RU2545381C1 - Method of profiling aspherical polished surface - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: profile of a polished aspherical surface of a large optical component is measured using a linear three-point spherometer with an additional lateral height-adjustable leg, which is nullified in a reference aspherical mirror; installing the spherometer with outermost legs perpendicular to the diametrical section in the peripheral area of the component; moving the spherometer with the outermost legs into an area in which the central leg with an indicator was previously located; continuing the process of taking readings of the indicator to the centre of the component or to the centre opening of the component and then, based on geometric ratios, constructing the absolute profile of deviations of the surface from a given (theoretical) profile with the required vertex radius and eccentricity and the necessary allowance.

EFFECT: constructing the absolute profile of deviations of the shape of an aspherical surface of an optical component from the required theoretical shape with the necessary accuracy and achieving the required value of the vertex radius during shaping.

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Description

The invention relates to mechanical means for measuring contours and profiles and can be used in the shaping of axial and off-axis high-precision aspherical surfaces of large optical parts, in particular telescope mirrors.

Known methods for measuring the profile of an aspherical surface using a three-point spherometer, for example, according to ed. testimonial. USSR No. 619779, publ. 08/15/1978 Two measuring supports and a meter (sensor) located on the same line and three adjustable stops are fixed in the housing of the spherometer. During the measurement, the spherometer is moved around the controlled surface zone from point to point, the stops are pushed and extended, the meter contacts the controlled surface and the deviation of the arrow of curvature is recorded at each given point. The measurement process is quite cumbersome and time consuming.

There is a mechanized method for measuring the profile of an aspherical mirror of a telescope (Proc. Of SPIE Vol.7018, 701818, p.701818-10 ÷ 701818-12, 2008), according to which the measuring head, mounted on a rotary inclined rod, is sequentially moved mechanically along large arcs along controlled surface and using the recorder take the readings of the indicator of the measuring head. However, for reasons of rod rigidity and the necessary measurement accuracy, the method is applicable for monitoring mirrors of a relatively small diameter (not more than 1.5 m).

Closest to the proposed technical essence can serve as a way to control the processing of the aspherical surface of the optical part according to ed. testimonial. USSR No. 4131117, publ. 01/30/1974, according to which, using a three-point spherometer or a metal ruler with two agate legs at the ends and a spring indicator head with a division price of 0.1 μm, installed in the middle, with a spherometer base equal to "a" (the distance between the two extreme agate legs of the spherometer ), measure the deflection arrows along the diametrical direction or along the chord tangent to the central hole on the part (for parts with a central hole), sequentially shifting the spherometer by a / 2 in such a way that one extreme The spherometer’s throat leg moved to the position of the central leg, central to the position of the second extreme leg, and the second extreme leg to a new position, thus passing the entire diametrical segment or chord with a step of half the base of the spherometer, and the radius of the part (diameter, chord) is divided into Separate gaps “a”, lying on the full radius of the part, compare the results with the calculated values of the deflection arrows for each position of the spherometer and, based on these measurements, construct a relative profile of deviations from the nearest ac of spherical surface for performing the grinding process.

Usually, for the stability of the spherometer on a concave or convex surface and for unloading its weight, the spherometer is equipped with at least one auxiliary side leg-stop. So, when controlling aspherical surfaces according to patent application RU 2013 147718/28, prior. 10.28.2013, use a spherometer with three additional support legs, of which one is located on the side of the indicator (sensor) and can be adjusted in height.

The specified method does not solve the problem, because the discreteness of the constructed profile is half the base of the spherometer, a decrease in the base of the spherometer leads to an increase in the error in determining the profile, and also does not determine the vertex radius of the surface and eccentricity. The resulting deviation profile from the nearest aspherical surface can significantly differ from that required, especially for a high aspherical surface (up to 1000 μm in diameter up to 4 m) with very small tolerances for deviations from the vertex radius and eccentricity that are currently being processed.

The technical result of the invention is the construction of an absolute profile of deviations of the shape of the aspherical surface of the optical part from the required theoretical with the required accuracy (deviation of the vertex radius from the specified less than 0.03-0.05%) and the achievement of this value of the vertex radius in the process of forming.

, в которой до этого располагалась центральная ножка с индикатором, процесс снятия показаний индикатора продолжают до центра детали или до центрального отверстия детали и затем на основании геометрических соотношений строят абсолютный профиль отклонений поверхности от заданного (теоретического) профиля с требуемым вершинным радиусом и эксцентриситетом и необходимым допуском на них.The technical result is achieved by the fact that in the method for determining the profile of a polished aspherical surface by placing the legs of a three-point linear spherometer with a base “a” with the indicator in the middle at pre-calculated points, sequentially moving the spherometer in diameter, taking readings of the indicator about the deflection arrows and calculating surface shape deviations from theoretical, unlike the known one, a spherometer with an additional lateral height-adjustable leg is used, the spherometer is reset to zero on a control glass known surface radius close to the interval radii aspheric surfaces outermost legs mounted perpendicular diametrical cross section in the edge parts zone with radius R _i, is moved spherometer outermost legs in a zone with a radius $$R_{i+\mathrm{one}}=\sqrt{R_i^2-{(a/2)}^2}$$

, in which the central leg with the indicator was located before, the process of taking the indicator readings is continued to the center of the part or to the central hole of the part, and then, based on geometric relationships, an absolute profile of surface deviations from the given (theoretical) profile with the required vertex radius and eccentricity and necessary tolerance is built on them.

The method is illustrated by drawings, where:

Fig. 1 shows a diagram of the installation of the spherometer legs on the surface and a diagram for calculating the installation points;

Fig. 2 is an indicator layout;

Fig. 3 is a diagram of reference points and segments;

Fig. 4 is a graph of the construction of the measured profile.

The proposed method is implemented as follows. The measurements were carried out on a mirror with a diameter of 3700 mm with a light measured diameter of 3670 mm, a vertex radius of curvature of the aspherical surface equal to 14639.0 mm, a conical constant K = 1.03296, and a hole diameter of 720 mm. For measurements, a linear three-point spherometer is used with an indicator head in the middle with a division price of 0.1 μm, with a base “a” (the distance between the extreme legs of the spherometer) equal to 1020 mm and a side height-adjustable auxiliary leg fixed to the side of the indicator at a distance of 40 mm . To zero the indicator, a control (test) glass was made with a radius of 14727.0 mm, given that the radius of the sphere closest to the aspheric is 14700.55 mm.

, в которой теоретическое значение должно быть Δs_2,теор определяется добавка к профилю Δр₂=Δs_2,измер-Δs_2,теор и отклонение профиля в точке Р₂=P₁+Δр₂, сферометр перемещают крайними ножками на зону, в которой располагалась центральная ножка, снова выполняют измерения стрелки прогиба и определяют отклонения профиля в точке P_i+1=P_i+Δp_i и процесс измерений продолжают до центра детали или до центрального отверстия P_n=P_n-1+Δp_n-1 и строят абсолютный профиль с отклонениями от поверхности с требуемым вершинным радиусом и эксцентриситетом.A spherometer with a base “a” (A ₁ -B ₁ in Fig. 1), a distance of “b” to the 4th lateral leg from the central (Fig. 2), which ensures the spherometer is normal to the surface, is placed on a control glass, zeroed, set with the extreme legs on the measured part perpendicular to the diametrical section and normal to the surface (Fig. 2) in the first edge zone of the part (at points A ₁ , B ₁ , Fig. ₁ , Fig. 3) with a radius R _A1 in the XY plane, which the deviation of the profile is taken equal to P ₁ = 0, take the readings of the spherometer Δs _{1, measured} relative to the reference sphere at point T ₂ on s one with the distance from the center to $${\mathrm{<figure-callout\; id="2"\; label="R\; A"\; filenames="00000007.png"\; state="\{\{state\}\}">R\; </figure-callout>}}_A=\sqrt{R_{A\mathrm{one}}^2-{(a/2)}^2}$$

in which the theoretical value should be Δs _{2, theor} is determined by the addition to the profile Δp ₂ = Δs _{2, measured} -Δs _{2, theor} and the deviation of the profile at the point P ₂ = P ₁ + Δp ₂ , the spherometer is moved with its extreme legs to the zone in which the central leg was located, the deflection arrows are measured again and the profile deviations are determined at the point P _{i + 1} = P _i + Δp _i and the measurement process continues to the center of the part or to the central hole P _n = P _n-1 + Δp _n-1 and build absolute profile with deviations from the surface with the required vertex radius and eccentricity.

Δs _{i, theor} , is determined from the equation of the aspherical surface, which is generally written as follows:

,

,

where S ² = x ² + y ² ;

c = 1 / R ₀ is the reciprocal of the vertex radius;

K = -e ² , where e is the eccentricity of the surface;

A ₁ , A ₂ , A ₃ , A ₄ - aspheric coefficients for surfaces of a higher order (above the 2nd).

Depending on the value of the conic constant, the following surface forms are distinguished:

K <-1 - hyperboloid

K = -1 - paraboloid

-1 <K <0 - ellipsoid of revolution relative to the main axis (ellipsoid or elongated spheroid)

K = 0 - sphere

K> 1 - ellipsoid of revolution relative to the minor axis (oblate spheroid)

We determine the values of z _A1 , z _A2 , z _T2 , determine the arrow minus the arrows of the reference sphere arrow of the _sphere :

Δs _{i, theor} = (z _A1 -z _T2 -arrow _spheres ) cos (α),

where angle α is the angle between the vertical and the normal to the surface at the measured point.

Figure 4 shows the results of calculating the profile according to the described method. The graph shows the obtained deviations of the Delta _asf (in Fig. 4 Y _tr . _Legs , Z _{tr. Legs} - the third stationary leg). PS _theory and PS _fact - theoretical and actual deviations of the deflection arrow from the reference spherical surface, Y - coordinate of the profile along the radial direction from the edge of the part to the center, Z _theory and Z _fact - theoretical and actual value of the Z coordinate. Asf. _Theory and Asf. _fact - theoretical and obtained actual value of asphericity from the nearest sphere. In the last column of Arr. def. - the value of the correction in the readings of the spherometer, taking into account the deformation of the spherometer when it is inclined relative to the working surface. This correction is determined experimentally for various angles of inclination of the spherometer a (Fig. 2) relative to the vertical position. Taking this strain correction into account significantly increases the accuracy of measurements.

Actual measurements of the vertex radius made after preliminary polishing of the surface gave a value of R ₀ = 14639 ± 5 mm (the required value is ± 7 mm), which amounts to a deviation from the set value of 0.03%.

The results shown in Fig. 4 show the high efficiency and reliability of the proposed method for measuring the profile of a polished aspherical surface and practically confirm the achievement of the technical result: constructing an absolute profile of deviations of the shape of the aspherical surface of the optical part from the required theoretical one with the required accuracy (the deviation of the vertex radius from the set is less than 0 , 03-0.05%) and the achievement of a given value of the vertex radius in the process of shaping.

Claims (1)

The method of determining the profile of an aspherical polished surface by placing the legs of a three-point linear spherometer with a base “a” with the indicator in the middle at pre-calculated points, sequentially moving the spherometer in diameter, taking readings of the indicator on the deflection arrows and calculating deviations of the surface shape from the theoretical one, characterized in that they are used a spherometer with an additional lateral height-adjustable leg; the spherometer is reset to zero on a control glass with a known surface radius close to shaft radii of the aspheric surfaces outermost legs mounted perpendicular diametrical cross section in the part edge area with a radius R _i, is moved spherometer outermost legs in a zone with a radius $$R_{i+\mathrm{one}}=\sqrt{R_i^2-{(a/2)}^2}$$

, in which the central leg with the indicator was located before, the process of taking the indicator readings is continued to the center of the part or to the central hole of the part, and then, based on geometric relationships, an absolute profile of surface deviations from the given (theoretical) profile with the required vertex radius and eccentricity and necessary tolerance is built on them.

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