RU2793080C1 - Method for axisymmetric correction of optical parts of arbitrary shape - Google Patents

Abstract

FIELD: optical technology.

SUBSTANCE: technological process for formation of optical elements from optical materials of a given surface shape. According to the invention, the rotation axis of the optical part is searched both inside the aperture of the part and outside, the global minimum of the surface is found by sorting through positions of the rotation axis available in the setup geometry. An etch profile is calculated for each axis, and then a rotation axis is selected that provides the minimum amount of surface shape error after etching.

EFFECT: invention provides the maximum reduction of the shape error of the surface of the optical part, thereby reducing the processing time of the optical part.

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Description

The invention relates to a technological process for the formation of optical elements from optical materials, in particular, fused quartz, a given surface shape with a surface generatrix having an axis of symmetry passing through an arbitrary point in space.

A well-known method that provides a minimum error in the shape of the surface of optical elements during their production is lapping. Lapping is carried out when the workpiece is in contact with the polishing pad over its entire surface, which ensures the best processing results. This method produces flat and spherical optical elements of sufficiently high quality - the resulting standard deviation of the surface shape from the calculated one is at the level of 10 nm. But this does not satisfy the requirements of the soft x-ray (MP) and extreme ultraviolet (EUV) wavelength ranges, for which the required shape accuracy is RMS (root-mean square - standard deviation) ~ 0.5-5 nm. The specificity of the method (lapping is carried out during the rotation of the polishing pad) leads to the fact that a significant proportion of the deviation of the surface shape from the calculated one is axisymmetric errors that require subsequent correction. Moreover, to solve a wide range of problems, such as expanding the field of view of an optical system, surfaces with a significant profile deviation from a sphere (aspherical surfaces) are required. The manufacture of such surfaces by the lapping method is not possible. Aspherical surfaces are formed mainly by surface treatment with a small cutting tool.

For example, in documents (patent RU 2609610 "Method for shaping aspherical surfaces of large-sized optical parts and a device for its implementation" (published on February 2, 2017, IPC B24B 13/06); US patent 7164964 "Method for producing an aspherical optical element" (publ. 16.01.2007, IPC G06F 19/00), copyright certificate SU 947113 "Method of shaping the surfaces of optical parts" (publ. 30.07.1982, IPC С03С 23/00) and CN 101376229 A "Processing method and device for forming aspheric surface part by numerical control tangent line turning method” (published on March 4, 2009, IPC B24B 13/04)) describes various types of cutting or polishing tools and control methods that make it possible to create aspherical optical elements, both axisymmetric and and off-axis. However, this approach leads to a significant deterioration in the quality of the surface, due to the beating of the tool and / or workpiece, high-frequency errors in the surface shape are formed (M.N. Toropov, A.A. Akhsakhalyan, I.V. Malyshev, M.S. Mikhailenko, A. E. Pestov, N. N. Salashchenko, A. K. Chernyshov, N. I. Chkhalo, “Lens wavefront corrector for studying flat surfaces”, Journal of Technical Physics, 2021, v. 91, issue 10, p. 1583-1587), which also does not allow the use of optical elements obtained by this technique in imaging systems of the MP and EUV wavelength ranges.

Thus, in order to bring the surface to the requirements of the MP and EUV wavelength ranges, it is necessary to carry out a finishing correction, which is carried out by the method of ion beam etching (IBF - ion beam figuring). Correction is carried out by scanning with a small-sized ion beam over the surface of the part. Using this approach, it is possible to obtain surfaces with a shape accuracy in the RJV1S parameter of 1 nm or less (Y. Lu, X. Xie, L. Zhou, Z. Dai, G. Chen, "Improve optics fabrication efficiency by using a radio frequency ion beam figuring tool", Applied Optics, 2017, 56, 260-266; Zhang Y., Fang F., Huang W., Fan W, "Dwell Time Algorithm Based on Bounded Constrained Least Squares Under Dynamic Performance Constraints of Machine Tool in Deterministic Optical Finishing)), International Journal of Precision Engineering and Manufacturing-Green Technology, 2021, 8, 1415-1427). For these purposes, ion sources with an ion beam size up to several mm in diameter and an ion current in the beam up to several mA are used. For example, in the patent CN 105328535 "Nanometer-precision optical curved-face ion beam processing method based on non-linear modeling)) (published on 07.11.2017, IPC B24B 1/00, B24B 13/00) and in the CN patent 103831675 "Device and method for processing ion beam of large-diameter optical element") (published on March 30, 2016, IPC B24B 1/00), algorithms for calculating the correction process and sources of accelerated ions that form a small-sized ion beam are proposed. Moreover, in CN 105328535 it is proposed to set the beam diameter through the use of cutting diaphragms, which is not advisable, since with a decrease in the hole diameter, the ion current and, accordingly, the processing speed drop quadratically. CN 103831675 proposes to use a focusing ion beam source, which is more efficient, but even then the surface treatment speed will be very slow due to the small size of the ion beam and the ion current. Therefore, such a two-stage process (mechanical aspherization followed by correction) is extremely complex and time-consuming.

As an alternative method, the surface shape aspherization method can be considered by applying thin-film coatings on an initially spherical substrate made using the lapping technology. For example, in the patent US 5745286 "Forming aspheric optics by controlled deposition)) (published on April 28, 1998, IPC G02B 3/02, G02B 5/10, G02B 005/08, G02B 001/10) it is proposed to apply such a coating by the method magnetron sputtering through a figured diaphragm rotating in front of the part, coaxial with it. This is a well-controlled process that produces an accurate distribution of film thickness over the surface, however, this method has a number of disadvantages. Firstly, this approach is applicable only in the manufacture of substrates for mirrors; it will not be possible to form refracting optical elements with its help. Secondly, due to the low rate of magnetron sputtering, it is possible to form aspherics with a height difference of no more than a few microns. Thirdly, due to the strong expansion of the particle flow, it is also very difficult to create a large thickness gradient along the radius.

Therefore, recently it has been increasingly proposed to carry out aspherization for optical systems in the short-wavelength range of wavelengths according to the method proposed at the end of the 20th century (Eisenberg N.P., Carouby R., Broder J, "Aspheric generation on glass by ion beammilling", Proceedings of SPIE, 1988 , 1038, 279-287), namely, by rotating the part behind the figured diaphragm that limits the wide ion beam. There are sources with very high (several hundred mA) ion currents and high parallelism of the ion beam (N.I. Chkhalo, LA. Kaskov, I.V. Malyshev, M.S. Mikhaylenko, A.E. Pestov, V.N. Polkovnikov, N.N. Salashchenko, M.N. Toropov, I.G. Zabrodin, “High-performance facility and techniques for high-precision machining of optical components by ion beams”, Precision Engineering, 2017, 48, 338-346), which allows significant material removal at a rate of several microns per hour and the formation of an almost arbitrarily large etch depth gradient along radius. The errors arising from this method of formation (rotation around the axis of symmetry) of aspherical surfaces (errors in the processing time, in the shape and position of the diaphragm) will have a significant axisymmetric component. Such errors can be effectively removed by the same technique if the axisymmetric component is separated from the total shape error.

The invention closest in technical essence is presented in patent CN 106736990 “Aspherical ion beam forming device and aspherical ion beam forming method” (published on 03/05/2019, IPC B24B 13/00), which describes a device and a method for forming aspherical surfaces by ionic beam. The prototype method includes searching for a section of the diaphragm that forms the profile of the ion beam, and rotating the part behind this diaphragm around the axis, which is the axis of symmetry of the optical part. This approach is very promising and makes it possible to obtain high-quality aspherical surfaces without the formation of high-frequency shape errors. The method makes it possible to produce both reflective and refractive optical elements, since no sputtering is performed on the workpiece surface. The disadvantage of the described method is the inability to form optical parts of arbitrary shape, including off-axis aspherical parts.

The problem to be solved by this invention is the development of a method for forming optical elements of various shapes by axisymmetric removal of material from the surface of optical elements by a wide quasi-parallel ion beam through a figured diaphragm, providing a minimum amount of error in the surface shape, thereby reducing the processing time of the optical part.

The technical result is achieved due to the fact that the developed method for axisymmetric removal of material from the surface of optical parts by a wide quasi-parallel ion beam, like the prototype method, includes searching for the axis of rotation of the optical part, calculating the section of the forming diaphragm, rotating the optical part behind this diaphragm, which forms the profile of the ion beam. What is new is that the axis of rotation of the optical part is searched both inside the aperture of this part and outside it, and the etching profile is calculated in such a way that the error in the shape of the surface of the optical part is minimized. To do this, the global minimum of the surface is found, the positions of the rotation axis available in the geometry of the rotation axis are sorted, the surface is divided into concentric rings relative to each axis of rotation, the etching depth is calculated on each ring to achieve the global minimum of the surface, the etching profile is calculated for each axis of rotation, and the volume of the shape error is calculated surface after etching, then choose the axis of rotation, providing a minimum amount of error in the shape of the surface after etching.

In a particular case of implementing the method for a part of arbitrary shape, an axis of rotation is found that does not pass through the geometric center of the part.

In another particular case, for a round symmetrical part, an axis of rotation is found that passes through the geometric center of the part, and the axisymmetric components of the surface shape error are isolated using Zernike polynomials.

The developed method is illustrated by the following figures.

In FIG. 1 schematically shows an installation for processing an optical part according to the claimed method.

In FIG. 2 is presented for a round part: a) map of surface shape errors (RMS=38.4 nm), b) axisymmetric part of shape errors (RMS=36.0 nm), c) profile of axisymmetric part of surface shape errors, d) figured diaphragm for removal of material from the surface of the part, e) map of surface shape errors after ion correction (RMS=3.5 nm).

In FIG. 3 is presented for a part of arbitrary shape: a) scheme of the method, b) profile of the axisymmetric part of the shape errors, c) figured diaphragm for removing material from the surface of the part.

In FIG. 4 is presented as an example for a rectangular part: a) map of surface shape errors before ion correction (RMS=102 nm); b) map of surface shape errors after ion correction (RMS=2.7 nm).

The authors proposed a method for correcting the surface shape with a wide-aperture high-current ion beam, which makes it possible to significantly reduce the duration of the most time-consuming and time-consuming procedure - the final correction of local shape errors with a small-sized ion beam (IBF). The method proposes the calculation of a figured diaphragm that limits the beam profile in such a way that when the workpiece rotates behind the diaphragm, material is removed on its surface, specified by the calculated profile.

In the case of round parts, for which the center of axisymmetric errors coincides with the center of the part, rotation is performed around the axis of symmetry of the part. The etch profile is determined from the surface shape error map. The axisymmetric part of the shape error is extracted by zeroing out all nonaxisymmetric Zernike polynomials that describe the deviation of the surface shape from the ideal one.

In the case of parts of arbitrary shape, where it is impossible to unambiguously identify the axisymmetric part of the surface shape error using Zernike polynomials, a search is made for the axis of rotation passing through an arbitrary point in space, which ensures the maximum reduction in the surface shape error. In a particular case, the search is carried out within the limits of possible movements of the motorized table of the used installation. The authors used the setup described in the article (N.I. Chkhalo, L.A. Kaskov, I.V. Malyshev, M.S. Mikhaylenko, A.E. Pestov, V.N. Polkovnikov, N.N. Salashchenko, M.N. Toropov, I.G. Zabrodin “High-performance facility and techniques for high-precision machining of optical components by ion beams", Precision Engineering, 2017, V. 48, p. 338-346). As a criterion for searching for the etching profile, we chose to minimize the residual volume of material that must be removed to bring the surface shape to the required accuracy.

Thus, the developed method allows for aspherization and/or correction of the surface profile of axisymmetric and off-axis parts. The claimed method works as follows.

Wide-aperture ion source 1 with a flat ion-optical system forms a quasi-parallel beam of accelerated ions 2 (Fig. 1). This beam 2, passing through the diaphragm 3 forming the profile of the ion beam, is converted into a beam of the required cross section 4 and falls on the optical part 5 rotating around some axis, fixed on the turntable 6. Thus, when the part 5 rotates, part of the material will be removed from its surface , which is a certain figure of rotation, limited by the generatrix - the etching profile.

The search for the axis of rotation of the optical part 5 is carried out both inside the aperture of this part 5 and outside it. For a part 5 of arbitrary shape, an axis of rotation is found that does not pass through its geometric center. And for a round symmetrical part 5, an axis of rotation is found that passes through its geometric center, which is also the axis of symmetry of such part 5.

Next, the etching profile is calculated in such a way as to ensure the maximum decrease in the error in the shape of the surface of the optical part 5. To do this, the global minimum of the surface is found and the positions of the rotation axis available in the setup geometry are sorted. With respect to each axis of rotation, the surface is divided into concentric rings, and the depth of etching is calculated on each ring to achieve a global minimum of the surface. For each axis of rotation, an etch profile is calculated and the amount of surface shape error after etching is calculated. Then choose the axis of rotation, providing a minimum amount of error in the shape of the surface after etching.

The etching profile can be determined by the task of aspherization or extracted from surface shape errors, and the center of the etching profile can either coincide with the axis of symmetry of part 5 or not, in the general case, the rotation axis can pass through an arbitrary point in space.

The algorithm for calculating aperture 3 is reduced to pointwise convolution of the desired etching profile and the distribution of the ion current in beam 4.

where ϕ(r) is the mask shape function in polar coordinates (column vector of radii and their corresponding opening angles),

ω - angular speed of rotation of the workpiece 5 in revolutions/minute (characteristic of the turntable 6),

F(r) is the required etching profile in the form of a one-dimensional map, that is, the dependence of the etching depth on the radius of part 5,

v(r) is the etching rate distribution obtained by normalizing the distribution of the ion current in beam 4 to the etching rate for a given target gas-material pair.

In the case of a round part 5, the etch profile for correcting the surface shape can be extracted directly from the shape error map obtained on the interferometer, which can be represented as a series expansion in Zernike polynomials. There are even and odd Zernike polynomials. Even polynomials are defined as follows:

Odd polynomials are defined as:

where m and n are non-negative integers, n>=m,

ρ - radius,

ϕ - azimuth angle.

The radial part of polynomials is defined as follows:

By extracting even polynomials with m=0, one can describe the axisymmetric part of the aberration.

In the case of elements with an arbitrary shape of the boundary, the Zernike polynomial expansion is ambiguous; to the best result. To assess the quality of the processing, it is necessary to introduce a metric in the solution space that would show how good the constructed solution is. There are many options for describing the quality of the surface, for example, by the RMS parameter, by building the power spectral density function PSD (power spectral density), etc. For each of them, it is possible to evaluate the ongoing processing and control the change in the surface. In this case, the criterion for minimizing the volume of surface shape errors is used.

Minimizing the volume of shape errors remaining after processing by beam 4 from a wide-aperture source 1 leads to a decrease in the time for finishing processing with a small-sized ion beam (IBF method). This is reasonable, since local shape correction by a small-sized ion beam makes it possible to obtain a surface with a given accuracy, but the processing speed is several times lower than when using a wide-aperture source 1.

The surface shape error map is specified in the format (x, y, z) on a grid with a fixed step. Thus, the volume of the surface shape error map can be considered the sum of the height values on the surface shape error map relative to the level of the lowest point (the global minimum of the surface), multiplied by the area of one grid cell.

where H _i is the value of the surface error at the i-th point,

H _ms - global minimum on the surface map,

S _cells - the area of one cell of the coordinate grid.

In axisymmetric processing, the material removed from the surface during etching is described by a figure of rotation. This means that the depth of etching at a particular point on the surface depends on the radius at which the given point is located relative to the axis of rotation, and does not depend on the angle.

Consider the case when the etch profile H(r) is given as follows:

In this case, etching will occur only within the ring with an inner radius r ₀ and an outer radius r ₀ +δr. During such processing, material will be removed evenly over the entire area of the ring to a depth of X.

Let us write down the change in the surface volume depending on the etching depth X. Two cases can be distinguished: the global minimum of the surface changes or not, formulas (7) and (8), respectively.

If the etch depth X is less than the difference between the minimum value on the ring H _mr and the global minimum of the surface H _ms :

X<(H _mr -H _ms ), that is, the global minimum does not change, then

If X>(H _mr -H _ms ), that is, the global minimum changes, then

where V ₀ is the volume of the surface map before etching,

V is the volume of the surface map after etching,

X - etching depth on the ring,

S _{of the ring} - the area of the ring,

S _{of the surface} - the area of the entire surface,

H _mr - minimum value of the surface shape error on the ring,

H _ms - the minimum value of the shape error of the entire surface.

That is, when etching on the ring to a depth that is below the global minimum of the entire surface, this global minimum is replaced, and the remaining volume on the error map begins to increase.

Let's open the brackets in equation (8) and get equation (9):

It can be seen from this equation that under the condition S _{of the surface} >2 * S _{of the ring,} the volume will increase with increasing X. Due to the fact that δ _r can be taken arbitrarily small, we can satisfy the condition that the area of the ring is small compared to the area of the entire surface for any r ₀ .

стремится к 0 при δr стремящимся к 0.

tends to 0 as δr tends to 0.

Thus, to achieve the best result (minimizing the volume of the surface shape error map), it is necessary that after processing the minimum value on each of the radii is equal to the minimum value on the entire surface (10).

Thus, the algorithm for finding the axis of rotation and the etching profile for parts is as follows:

- find the global minimum of the surface,

- iterate over the possible axes of rotation, in particular, the axes of rotation available in the installation geometry,

- break the surface into concentric rings about each axis of rotation,

- on each ring find the depth of etching to achieve a global minimum surface,

- for each axis of rotation, the etch profile is calculated and the amount of surface shape error after etching is calculated,

- choose the axis of rotation, providing a minimum amount of error in the shape of the surface after etching.

The same approach is valid for the formation of off-axis aspherical elements or circular optical elements, where it is impossible to isolate the axisymmetric component of the surface shape error. In the first case, the axis of rotation and the etching profile will be predetermined (calculated aspherization profile of the optical element from the aspherization problem). In the second case, the search for the axis of rotation is also carried out according to the algorithm described above.

According to the proposed method, the authors made two parts: round, shown in Fig. 2 and a free-form detail (FIG. 3).

In FIG. 2 shows the substrate of the collector mirror. To ensure the calculated size of the focusing spot from a source with a size of 50 μm, the aberrational distortions of the wave front in terms of the RMS parameter should be no more than 5 nm. Initial shape errors were RMS=38.4 nm (FIG. 2a). The processing of such a surface by a small-sized ion beam, according to the calculation, takes about 38 hours. The time of shape correction by wide-aperture beam 4 through diaphragm 3 was 36 min. In FIG. Figure 2d shows a figured diaphragm 3 through which a beam of accelerated ions 2 passed, and a beam of the required cross section 4 fell on part 5. For a round part 5, the axis of rotation (center of rotation 7) passes through the geometric center of part 5. parameters was 3.5 hours. Thus, the total processing time for part 5 was reduced by almost 10 times from 38 hours to 4 hours. After corrections (one axisymmetric by a wide-aperture ion beam and two local small-sized ion beams) of the mirror surface shape, the wavefront errors were reduced to RMS ~ 3.5 nm (Fig. 2e).

In FIG. Figure 3 shows detail 5 of arbitrary shape Si<110> crystal monochromator for the ESRF synchrotron (overall dimensions 80×30×30 mm, working surface area 75×25 mm). The angles of incidence of radiation on the surface of the element lie within 0.5° from the surface (grazing incidence). In this case, the angular RMS _∠ (angle spread from the plane) should be minimized on the surface. Initial parameters: RMS _∠ ~ 15 μrad (corresponding to RMS ~ 100 nm). Requirements: RMS _∠ ~ 0.2 μrad (i.e. RMS ~ 6 nm). Thus, it is necessary to reduce the surface RMS from ~100 nm to ~6 nm. Surface treatment of such a surface with a small-sized ion beam, according to the calculation, takes ~22 hours. The time for correcting the shape through diaphragm 3 with wide-aperture beam 4 was 105 min. In this case, the calculated center of rotation 7 was outside the part 5 (see Fig. 3a). Part 5 during processing rotates around the center of rotation 7 and is inside the ring limited by radii Rmin and Rmax (Rmin is the minimum distance from the center of rotation 7 to the edge of part 5, Rmax is the maximum distance from the center of rotation 7 to the extreme point of part 5). Finishing correction with a small-sized ion beam took 3.5 hours to achieve the required parameters. Thus, the total processing time for part 5 was reduced by almost 4 times from 22 hours to 5 hours and 15 minutes. After corrections (one axisymmetric with a wide-aperture ion beam and three local small-sized ion beams), the surface shape errors were reduced to RMS ~ 2.7 nm (Fig. 4).

Thus, the proposed method makes it possible to process optical parts of arbitrary shape by axisymmetric removal of material from the surface of optical elements with a wide quasi-parallel ion beam through a figured diaphragm. The developed method provides a significant reduction in the processing time of the optical part and minimization of the surface shape error.

Claims (3)

1. A method for axisymmetric removal of material from the surface of optical parts by a wide quasi-parallel ion beam, including searching for the axis of rotation of the optical part, calculating the section of the forming diaphragm, rotating the optical part behind this diaphragm, which forms the profile of the ion beam, characterized in that the axis of rotation of the optical part is searched as inside the aperture of this part, and outside it, and the calculation of the etching profile in such a way that ensures the maximum reduction in the shape error of the surface of the optical part, for this, the global minimum of the surface is found, iterates over the positions of the rotation axis available in the geometry of the settings, relative to each axis of rotation, the surface is divided into concentric rings, on each ring calculate the etch depth to achieve the global surface minimum, calculate the etch profile for each axis of rotation and calculate the amount of surface shape error after etching, then choose the axis of rotation that provides the minimum amount of surface shape error after etching. 2. The method of axisymmetric removal of material from the surface of optical parts by a wide quasi-parallel ion beam according to claim 1, characterized in that for an arbitrary-shaped part, an axis of rotation is found that does not pass through the geometric center of the part. 3. The method of axisymmetric removal of material from the surface of optical parts with a wide quasi-parallel ion beam according to claim 1, characterized in that for a round symmetrical part, an axis of rotation is found passing through the geometric center of the part, and the axisymmetric components of the surface shape error are isolated using Zernike polynomials.

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