CN102848287B - 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, with there being large-area space geometry contact form between optical element, is conducive to the successional generation of face shape error, and error shows as macro-scale, i.e. low frequency form error; And micro-nano magnitude polishing abrasive material is with the mechanochemistry comprehensive function between optical element material, the error that major embodiment is micro-scale develops, i.e. high frequency roughness error.Therefore, in the resulting surface of the work error of traditional manufacturing process (as classic polishing, ring throwing etc.), substantially do not comprise serious medium-high frequency error form, can guarantee the favorable optical performance of optical element.

The development of modern advanced optical fabrication methods, trends towards adopting computer control small tool to carry out the removal of certainty controllable material to optical surface, belongs to the category of footpath, computer control rim of the mouth polishing technology.Because the small tool size adopting is generally all far smaller than workpiece size, therefore, in realizing the process of the definite convergence of low frequency face shape error, more and more tend to form periodic small scale foozle feature in medium-high frequency section.What people were popular is classified as medium-high frequency error this class small scale foozle feature, and 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 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 MRF belongs to a kind of flexible polishing mode.This flexible removing method, has determined that it is adding man-hour to optical surface error, and magnetic flow liquid can keep good contact condition with optical surface.When the magnetic flow liquid under high strength gradient magnetic carries out material removal to surface of the work, the flexible polishing mould that magnetic flow liquid forms is with machining area generation comprehensive engagement, and the polish abrasive of magnetic flow liquid is all had an effect with surface of the work error.Owing to material being removed to active shearing force, be not substantially subject to the impact of face shape error micro Distribution, no matter be therefore protruding peak or the groove of optical element surface, flexible polishing mould is basically identical to its removal efficiency.In other words, if utilize MRF to carry out material to optical element surface, evenly remove, 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, by distributing residence time can realize certain medium-high frequency error correction, thereby control the means that provide for medium-high frequency error.

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

Yet, in prior art, generally all adopt single removal mechanisms at work to control the medium-high frequency error of optical element, and single removal mechanisms at work is difficult to realize effective control of medium-high frequency error, and the directly related machining feature of residual same removal mechanisms at work usually, 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 technical advantage separately of MRF and CCOS 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 first to treat processing optical part to carry out the assessment of medium-high frequency error machinability, then according to assessment result, selectively carry out following operation (a) or operation (b), wherein:

Described medium-high frequency error machinability assessment comprises the following steps: the face shape error that first utilizes interferometer measurement optical element to be processed, then the face shape error obtaining being carried out to PSD (wavefront power spectral density) analyzes, obtain the PSD curve of face shape error, the object that obtains PSD curve is exactly in order to observe face shape error at the distribution character of frequency domain, according to its distribution character, just can carry out suitable judgement by 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 is mainly reflected in the shape and efficiency of optimizing removal function removal function model after being optimized, the feature of removing function by change can change process time and machining accuracy, thereby according to process time and machining accuracy realizing the combined optimization of removing function); Removal function model after optimizing is carried out to spectrum analysis, obtain removing the amplitude spectral line of function; According to this amplitude spectral line, obtain the cut-off frequency of removing function again, and this cut-off frequency is distributed and compared with the aforementioned medium-high frequency error frequency that needs to control; If there is the medium-high frequency the revised error lower than cut-off frequency during medium-high frequency error frequency distributes, forward following step (a) to and to this, can revise medium-high frequency error and process; During if medium-high frequency error frequency distributes, exist higher than cut-off frequency can not revise medium-high frequency error, forward following step (b) to and to this, can not revise medium-high frequency error and process;

Described operation (a) refers to: described in employing MRF processes, can revise medium-high frequency error, until meet surface figure accuracy requirement, stop processing;

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

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

The process of MRF be in essence remove function at surface of the work the two-dimensional convolution process with residence time, by computer realization certainty material, removing control is the inverse process of said process, input face shape error and removal function before processing, utilize Mathematical Modeling output residence time, and the continuous variation by speed on machining path realizes material and removes; 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 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), after being converted, formula (1) can obtain following formula (2):

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

From the angle of signal, remove the effect that function serves as wave filter in process, as shown in Figure 1.Signal T obtains " pure " signal D ' by system R filtering, signal D ' is polluted and obtains actual signal D by E, H represents that (solving of residence time is the process of liftering that signal is carried out to liftering system, specifically using optical element face shape error with remove function as input, obtain residence time output, by lathe, to residence time, output realizes, 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 it is typical low pass filter; The characteristic that removal function blocks 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, need first the modification capability (removing the ability of function correction optical surface error) of MRF removal function to be defined; Evaluate the modification capability of removing function, generally from removing the frequency spectrum of function, start with, owing to removing function, present certain bandwidth characteristic on 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 is greater than cut-off frequency, remove function it is carried out to signal cutout, remove function the error higher than cut-off frequency is lost to modification capability.

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

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 convolution effect, thus the small scale medium-high frequency error character of introducing CF.The specific medium-high frequency error that convolution effect is introduced is directly directly related with the planning form of machining path.Such as grating machining path can be introduced the medium-high frequency error character with feeding step pitch respective frequencies on perpendicular to discrete direction of feed, and concentric circles machining path can be introduced the medium-high frequency error character with feeding pitch respective frequencies at circular optical element generatrix direction, their unifications on PSD curve show as the needle pattern frequency band error at CF place.Therefore,, in the process of utilizing MRF to revise part medium-high frequency error, 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, make error correction path present 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 conventional random line machining path, generally comprise following some: the predefined all discrete dwell point of (1) traversal path; (2) experience all discrete dwell point in path 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, has spatial continuity.Analyze accordingly, the planning process of random line machining path is the path curve of all discrete dwell point of traversal of search in essence.The grid of the discrete dwell point of typical case is even orthohormbic structure, has 8 points in its any discrete dwell point neighborhood, supposes on path to be some p _i-1, current point is p _i, lower is some p _i+1, under path, a bit there are 7 theoretical positions, as shown in Figure 2.Consider the steady realization in machine tool motion performance and path, by 7 p shown in Fig. 2 _i+1the path that discrete dwell point forms is divided into three classes: stabilizing path, migration path and unstable path.Dotted path direct of travel in Fig. 2 acutangulates with the current direction in path, now requires lathe one axle snap back and another axle starts fast, and this easily causes that lathe trembles, and is unstable path; 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 lower than unstable path machine dynamic characteristics, is migration path; Solid-line paths direct of travel becomes obtuse angle with the current direction in path, only needs the lathe normal acceleration and deceleration of one axle and another axle startup, minimum to machine dynamic characteristics requirement, is stabilizing path.As can be seen here, in described random line machining path, three adjacent discrete dwell point define two continuous machining cell paths; Described stabilizing path refers to the machining path when angle in two machining cell paths is greater than 90 °; Described migration path refers to the machining path when angle in two machining cell paths equals 90 °; Described unstable path refers to the machining path when angle in two machining cell paths is less than 90 °.As preferred scheme, described random line machining path is to 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 described operation (b), the concrete steps that can not revise medium-high frequency error described in described computer controlled optical surfacing forming technology processing preferably include: first according to the pitch dish that in described medium-high frequency error machinability evaluation process, definite medium-high frequency error frequency distribution characteristics is used computer controlled optical surfacing forming technology, be optimized, optimize the content comprises determines that the material of bottom supporting dish is, 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 for changing the removal efficiency of pitch dish to optical element surfacing by setting the parameters such as public rotational velocity, polish pressure of pitch dish, thereby makes the fairing effect that as far as possible reaches pursued within the predefined fairing of the processor time; Finally utilize the pitch dish after optimizing and described optical element to be processed carried out to the fairing of medium-high frequency error according to the technological parameter after optimizing.

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

$\begin{array}{cc}{\▿}^2\mathrm{\Φ}=-\frac{q}{D}& \\ {\▿}^{2}w=-\mathrm{\Φ}-\frac{q}{D_s}& \\ ({\▿}^2-{\mathrm{\β}}^2)\mathrm{\Ψ}=0& {\mathrm{\β}}^2=\frac{{2D}_s}{D(1-v)}\end{array}----\left(3\right)$

In formula (3), the shear stiffness that represents pitch dish, the bending rigidity that represents 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 acting on pitch dish, for Laplace operator,

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

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

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

Use q ₀the impressed pressure that represents to act on polishing disk, the actual pressure q acting on polishing disk can be expressed as:

q＝p-q ₀＝k _c(s-w)-q ₀ (5)

By first two of formula (3), can to obtain quadravalence equation as follows:

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

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

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

By second in formula (5) substitution formula (3), can obtain following formula:

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

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

$\begin{array}{c}D{\▿}^2{\▿}^{2}w-\frac{k_{c}D}{D_s}{\▿}^{2}w+k_{c}w=-q_0+k_c[1-\frac{D}{D_s}{\▿}^2]s\\ \mathrm{\Φ}=-{\▿}^{2}w+\frac{k_c}{D_s}w-\frac{k_{c}s-q_0}{D_s}\\ \begin{array}{cc}\left({\▿}^{2-{\mathrm{\β}}^2}\right)\mathrm{\Ψ}=0& ({\mathrm{\β}}^2=2D_s/(1-v)D)\end{array}\end{array}---\left(3\right)$

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

$s=(u\cos \frac{\mathrm{\πx}}{a}+v\sin \frac{\mathrm{\πx}}{a})\cos \frac{\mathrm{\πy}}{b}+(u^{*}\cos \frac{\mathrm{\πx}}{a}+v^{*}\sin \frac{\mathrm{\πx}}{a})\sin \frac{\mathrm{\πy}}{b}---\left(10\right)$

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 obtained to the suffered actual pressure of polishing disk, that is:

$p=q_0+k_c(1-\frac{{\mathrm{\α}}_1}{{\mathrm{\α}}_2})s---\left(11\right)$

Wherein, $\begin{array}{cc}{\mathrm{\α}}_1=k_c[1+\frac{D}{D_s}(\frac{{\mathrm{\π}}^2}{a^2}+\frac{{\mathrm{\π}}^2}{b^2})]& {\mathrm{\α}}_2={\mathrm{\α}}_1+D{(\frac{{\mathrm{\π}}^2}{a^2}+\frac{{\mathrm{\π}}^2}{b^2})}^2\end{array};$ In frequency domain analysis the problems referred to above, have further known (ζ, ξ all represent error frequency, and just the value of the two is different):

$a^2=\frac{1}{4{\mathrm{\ξ}}^2},b^2=\frac{1}{4{\mathrm{\ζ}}^2},{\mathrm{\α}}_1=k_c(1+{4\mathrm{\π}}^2\frac{D}{D_s}({\mathrm{\ξ}}^2+{\mathrm{\ζ}}^2)),{\mathrm{\α}}_2={\mathrm{\α}}_1+{16\mathrm{\π}}^{4}D{({\mathrm{\ξ}}^2+{\mathrm{\ζ}}^2)}^2---\left(12\right)$

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

p＝q ₀+γs (13)

Wherein $\mathrm{\γ}=\frac{1}{\frac{1}{16{\mathrm{\π}}^{4}D{\mathrm{\ξ}}^4}+\frac{1}{4{\mathrm{\π}}^2{D}_s{\mathrm{\ξ}}^2}+\frac{1}{k_c}}.$

From formula (13), polish pressure p is the linear function of face shape error s, and γ is polish pressure coefficient.From signal angle, understand, face shape error s can be considered as to input signal, polish pressure p is considered as output signal, 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, can eliminate the medium-high frequency error in face shape error).

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

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

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 fixed frequency face shape error, the distortion of different-thickness pitch dish is mainly divided into three phases: when polishing disk thickness hour, polishing disk be take detrusion as main, polish pressure, along surface of the work tangential direction, shows as shearing force, easily destroys the original face shape error of optical surface; When pitch disc thickness increases, polishing disk be take flexural deformation gradually as main, and polish pressure is along 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 the now crimp of pitch occupies leading role gradually.Pitch dish deformation process can be understood as: the thickness of pitch dish increases, and corresponding polish pressure is also larger, because pitch dish needs larger pressure to realize flexural deformation.Meanwhile, along with pitch disc thickness increases, its high-order distortion is more and more difficult, therefore for higher frequency error, mainly take the crimp of pitch as main.

According to above-mentioned analysis, revise face shape error more than certain frequency, need the thickness of reasonably optimizing pitch dish, to guarantee for this error more than frequency, the flexural deformation of pitch dish and the crimp of pitch occupy leading role therein.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 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)

By D _swith the expression formula substitution above 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 in equation and does not comprise elastic modulus E, parameter only has Poisson's ratio ν and polishing disk thickness h.According to formula (16), can obtain critical thickness h ₀for:

$h_0=\frac{\sqrt{6(1-v)}}{2\mathrm{\&pi;\&xi;}}---\left(17\right)$

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 pitch dish is elastic sheet.According to the condition of thin plate, known pitch disc thickness h is with having following relationship between diameter d:

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

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

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

Pitch disc thickness is less, and stability is more unreliable, and under general technology Parameter Conditions, polishing disk can not become lamina membranacea (thickness with diameter than the thin plate that is less than 1/80), and the optimal conditions that therefore can obtain 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 pitch disk material is definite, carry out fairing to the face shape error of higher frequency composition, the pitch disc thickness needing 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 of at 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 it is suitable to realize the efficient light of medium-high frequency error.

As the further improvement to technique scheme, after completing described operation (a), if also exist and can not revise medium-high frequency error, proceed described operation (b).Generally speaking, if after complete operation (a), the medium-high frequency error that optical element exists can meet the surface figure accuracy requirement that optical element is used, after operation (a), can stop processing, if but the medium-high frequency error of can not revising existing after complete operation (a) requires to still have considerable influence to the surface figure accuracy of optical element application, can superpose and operate (b) afterwards in operation (a), so that optical element to be processed reaches better surface figure accuracy, fully revise the medium-high frequency error existing in optical element.If adopt this preferred technical scheme, in follow-up operation (b), should be noted that the low frequency surface figure accuracy keeping after operation (a) correction of the flank shape is not destroyed.If in subsequent operation (b) heavy damage the low frequency surface figure accuracy that obtains of operation (a), so also need further to operate (a) to improve 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 in conjunction with MRF and CCOS technical advantage separately, form combined type control technique, when meeting 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.

Accompanying drawing explanation

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

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

Fig. 3 is signal model schematic diagram in 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 present invention 1.

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

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

Fig. 8 is the random line machining path figure generating in the embodiment of the present invention 1.

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

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

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

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

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

The specific embodiment

Below in conjunction with Figure of description and specific embodiment, the invention will be further described.

Embodiment 1:

A combined type processing method for optical element medium-high frequency error of the present invention, the processing object of the present embodiment processing method is the paraboloidal mirror of a bore 200mm, vertex curvature radius 640mm, the processing method of the present embodiment comprises the following 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 analyzes: first the face shape error of above-mentioned optical element paraboloidal mirror to be processed is carried out to PSD analysis, obtain the PSD curve (referring to Fig. 6) of face shape error, the criteria for classifying with reference to U.S. QED company to the basic, normal, high frequency range of optical element, be to be respectively >D/5, D/5～D/30, <D/30 (D is clear aperture) error space cycle, based on PSD curve, determine the present embodiment medium-high frequency error frequency distribution characteristics, the error frequency of the present embodiment medium-high frequency error should be greater than 0.025mm ^-1;

1.2 remove 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: removal function length is 22mm, and width is 8mm.It should be noted that, 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 frequencies solve: the removal function model after above-mentioned steps 1.2 is carried out to spectrum analysis, obtain removing the amplitude spectral line of function as shown in Figure 5; According to the cut-off frequency of removing function in this amplitude spectral line acquisition the present embodiment, be 0.1053mm again ^-1(for removing the amplitude spectral line of function, dropping to the frequency at 5% place of peak value).

1.4 frequency characteristic comparisons: above-mentioned cut-off frequency is distributed and compared with the aforementioned medium-high frequency error frequency that needs to control; According to the PSD curve of paraboloidal mirror in the cut-off frequency characteristic of the present embodiment and the present embodiment Fig. 6, we think in this paraboloidal mirror face shape error lower than 0.1053mm ^-1medium-high frequency error be machinable, therefore, determine to adopt MRF technique to be positioned at 0.025mm to frequency ^-1and 0.1053mm ^-1between 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 errors discrete: first carry out discrete processes to measuring the face shape error of gained in step 1;

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

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

2.4 generate random line machining path: raw the present embodiment of shape of the paraboloidal mirror based on above-mentioned becomes the machining path of MRF technique; Route characteristic can be defined as to path constraint condition, stabilizing path characterizing definition is route searching feature, simultaneously by migration path feature and unstable route characteristic route searching feature as a supplement, thereby pathway search mechanisms, by computer program, search for attainable random line machining path, 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 this unrest line machining path is to take stabilizing path as main, take migration path and unstable path as auxiliary.

2.5 MRFs: finally according to the random line machining path shown in Fig. 8, the residence time that solves gained is distributed and is converted to the resident VELOCITY DISTRIBUTION along machining path direction, and above-mentioned paraboloidal mirror is carried out to the correction of medium-high frequency error according to resident VELOCITY DISTRIBUTION.Result after processing is carried out to PSD analysis, and the PSD curve of the paraboloidal mirror after being processed 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 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.In the present embodiment, by MRF processes, can make optical element substantially meet surface figure accuracy requirement, not need to carry out again follow-up computer controlled optical surfacing forming technology processing.

Embodiment 2:

A combined type processing method for optical element medium-high frequency error of the present invention, the processing object of the present embodiment processing method is the level crossing of a bore 100mm, the processing method of the present embodiment comprises the following 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 analyzes: first the face shape error of above-mentioned optical element level crossing to be processed is carried out to PSD analysis, obtain the distribution of face shape error as shown in Figure 9, the PSD curve obtaining as shown in figure 13, visible, and in face shape error, Existential Space frequency is 0.2mm ^-1sinusoidal face shape error structure; According to the criteria for classifying of medium-high frequency error, this face shape error becomes to belong to medium-high frequency error character;

1.2 remove 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: removal function length is 16mm, and width is 8mm.

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

1.4 frequency characteristic comparisons: 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 to carry out fairing processing to this medium-high frequency error.

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

The 2.1 pitch dishes of CCOS being used according to above-mentioned definite medium-high frequency error frequency distribution characteristics are optimized, and optimize the content comprises determines that the material of bottom supporting dish is, diameter and the thickness of pitch dish; Working process parameter is optimized according to predefined fairing time (processor's expectation process time while adopting CCOS technique to carry out fairing) and medium-high frequency error amplitude characteristic; After the present embodiment optimization, obtain concrete machined parameters as follows: polishing disk is 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 function diameter is 35mm, and revolution speed is 150rpm, and rotational velocity is 155rpm;

In the present embodiment, stainless Poisson's ratio is 0.3, and the frequency of the error of fairing is 0.2mm ^-1by 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 optimization is 25mm, thickness is 4mm, and the pitch dish diameter in the present embodiment and thickness meet 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 carried out to the fairing of medium-high frequency error according to the technological parameter after optimizing, the processing conditions that above-mentioned parameter forms obviously can be to frequency higher than 5mm ^-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 face shape error distribution as shown in figure 11.

For directly perceived convergence effect of observing the present embodiment fairing process different phase face shape error, face shape error PV value and the RMS value of different process times are arranged, can obtain their relation curves with process time, as shown in figure 12.Face shape error before and after fairing is carried out to PSD analysis, obtain PSD curve as shown in figure 13, normal is after fairing process, and not only the medium-high frequency error character in face shape error obtains fairing, and face shape error also obtains effective convergence.Therefore, this experimental verification in the not machinable situation of face shape error, adopt CCOS can centering high frequency error to carry out efficient light suitable, thereby provide 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 first to treat processing optical part to carry out the assessment of medium-high frequency error machinability, then according to assessment result, selectively carry out following operation (a) or operation (b), wherein:

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

Described operation (a) refers to: described in employing MRF processes, can revise medium-high frequency error, until meet surface figure accuracy requirement, stop processing;

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

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

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

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 to take stabilizing path as main, take migration path and unstable path as auxiliary; In described random line machining path, three adjacent discrete dwell point define two continuous machining cell paths; Described stabilizing path refers to the machining path when angle in two machining cell paths is greater than 90 °; Described migration path refers to the machining path when angle in two machining cell paths equals 90 °; Described unstable path refers to the machining path when angle in two machining cell paths is less than 90 °.

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

7. the combined type processing method of optical element medium-high frequency error according to claim 6, is characterized in that, in described operation (b), the diameter d of described pitch dish and thickness h meet 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. according to the combined type processing method of the optical element medium-high frequency error described in any one in claim 1～5, it is characterized in that, complete after described operation (a), if also exist and can not revise medium-high frequency error, proceed described operation (b).