RU2810680C1 - Method of forming astigmatism and higher orders of zernike polynomials with coefficients n=m (n≥2) on surface of optical elements - Google Patents

Abstract

FIELD: optical instrument making.

SUBSTANCE: invention concerns a method of forming astigmatism and higher orders of Zernike polynomials on the surface of optical elements. The method includes calculating the cross sections that form the ion beam of the diaphragms, calculating the dependence of the rotation speed on the angular position of the part, and rotating the optical part in accordance with the calculated speed behind the calculated diaphragm forming the profile of the ion beam. Processing is performed in two stages. At the first stage, non-axisymmetric processing is performed first calculating the diaphragm corresponding to the non-axisymmetric component of the aspherization profile and the dependence of the rotation speed of the part on its angular position relative to the diaphragm forming the ion beam. At the second stage, axisymmetric processing is performed first calculating the forming diaphragm corresponding to the axisymmetric component of the aspherization profile.

EFFECT: possibility of manufacturing aspherical optical elements with a non-axisymmetric surface profile.

1 cl, 4 dwg

Description

The invention relates to a technological process for forming optical elements from optical materials, in particular fused quartz, that compensate for astigmatism or other wavefront aberrations described by Zernike polynomials with m=n, where m and n are positive integers and greater than or equal to 2.

A well-known method for manufacturing aspherical optical elements with a non-axisymmetric surface profile is turning with a small-sized polishing pad on a CNC machine. This method makes it possible to obtain high-quality optical surfaces for the visible and IR wavelength ranges (the error in the shape of the resulting surface in terms of standard deviation (RMS) from the calculated one is 100 nm). However, such parameters do not satisfy the requirements of the soft X-ray (MP) and extreme ultraviolet (EUV) wavelength ranges, for which, due to the short wavelength (λ = 1-30 nm), the required shape accuracy is at the level of ~ 1-5 nm according to the standard deviation parameter. The specificity of this wavelength range is the absence of refractive optics, and mirror optics is based on multilayer interference structures - X-ray mirrors, which are highly sensitive to surface roughness. Thus, in addition to the precise shape, the surface of the optical elements must have low roughness. While when processing the surface of optical elements with a small-sized cutting tool, roughness develops on the surface (during turning, the near-surface layer of the workpiece is destroyed), and a relief with lateral dimensions corresponding to the cutter pitch is formed, which leads to a significant decrease in the reflectance of multilayer X-ray mirrors and deterioration of the resolution of the X-ray optical system.

For example, in documents (patent RU 2609610 “Method for shaping aspherical surfaces of large-sized optical parts and a device for its implementation” (published 02.02.2017, IPC V24V 13/06); patent US 7164964 “Method for producing an aspherical optical element) ) (published 01/16/2007, IPC G06F 19/00), copyright certificate SU 947113 “Method of shaping the surfaces of optical parts)) (published 07/30/1982, IPC S03C 23/00) and CN 101376229 A (( Processing method and device for forming aspheric surface part by numerical control tangent line turning method)) (published 03/04/2009, IPC B24B 13/04)) describes various types of cutting or polishing tools and control methods that allow the creation of aspheric optical elements both axisymmetric and off-axis. However, this approach leads to surface shape errors; due to tool and/or part runout, high-frequency surface shape errors are formed, which have periodicity in radius and angle (M.N. Toropov, A.A. Akhsakhalyan, I.V. Malyshev , M. S. Mikhailenko, A. E. Pestov, N. N. Salashchenko, A. K. Chernyshev, N. I. Chkhalo, “Lens wave front corrector for studying flat surfaces)”, Journal of Technical Physics, 2021, t 91, issue 10, p. 1583-1587), which also does not allow the use of optical elements obtained using this technique in imaging systems of the MP and EUV wavelength ranges. However, it is worth noting that the profile of such errors in the case of axisymmetric aspherization often has a significant contribution of errors described by Zernike polynomials with coefficients n=m.

Thus, in order to bring the surface to the requirements of the MP and EUV wavelength ranges, it is necessary to carry out finishing correction, which is carried out by the ion beam etching method (IBF). Correction is carried out by scanning a small-sized ion beam over the surface of the part. Using this approach, it is possible to obtain surfaces with shape accuracy in terms of the standard deviation parameter at a level 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 computing 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 from several centimeters to submillimeter and an ion current in the beam of up to several mA are used. For example, in the CN patent 105328535 “Nanometer-precision optical curved-face ion beam processing method based on non-linear modeling)) (published 11/07/2017, 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 March 30, 2016, IPC B24B 1/00) algorithms for calculating the correction process are proposed and sources of accelerated ions that form a small-sized ion beam are proposed. Moreover, CN 105328535 proposes to set the beam diameter through the use of cutting diaphragms, which is not advisable, since as the hole diameter decreases, the ion current and, accordingly, the processing speed decrease quadratically. The CN 103831675 patent suggests using a focused ion beam source, which is more efficient, but even then the surface processing speed will be very low due to the small size of the ion beam and the low ion current. Therefore, such a two-stage process (mechanical aspherization followed by correction) is extremely complex and time-consuming.

Therefore, recently it has increasingly been proposed to carry out aspherization for optical systems in the short-wave range according to the technique 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 shaped diaphragm that limits the wide ion beam. There are sources with very large (several hundred mA) ion currents and high parallelism of the ion beam (N.I. Chkhalo, I.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, 48, 338-346), which allows for significant material removal at a rate of several microns per hour and the formation of an almost arbitrarily large gradient of etching depth along the radius .

The invention that is closest in technical essence is presented in patent RU 2793080 C1 “Method for axisymmetric correction of optical parts of arbitrary shape” (published on March 28, 2023, IPC V24V 13/06), which describes a method for forming aspherical axisymmetric surfaces with an ion beam. The prototype method involves searching for the aspheric profile, the cross-section of the diaphragm that forms the ion beam profile, and rotating the part behind this diaphragm around an axis passing either through the center of the part or through a certain point in space, which is the axis of the aspheric profile (for off-axis aspherics). 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 deposition is performed on the surface of the workpiece. The disadvantage of the described method is the inability to form optical parts with a profile that does not have axial symmetry.

One of the simplest cases of asphericity without axial symmetry is astigmatism, which is a common error in the manufacture of spherical parts. Astigmatism occurs in the case of elastic deformation of a part in the frame during its manufacture using the lapping method, when the part is removed from the frame and the deformation is straightened out. In this case, as a rule, a shape error occurs - astigmatism. In addition, it is often necessary to compensate for wave aberrations such as astigmatism and higher order aberrations similar in nature, which arise when using optical elements in circuits with off-axis radiation incidence, or such errors are already present on the surface of the part (appear during manufacturing due to tool runout and/ or parts when making a part on a cutting machine) and must be eliminated. Such wavefront deformations are described by Zernike polynomials (see formulas 1 and 2) with expansion coefficients m=n (m and n are integers, positive).

Even Zernike polynomials are defined as follows:

Odd polynomials are defined as:

where m and n are non-negative integers, n≥m≥0,

ρ - radius,

ϕ - azimuthal angle.

The radial part of the polynomials is defined as follows:

Astigmatism corresponds to a polynomial with m=n=2.

The problem to be solved by this invention is the development of a method for forming optical elements with an aspherical surface shape such as astigmatism and higher orders of Zernike polynomials with expansion coefficients n=m. Those. expressions 1-3 are reduced to the form:

Even polynomials:

Odd:

The surface profile described by these expressions can be decomposed into two components, axisymmetric and non-axisymmetric.

The axisymmetric component is described by the expression:

The non-axisymmetric component is described by the expression:

where C is a constant, C>1. Selected from the conditions available for the real process (determined by the maximum possible rotation speed of the part). Thus, the technical result is achieved in two stages. At the first stage, it is necessary to form an axisymmetric component of the surface shape profile, and at the second, a non-axisymmetric component. It turned out that to implement a non-axisymmetric profile, described by expression (8), it is possible to use the same geometry of the technological process as for the axisymmetric one, described by expression (7), but with a changing angular velocity of rotation of the part behind the diaphragm forming the beam. The technical implementation of the method consists in controlling the rotation speed of the stepper motor shaft by increasing or decreasing the frequency of control pulses supplied to its windings.

To form the required distribution, the angular velocity of rotation must change according to expression 9:

The cross section of the ion beam-forming diaphragm to create a given non-axisymmetric profile, described by expression (8), in this case is determined by the expression:

At the second stage, it is necessary to create an axisymmetric component. To do this, a diaphragm is cut out with a cross section described by the following expression:

The rotation of the part behind the diaphragm with such a cross-section is already carried out at a uniform angular velocity.

To illustrate the presented method, let us consider the simplest case - astigmatism (m=n=2), provided that the ion beam has a uniform current density throughout the entire aperture. In this case, the diaphragms forming the profile of the ion beam are given by the equations

The coefficients in these formulas are introduced so that the largest aperture opening is ±45° (see Fig. 2) The rotation speed law is expressed as

The method is illustrated by the following figures.

In fig. 1. shows a schematic representation of the process of processing an optical part according to the claimed method.

According to the proposed method, processing occurs in two stages. During one of the stages, the workpiece being processed rotates behind the ion beam-forming diaphragm in FIG. 2a with variable angular velocity, the law of change of which corresponds to formula (14) and is illustrated in figure 3. As a result of such processing, a non-axisymmetric relief is formed on the surface of the part, shown in figure 4b.

At the next stage, the workpiece rotates at a constant angular velocity, while the diaphragm that forms the ion beam is shown in figure 2b. As a result of processing the part, an aspherical profile is formed on its surface, shown in figure 4c.

The result of two-stage processing is an aspherical surface described by the Zernike polynomial (5) with n=2. The map of the resulting surface is the sum of the surface maps (Fig. 4d) obtained at each of the processing stages, and itself has the shape shown in Figure 4a.

In fig. Figure 2 shows a cross-section of the ion beam-forming diaphragms for the formation of a) the non-axisymmetric component and b) the axisymmetric component of the aspherization profile.

In fig. Figure 3 shows the dependence of the rotation speed of the part on the angle W(ph) for the case of the formation of a non-axisymmetric component.

In fig. 4 Aspheric map formed according to the specified method (a), non-axisymmetric map describing material removal at the processing stage with variable rotation speed (b); axisymmetric map describing material removal at the processing stage with a constant rotation speed (c); scheme for forming the required aspherics in two stages (d).

Thus, the authors have proposed a method for manufacturing aspherical optical elements with a non-axisymmetric surface profile described by Zernike polynomials with coefficients n-m≥2. The method offers a two-stage surface treatment with a wide parallel ion beam through diaphragms that form the ion beam profile, the cross section of which is determined by the degree of the Zernike polynomial, the shape of which must be formed on the surface of the workpiece

At the first stage, rotation is carried out behind the diaphragm, the opening angle of which, depending on the radius, is described by the expression:

ϕ(ρ)~ρ ⁿ

In this case, the part rotates around an axis coinciding with the center of the diaphragm (point R=0), with an angular velocity also determined by the degree of the Zernike polynomial, the shape of which must be formed on the surface of the workpiece.

At the second stage, processing is carried out with uniform rotation through a diaphragm, the cross section of which is also determined by the degree of the Zernike polynomial and is described by the expression:

The axis of rotation of the part also coincides with the center of the diaphragm (point R=0).

The proposed method makes it possible to form an aspherical profile on the surface of an optical part, compensating for aberrations such as astigmatism or a higher order with n=m.

Claims (1)

A method for forming astigmatism and higher orders of Zernike polynomials with coefficients n=m (n≥2) on the surface of optical elements, including calculation of cross sections of diaphragms forming the ion beam, calculation of the dependence of the rotation speed on the angular position of the part, rotation of the optical part in accordance with the calculated speed behind a calculated diaphragm that forms the ion beam profile, characterized in that the processing occurs in two stages, in the first of which non-axisymmetric processing is performed, for which the diaphragm corresponding to the non-axisymmetric component of the aspherization profile is calculated and the dependence of the rotation speed of the part on its angular position relative to the diaphragm forming the ion beam is calculated , and at the second stage, axisymmetric processing is performed, for which the forming diaphragm corresponding to the axisymmetric component of the aspherization profile is calculated.