CN109227226A - Uniform-sliding method for residence time in optical element processing process - Google Patents
Uniform-sliding method for residence time in optical element processing process Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
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Abstract
The invention discloses a residence time smoothing method in the optical element processing process, which diffuses residence time distribution obtained by conventional calculation by introducing a time diffusion model so as to realize residence time smoothing. Compared with the original residence time, the residence time after the uniform sliding treatment is relatively small in time difference value on the adjacent discrete points, so that smooth transition between the adjacent discrete points is realized, and further the influence of frequent acceleration and deceleration of the polishing tool on the stability of the machine tool in the machining process is reduced. The residence time smoothing method in the optical element processing process can improve the calculated convergence effect through time diffusion processing, can reduce the jump degree of the residence time between adjacent discrete points through the residence time smoothing processing, is favorable for improving the stability of numerical control processing, and further reduces medium and high frequency errors caused by frequent jitter of a polishing tool on elements.
Description
Technical field
The invention belongs to the manufacture fields of optical element, and in particular to residence time in a kind of optical element process
Even sliding method.
Background technique
As the rapid development of optical technology and its continuous expansion of application range are opened up, face shape essence of the people to optical element
The technical indicators such as degree, surface roughness propose increasingly higher demands, and aspherical, large relative aperture, nano-precision become
The development trend of contemporary optics element.It is processed to effectively improve optical element surface processing quality and meet modernization high-precision
The demand of technology, technical staff start the processing that optical element is carried out using NC machining lathe.In numerical control processing
Cheng Zhong, polishing tool form certain speed of related movement and pressure in processed element surface, are processed element to remove
The excess stock on surface.Due to the introducing of digitizing technique, polishing tool can be approximate in the motion profile for being processed element surface
Regard the continuous moving on various discrete point as, within the unit time, polishing tool is on single discrete point to processed member
The removal amount of part is known as removing function, and residence time of the polishing tool on various discrete point is residence time.Therefore, such as
What planning polishing tool is the key that realize NC machining in the residence time distribution for being processed element surface.
In the prior art, the method for solving residence time is broadly divided into global optimum's optimal solution in solution drawn game portion:
1, global optimum's solution
When the amount to be removed for removing function and processed element is known, the classic algorithms meter such as least square method can be passed through
It calculates and obtains one group of optimal residence time distribution so that the face shape residual error of element surface is minimum after processing, and this organizes optimal be resident
Annual distribution is globally optimal solution.But in the processing of actual high-precision, data volume and operand which is related to
It is very huge, cause to be difficult to acquire globally optimal solution.
2, local optimum solution
It is distributed in order to which one group of preferably residence time is calculated in finite time, makes the face shape of element surface after processing
Residual error is as small as possible, it will usually residence time is solved using estimation iterative method, pulse iterative method scheduling algorithm in proportion, and this group is stayed
Staying Annual distribution is locally optimal solution.However, this method is primarily adapted for use in polishing tool in the removal function of element surface
The case where circularly symmetric distribution, should when for magnetorheological polishing machine etc., to remove function be non-circular symmetrical polissoir
The calculating convergence effect of method is to be improved.
However, above two method does not consider the even sliding problem of residence time distribution；When being resident between adjacent discrete point
Between variable quantity it is excessive when, i.e., residence time is distributed not even enough cunning, and polishing tool is likely to occur during the motion frequently to be accelerated, subtracts
Phenomena such as fast, to influence caused by machine stability, and then leaves movement trace in processed element surface.Usual situation
Under, the bulk of the movement trace is suitable with the spacing of adjacent discrete point on the order of magnitude, corresponds to medium, high frequency face shape and misses
Difference.Since the face shape error is that process equipment introduces in process, and the amendment of medium, high frequency face shape error is today's numerical control
The technological difficulties of processing, so being difficult to be modified it by secondary operation.
Summary of the invention
In the presence of overcoming the shortcomings of the prior art, a kind of optical element process is provided
The even sliding method of middle residence time, this method by introduce a time diffusion model to locally optimal solution method in an iterative process
The residence time distribution being calculated is diffused, to realize the even sliding processing of residence time；And inherit local optimum
The advantages of solution, calculation amount are much smaller than global optimum's solution.
The technical solution adopted by the present invention are as follows: a kind of even sliding method of residence time in optical element process passes through
It introduces a time diffusion model to be diffused the residence time distribution that conventionally calculation obtains, to realize the even of residence time
Sliding processing, comprises the concrete steps that:
Step 1: settling time diffusion model D (x, y), center are D (x0,y0), and D (x, y) meets total amount normalizing
Change and require:
∑I, jD(xi, yj)=1 (1)
Wherein D (xi,yj) indicate (x after time diffusioni,yj) position relative time change rate；For any time amount t,
With its position as central point (x0,y0), time quantum t is diffused using diffusion model D (x, y), then tD (xi,
yj) indicate (x after time diffusioni,yj) position time quantum.
Step 2: the face shape error of element to be processed is M (x, y), and removal function of the polishing tool within the unit time is I
(x, y) is T by the residence time that single iteration solves in iterative process1(x,y)；In residence time T1(x,
Y) in, the difference of the face shape error M (x, y) of theoretical removal amount and element to be processed is to calculate residual error E1(x, y) can be indicated
Are as follows:
E1(x, y)=M (x, y)-T1(x, y) * * I (x, y) (2)
In formula, * * indicates convolution, T1(x, y) * * I (x, y) is indicated in residence time T1In (x, y), polishing tool is to be added
The removal amount of work element；
Step 3: being directed to T1Each of (x, y) discrete coordinate (xi,yj), by time diffusion model D (x, y) in X, Y
It is translated on direction, makes its center (x0,y0) it is moved to (xi,yj), it is denoted as Dij(x, y):
Dij(x, y)=D (x-xi, y-yj) (3)
Then, using spread function Dij(x, y) is to point T1(xi,yj) DIFFUSION TREATMENT of progress from point to surface, to be expanded
Annual distribution K after dissipatingij(x, y):
Kij(x, y)=Dij(x, y) T1(xi, yj) (4)
Due to Dij(x, y) equally meets the normalization of total amount shown in formula (1) and requires, so that
∑I, jKij(x, y)=T1(xi, yj) (5)
kij(x, y) * * I (x, y) ≈ T1(xi, yj) I (x, y) (6)
Step 4: can obtain being directed to various discrete point (x according to step 3i,yj) the Annual distribution K that is diffused that treatedij
(x, y), then the residence time after even cunning is distributed T1' (x, y) may be expressed as:
T′1(x, y)=∑I, jKij(x, y) (7)
And the residence time after even cunning is distributed T1' (x, y) corresponding removal amount, T should be distributed with the residence time before even cunning1
(x, y) corresponding removal amount is approximately equal:
T′1(x, y) * * I (x, y) ≈ T1(x, y) * * I (x, y) (8)
Step 5: the residence time after face shape error M (x, y) to be processed and even cunning is distributed T1' (x, y) corresponding removal amount
Difference, as the even cunning of single residence time treated calculate residual error E1' (x, y):
E′1(x, y)=M (x, y)-T '1(x, y) * * I (x, y) (9)
Step 6: residual error E will be calculated1' it is used as shape M in face to be processed, it repeats step 2 and arrives step 5, be iterated calculating, until
After the completion of nth iteration calculates, corresponding calculating residual error En' meet the requirements, to obtain even cunning treated total residence time
It is distributed T ' (x, y):
In formula, n represents the total degree of loop iteration；It is achieved in the even sliding processing of optical element processing residence time.
Possessed advantage and beneficial technical effect are as follows compared with prior art by the present invention:
(1), in a kind of optical element process of the present invention residence time even sliding method, can be to polishing tool
It is that non-circular symmetrical situation plays compensation effect in the removal function of element surface, improves the convergence effect of iterative calculation.
(2), in a kind of optical element process of the present invention residence time even sliding method, can iterate to calculate
In the process by the even sliding processing to residence time, residence time jumps degree between reducing adjacent discrete point, to reduce processing
Polishing tool frequently accelerates in the process, slowing down influences caused by machine stability, so reduce process in equipment to quilt
The medium-high frequency face shape error that machine component introduces.
Detailed description of the invention
Fig. 1 is the flow chart for realizing the even sliding method of residence time in a kind of optical element process of the present invention；
Fig. 2 is the distribution of removal function and time diffusion model used in embodiment, and Fig. 2 (a) is used in embodiment
Function distribution is removed, Fig. 2 (b) is time diffusion model used in embodiment；
Fig. 3 is face shape error to be processed initial in embodiment；
Fig. 4 is to calculate the root-mean-square value (RMS) of residual error in embodiment (wherein solid line is with the trend chart of the number of iterations
The root-mean-square value of residual error is calculated when the even sliding method of residence time in a kind of optical element process of the present invention is not used
(RMS) with the changing rule of the number of iterations, dotted line is using residence time in a kind of optical element process of the present invention
Even sliding method when calculate residual error root-mean-square value (RMS) with the number of iterations changing rule)；
Fig. 5 is the comparison diagram that residual error is calculated in embodiment, and wherein Fig. 5 (a) is that a kind of optics member of the present invention is not used
Calculating residual error in part process when the even sliding method of residence time, Fig. 5 (b) are using a kind of optical element of the present invention
Calculating residual error in process when the even sliding method of residence time；
Fig. 6 be in embodiment calculate residual error power spectral density (PSD) distribution (wherein solid line be not used it is of the present invention
Power spectral density (PSD) distribution of residual error, dotted line are calculated in a kind of optical element process when the even sliding method of residence time
It is using the power spectrum for calculating residual error in a kind of optical element process of the present invention when the even sliding method of residence time
Spend (PSD) distribution)；
Fig. 7 is the residence time comparison diagram obtained in embodiment by iterative calculation, and wherein Fig. 7 (a) is that this hair is not used
Residence time distribution in a kind of bright optical element process when the even sliding method of residence time, Fig. 7 (b) are to use this
Invent residence time distribution when the even sliding method of residence time in a kind of optical element process；
Fig. 8 be residence time in embodiment power spectral density (PSD) distribution (wherein solid line be not used it is of the present invention
In a kind of optical element process when the even sliding method of residence time residence time power spectral density (PSD) distribution, dotted line
Be using in a kind of optical element process of the present invention when the even sliding method of residence time residence time power spectrum
Spend (PSD) distribution).
Specific embodiment
Invention is further described in detail with reference to the accompanying drawing and with specific embodiment, it is necessary to be pointed out that described
Embodiment is only intended to further describe of the invention, and is not meant to be any restriction to the scope of the present invention.
The even sliding method of residence time, implementation process such as Fig. 1 in a kind of optical element process proposed by the present invention
It is shown.
The first step is established real according to the corresponding removal function model I (x, y) of used machining tool and process equipment
Time diffusion model D (x, y) used in the even sliding method of residence time in a kind of existing optical element process of the present invention；
Second step is solved by single iteration and is resident according to face shape M (x, y) to be processed and removal function I (x, y)
Time Tn(x,y)；
Third step, using time diffusion model D (x, y) to residence time Tn(x, y) carries out even sliding processing, after obtaining even cunning
Residence time Tn'(x,y)；
4th step, by even cunning treated residence time Tn' (x, y) and face shape M (x, y) to be processed, it solves and is calculated
Residual error En'(x,y)；
5th step, calculating residual error En' (x, y) as face shape M (x, y) to be processed, repetition second step to the 4th step is carried out
Iterative calculation calculates residual error E after the completion of nth iteration calculatingn' (x, y) meet the requirements；
6th step, the residence time T that will be calculated every timen' (x, y) is cumulative obtains total residence time T ' after even cunning
(x, y), and enter following process link.
Embodiment
The present embodiment for the circular flat mirror of 100mm is to be added with diameter using magnetorheological numerical control polishing as process equipment
Work element, and Fig. 2 to Fig. 7 is combined, a specific embodiment of the invention is illustrated.It, will during subsequent descriptions
The even sliding method of residence time is referred to as even sliding method in a kind of optical element process of the present invention.In regular situation
Under, in non-circular symmetrical, Fig. 2 (a) is Magnetorheological Polishing head in x=0, the coordinate of y=0 for the removal function of magnetorheological polishing machine
Removal function when being resident 3 seconds on point is distributed I (x, y).The present embodiment is with the distribution of removal function shown in Fig. 2 (a) about x=0, y
Distribution of shapes after=0 coordinate points rotation 180 degree is as time diffusion model D (x, y), shown in distributional pattern such as Fig. 2 (b)；
And total amount normalized is carried out to the time diffusion model, so that it is met formula (1).
Fig. 3 is the initial face shape error M (x, y) to be processed of element to be processed, and face shape peak-to-valley value (PV) is
200.076nm, root-mean-square value (RMS) are 36.115nm.Face shape error M (x, y) to be processed and removal function I (x, y) are substituted into
Formula (2) can solve to obtain residence time distribution T when the even sliding method of unused time1(x, y) and corresponding calculating residual error
E1(x,y).For above-mentioned residence time T1(x, y), using time diffusion model D (x, y) shown in Fig. 2 (b) according to formula (3)
~(8) carry out even sliding processing to it, can be obtained using the residence time distribution T after even sliding method1' (x, y), and can be by formula
(9) it is calculated using the calculating residual error E after even sliding method1’(x,y)。
When not using even sliding method, by above-mentioned calculating residual error E1(x, y) is used as face shape error M (x, y) to be processed, and generation
Enter circulation and is iterated calculating；When using even sliding method, by above-mentioned calculating residual error E1' (x, y) conduct face shape error M to be processed
(x, y), and substitute into circulation and be iterated calculating.
Fig. 4 gives in 20 iterative calculation, and the root-mean-square value (RMS) for calculating residual error is advised with the variation of the number of iterations
Rule；Wherein, solid line is that the root-mean-square value (RMS) of residual error is calculated when even sliding method is not used with the changing rule of the number of iterations, empty
Line be using after even sliding method calculate residual error root-mean-square value (RMS) with the number of iterations changing rule.From fig. 4, it can be seen that
The root-mean-square value (RMS) for calculating residual error shows the trend being gradually reduced with the increase of the number of iterations, and is using even cunning side
After method, the convergence rate and convergence effect for calculating the root-mean-square value (RMS) of residual error are superior to the case where not using even sliding method.When
Calculating residual error E when without using even sliding method, after the completion of the 20th iterative calculation20(x, y) such as Fig. 5 (a) is shown, corresponding peak valley
Being worth (PV) is 96.258nm, and root-mean-square value (RMS) is 12.263nm；And after using even sliding method, the 20th iterative calculation is completed
Calculating residual error E afterwards20' (x, y) such as shown in Fig. 5 (b), corresponding peak-to-valley value (PV) is 86.432nm, root-mean-square value (RMS) is
7.835nm.Compared with Fig. 5 (a), the corresponding face shape of Fig. 5 (b) is distributed more uniform, gentle, peak-to-valley value (PV) and root-mean-square value
(RMS) also smaller, show that the even sliding method can improve the convergence effect of iterative calculation, even polishing tool is in element surface
Removal function is non-circular symmetrical situation, and preferable convergence effect can be also reached after sliding method even using this.Shown in Fig. 6,
Calculating residual error E when compared without using even sliding method20(x, y) and use the calculating residual error E after even sliding method20' (x, y)
Power spectral density (Power Spectral density, PSD) distribution.Power spectral density (PSD) is the known content of this field,
It does not do and further tells about herein, numerical computational formulas are as follows:
In formula, △ x=L/N is the sampling interval, and L is sampling length, and N is efficiently sampling points, and M (n) is error function.From
Fig. 6 can be seen that compared with when even sliding method is not used, and after using even sliding method, calculate in the shape of residual error face, spatial frequency is low
In 0.2mm-1Part (in generally corresponding to, low frequency aberration) reduced, and then show that the even sliding method can improve processing
Equipment is in, the processing effect of low frequency part.
Shown in Fig. 7, the residence time that compared without using even sliding method and solve when having used even sliding method is distributed.Its
In, bulk corresponding to each discrete point is 0.0383mm2, that is, used 512 × 512 a length of 100mm of discrete point opposite side
Square region carry out discrete processes；When Fig. 7 (a) is without using even sliding method, obtained after the completion of the 20th iterative calculation total
Residence time T (x, y) distribution, T (x, y) meetIts corresponding peak-to-valley value (PV) is 0.107
Second, root-mean-square value (RMS) is 0.013 second；7 (b) are after having used time even sliding method, total after the completion of the 20th iterative calculation
Residence time T ' (x, y) distribution, T ' (x, y) meetIts corresponding peak-to-valley value (PV) is 0.038
Second, root-mean-square value (RMS) is 0.006 second.It is therefore seen that compared with the residence time being calculated when not using even sliding method,
Reduced for the use of peak-to-valley value (PV) and root-mean-square value (RMS) using the residence time that even sliding method is calculated, at that time
Between be distributed it is more uniform, gentle.Fig. 8 compared residence time T (x, y) and T ' (x, y) in space from the angle of power spectral density
Distribution character in frequency.From figure 8, it is seen that compared with when not using even sliding method, it is resident after using even sliding method
In Annual distribution, spatial frequency is higher than 0.05mm-1Part (generally corresponding to medium, high frequency error) reduced；Show this
Even sliding method can reduce frequent movement degree of the polishing tool in small size space, in process, reduce because throwing
Optical tool frequently shakes the medium, high frequency error introduced to element.
Through the foregoing embodiment, the even cunning of residence time in a kind of optical element process of the present invention is shown
Method can improve the convergence effect iterated to calculate in residence time solution procedure, improve process equipment to processed element surface
In, the working ability of low frequency aberration；In addition, in a kind of optical element process of the present invention residence time even cunning side
Method reduces the jump degree of residence time between adjacent discrete point, to reduce processing by the even sliding processing to residence time
Polishing tool frequently accelerates in the process, slowing down influences caused by machine stability, and then reduces because polishing tool is frequently shaken
The medium, high frequency error that processed element is introduced.
Claims (2)
1. a kind of even sliding method of residence time in optical element process, it is characterised in that: expanded by introducing a time
Model is dissipated to be diffused the residence time distribution that conventionally calculation obtains, thus realize the even sliding processing of residence time, it is specific
Step is:
Step 1: settling time diffusion model D (x, y), center are D (x0,y0), and D (x, y) meets total amount normalization and wants
It asks:
∑I, jD(xi, yj)=1 (1)
Wherein D (xi,yj) indicate (x after time diffusioni,yj) position relative time change rate；For any time amount t, with it
Position is as central point (x0,y0), time quantum t is diffused using diffusion model D (x, y), then tD (xi,yj) table
Show the time diffusion after (xi,yj) position time quantum；
Step 2: the face shape error of element to be processed be M (x, y), removal function of the polishing tool within the unit time be I (x,
It y), is T by the residence time that single iteration solves in iterative process1(x,y)；In residence time T1(x,y)
Interior, the difference of the face shape error M (x, y) of theoretical removal amount and element to be processed is to calculate residual error E1(x, y) may be expressed as:
E1(x, y)=M (x, y)-T1(x, y) * * I (x, y) (2)
In formula, * * indicates convolution, T1(x, y) * * I (x, y) is indicated in residence time T1In (x, y), polishing tool is to member to be processed
The removal amount of part；
Step 3: being directed to T1Each of (x, y) discrete coordinate (xi,yj), by time diffusion model D (x, y) in X, Y-direction
On translated, make its center (x0,y0) it is moved to (xi,yj), it is denoted as Dij(x, y):
Dij(x, y)=D (x-xi, y-yj) (3)
Then, using spread function Dij(x, y) is to point T1(xi,yj) DIFFUSION TREATMENT of progress from point to surface, thus after obtaining diffusion
Annual distribution Kij(x, y):
Kij(x, y)=Dij(x, y) T1(xi, yj) (4)
Dij(x, y) equally meets the normalization of total amount shown in formula (1) and requires, so that
∑I, jKij(x, y)=T1(xi, yj) (5)
kij(x, y) * * I (x, y) ≈ T1(xi, yj)-I (x, y) (6)
Step 4: can obtain being directed to various discrete point (x according to step 3i,yj) the Annual distribution K that is diffused that treatedij(x, y),
Then the residence time after even cunning is distributed T1' (x, y) may be expressed as:
T′1(x, y)=∑I, jKij(x, y) (7)
And the residence time after even cunning is distributed T1' (x, y) corresponding removal amount, T should be distributed with the residence time before even cunning1(x,y)
Corresponding removal amount is approximately equal:
T′1(x, y) * * I (x, y) ≈ T1(x, y) * * I (x, y) (8)
Step 5: the residence time after face shape error M (x, y) to be processed and even cunning is distributed T1' (x, y) corresponding removal amount difference,
As the even cunning of single residence time treated calculate residual error E1' (x, y):
E′1(x, y)=M (x, y)-T '1(x, y) * * I (x, y) (9)
Step 6: residual error E will be calculated1' it is used as shape M in face to be processed, it repeats step 2 and arrives step 5, calculating is iterated, until n-th
After the completion of iterative calculation, corresponding calculating residual error En' meet the requirements, to obtain even cunning treated total residence time distribution T '
(x, y):
In formula, n represents the total degree of loop iteration；It is achieved in the even sliding processing of optical element processing residence time.
2. the even sliding method of residence time in a kind of optical element process according to claim 1, it is characterised in that:
Even sliding processing is carried out to residence time using time diffusion model, and can be by adjusting time diffusion model come when improving resident
Between even sliding effect.
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| CN201811336114.8A CN109227226B (en) | 2018-11-12 | 2018-11-12 | Uniform-sliding method for residence time in optical element processing process |
| US16/681,209 US20200147753A1 (en) | 2018-11-12 | 2019-11-12 | Method for controlling dwell time during processing to optical component |
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| CN201811336114.8A CN109227226B (en) | 2018-11-12 | 2018-11-12 | Uniform-sliding method for residence time in optical element processing process |
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| CN117473802A (en) * | 2023-12-28 | 2024-01-30 | 中国科学院长春光学精密机械与物理研究所 | Method for rapidly solving polishing residence time of large-caliber optical element |
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| CN117473802A (en) * | 2023-12-28 | 2024-01-30 | 中国科学院长春光学精密机械与物理研究所 | Method for rapidly solving polishing residence time of large-caliber optical element |
| CN117473802B (en) * | 2023-12-28 | 2024-03-19 | 中国科学院长春光学精密机械与物理研究所 | Method for rapidly solving polishing residence time of large-caliber optical element |
| CN118081494A (en) * | 2024-04-28 | 2024-05-28 | 中国科学院长春光学精密机械与物理研究所 | Magnetorheological polishing processing method based on optimal removal function selection |
| CN118123694A (en) * | 2024-05-06 | 2024-06-04 | 中国科学院长春光学精密机械与物理研究所 | Processing capability evaluation method based on hybrid robot magneto-rheological optical processing equipment |
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