removal function model after the described optimization is carried out discrete processes; Finding the solution the required residence time of MRF technique distributes; Generate the machining path of MRF technique based on the shape of described optical element to be processed; According to machining path the residence time of gained being distributed at last is converted to resident VELOCITY DISTRIBUTION along the machining path direction, and according to resident VELOCITY DISTRIBUTION described optical element to be processed is carried out the correction of medium-high frequency error.

In the operation (a) of combinations thereof formula processing method, the removal function of MRF can be revised the medium-high frequency error that certain frequency distributes, but the discretization of computer control process can be introduced the convolution effect, thereby introduces the small scale medium-high frequency error character of CF.The specific medium-high frequency error that the convolution effect is introduced is directly directly related with the planning form of machining path.Can be in the medium-high frequency error character of introducing perpendicular to discrete direction of feed with feeding step pitch respective frequencies such as the grating machining path, and the concentric circles machining path can be in the medium-high frequency error character of circular optical element generatrix direction introducing with feeding pitch respective frequencies, and they are in the unified needle pattern frequency band error that shows as at the CF place of PSD curve.Therefore, in the process of utilizing MRF that part medium-high frequency error is revised, also need to suppress the specific medium-high frequency error percentage that this convolution effect is introduced.Suppress the specific medium-high frequency error percentage of this class, need to reduce strong regularity and the systematicness of machining path, so that the error correction path presents the eigenstate of " unordered in a jumble ".Therefore, the machining path of the technique of MRF described in the present invention preferably adopts " random line machining path ", and described random line machining path refers to that machining path presents irregular, random mixed and disorderly randomness feature and distributes.

As preferred, analyze the characteristic feature of random line machining path commonly used, generally comprise following some: predefined all the discrete dwell point of (1) traversal path; (2) path experiences that all discrete dwell point have and only once; (3) path should be from (or the claiming non-selfing) of avoiding; (4) path should be unicursal, and middle not interruption namely has spatial continuity.Analyze accordingly, the planning process of random line machining path is the path curve of all discrete dwell point of a traversal of search in essence.The grid of the discrete dwell point of typical case is even orthohormbic structure, and there are 8 points in it in discrete dwell point neighborhood arbitrarily, supposes a bit to be on the path p _I-1, current point is p _i, lower is p a bit _I+1, then a bit have 7 theoretical positions under the path, as shown in Figure 2.Consider the steady realization in machine tool motion performance and path, with 7 p shown in Fig. 2 _I+1The path that discrete dwell point consists of is divided into three classes: stabilizing path, migration path and unstable path.Dotted path direct of travel among Fig. 2 acutangulates with the current direction in path, and require lathe one axle snap back and another axle starts fast this moment, and this causes that easily lathe trembles, and is unstable path; The dashed path direct of travel meets at right angles with the current direction in path, requires lathe one axle to stop fast and another axle starts fast, and it requires to be lower than unstable path to machine dynamic characteristics, is migration path; The solid-line paths direct of travel becomes the obtuse angle with the current direction in path, only needs the normal acceleration and deceleration of lathe one axle and another axle startup, and is minimum to the machine dynamic characteristics requirement, is stabilizing path.This shows, three adjacent in the described random line machining path discrete dwell point define two continuous machining cell paths; The machining path of the angle that described stabilizing path refers to two machining cell paths during greater than 90 °; Machining path when described migration path refers to that the angle in two machining cell paths equals 90 °; The machining path of the angle that described unstable path refers to two machining cell paths during less than 90 °.As preferred scheme, described random line machining path is take stabilizing path as main, take migration path and unstable path as auxiliary.

The combined type processing method of above-mentioned optical element medium-high frequency error, in the described operation (b), the described concrete steps that can not revise the medium-high frequency error of described computer controlled optical surfacing forming technology processing preferably include: the pitch dish of according to the medium-high frequency error frequency distribution characteristics of determining in the described medium-high frequency error machinability evaluation process computer controlled optical surfacing forming technology being used first is optimized, and optimize the content comprises the material of determining the bottom supporting dish, diameter and the thickness of pitch dish; According to predefined fairing time and medium-high frequency error amplitude characteristic (this characteristic mainly refers to the amplitude size of the upper high band part of aforementioned PSD curve) working process parameter is optimized, the genus routine techniques means of the equal this area of optimizing process, main manifestations is to change the pitch dish to the removal efficient of optical element surfacing by parameters such as the public rotational velocity of setting the pitch dish, polish pressures, thereby so that within the predefined fairing of the processor time, reach the fairing effect of pursuing as far as possible; Pitch dish after utilize optimizing at last also carries out the fairing of medium-high frequency error according to the technological parameter after optimizing to described optical element to be processed.

The mechanism of CCOS process medium pitch dish centering high frequency error satisfies " bridge model ", be that the optical surface error is that height joins continuously, when the pitch dish comes in contact with the optics surface under predetermined pressure, its zone that contacts at first is the ridge that error distributes, at this moment the pitch dish just as set up a bridge block between the high point of error, therefore claims this model to be " bridge model ".Because the pitch dish is generally thinner, belongs to the thin flat plate in the mechanics, therefore adopt the Kirchoff plate theory that it is carried out force analysis, and introduce shear stiffness, the Mathematical Modeling that can set up the change of pitch dish type is as follows:

${\▿}^2\mathrm{\Φ}=-\frac{q}{D}$

${\▿}^{2}w=-\mathrm{\Φ}-\frac{q}{D_s}---\left(3\right)$

$\begin{array}{cc}({\▿}^2-{\mathrm{\β}}^2)\mathrm{\Ψ}=0& {\mathrm{\β}}^2=\frac{2D_s}{D(1-v)}\end{array}$

In the formula (3),

The shear stiffness of expression pitch dish,

The bending rigidity of expression pitch dish; Wherein, E is the Young's modulus of elasticity of pitch dish, and h is the thickness of pitch dish, and ν is Poisson's ratio, and q is the actual pressure that acts on the pitch dish,

Be Laplace operator,

In the process, there are two kinds of situations in polishing disk (being the pitch dish) with the contact condition on optics surface: the flexural deformation of polishing disk generation low order changes to adapt to the surface; Pitch is compressed to fill up polishing disk with the gap between the optics piece surface.In fact, certain low order deformation occurs in polishing disk, changes but be not enough to adapt to surface error, and this moment, polishing disk was filled up by pitch with the gap between the optics surface.Crimp occurs under the stressed effect in pitch outside, if surface error is less, thinks that so the rear polishing disk of distortion can coincide with the optics surface, then pitch crimp w _cP is proportional with polish pressure, that is:

$w_c=s-w=\frac{p}{k_c}---\left(4\right)$

In the formula (4), k _cBe the compression stiffness of pitch, s is that the optical surface error distributes (being face shape error), and w is the strain of metallic plate;

Use q ₀Expression acts on the impressed pressure of polishing disk, and the actual pressure q that then acts on the polishing disk can be expressed as:

q＝p-q ₀＝k _c(s-w)-q ₀ (5)

Can to get the quadravalence equation as follows by front two of formula (3):

${\▿}^2{\▿}^{2}w=\frac{q}{D}-\frac{{\▿}^{2}q}{D_s}---\left(6\right)$

Formula (5) substitution formula (6) can be got following formula (q ₀Be constant, in conversion, can become zero):

$D{\▿}^2{\▿}^{2}w=(k_{c}s-q_0)-k_{c}w-\frac{k_{c}D}{D_s}{\▿}^2(s-w)---\left(7\right)$

Can get following formula with second in formula (5) the substitution formula (3):

$\mathrm{\Φ}=-{\▿}^{2}w-\frac{k_{c}s-q_0}{D_s}+\frac{k_c}{D_s}w---\left(8\right)$

It is as follows that in simultaneous following formula (7), formula (8) and the formula (3) the 3rd can get equation group:

$D{\&dtri;}^2{\&dtri;}^{2}w-\frac{k_{c}D}{D_s}{\&dtri;}^{2}w+k_{c}w=-{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HDA00002140037700022.png,HDA00002140037700061.png"\; state="\{\{state\}\}">q</figure-callout>}}_0+k_c[1-\frac{D}{D_s}{\&dtri;}^2]s$

$\mathrm{\&Phi;}=-{\&dtri;}^{2}w+\frac{k_c}{D_s}w-\frac{k_{c}s-q_0}{D_s}---\left(9\right)$

$({\&dtri;}^2-{\mathrm{\&beta;}}^2)\mathrm{\&Psi;}=0\begin{array}{cc}& \end{array}({\mathrm{\&beta;}}^2=2D_s/(1-v)D)$

For analyzing the stressing conditions of polishing disk under each frequency error condition, can represent that the face shape error of optical surface distributes with certain frequency periodic function sum.The definition face shape error is the synthetic of a series of sin cos functionses, that is:

$s=(u\cos \frac{\mathrm{\&pi;x}}{a}+v\sin \frac{\mathrm{\&pi;x}}{a})\cos \frac{\mathrm{\&pi;y}}{b}+(u^{*}\cos \frac{\mathrm{\&pi;x}}{a}+v^{*}\sin \frac{\mathrm{\&pi;x}}{a})\sin \frac{\mathrm{\&pi;y}}{b}---\left(10\right)$

Wherein u, v, u ^*And v ^*Be respectively amplitude, a, b represent respectively the half-wavelength of X and Y-direction, s substitution equation group (9) can be got the suffered actual pressure of polishing disk, that is:

$p={\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HDA00002140037700022.png,HDA00002140037700061.png"\; state="\{\{state\}\}">q</figure-callout>}}_0+k_c(1-\frac{{\mathrm{\&alpha;}}_1}{{\mathrm{\&alpha;}}_2})s---\left(11\right)$

Wherein, ${\mathrm{\&alpha;}}_1=k_c[1+\frac{D}{D_s}(\frac{{\mathrm{\&pi;}}^2}{a^2}+\frac{{\mathrm{\&pi;}}^2}{b^2})]$ ${\mathrm{\&alpha;}}_2={\mathrm{\&alpha;}}_1+D{(\frac{{\mathrm{\&pi;}}^2}{a^2}+\frac{{\mathrm{\&pi;}}^2}{b^2})}^2;$ In frequency domain analysis the problems referred to above, then have

Further as can be known (ζ, ξ all represent error frequency, and just the value of the two is different):

$a^2=\frac{1}{4{\mathrm{\&xi;}}^2},$ ${\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA00002140037700061.png"\; state="\{\{state\}\}">b</figure-callout>}}^2=\frac{1}{4{\mathrm{\&zeta;}}^2},$ ${\mathrm{\&alpha;}}_1=k_c(1+4{\mathrm{\&pi;}}^2\frac{D}{D_s}({\mathrm{\&xi;}}^2+{\mathrm{\&zeta;}}^2)),$ α ₂＝α ₁+16π ⁴D(ξ ²+ζ ²) ² (12)

Because a, b represent respectively the half-wavelength of X and Y-direction, parameter b is infinitely great if make, and then this problem can be reduced to one-dimensional problem, and ζ=0 is arranged, and substitution formula (11) can get:

p＝q ₀+γd (13)

Wherein $\mathrm{\&gamma;}=\frac{1}{\frac{1}{16{\mathrm{\&pi;}}^{4}D{\mathrm{\&xi;}}^4}+\frac{1}{4{\mathrm{\&pi;}}^2{D}_s{\mathrm{\&xi;}}^2}+\frac{1}{k_c}}.$

By formula (13) as can be known, polish pressure p is the linear function of face shape error s, and γ is the polish pressure coefficient.Understand from signal angle, face shape error s can be considered as input signal, polish pressure p is considered as output signal, then the polish pressure coefficient gamma is served as the effect of wave filter, Fig. 3 has shown the signal model of polishing disk work in-process, the characteristic of polishing disk shows that γ is high-pass filter (corresponding to the LPF of process, namely can eliminate the medium-high frequency error in the face shape error).

There are three in the denominator of polish pressure coefficient, consider the relation between the three, have following approximated equation:

$\left\{\begin{array}{cc}\mathrm{\&gamma;}\&ap;16{\mathrm{\&pi;}}^{4}D{\mathrm{\&xi;}}^4& 16{\mathrm{\&pi;}}^{4}D{\mathrm{\&xi;}}^4<<\min (4{\mathrm{\&pi;}}^2{D}_s{\mathrm{\&xi;}}^2,k_c)\\ \mathrm{\&gamma;}\&ap;4{\mathrm{\&pi;}}^2{D}_s{\mathrm{\&xi;}}^2& 4{\mathrm{\&pi;}}^2{D}_s{\mathrm{\&xi;}}^2<<\min (16{\mathrm{\&pi;}}^{4}D{\mathrm{\&xi;}}^4,k_c)\\ \mathrm{\&gamma;}\&ap;k_c& k_c<<\min (16{\mathrm{\&pi;}}^{4}D{\mathrm{\&xi;}}^4,4{\mathrm{\&pi;}}^2{D}_s{\mathrm{\&xi;}}^2)\end{array},---\left(14\right)\right.$

16 π wherein ⁴D ξ ⁴The flexural deformation of the corresponding polishing disk of item, 4 π ²D _sξ ²The transverse shear deformation of corresponding polishing disk, k _cThe crimp of corresponding pitch.Therefore, for the fixed frequency face shape error, the distortion of different-thickness pitch dish mainly is divided into three phases: when polishing disk thickness hour, polishing disk is take detrusion as main, polish pressure shows as shearing force along the surface of the work tangential direction, easily destroys the original face shape error of optical surface; When the pitch disc thickness increased, polishing disk was gradually take flexural deformation as main, and polish pressure is along the surface of the work normal direction, and it is main showing as normal pressure, therefore can preferentially remove the medium-high frequency component of face shape error; Along with the further increase of pitch disc thickness, flexural deformation and the detrusion of generation are more and more less, and this moment, the crimp of pitch occupied leading role gradually.Pitch dish type change process can be understood as: the thickness of pitch dish increases, and then corresponding polish pressure is also larger, because the pitch dish needs larger pressure to realize flexural deformation.Simultaneously, along with the pitch disc thickness increases, its high-order distortion is more and more difficult, therefore for the higher frequency error mainly take the crimp of pitch as main.

According to above-mentioned analysis, revise the above face shape error of certain frequency, need the thickness of reasonably optimizing pitch dish, for this error more than frequency, the flexural deformation of pitch dish and the crimp of pitch occupy leading role therein with assurance.For high frequency error, the Main Function of pitch dish all shows as the crimp of pitch, therefore only needs to discuss the critical thickness h of flexural deformation and detrusion ₀, just can obtain the polish pressure coefficient as the cut-off frequency of high-pass filter.When flexural deformation equals transverse shear deformation, there is following formula:

16π ⁴Dξ ⁴＝4π ²D _sξ ² (15)

With D _sWith the expression formula substitution following formula (15) of D, the error frequency when obtaining flexural deformation and detrusion and equating is:

$\mathrm{\&xi;}=\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;h}}---\left(16\right)$

Error frequency when formula (16) has provided flexural deformation and detrusion and equates notices not comprise elastic modulus E in the equation that parameter only has Poisson's ratio ν and polishing disk thickness h.Can get critical thickness h according to formula (16) ₀For:

${\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002140037700022.png,HDA00002140037700061.png"\; state="\{\{state\}\}">h</figure-callout>}}_0=\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}}---\left(17\right)$

Formula (17) has been set up the relation of critical thickness isospace error frequency.It should be noted that above-mentioned Mathematical Modeling is to be based upon on the hypothesis that the pitch dish is elastic sheet.According to the condition of thin plate, pitch disc thickness h is with having following relationship between the diameter d as can be known:

$\frac{1}{80}<\frac{h}{d}<\frac{1}{5}---\left(18\right)$

According to formula (17) and formula (18), realize the fairing of medium-high frequency error, pitch dish diameter d then preferably satisfies following constraints:

$\frac{5\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}}<d<\frac{40\sqrt{6(1-v)}}{\mathrm{\&pi;\&xi;}}---\left(19\right)$

The pitch disc thickness is less, and stability is more unreliable, and polishing disk can not become lamina membranacea (thickness and diameter than less than 1/80 thin plate) under the general technology Parameter Conditions, and the optimal conditions that therefore can get pitch dish parameter is as follows:

$h>\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}};$ $d>\frac{5\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}}---\left(20\right)$

Formula (20) shows: in the situation that the pitch disk material is definite, carry out fairing to the face shape error of higher frequency composition, the pitch disc thickness that then needs is larger, and the diameter of pitch dish is also larger simultaneously.Therefore, for the higher error percentage of frequency, often need the pitch dish of larger diameter, larger thickness to carry out efficient light to it suitable, this also reasonable dismissal why in the situation that medium-high frequency error serious (" broken band "), can only use deep bid to carry out fairing, thereby remove medium-high frequency error wherein, obtain level and smooth face shape error and distribute.Formula (20) is to utilize the theoretical foundation of CCOS fairing medium-high frequency error, for the medium-high frequency error of certain frequency, need to carry out according to the frequency characteristic of error the optimization of pitch dish, thereby the efficient light of realizing the medium-high frequency error is suitable.

As to further improvement in the technical proposal, after finishing described operation (a), can not revise the medium-high frequency error if also exist, then proceed described operation (b).Generally speaking, if behind the complete operation (a), the medium-high frequency error that optical element exists can satisfy the surface figure accuracy requirement that optical element uses, then can stop processing after the operation (a), if but the surface figure accuracy that the medium-high frequency error uses optical element of can not revising that exists behind the complete operation (a) requires to still have considerable influence, then can superpose afterwards in operation (a) and operate (b), so that optical element to be processed reaches better surface figure accuracy, fully revise the medium-high frequency error that exists in the optical element.If adopt this preferred technical scheme, should be noted that in follow-up operation (b) that then the low frequency surface figure accuracy after maintenance operation (a) correction of the flank shape is not destroyed.If in the subsequent operation (b) heavy damage the low frequency surface figure accuracy that obtains of operation (a), so also need further to operate (a) with raising low frequency surface figure accuracy, thereby make the full frequency band surface figure accuracy of optical element reach practical application request.

Therefore, the different removal mechanisms at work of MRF and CCOS reveal different characteristics for the acting body of medium-high frequency error, adopt in the process that above-mentioned processing method of the present invention processes the medium-high frequency error of optical element, can fully form combined type control technique in conjunction with MRF and CCOS technical advantage separately, when satisfying the optical mirror plane high-precision requirement, realize effective control of centering high frequency error, realize the efficient uniform convergence of optical element full frequency band error, for the further lifting of optical element optical property provides effective way.

Description of drawings

Fig. 1 is the signal model schematic diagram of typical MRF process among the present invention.

Fig. 2 is dissimilar path planning schematic diagram in the MRF process of the present invention.

Fig. 3 is signal model schematic diagram in the CCOS process of the present invention.

Fig. 4 is the process chart of combined type processing method medium-high frequency error machinability assessment of the present invention.

Fig. 5 is the amplitude frequency spectrum figure that removes function in the embodiment of the invention 1.

Fig. 6 is the PSD curve before and after the paraboloidal mirror processing in the embodiment of the invention 1.

Fig. 7 is the algorithm flow chart that random line machining path generates in the embodiment of the invention 1.

Fig. 8 is the random line machining path figure that generates in the embodiment of the invention 1.

Fig. 9 is the embodiment of the invention 2 midplane mirror primary face shape error map.

Figure 10 is medium-high frequency error fairing process chart in the embodiment of the invention 2.

Figure 11 is the face shape error distribution map after the fairing in the embodiment of the invention 2.

Figure 12 is the face shape error profile diagram of fairing process in the embodiment of the invention 2.

Figure 13 is the PSD curve map before and after the fairing processing in the embodiment of the invention 2.

The specific embodiment

The invention will be further described below in conjunction with Figure of description and specific embodiment.

Embodiment 1:

A kind of combined type processing method of optical element medium-high frequency error of the present invention, the processing object of the present embodiment processing method are the paraboloidal mirror of a bore 200mm, vertex curvature radius 640mm, and the processing method of the present embodiment may further comprise the steps:

1. medium-high frequency error machinability assessment: the operating procedure of the medium-high frequency error machinability assessment of the present embodiment as shown in Figure 4.

1.1PSD analyze: at first the face shape error of above-mentioned optical element paraboloidal mirror to be processed carried out the PSD analysis, obtain the PSD curve (referring to Fig. 6) of face shape error, with reference to the criteria for classifying of U.S. QED company to the basic, normal, high frequency range of optical element, be be respectively in the error space cycle＞D/5, D/5～D/30,＜D/30 (D is clear aperture), determine the present embodiment medium-high frequency error frequency distribution characteristics based on the PSD curve, the error frequency of the present embodiment medium-high frequency error should be greater than 0.025mm ^-1

1.2 removal function optimization: consider process time and machining accuracy accessibility, the removal function of MRF instrument in the present embodiment is optimized, the removal function model after being optimized is as follows: the removal function length is 22mm, and width is 8mm.Need to prove, the choice and optimization of removing function is a combined process, and it is mainly determined jointly by the face shape error feature of processor predefined process time, machining accuracy and minute surface to be processed.Remove the optimization of function and general knowledge and the routine techniques that selection course belongs to this area.

1.3 cut-off frequency is found the solution: the removal function model after the above-mentioned steps 1.2 is carried out spectrum analysis, obtain removing the amplitude spectral line of function as shown in Figure 5; Be 0.1053mm according to the cut-off frequency of removing function in this amplitude spectral line acquisition the present embodiment again ^-1(dropping to the frequency at 5% place of peak value for the amplitude spectral line of removing function).

1.4 frequency characteristic relatively: above-mentioned cut-off frequency is compared with the aforementioned medium-high frequency error frequency distribution that needs control; According to the PSD curve of paraboloidal mirror among the cut-off frequency characteristic of the present embodiment and the present embodiment Fig. 6, we think and are lower than 0.1053mm in this paraboloidal mirror face shape error ^-1The medium-high frequency error be machinable, therefore, determine to adopt MRF technique that frequency is positioned at 0.025mm ^-1And 0.1053mm ^-1Between the medium-high frequency error process.

2. MRF processes: adopt the above-mentioned medium-high frequency the revised error of MRF processes.

2.1 face shape error is discrete: first the face shape error of measuring gained in the step 1 is carried out discrete processes;

2.2 remove the discrete of function: the removal function after optimizing in the above-mentioned steps 1 is carried out discrete processes;

2.3 find the solution residence time: find the solution the required residence time of the present embodiment MRF technique and distribute;

2.4 generate random line machining path: the shape based on above-mentioned paraboloidal mirror is given birth to the machining path that the present embodiment becomes MRF technique; Route characteristic can be defined as the path constraint condition, the stabilizing path characterizing definition is the route searching feature, simultaneously with migration path feature and unstable route characteristic route searching feature as a supplement, thereby pathway search mechanisms, search for attainable random line machining path by computer program, its algorithm principle as shown in Figure 7; In the present embodiment, utilize the random line machining path of this algorithm flow generation as shown in Figure 8.As seen from Figure 8, the random line machining path of the present embodiment MRF technique presents irregular, random mixed and disorderly randomness feature and distributes, and should unrest line machining path be take stabilizing path as main, take migration path and unstable path as auxiliary.

2.5 MRF: the residence time that at last will find the solution gained according to random line machining path shown in Figure 8 distributes and is converted to resident VELOCITY DISTRIBUTION along the machining path direction, and above-mentioned paraboloidal mirror is carried out the correction of medium-high frequency error according to resident VELOCITY DISTRIBUTION.Result after the processing is carried out PSD analyze, the PSD curve of the paraboloidal mirror after obtaining processing as shown in Figure 6.Observe the PSD curve of processing front and back, find that spatial frequency is lower than 0.1mm ^-1Error effectively revised, and spatial frequency is higher than 0.1mm ^-1Error substantially do not restrain.The cut-off frequency of removing function is 0.1053mm ^-1, this is consistent with the convergence property in the actual process.

The process of the present embodiment can show: on the one hand, the amplitude frequency spectrum figure that removes function can effectively realize the assessment of face shape error machinability; On the other hand, the effective retouch medium-high frequency error percentage of MRF.Can make optical element substantially satisfy the surface figure accuracy requirement by the MRF processes in the present embodiment, not need to carry out again follow-up computer controlled optical surfacing forming technology processing.

Embodiment 2:

A kind of combined type processing method of optical element medium-high frequency error of the present invention, the processing object of the present embodiment processing method are the level crossing of a bore 100mm, and the processing method of the present embodiment may further comprise the steps:

1. medium-high frequency error machinability assessment: the operating procedure of the medium-high frequency error machinability assessment of the present embodiment as shown in Figure 4.

1.1PSD analyze: at first the face shape error of above-mentioned optical element level crossing to be processed is carried out PSD and analyzes, obtain the distribution of face shape error as shown in Figure 9, the PSD curve that obtains as shown in figure 13, as seen, the Existential Space frequency is 0.2mm in the face shape error ^-1Sinusoidal face shape error structure; According to the criteria for classifying of medium-high frequency error, this face shape error becomes to belong to the medium-high frequency error character;

1.2 removal function optimization: consider process time and machining accuracy accessibility, the removal function of MRF instrument in the present embodiment is optimized, the removal function model after being optimized is as follows: the removal function length is 16mm, and width is 8mm.

1.3 cut-off frequency is found the solution: the removal function model after the above-mentioned steps 1.2 is carried out spectrum analysis, obtain removing the amplitude spectral line of function; Be 0.082mm according to the cut-off frequency of removing function in this amplitude spectral line acquisition the present embodiment again ^-1(dropping to the frequency at 5% place of peak value for the amplitude spectral line of the present embodiment removal function).

1.4 frequency characteristic relatively: continuity and cut-off frequency the approaching with correction medium-high frequency error frequency of considering face structure in the present embodiment, we think that the machinability of this removal function centering high frequency error is not enough, therefore adopt CCOS that this medium-high frequency error is carried out fairing processing.

2. computer controlled optical surfacing forming technology processing: adopt CCOS that the medium-high frequency error of above-mentioned minute surface is carried out fairing processing, concrete operation step generally as shown in figure 10.

2.1 according to above-mentioned definite medium-high frequency error frequency distribution characteristics the pitch dish that CCOS uses is optimized, optimize the content comprises the material of determining the bottom supporting dish, diameter and the thickness of pitch dish; Working process parameter is optimized according to predefined fairing time (processor's expectation process time when adopting CCOS technique to carry out fairing) and medium-high frequency error amplitude characteristic; Obtain concrete machined parameters after the present embodiment optimization as follows: polishing disk is the pitch dish, base material is stainless steel, pitch dish diameter 25mm, thickness 4mm, eccentric throw is 5mm, pitch mould thickness 5mm, impressed pressure 0.15MPa, removing the function diameter is 35mm, and revolution speed is 150rpm, and rotational velocity is 155rpm;

Stainless Poisson's ratio is 0.3 in the present embodiment, and the frequency of the error of fairing is 0.2mm ^-1With these parameters respectively substitution to calculate the minimum of a value that can obtain pitch dish diameter be 8.1453mm, the minimum of a value of pitch disc thickness is 1.63mm, the pitch dish diameter after the optimization is 25mm, thickness is 4mm, and namely the pitch dish diameter in the present embodiment and thickness satisfy following constraints: $d>\frac{5\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}};$ $h>\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}}.$

2.2 fairing processing: utilize the pitch dish after optimizing and above-mentioned level crossing is carried out the fairing of medium-high frequency error according to the technological parameter after optimizing, the processing conditions that above-mentioned parameter consists of obviously can be higher than 5mm to frequency ^-1Error percentage carry out fairing, adopt these parameters to test, through the fairing processing of 30min altogether, face shape error PV value is reduced to 0.062um by 1.102um, RMS value is reduced to 0.009um by 0.35um, finally the face shape error distribution as shown in figure 11.

Be convergence effect of observing the present embodiment fairing process different phase face shape error directly perceived, face shape error PV value and the RMS value of different process times are put in order, can obtain their relation curves with process time, as shown in figure 12.Face shape error before and after the fairing is carried out PSD analyze, obtain the PSD curve as shown in figure 13, after the normal process fairing process, not only the medium-high frequency error character in the face shape error obtains fairing, and face shape error also obtains effective convergence.Therefore, this experimental verification in the situation that face shape error can not be processed, adopt CCOS can the centering high frequency error to carry out efficient light suitable, thereby provide the basis for the high accuracy processing of optical element.

Claims (8)

1. the combined type processing method of an optical element medium-high frequency error, described combined type processing method is to treat first the processing optical part to carry out the assessment of medium-high frequency error machinability, then selectively carry out following operation (a) or operation (b) according to assessment result, wherein:

Described medium-high frequency error machinability assessment may further comprise the steps: the face shape error that at first utilizes interferometer measurement optical element to be processed, then the face shape error that obtains being carried out PSD analyzes, obtain the PSD curve of face shape error, determine medium-high frequency error frequency distribution characteristics based on the PSD curve; According to predetermined process time and machining accuracy the removal function of MRF instrument is optimized the removal function model after being optimized; Carry out spectrum analysis to removing function model, obtain removing the amplitude spectral line of function; Remove again the cut-off frequency of function according to this amplitude spectral line acquisition, and this cut-off frequency is compared with the aforementioned medium-high frequency error frequency distribution that needs control; If there is the medium-high frequency the revised error that is lower than cut-off frequency during the medium-high frequency error frequency distributes, then forwards following operation (a) to and can revise the medium-high frequency error to this and process; Exist during if the medium-high frequency error frequency distributes be higher than cut-off frequency can not revise the medium-high frequency error, then forward following operation (b) to and can not revise the medium-high frequency error to this and process;

Described operation (a) refers to: employing MRF processes is described revises the medium-high frequency error, until satisfy the surface figure accuracy requirement, stops processing;

Described operation (b) refers to: the processing of employing computer controlled optical surfacing forming technology is described can not revise the medium-high frequency error, until satisfy the surface figure accuracy requirement, stops processing.

2. the combined type processing method of optical element medium-high frequency error according to claim 1 is characterized in that, in the described medium-high frequency error machinability evaluation process, described cut-off frequency drops to the frequency at peak value 5% place for the amplitude spectral line of removing function.

3. the combined type processing method of optical element medium-high frequency error according to claim 1, it is characterized in that, in the described operation (a), the described concrete steps of revising the medium-high frequency error of MRF processes comprise: the face shape error of measuring gained in the first centering high frequency error machinability evaluation process carries out discrete processes, and the removal function model after the described optimization is carried out discrete processes; Finding the solution the required residence time of MRF technique distributes; Generate the machining path of MRF technique based on the shape of described optical element to be processed; According to machining path the residence time of gained being distributed at last is converted to resident VELOCITY DISTRIBUTION along the machining path direction, and according to resident VELOCITY DISTRIBUTION described optical element to be processed is carried out the correction of medium-high frequency error.

4. the combined type processing method of optical element medium-high frequency error according to claim 3, it is characterized in that, the machining path of described MRF technique adopts " random line machining path ", and described random line machining path refers to that machining path presents irregular, random mixed and disorderly randomness feature and distributes.

5. the combined type processing method of optical element medium-high frequency error according to claim 4 is characterized in that, described random line machining path is take stabilizing path as main, take migration path and unstable path as auxiliary; Three adjacent in the described random line machining path discrete dwell point define two continuous machining cell paths; The machining path of the angle that described stabilizing path refers to two machining cell paths during greater than 90 °; Machining path when described migration path refers to that the angle in two machining cell paths equals 90 °; The machining path of the angle that described unstable path refers to two machining cell paths during less than 90 °.

6. the combined type processing method of each described optical element medium-high frequency error according to claim 1～5, it is characterized in that, in the described operation (b), the described concrete steps that can not revise the medium-high frequency error of described computer controlled optical surfacing forming technology processing comprise: the pitch dish of according to the medium-high frequency error frequency distribution characteristics of determining in the described medium-high frequency error machinability evaluation process computer controlled optical surfacing forming technology being used first is optimized, and optimize the content comprises the material of determining the bottom supporting dish, diameter and the thickness of pitch dish; Working process parameter is optimized according to predefined fairing time and medium-high frequency error amplitude characteristic; Pitch dish after utilize optimizing at last also carries out the fairing of medium-high frequency error according to the technological parameter after optimizing to described optical element to be processed.

7. the combined type processing method of optical element medium-high frequency error according to claim 6 is characterized in that, in the described operation (b), the diameter d of described pitch dish and thickness h satisfy following restrictive condition:

$d>\frac{5\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}};$ $h>\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}};$

Wherein, ν represents Poisson's ratio, and ξ represents error frequency.

8. the combined type processing method of each described optical element medium-high frequency error according to claim 1～5, it is characterized in that, after finishing described operation (a), can not revise the medium-high frequency error if also exist, then proceed described operation (b).

Images