阅读说明：本技术 共轭校正检验非球面镜的光学系统及理论 (optical system and theory of conjugate correction inspection aspherical mirror ) 是由 郝沛明 郑列华 于 2019-09-23 设计创作，主要内容包括：本发明公开了一种共轭校正检验非球面镜的光学系统及理论。检测设备中发光点发出的光线经校正透镜成像于待检非球面镜的共轭物点；待检非球面镜将共轭物点成像于共轭像点；共轭像点作为自准校正透镜的物点,光线经自准校正透镜自准原路返回。校正透镜和自准校正透镜生成球差可校正待检非球面镜在两个共轭点生成球差。共轭前后点与前区、中区、后区三个区间是相关的,大大提高了像差校正能力；自准面位于自准校正透镜上,光线两次通过待检非球面镜；自准校正透镜位于共轭前点前,校正扁球面能力强；校正透镜与自准校正透镜光路连接,校正能力更强。共轭校正检验可实现大口径、大相对孔径甚至超大口径、超大相对孔径的非球面镜检验。(The invention discloses an optical system and theory of a conjugate correction inspection aspherical mirror. The light emitted by the luminous point in the detection equipment is imaged on a conjugate object point of the aspherical mirror to be detected through the correction lens; imaging the conjugate object point on the conjugate image point by the aspheric mirror to be detected; the conjugate image point is used as the object point of the autocollimation lens, and the light returns from the autocollimation path through the autocollimation lens. The spherical aberration generated by the correction lens and the self-calibration correction lens can correct the spherical aberration generated by the aspheric lens to be detected at two conjugate points. The front point and the rear point of conjugation are related to the front zone, the middle zone and the rear zone, so that the aberration correction capability is greatly improved; the self-collimating surface is positioned on the self-collimating correction lens, and the light rays pass through the aspheric lens to be detected twice; the self-aligning correcting lens is positioned in front of the conjugate front point, and the correcting oblate spheroid surface has strong capability; the correction lens is connected with the self-aligning correction lens through a light path, and the correction capability is stronger. The conjugate correction inspection can realize the inspection of the aspheric mirror with large caliber, large relative aperture, even ultra-large caliber and ultra-large relative aperture.)

1. An optical system of conjugate correction inspection aspherical mirror comprises a correction lens (2) and a self-aligning correction lens (3), the aspherical mirror (1) to be inspected has two conjugate points without spherical aberration, namely a post-conjugate point O 'and a pre-conjugate point O', and is characterized in that,

the light emitted by the detection equipment is reflected to the aspheric mirror (1) to be detected to the auto-calibration lens (3) after passing through the calibration lens (2), is reflected to the aspheric mirror (1) to be detected by the lens surface plated with the semi-transparent semi-reflective film in the auto-calibration lens (3), is reflected to the auto-calibration lens (3) by the aspheric mirror (1) to be detected, and is transmitted by the auto-calibration lens (3) and transmitted by the calibration lens (2) to return to the detection equipment;

The correction lens (2) images the light rays emitted by the detection equipment on a post-conjugation point O 'or a pre-conjugation point O' of the aspherical mirror (1) to be detected, and the point is used as a conjugate object point of the aspherical mirror to be detected; the aspheric mirror (1) to be detected images the conjugate object point on another conjugate point, and the point is a conjugate image point; the point O 'before conjugation and the point O' after conjugation are conjugated to be an object-image relation point; dividing the space into a conjugate back point, a conjugate front point, a middle area O' between the conjugate back point and the conjugate front point, a back area behind the conjugate back point and a front area before the conjugate front point, wherein the conjugate front point and the conjugate back point are related to the front area, the middle area and the back area; the spherical aberration generated by the correction lens (2) and the autocollimation correction lens (3) corrects the spherical aberration generated by the aspheric mirror (1) to be detected at two conjugate points; the self-correcting lens (3) is arranged at a conjugate rear point O ', a conjugate front point O', and a middle area, a rear area or a front area; the diaphragm is located the autocollimation face of autocollimation correction lens (3), and the autocollimation face has plated half-transparent half-reflection membrane, and the aspheric mirror (1) of waiting to examine is waited twice to light.

2. The conjugate corrective inspection aspheric lens optical system as defined in claim 1 in which: the correcting lens (2) and the self-aligning correcting lens (3) can be combined into one lens.

3. a conjugate calibration verification aspherical mirror theory based on the optical system of the conjugate calibration verification aspherical mirror of claim 1, characterized in that: the method for determining the normalization parameters of the correction lens (2) and the self-alignment correction lens (3) is as follows:

The parameters are defined as h₀Is the incident height h of light on the aspherical mirror (1) to be detected_SchoolThe incident height h of the light on the correction lens (2)_{Self-calibration}Is the incident height of light on the autocorrection lens (3), r₀For the radius of curvature, u, of the vertex of the aspherical mirror (1) to be examined₀The curvature center of the aspheric mirror (1) to be detected reaches the half aperture of the aspheric mirror (1) to be detected and forms an angle with the aperture of an optical axis, u and u 'are angles between the incident light and the aperture of the optical axis of the aspheric mirror (1) to be detected and reflected, n and n' are refractive indexes n which are 1 and n which are-1 of the incident light and the reflected light of the aspheric mirror (1) to be detected; the O 'point and the O' point are two conjugate points of an object-image relationship, the O 'point is a point after conjugation, and the O' point is a point before conjugation; l is the pre-conjugation intercept, l' is the post-conjugation intercept,And K_{Is not}For the primary spherical aberration parameter of the aspherical mirror (1) to be examined, e²For the aspheric mirror (1) to be examined the eccentricity squared, S_{1 is not}Is the primary spherical aberration coefficient, P, of the aspherical mirror (1) to be examined_SchoolFor correcting the primary spherical aberration parameter, S, of the lens (2)_{1 school}In order to correct the primary spherical aberration coefficient of the lens (2),For self-aligning the primary spherical aberration parameters of the lens (3), S_{1 self-calibration}For self-aligning the primary spherical aberration coefficient, S, of the lens (3)₁Primary spherical aberration coefficients of the system are checked; h is₀、h_School、h_{Self-calibration}、r₀、u₀、u、u′、n、n′、l、l′、K_{Is not}、e²、S_{1 is not}、P_School、S_{1 school}、S_{1 self-calibration}The relationship between the various parameters is as follows,

Regulation of conditions

for concave aspherical mirrors u₀＝1,h₀＝-1,r₀＝-1；

For convex aspherical mirrors u₀＝1,h₀＝1,r₀＝1；

by using paraxial formula, for the convex-concave aspheric mirror to be detected,

h₀＝lu＝l′u′ (3)

u′+u＝2 (5)

Primary spherical aberration parameter of aspheric mirror (1) to be detectedAnd K_{is not}Coefficient of spherical aberration with primary_{1 is not}The relationship is as in equation (8),

substituting equation (6) and equation (7) into the primary spherical aberration coefficient S_{1 is not}In the expression (8), the expression (9) can be derived,

S_{1 is not}＝2h₀[e²-(1-u)²]＝2h₀[e²-(u′-1)²] (9)

For concave aspheric mirror to be inspected, r₀＝-1,h₀Equation (9) becomes equation (10) when it is-1,

S_{1 is not}＝-2[e²-(1-u)²]＝2[(1-u)²-e²]≠0 (10)

For convex aspheric mirror to be inspected r₀＝1,h₀Equation (9) becomes equation (11) when 1 is satisfied,

S_{1 is not}＝2[e²-(1-u)²]≠0 (11)

Primary spherical aberration coefficient S of optical system₁And S_{1 is not}、S_{1 school}、S_{1 self-calibration}The relationship is

For the concave aspheric mirror to be inspected, formula (12) is changed into formula (13),

For convex aspheric mirrors to be inspected, formula (12) is changed to formula (14),

Given an initial h_School、h_{Self-calibration}The u parameter values are calculated, and the normalization parameters P of the correction lens (2) and the self-aligning correction lens (3) can be obtained by solving the formulas (2), (3), (4), (5), (13) and (14)_SchoolAnd

Technical Field

The invention relates to aspheric mirror inspection of large caliber and large relative aperture, even aspheric mirror inspection of ultra-large caliber and ultra-large relative aperture, in particular to a basic theory for inspecting the aspheric mirror based on a conjugate correction principle.

Background

The aspheric mirror optics comprises main parts such as aberration theory, aspheric mirror optical system design, auxiliary optical system design, processing technology and image quality evaluation, wherein the auxiliary optical system design plays a role of a bridge between the aspheric mirror optical system design and aspheric mirror processing, and the aspheric mirror design processing is realized by inspecting the aspheric mirror through the auxiliary optical system. Reviewing the history of development of secondary optical system designs, aspherical mirror inspection can be divided into two main types:

1. Classical aspheric mirror inspection

Self-alignment inspection is carried out by utilizing the self-aberration-eliminating point of the aspherical mirror, the diaphragm is positioned on the auxiliary surface, and light passes through the aspherical mirror to be inspected twice. Typical methods are represented as follows: (1) and (4) self-calibration of the concave paraboloid. And (5) utilizing the auxiliary plane mirror to automatically check the concave paraboloid. (2) Hendel (Hindle 1931) convex hyperboloid test. The convex hyperboloid is self-calibrated by using an auxiliary spherical mirror. (3) Simpson (Simpson 1974) convex hyperboloid test. The convex hyperboloid is self-checked by using the semi-reflecting and semi-permeable self-aligning auxiliary spherical surface. (4) Inspection with a transmission convex aspherical mirror (Heiperming 1991). The self spherical aberration of the convex aspherical mirror to be detected is eliminated, and a self-aligning auxiliary spherical mirror is added on one side of the spherical aberration eliminating point of refraction, so that the convex aspherical mirror can be automatically and accurately detected.

The self-calibration inspection method for the self-aberration-eliminating point of the aspherical mirror is suitable for inspecting aspherical mirrors with general apertures and small relative apertures.

2. Zero compensation aspherical mirror inspection

And compensating the normal distance difference of the concave aspheric lens to be detected by utilizing the spherical aberration generated by the compensation lens, and performing self-alignment detection. The concave aspherical mirror to be detected is a self-aligning surface, the diaphragm is positioned on the concave aspherical mirror to be detected, and light passes through the concave aspherical mirror to be detected once. Typical methods are represented as follows: (1) dall 1947 concave aspherical mirror test. The concave paraboloid is detected by utilizing a compensation positive lens positioned between the concave paraboloid to be detected and the spherical center of the curvature radius, and the concave paraboloid to be detected is a self-collimating surface which is detected by a front zero compensation aspherical mirror. (2) Modified dalle (Dall) oblate spheroid test. The concave oblate surface is inspected by using a compensation negative lens positioned between the concave oblate surface to be inspected and the spherical center of curvature radius, the concave oblate surface to be inspected is a self-aligning surface, and the self-aligning surface is inspected by using a front zero compensation aspherical mirror. (3) The Ovonier (Offner 1863) concave aspherical mirror test. The concave paraboloid is detected by utilizing the compensation positive lens positioned behind the curvature radius sphere center of the concave aspheric mirror to be detected, the concave paraboloid to be detected is a self-collimating surface, and the self-collimating surface is used for detecting the rear zero compensation aspheric mirror. (4) Concave aspherical mirror inspection by Mark Sokov (Maksutov 1957). The concave paraboloid is detected by utilizing the compensation concave reflecting mirror positioned between the concave aspherical mirror to be detected and the spherical center of the curvature radius, and the concave paraboloid to be detected is a self-aligning surface which is used for detecting the front zero compensation aspherical mirror. (5) Safel (Shafer 1979) concave aspherical mirror test. The spherical aberration generated by the combination of the three lenses without focal power between the concave paraboloid to be detected and the spherical center with the curvature radius is used for compensating the normal distance difference of the concave paraboloid to be detected, and the concave paraboloid to be detected is a self-collimating surface which is used for the detection of the front zero compensation aspherical mirror.

The zero compensation aspherical mirror inspection method can realize large-caliber concave aspherical mirror inspection by using a smaller compensation lens or reflector, but the inspection of the concave aspherical mirror with larger caliber and larger relative aperture is difficult by using the methods for zero compensation aspherical mirror inspection.

In order to realize the inspection of the aspheric mirror with large caliber and large relative aperture, even the inspection of the aspheric mirror with super large caliber and super large relative aperture, the theory of conjugate correction inspection of the aspheric mirror is provided, and the principle is as follows: the aspheric mirror to be detected can generate a conjugate front point and a conjugate back point (two conjugate points do not eliminate spherical aberration), the correction lens images an object point (a luminous point) on one conjugate point, the aspheric mirror to be detected images one conjugate point on the other conjugate point, the other conjugate point is a self-alignment point of the self-alignment correction lens, the two conjugate points are in an object-image relationship, and the spherical aberration generated by the aspheric mirror to be detected can be corrected by utilizing the spherical aberration generated by the correction lens and the self-alignment correction lens. The diaphragm is positioned on the self-collimating surface (internal reflection self-collimating) of the self-collimating correction lens, and the light rays pass through the aspheric lens to be detected twice. For classical aspheric mirror inspection and zero compensation aspheric mirror inspection, the conjugate correction inspection aspheric mirror is distinguished in that:

1. The classical aspheric mirror inspection utilizes the self-sphere-eliminating difference point of a convex or concave aspheric mirror to carry out self-calibration inspection, and is suitable for the inspection of aspheric mirrors with general apertures and small relative apertures.

2. The zero compensation inspection is divided into front compensation and rear compensation by taking a paraxial curvature center as a boundary; the self-aligning surface is positioned on the concave aspheric mirror to be detected, and light only passes through the concave aspheric mirror to be detected once for reflection. The zero compensation inspection is divided into a front zero compensation inspection and a back zero compensation inspection, and the two intervals are irrelevant, so that the compensation (correction) capability is greatly reduced, and the zero compensation inspection of the concave aspheric mirror with large caliber and large relative aperture is difficult to realize.

3. The conjugate correction test is divided into a front region, a middle region and a rear region by taking conjugate front and rear points as boundaries, and the conjugate front and rear points and three regions are related, so that the correction capability is greatly improved; the self-collimating surface is positioned on the self-collimating correction lens, and the light rays are reflected by the aspheric surface to be detected twice; the self-aligning correction negative lens is positioned in front of the conjugate front point, and the correction oblate spheroid surface capability is strong; the correction lens is connected with the self-aligning correction lens through a light path, and the purpose of stronger correction capability is achieved. The inspection of the conjugate correction aspheric mirror can realize the inspection of the aspheric mirror with large caliber and large relative aperture, and even realize the inspection of the aspheric mirror with super large caliber and super large relative aperture.

disclosure of Invention

The conjugate correction inspection aspheric mirror is suitable for inspecting convex and concave aspheric mirrors, and provides a basic theory for researching the inspection of the aspheric mirror with large caliber, large relative aperture, even ultra-large caliber and ultra-large relative aperture. An optical system of conjugate correction inspection aspheric mirror comprises a correction lens 2 and a self-aligning correction lens 3, wherein the aspheric mirror 1 to be inspected has two conjugate points of non-spherical aberration, namely a post-conjugate point O 'and a pre-conjugate point O', and is characterized in that light emitted by a detection device is reflected to the aspheric mirror 1 to be inspected to the self-aligning correction lens 3 through the correction lens 2, is reflected back to the aspheric mirror 1 to be inspected through a lens surface plated with a semi-transparent semi-reflective film in the self-aligning correction lens 3, is reflected to the self-aligning correction lens 3 through the aspheric mirror 1 to be inspected, and is transmitted through the self-aligning correction lens 3 and transmitted through the correction lens 2 to return to the detection device.

The correction lens 2 images light rays emitted by detection equipment on a post-conjugation point O 'or a pre-conjugation point O' of the aspherical mirror 1 to be detected, and the point is used as a conjugate object point of the aspherical mirror to be detected; the aspheric mirror 1 to be detected images the conjugate object point on another conjugate point, and the point is a conjugate image point; the point O 'before conjugation and the point O' after conjugation are conjugated to be an object-image relation point; dividing the space into a conjugate back point, a conjugate front point, a middle area O' between the conjugate back point and the conjugate front point, a back area behind the conjugate back point and a front area before the conjugate front point, wherein the conjugate front point and the conjugate back point are related to the front area, the middle area and the back area; the spherical aberration generated by the correction lens 2 and the autocorrection lens 3 corrects the spherical aberration generated by the aspheric mirror 1 to be detected at two conjugate points; the self-collimating lens 3 is placed at the post-conjugate point O', the pre-conjugate point O ", the middle, rear or front zone; the diaphragm is located the autocollimation face of autocollimation correction lens 3, and the autocollimation face has plated half-transparent half-reflection membrane, and the aspheric mirror 1 of waiting to examine is crossed twice to light.

both the correction lens 2 and the autocollimation lens 3 according to the invention can be combined into the same lens.

The theory of the conjugate correction inspection aspherical mirror of the optical system of the conjugate correction inspection aspherical mirror is characterized in that: the method for determining the normalization parameters of the correcting lens 2 and the self-aligning correcting lens 3 is as follows:

The parameters are defined as h₀Is the incident height h of light on the aspherical mirror (1) to be detected_Schoolthe incident height h of the light on the correction lens (2)_{Self-calibration}Is the incident height of light on the autocorrection lens (3), r₀For the radius of curvature, u, of the vertex of the aspherical mirror (1) to be examined₀To wait to examine aspherical mirror (1) curvature center to wait to examine aspherical mirror (1) half bore department and optical axis aperture angle, u and u 'wait to examine aspherical mirror (1) light and optical axis aperture angle for incidence and reflection, n and n' are the refractive index n that looks at aspherical mirror (1) light for incidence and reflection 1, n ═ 1. The O 'point and the O' point are two conjugate points of an object-image relationship, the O 'point is a point after conjugation, and the O' point is a point before conjugation; l is the pre-conjugation intercept, l' is the post-conjugation intercept,And K_{Is not}for the primary spherical aberration parameter of the aspherical mirror (1) to be examined, e²for the aspheric mirror (1) to be examined the eccentricity squared, S_{1 is not}Is the primary spherical aberration coefficient, P, of the aspherical mirror (1) to be examined_SchoolFor correcting the initial lens (2)Level spherical aberration parameter, S_{1 school}In order to correct the primary spherical aberration coefficient of the lens (2),For self-aligning the primary spherical aberration parameters of the lens (3), S_{1 self-calibration}For self-aligning the primary spherical aberration coefficient, S, of the lens (3)₁To check the primary spherical aberration coefficient of the system. h is₀、h_School、h_{Self-calibration}、r₀、u₀、u、u′、n、n′、l、l^′、K_{Is not}、e²、S_{1 is not}、P_School、S_{1 school}、S_{1 self-calibration}The relationship between the various parameters is as follows,

regulation of conditions

For concave aspherical mirrors u₀＝1,h₀＝-1,r₀＝-1；

For convex aspherical mirrors u₀＝1,h₀＝1,r₀＝1；

By using paraxial formula, for the convex-concave aspheric mirror to be detected,

h₀＝lu＝l′u′ (3)

u′+u＝2 (5)

Primary spherical aberration parameter of aspheric mirror 1 to be detectedAnd K_{Is not}Coefficient of spherical aberration with primary_{1 is not}The relationship is as in equation (8),

Substituting equation (6) and equation (7) into the primary spherical aberration coefficient S_{1 is not}in the expression (8), the expression (9) can be derived,

S_{1 is not}＝2h₀[e²-(1-u)²]＝2h₀[e²-(u′-1)²] (9)

For concave aspheric mirror to be inspected, r₀＝-1,h₀Equation (9) becomes equation (10) when it is-1,

S_{1 is not}＝-2[e²-(1-u)²]＝2[(1-u)²-e²]≠0 (10)

For convex aspheric mirror to be inspected r₀＝1,h₀Equation (9) becomes equation (11) when 1 is satisfied,

S_{1 is not}＝2[e²-(1-u)²]≠0 (11)

Primary spherical aberration coefficient S of optical system₁And S_{1 is not}、S_{1 school}、S_{1 self-calibration}The relationship is

For the concave aspheric mirror to be inspected, formula (12) is changed into formula (13),

For convex aspheric mirrors to be inspected, formula (12) is changed to formula (14),

Given an initial h_School、h_{Self-calibration}The u parameter values are calculated by the formulas (2), (3), (4), (5) and the formulas (13) and (14) to obtain the normalization parameters P of the correction lens 2 and the self-aligning correction lens 3_schoolandFrom P_School、The lens specification parameters can be obtained by combining the specific structure form of the lens.

The aspheric mirror 1 to be detected for reflection has two conjugate points, wherein O 'is a point after conjugation, O' is a point before conjugation, the two conjugate points are in an object-image relationship with each other, and the two conjugate points have spherical aberration generated by the aspheric mirror 1 to be detected. For r₀＝-1,h₀The point on the right side of the paraxial curvature center of the concave aspheric mirror 1 to be detected is a conjugate front point O ', and the point on the left side of the paraxial curvature center is a conjugate back point O'. For r₀＝1,h₀1 protruding aspheric mirror 1 of examining of waiting is 1, and the point on the right of aspheric mirror 1 of examining in the reflection is conjugation front point O ", and the point on the left of aspheric mirror 1 of examining in the reflection is conjugation back point O'.

The aspheric mirror 1 to be detected in reflection is divided into areas according to two conjugate points, a middle area O' is arranged between a point after conjugation, a point before conjugation and a point before conjugation, a back area is arranged behind the point after conjugation and a front area is arranged before the point before conjugation. The front, middle and rear regions are divided into two regions due to the difference between the height of the incident light and the height of the self-collimating lens 3. The conjugate front and back points and the front, middle and back regions are correlated, and the aberration correction capability is stronger.

The spherical aberration generated by the correction lens 2 and the self-calibration correction lens 3 can correct the spherical aberration generated by the aspherical mirror 1 to be detected at two conjugate points. The distance between the pre-conjugate point O ″ and the post-conjugate point O' (conjugate point distance) is related to the position of the autocollimator lens 3 and the incident height of the light ray on the autocollimator lens. The self-collimating lens 3 can be placed at the post conjugate point O' or the pre conjugate point O ", and can also be placed between the middle, rear and front zones. By determining the position and height of the autocollimation lens 3, the configuration of the optical system can be determined.

from the principle analysis and design results of the conjugate correction inspection aspheric mirror, the inspection capability of the conjugate correction aspheric mirror is far superior to that of the zero compensation aspheric mirror and the classical aspheric mirror. The classical aspheric mirror inspection uses the self-sphere-eliminating difference point of a convex or concave aspheric mirror to carry out self-calibration inspection, and is only suitable for the inspection of aspheric mirrors with general apertures and small relative apertures. The zero compensation inspection is divided into front compensation and rear compensation by taking a paraxial curvature center as a boundary; the light only passes through the concave aspheric mirror to be detected for one time for reflection; the front zero compensation inspection and the rear zero compensation inspection are irrelevant, so that the compensation correction capability is greatly reduced, and the inspection of the concave aspheric mirror with large caliber and large relative aperture by using the zero compensation is difficult; the method adopted at home and abroad is to change the aspherical mirror of the spherical compensation system into a mirror, so as to improve the compensation capability, but the precision of the aspherical mirror to be processed is reduced and the processing period is prolonged, and even if the aspherical mirror of the spherical compensation system is changed into the mirror, the inspection of the aspherical mirror with super-large caliber and super-large relative aperture is difficult to realize. The conjugate correction optical systems are spherical surfaces, and the structure is simple; the conjugate correction test is divided into a front region, a middle region and a rear region by taking the front and rear conjugate points as boundaries, and the front and rear conjugate points and three regions are related, so that the aberration correction capability is greatly improved; the self-collimating surface is positioned on the self-collimating correction lens, and the light rays are reflected by the aspheric surface to be detected twice; the self-aligning correction negative lens is positioned in front of the conjugate front point, and the correction oblate spheroid surface capability is strong; the correction lens is connected with the self-aligning correction lens through a light path, and the purpose of stronger correction capability is achieved. The inspection of the conjugate correction aspheric mirror can realize the inspection of the aspheric mirror with large caliber and large relative aperture, and even realize the inspection of the aspheric mirror with super large caliber and super large relative aperture.

Drawings

FIG. 1 shows a conjugate inspection light path of an aspherical mirror, wherein 1 is the aspherical mirror to be inspected, 2 is a correction lens, and 3 is a self-alignment correction lens.

FIG. 2 is a diagram of a three-lens conjugate calibration inspection optical path, in which 1 is a concave aspherical mirror to be inspected, 2-1 is a first calibration lens, 3 is a self-calibration lens, and 2-2 is a second calibration lens.

Detailed Description

The invention provides an optical system and a basic theory for conjugate correction inspection of an aspherical mirror. The invention is described in further detail below with reference to the figures and specific examples. The specific embodiments described are merely illustrative of the invention and do not limit the invention.

The self-calibration correction lens 3 and the second correction lens 2-2 are positioned at the center of the sphere of the concave aspheric surface to be detected. As shown in FIG. 2, the light ray is emitted from the on-axis point O and passes through the spherical surface R of the first correcting lens 2-1₁And the spherical surface R₂Spherical surface R of transmission and autocorrection lens 3₃And R₄Transmission, and spherical surface R of the second correction lens 2-2₅And R₆The light is refracted to the concave aspheric mirror 1 to be detected (forming a virtual image at a conjugate rear point O 'of the concave aspheric mirror 1 to be detected), reflected by the concave aspheric mirror 1 to be detected to form an image at a conjugate front point O', the light is incident to the second correcting lens 2-2 and the self-aligning correcting lens 3, and after being reflected by the self-aligning correcting lens 3 from the aligning surface, the light is transmitted by the second correcting lens 2-2, reflected by the concave aspheric mirror 1 to be detected, transmitted by the second correcting lens 2-2, transmitted by the self-aligning correcting lens 3 and transmitted by the first correcting lens 2-1, and then returns to the image point O according to the original path.

the steps of conjugate correction and inspection of the concave aspherical mirror are as follows:

1. And (4) defining symbols. The arrow above the symbol is → when following the light path. When the light path is reversed, the arrow above the symbol is ←.

2. The direction in which the light is emitted. To satisfy the incident height h of the concave aspherical mirror 1 to be inspected₀₃The on-axis object point emits light directed below the optical axis, for the normalized condition of-1.

3. Imaging relation of the concave aspherical mirror to be detected. The point O 'after conjugation is the object point, and the point O' before conjugation is the image point.

4. The incident height of the light on each face is h, and the primary spherical aberration parameter is P, K. Spherical surface R of correction lens 2-1₁And the spherical surface R₂formed primary spherical aberration coefficient h₁P_1-2Spherical surface R of the self-collimating lens 3₃and R₄Formed primary spherical aberration coefficient h₃P_3-4Spherical surface R of second correction lens 2-2₅And R₆Formed primary spherical aberration coefficient h₃P_5-6Primary spherical aberration coefficient formed by concave aspherical mirror 1 to be inspectedThe primary spherical aberration coefficient of the light reflected by the concave aspherical mirror 1 to be detected and incident on the second correcting lens 2-2Then passes through the primary spherical aberration coefficient formed by the self-calibration of the self-calibration correction lens 3

5. And (5) regulating condition setting. The curvature radius of the mirror surface is r, and the curvature radius r of the concave aspheric mirror 1 to be detected₀₇spherical surface R of correction lens 2-1₁、R₂Radius of curvature r₁、r₂Spherical surface R of the self-collimating lens 3₃、R₄Radius of curvature r₃、r₄Spherical surface R of second correction lens 2-2₅、R₆Radius of curvature r₅、r₆(ii) a The aperture angle of each incident optical surface is u, and the aperture angle of each incident concave aspheric lens to be detected is u₀₇2-1 spherical surface R of correction lens₁Incident ray aperture angle of u₁. Normalized condition of r₀₇＝-1.0,h₀₇＝-1.0,u₀₇＝h₀₇/r₀₇＝1。

6. And (6) correcting spherical aberration. e.g. of the type₇2 is the eccentricity square of the concave aspherical mirror 1 to be detected, and the conjugate of the combination of the first correction lens 2-1, the self-alignment correction lens 3 and the second correction lens 2-2The aspheric deghost of the correction test is expressed as

Wherein h is₃(P_3-4+P_5-6) Andthe generated spherical aberration is small.

7. The first correction lens 2-1, the second correction lens 2-2 and the self-collimating correction lens 3 are solved. Given h₈＝0.10、h₆＝-0.10h₁＝0.1、u₁A value of-0.5 whenThen, the primary spherical aberration parameters P of the first correction lens 2-1, the auto-collimation correction lens 3 and the second correction lens 2-2 are obtained by solving according to the formula (13) and the formula (15)_1-2＝10、From P_1-2＝10、By combining the specific structural form of the lens and adopting the glass material K9, the normalized curvature radiuses of the first correction lens 2-1, the self-alignment correction lens 3 and the second correction lens 2-2 are respectively as follows:

r₁＝0.0351、r₂＝3.3525、r₃＝0.7382、r₄＝-0.087、r₅＝-0.0378、r₆＝-0.0375。