CN102393565B - Reverse type inverse compensator - Google Patents

Abstract

The invention is a catadioptric inverse compensator, which is used to calibrate an aspheric zero detection compensator, including an interferometer, a lens, a negative lens and a reflective spherical mirror, and an aspheric surface to be calibrated is arranged between the interferometer and the lens Zero detection compensator; a negative lens is set between the reflective spherical mirror and the lens, the lens is used to correct advanced spherical aberration, and the negative lens is used to produce quantitative spherical aberration; after the light passes through the negative lens and the lens twice, the spherical aberration produced by the lens and the lens The sum of the differences is equal to the theoretical spherical aberration of the aspheric zero-detection compensator, and the sign is opposite; the single-wavelength divergent spherical wave emitted by the interferometer passes through the aspheric zero-detection compensator to form a divergent spherical wave, and the divergent spherical wave with spherical aberration The light beam passes through the lens and the negative lens in turn to reach the reflective spherical mirror. After being reflected by the reflective spherical mirror, the light beam passes through the negative lens and the lens for the second time, and then reaches the interferometer after passing through the aspheric zero detection compensator. System aberrations are detected.

Description

A catadioptric inverse compensator

technical field

The invention relates to a catadioptric inverse compensator for calibrating an aspherical zero-detection compensator, which is mainly used for calibrating the aspheric zero-detection compensator.

Background technique

Aspheric surfaces play an important role in optics. In most large optical systems, the primary mirrors are aspherical, especially secondary aspheric surfaces. But so far, it is much more difficult to manufacture aspheric surfaces than spherical surfaces. The important reason is that the detection of aspheric surfaces is much more difficult than that of spherical surfaces.

The current main means of inspection of large-aperture aspheric mirrors is the zero-detection compensator, and the representative zero-detection compensator is the Offner compensator. Because the detection accuracy of this method is high, and the diameter of the compensator is much smaller than the diameter of the aspheric mirror to be tested, it is more and more widely used. The Offner compensator belongs to normal aberration compensation, which is composed of two positive lenses, a compensation mirror and a field mirror. The compensation mirror almost completely compensates the spherical aberration produced by the aspheric surface, and the field lens images the compensation mirror on the aspheric surface. The light emitted by the light source reaches the aspheric surface through the compensation mirror and the field lens, and all the light rays are incident on the aspheric surface to be tested along the normal line. The essence of this compensation method is to convert the plane or spherical wave into an aspheric wave with the help of a compensator and coincide with the theoretical shape of the tested aspheric surface. The wavefront emitted by the compensator can be regarded as a glass sample stacked on the tested aspheric surface. In essence, the deviation of the reference wavefront generated by the tested aspheric surface to the compensator is amplified to twice and transmitted to the wavefront returned by the compensator, which is exactly the same as the glass sample method. Therefore, the Offner compensation method can be understood as the use of a small-caliber compensator to produce a large-diameter non-contact glass sample while maintaining the basic advantages of the glass sample method. The feature of this technology is that a field lens near the center of curvature of the apex of the aspheric surface projects the aspherical surface onto the compensating mirror, which can greatly reduce the residual aberration, see "A Null Corrector for Paraboloidal Mirrors" Abe Offner.AppliedOptics Vol.2 No.2. However, this type of zero-detection compensator suffers from several drawbacks:

First, the field of view of the Offner compensator is very small, only about a few tenths of a millimeter, so the coaxiality of the optical path is very high in the actual inspection of large-aperture aspheric mirrors. However, the inspection optical path of a large aspheric primary mirror often reaches more than ten meters or even longer, and it is very difficult to meet the coaxiality requirement.

Second, Offner compensator assembly is quite difficult. For example, to detect the Offner compensator for the Φ1800mm (F/1.5) parabolic primary mirror, the distance between each mirror is required to be about 5 microns, and the eccentricity error is about 7 seconds. Such assembly requirements have almost reached the engineering limit, and any negligence will lead to serious system errors.

The data of the compensation inspection of the large-aperture aspheric primary mirror directly guides the processing of the primary mirror, and whether it is correct or not directly determines the final processing result of the primary mirror. The spherical aberration required to be compensated by the compensator is proportional to the first power of the primary mirror aperture and the third power of the relative aperture. Therefore, as far as the compensator itself is concerned, it is a large spherical aberration system, especially for large-aperture and high-steep primary mirrors. This also determines that the compensator is very sensitive to errors, and small errors and negligence will lead to disastrous consequences. There have been major accidents caused by compensator problems in history. Therefore, how to achieve high-precision calibration of the compensator, improve the reliability of the compensator, and prevent similar accidents has become one of the primary tasks in the processing of large-aperture aspheric primary mirrors. Existing compensation methods mainly rely on computational holography. Computational holograms (Computer-generated holograms, referred to as CGH) were proposed by American scientists A.J.Macgovern and J.C.Wyant in 1971 on the basis of optical holography. Its essence is to use a computer to synthesize a hologram, which does not require the actual existence of the object, but after inputting the mathematical description of the physical wave into the computer, it controls the production equipment to process the hologram. Using CGH to calibrate the compensator is to use the diffraction wave surface of CGH to simulate the reflection wave surface of the primary mirror, so that the reflection wave surface of the ideal large-aperture aspheric primary mirror can be completely simulated in the case of short distance and small aperture; and then use large-scale integration Circuit equipment to produce diffraction holograms. However, there are many error sources in the CGH manufacturing process, such as the surface shape of the CGH substrate, the step etching depth, and the position error of the scribe line, etc., which will greatly affect the calibration accuracy. In particular, the position error of the reticle has a great influence on the accuracy of the diffraction wave surface of CGH, but it is not possible to accurately determine the position error of the reticle by directly measuring the position and radius of the reticle, so the accuracy of the produced hologram is uncertain. . There is a great risk in using it to calibrate the compensator. The different diffraction orders of the hologram will also adversely affect the detection, and will form additional interference noise that is unfavorable to the detection, and the contrast is poor. With the increase of the caliber of the aspheric primary mirror and the increase of the relative caliber, the asphericity of the aspheric surface increases rapidly. To simulate the reflected wave surface of the primary mirror, the holographic film needs to etch a very small line width. The existing equipment guarantees enough engraving. Eclipse accuracy faces major challenges. Therefore, generally speaking, the current calibration methods for aspheric compensators have great technical risks.

Contents of the invention

The technical problem to be solved by the present invention is: compared with the shortcomings of the existing aspheric compensator calibration method CGH accuracy, poor contrast, difficult production, etc., the purpose of the present invention is to provide a low production cost, the main error source can be precisely measured, A catadioptric inverse compensator with good contrast and simple processing for calibrating aspheric zero-detection compensators.

In order to achieve the stated purpose, the technical solutions adopted by the catadioptric compensator provided by the present invention to solve technical problems include: an interferometer, a lens, a negative lens and a reflective spherical mirror, wherein: a calibrated The aspherical zero-detection compensator; a negative lens is set between the reflective spherical mirror and the lens, the lens is used to correct advanced spherical aberration, and the negative lens is used to generate quantitative spherical aberration; after the light passes through the negative lens and the lens twice, the lens and the lens The sum of the spherical aberrations generated is equal to the theoretical spherical aberration of the aspherical zero-detection compensator; the single-wavelength divergent spherical wave emitted by the interferometer forms a divergent spherical wave after passing through the aspheric zero-detection compensator. The poor diverging spherical wave passes through the lens and the negative lens in turn to reach the reflective spherical mirror. After the light beam is reflected by the reflective spherical mirror, it passes through the negative lens and the lens for the second time, and then reaches the interferometer after passing through the aspheric zero detection compensator. The system aberrations of the zero detection compensator are detected.

Beneficial effects of the present invention: compared with the prior art, it has the following advantages,

The catadioptric inverse compensator only includes three optical elements, among which the negative lens bears most of the spherical aberration. The lens is mainly used to compensate the high-level spherical aberration that the negative lens has not yet compensated. The function of the reflective spherical mirror is to make the light along the Backtrack. The entire catadioptric inverse compensator has low manufacturing cost and relatively simple processing, and conventional optical processing can achieve the required precision requirements.

Parameters such as refractive index, uniformity, surface error, thickness error, assembly interval error, and eccentricity error of each component can be precisely measured. Therefore, the reliability of the catadioptric reverse compensator is greatly improved.

The catadioptric inverse compensator has no interference problem of different orders, and the contrast of the interference fringes can approximately reach 100%.

Description of drawings

Fig. 1 is the catadioptric reverse compensator of the present invention;

Fig. 2 is a schematic diagram of the meanings of symbols in the present invention.

Description of components in the figure:

1 is a light source or an interferometer;

2 is an aspheric zero detection compensator;

2a is the first lens of the aspheric zero detection compensator (the lens near the interferometer);

2b is the second lens of the aspheric zero detection compensator;

3 is a lens;

3q is the first surface of the lens;

3h is the second surface of the lens;

4 is a negative lens;

4q is the first side of the negative lens;

4h is the second surface of the negative lens;

5 is a reflective spherical mirror;

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 shows the catadioptric inverse compensator of the present invention, the catadioptric inverse compensator is used to calibrate the aspheric zero detection compensator, the catadioptric inverse compensator of the present invention comprises an interferometer 1, a lens 3, a negative Lens 4 and reflective spherical mirror 5. Among them, a calibrated aspheric zero detection compensator 2 is provided between the interferometer 1 and the lens 3; a negative lens 4 is provided between the reflective spherical mirror 5 and the lens 3, the lens 3 is used to correct high-level spherical aberration, and the negative lens 4 is used to generate quantitative spherical aberration; after the light passes through negative lens 4 and lens 3 twice, the sum of spherical aberration generated by lens 4 and lens 3 is equal to and opposite to the theoretical spherical aberration of aspheric zero detection compensator 2; the interferometer The single-wavelength divergent spherical wave emitted by 1 passes through the aspherical zero-detection compensator 2 to form a divergent spherical wave. The divergent spherical wave with spherical aberration passes through lens 3 and negative lens 4 to reflective spherical mirror 5 in turn, and the beam passes through the reflective spherical mirror. 5 After reflection, it passes through the negative lens 4 and lens 3 for the second time, and then reaches the interferometer 1 after passing through the aspheric zero detection compensator 2, and the system aberration of the aspheric zero detection compensator 2 is detected by the interferometer 1.

The spherical aberration coefficient _S2 of the lens 3 satisfies:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="S"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">S</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$

$<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">L</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="S"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">S</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}$

In the formula, S ₀ is the spherical aberration coefficient of the aspheric zero detection compensator 2; S ₃ is the spherical aberration coefficient of the negative lens 4, and I ₁ , I′ ₁ , U ₁ , L ₁ are the first The incident angle, refraction angle, object space aperture angle and object space intercept of surface 3q;

In the formula, n _a is the refractive index of lens 3; I ₂ , I′ ₂ , U ₂ , and L ₂ are respectively the incident angle, refraction angle, object-side aperture angle, and object-side angle of light to the second surface 3h of lens (3). intercept;

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

U ₂ =U ₁ +I ₁ -I′ ₁ ,

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">L</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="r"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

I' ₂ = arcsin(n _a ×sin(I ₂ ));

In the formula: r ₁ is the radius of the first surface 3q of the lens 3; U′ ₁ is the image square aperture angle of the light to the first surface 3q of the lens 3; d ₁ is the thickness of the lens 3; r ₂ is the second surface 3h of the lens 3 of the radius.

The negative lens 4 of the described catadioptric reverse compensator is characterized in that: its spherical aberration coefficient S ₃ satisfies:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="S"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">S</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="L"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">L</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$

$<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$

$<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}$

In the formula, S ₀ is the spherical aberration coefficient of _the aspheric zero _detection compensator 2 _; n _b is the refractive index of the negative lens ₄ ; The angle of incidence, angle of refraction, object space aperture angle, and object space intercept.

In the formula, I ₄ , I ₄ ′, U ₄ , and L ₄ are the incident angle, refraction angle, object-side aperture angle, and object-side intercept of light to the second surface 4h of the negative lens 4, respectively;

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="r"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

I' ₃ =arcsin(sin(I ₃ )/n _b ),

U ₄ =U ₃ +I ₃ -I′ ₃ ;

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="r"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="r"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="sin\; u"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">sin</figure-callout></span><figure-callout\; id="3"\; label="sin\; u"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}_{}^{}{\mathrm{<span\; class="notranslate">u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="HDA0000101078540000011.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

I′ ₄ =arcsin(n _b ×sin(I ₄ ));

In the formula, r ₃ is the radius of the first surface 4q of the negative lens 4; U ₃ ′ is the image square aperture angle of the light to the first surface 4q of the negative lens 4; d ₂ is the thickness of the negative lens 4; r ₄ is the 4th surface of the negative lens 4 Radius of two sides 4h.

The light rays pass through the lens 3 and the negative lens 4 to form divergent spherical waves.

The spherical center of the reflective spherical mirror 5 coincides with the spherical center of the divergent spherical wave formed after the light passes through the lens 3 and the negative lens 4 . Therefore, after the light is reflected by the mirror 5, it returns to the original path, passes through the negative lens 4 and the lens 3 again, and then reaches the interferometer through the compensator to complete the detection.

The aspherical zero-detection compensator 2 (the aspheric zero-detection compensator 2 shown in Figure 1, consisting of a first lens 2a and a second lens 2b) is calibrated by using a catadioptric inverse compensator. The parameters are shown in Table 1:

Table 1

Optical parameters and performance indicators:

Numerical aperture NA = 0.13,

Working wavelength λ=0.6328μm,

Aspherical zero detection compensator spherical aberration coefficient S ₀ =2.735

Spherical aberration coefficient S ₂ of lens (3) = 0.00079

Spherical aberration coefficient S ₃ of negative lens (4) =-1.367

Wavefront aberration: PV=0.025λ, RMS=0.005λ,

Maximum Optical Component Aperture:

Fig. 2 is the schematic diagram of meaning of each symbol of the present invention, wherein, ∑ is a working surface of a certain element, I _i is incident angle, I _i ' is refraction angle, U _i is object space aperture angle, U _i ' is image square aperture _ri is the radius of the working surface Σ, O _i is the vertex of the working surface Σ, L _i is the object space intercept, L _i ' is the image space intercept, A is the object point, and A' is the image point.

Parts not described in detail in the present invention belong to the well-known technology in the art.

The above is only a specific implementation mode in the present invention, but the scope of protection of the present invention is not limited thereto. Anyone familiar with the technology can understand the conceivable transformation or replacement within the technical scope disclosed in the present invention. All should be covered within the scope contained in the claims of the present invention.

Claims (5)

1. A catadioptric reverse compensator, characterized in that it comprises: an interferometer, a first lens, a first negative lens and a reflective spherical mirror, wherein: A calibrated aspheric zero detection compensator is arranged between the interferometer and the first lens; A first negative lens is arranged between the reflective spherical mirror and the first lens, the first lens is used to correct high-level spherical aberration, and the first negative lens is used to generate quantitative spherical aberration; After the light passes through the first negative lens and the first lens twice, the sum of the spherical aberration generated by the first negative lens and the first lens is equal to the theoretical spherical aberration of the aspheric zero detection compensator; the single wavelength emitted by the interferometer The divergent spherical wave forms a divergent spherical wave after passing through the aspherical zero-detection compensator. The divergent spherical wave with spherical aberration passes through the first lens and the first negative lens in turn to reach the reflective spherical mirror. After the light beam is reflected by the reflective spherical mirror, the second After passing through the first negative lens and the first lens, and passing through the aspheric zero detection compensator, it reaches the interferometer, and the system aberration of the aspheric zero detection compensator is detected by the interferometer. 2. The catadioptric inverse compensator according to claim 1, characterized in that: the spherical aberration coefficient S2 of the first lens satisfies: ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$ $<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$ $<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}$ In the formula, S ₀ is the spherical aberration coefficient of the aspheric zero detection compensator; S ₃ is the spherical aberration coefficient of the first negative lens, and I ₁ , I _′ 1, U ₁ , L ₁ are the first The incident angle, refraction angle, object space aperture angle and object space intercept of the surface; In the formula, n _a is the refractive index of the first lens; I ₂ , I′ ₂ , U ₂ , and L ₂ are the incident angle, refraction angle, object-side aperture angle, and object-side intercept angle of light on the second surface of the first lens, respectively. distance; ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>$ U ₂ =U ₁ +I ₁ -I′ ₁ , ${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$ ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ I' ₂ = arcsin(n _a ×sin(I ₂ )); In the formula: r ₁ is the radius of the first surface of the first lens; U ₁ ′ is the image square aperture angle of the light to the first surface of the first lens; d ₁ is the thickness of the first lens; r ₂ is the first lens The radius of the second surface of the first lens; the first surface of the first lens is a surface close to the aspheric zero detection compensator, and the second surface of the first lens is a surface away from the aspheric zero detection compensator. 3. The catadioptric reverse compensator according to claim 1, characterized in that: the spherical aberration coefficient _S3 of the first negative lens satisfies: ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$ $<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}$ $<span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}$ In the formula, S ₀ is the spherical aberration coefficient of the aspheric zero detection compensator; n _b is the refractive index of the first negative lens; I ₃ , I ₃ ', U ₃ , and L ₃ are the first The incident angle, refraction angle, object space aperture angle and object space intercept of the surface; In the formula, I ₄ , I ₄ ′, U ₄ , and L ₄ are the incident angle, refraction angle, object-side aperture angle, and object-side intercept of light on the second surface of the first negative lens, respectively; ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ I' ₃ =arcsin(sin(I ₃ )/n _b ), U ₄ =U ₃ +I ₃ -I′ ₃ ; ${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arcsin</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ I′ ₄ =arcsin(n _b ×sin(I ₄ )); In the formula, r ₃ is the radius of the first surface of the first negative lens; U ₃ ' is the image square aperture angle of the light to the first surface of the first negative lens; d ₂ is the thickness of the first negative lens; r ₄ is the first negative lens The radius of the second surface of a negative lens; the first surface of the first negative lens is the surface away from the reflective spherical mirror, and the second surface of the first negative lens is the surface close to the reflective spherical mirror. 4 . The catadioptric inverse compensator according to claim 1 , wherein the light rays form divergent spherical waves after passing through the first lens and the first negative lens. 5 . The catadioptric inverse compensator according to claim 1 , wherein the spherical center of the reflective spherical mirror coincides with the spherical center of the divergent spherical wave formed after the light passes through the first lens and the first negative lens.

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