CN106092514A - Optical heterogeneity measurement apparatus and method based on dual wavelength fizeau interferometer - Google Patents

Abstract

The invention discloses an optical non-uniformity measurement device and method based on a dual-wavelength Fizeau interferometer. In the dual-wavelength Fizeau interferometer device, the interference patterns of reference light waves and reflected light waves on the front surface of a plane mirror to be measured are successively collected. , the wavefront aberration data ΔW ₁₁ (x, y) and ΔW ₂₁ (x, y) corresponding to the wavelengths λ ₁ and λ ₂ are obtained through the first phase shift measurement; Measure the interferogram of the light waves reflected by the rear surface of the plane mirror, and obtain the wavefront aberration data ΔW ₁₂ (x, y) and ΔW ₂₂ (x, y) corresponding to the wavelengths λ ₁ and λ ₂ through phase shift measurement. The optical non-uniformity of the plane mirror to be tested is obtained by calculating the difference value of the corresponding wavelength wavefront aberration data obtained by the two-step measurement. The invention does not need to introduce a standard reflector, completely eliminates the influence of the surface shape of the standard reflector on the measurement result, has simple measurement steps, and makes up for the shortcomings of the traditional absolute measurement method, which are cumbersome and easily disturbed by air.

Description

Device and method for measuring optical non-uniformity based on dual-wavelength Fizeau interferometer

technical field

The invention belongs to the technical field of optical measurement, in particular to an optical non-uniformity measurement device and method based on a dual-wavelength Fizeau interferometer.

Background technique

Optical transmission materials are an important part of optical materials, and their optical properties play an important role in the entire optical system. The indicators used to evaluate the performance of optically transparent materials include dispersion, surface shape, optical non-uniformity, radius of curvature, stress birefringence, stripes and bubbles, etc. Among them, optical non-uniformity reflects the inconsistency of the refractive index inside the same piece of optical material. If the internal refractive index of the optical material is inconsistent, it will cause the change of the transmitted wavefront, change the wave aberration of the optical system, and then affect the performance of the optical system. The optical non-uniformity of the magnitude will bring the wave aberration of the wavelength magnitude, so it is very urgent and necessary to detect the optical non-uniformity of the optical material with high precision.

The optical inhomogeneity of the optical material will directly lead to the change of the transmitted wavefront, so the optical inhomogeneity distribution of the optical material can be obtained by measuring the change of the wave aberration of the transmitted wavefront. Among the current detection methods, interferometry is widely used as a non-contact high-precision detection method. Currently, there are many methods for measuring non-uniformity in optical components. In 2003, Guo Peiji and others proposed three absolute measurement methods for measuring the non-uniformity of optical glass in the article "Absolute Measurement Technology for Optical Uniformity of Optical Glass", and developed a high-precision optical non-uniformity measurement method for optical glass materials. The measuring instrument realizes high-precision measurement of the non-uniformity of optical glass, but the instrument is expensive and cannot be widely used. In 2008, Wang Jun et al. proposed a new method in the article Measuring the Optical Uniformity of Parallel Flat Glass with a Short Coherent Light Source. Using the coherence of the short coherent light source, the high precision of the optical non-uniformity of the parallel flat plate was realized. However, due to the short-coherence characteristics of the short-coherent light source, the reference light and the test light must be at the position of zero optical path difference, which brings great difficulty to the adjustment of the experimental optical path.

Contents of the invention

The purpose of the present invention is to provide an optical non-uniformity measurement device and method based on a dual-wavelength Fizeau interferometer, which solves the problems of cumbersome steps and susceptibility to air disturbance in the traditional absolute measurement method.

The technical solution to realize the object of the present invention is: an optical non-uniformity measuring device based on a dual-wavelength Fizeau interferometer includes a first laser, a second laser, a folding mirror, a switching mirror, a beam expander, and a beam splitting prism , refracting mirror, collimating objective lens, reference plane mirror, aperture stop, imaging lens group, CCD detector, plane mirror to be tested; the common optical axis is set in order to refract mirror, collimating objective lens, reference plane mirror, and plane mirror to be tested, And the optical axis where the above-mentioned components are located is the first optical axis; the common optical axis is sequentially arranged with a dichroic prism, an aperture stop, an imaging lens group, and a CCD detector, and the optical axis where the above-mentioned components are located is the second optical axis, and the first The optical axis is parallel to the second optical axis; the common optical axis is provided with a folding mirror, a switching mirror, a beam expander, a dichroic prism, and a folding mirror in sequence, and the optical axis where the above-mentioned components are located is the third optical axis. The three optical axes are perpendicular to the first optical axis, and the switching mirror moves in a direction parallel to the first optical axis; all optical elements are coaxially equal in height relative to the base, that is, coaxially equal in height relative to the optical platform or the instrument base.

Wherein, the deflecting mirror, collimating objective lens, reference plane mirror, and the plane mirror to be tested are arranged in sequence along the optical path direction to form a test optical path; The wavelength of the laser is λ ₁ and the wavelength of the second laser is λ ₂ .

Move the switching mirror out of the third optical axis, and the laser emitted by the first laser passes through the deflection mirror and is reflected to the beam expander to realize the expansion of the beam. The objective lens becomes a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes a reference beam, and the other part is transmitted through the reference plane mirror into the plane mirror to be tested, reflected by the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror; The reference beam and the test beam combine on the back surface of the reference plane mirror, return to the folding mirror along the optical path, reflect to the beam splitting prism through the folding mirror, and focus on the aperture stop after being reflected by the beam splitting prism, and then pass through the imaging lens group to form an image on the _On the target surface of the CCD detector, the interference image corresponding to the wavelength λ1 is obtained.

Move the switching mirror into the third optical axis, and the laser emitted by the second laser passes through the switching mirror and is reflected to the beam expander to realize the expansion of the beam. , becomes a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes the reference beam, and the other part is transmitted through the reference plane mirror into the plane mirror to be tested, and is reflected by the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror; The light beam and the test beam combine on the back surface of the reference plane mirror, return to the folding mirror along the optical path, reflect to the beam splitting prism through the folding mirror, and focus on the aperture stop after being reflected by the beam splitting prism, and then pass through the imaging lens group to be imaged on the CCD _On the target surface of the detector, the interference image corresponding to the wavelength λ2 is obtained.

In the optical non-uniformity measurement device based on the dual-wavelength Fizeau interferometer, the reference plane mirror is connected to the PZT to realize phase shift measurement.

In the optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer, the center wavelength of the first laser is λ ₁ , the center wavelength of the second laser is λ ₂ , and λ ₁ ≠ λ ₂ . .

The measurement method of the optical non-uniformity measuring device based on the dual-wavelength Fizeau interferometer, the steps are as follows:

Step 1. Build an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer:

An optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer, including a first laser, a second laser, a folding mirror, a switching mirror, a beam expander, a beam splitting prism, a folding mirror, a collimating objective lens, and a reference Plane mirror, aperture stop, imaging lens group, CCD detector, plane mirror to be tested; the common optical axis is arranged in turn with a folding mirror, a collimating objective lens, a reference plane mirror, and a plane mirror to be tested, and the optical axis of the above-mentioned components is the first Optical axis; the common optical axis is provided with a dichroic prism, an aperture stop, an imaging lens group, and a CCD detector in sequence, and the optical axis where the above components are located is the second optical axis, and the first optical axis is parallel to the second optical axis; the common optical axis The axes are arranged in turn with a folding mirror, a switching mirror, a beam expander, a dichroic prism, and a folding mirror, and the optical axis where the above components are located is the third optical axis, the third optical axis is perpendicular to the first optical axis, and the switching The reflector moves along a direction parallel to the first optical axis; all optical elements are coaxially and equally high relative to the base, that is, coaxially and equally high relative to the optical platform or the instrument base.

The position of the plane mirror to be tested is adjusted so that the front surface of the plane mirror to be tested is perpendicular to the first optical axis, so as to realize the interference of the reflected light wave from the front surface of the plane mirror to be tested and the reflected light wave from the reference plane mirror.

Step 2, obtain the first phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ respectively:

Move the switching mirror out of the third optical axis, and the laser emitted by the first laser passes through the deflection mirror and is reflected to the beam expander to realize the expansion of the beam. The objective lens becomes a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes the reference beam, and the other part is transmitted through the reference plane mirror into the plane mirror to be tested, reflected by the front surface of the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror Plane mirror; the reference beam and the test beam combine on the back surface of the reference plane mirror, return to the folding mirror along the optical path, reflect to the beam splitting prism through the folding mirror, and focus on the aperture stop after being reflected by the beam splitting prism, and then pass through the imaging lens group, Imaging on the target surface _of the CCD detector to obtain the interference image corresponding to the wavelength λ1, the PZT drives the reference plane mirror for phase shifting, and obtains the phase shifting interferogram formed by the interference between the front surface of the plane mirror to be measured and the rear surface _of the reference plane mirror at the wavelength λ1.

Move the switching mirror into the third optical axis, and the laser emitted by the second laser passes through the switching mirror and is reflected to the beam expander to realize the expansion of the beam. , to become a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes the reference beam, and the other part is transmitted through the reference plane mirror into the plane mirror to be tested, reflected by the front surface of the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror The reference beam and the test beam combine on the rear surface of the reference plane mirror, return to the folding reflector along the optical path, reflect to the beam splitting prism through the bending mirror, reflect and focus on the aperture diaphragm through the beam splitting prism, and then pass through the imaging lens group to form an image _On the target surface of the CCD detector, the interference image corresponding to the wavelength λ2 is obtained, and the PZT drives the reference plane mirror for phase shifting to obtain the phase _- shifting interferogram formed by interference between the front surface of the plane mirror to be measured and the rear surface of the reference plane mirror at the wavelength λ2.

Step 3, adopt corresponding phase-shifting algorithm according to the phase shift interferogram ₅ corresponding to wavelength λ ₁ and λ ₂ for the first time, obtain the phase information corresponding to wavelength λ ₁ and λ ₂ respectively, and eliminate the phase information under the two wavelengths The constant term and the de-tilt term are processed to obtain the wavefront aberration at any point on the front surface of the plane mirror to be measured corresponding to the wavelengths λ ₁ and λ ₂

ΔW ₁₁ (x, y)=2n _a A(x, y)+2S(x, y)

ΔW ₂₁ (x, y)=2n _a A(x, y)+2S(x, y)

In the formula, ΔW ₁₁ (x, y) is the wavefront aberration corresponding to the first measurement wavelength λ ₁ , ΔW ₂₁ (x, y) is the wavefront aberration corresponding to the first measurement wavelength λ ₂ , A(x, y) is the surface deviation of the front surface of the plane mirror to be measured, S(x, y) is the systematic error of the interferometric system, and n _a is the air refractive index.

Step 4, obtain the phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ for the second time respectively:

Adjusting the pitch and inclination of the plane mirror to be measured, so that the rear surface of the plane mirror to be measured is perpendicular to the first optical axis, so that the light wave transmitted through the plane mirror to be measured and reflected by the back surface of the plane mirror to be measured interferes with the light wave reflected by the reference plane mirror;

Move the switching mirror out of the third optical axis, and the laser emitted by the first laser passes through the deflection mirror and is reflected to the beam expander to realize the expansion of the beam. The objective lens becomes a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes the reference beam, and the other part is transmitted through the reference plane mirror into the plane mirror to be tested, reflected by the back surface of the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror Plane mirror; the reference beam and the test beam combine on the back surface of the reference plane mirror, return to the folding mirror along the optical path, reflect to the beam splitting prism through the folding mirror, and focus on the aperture stop after being reflected by the beam splitting prism, and then pass through the imaging lens group, Imaging on the target surface _of the CCD detector to obtain the interference image corresponding to the wavelength λ1, the PZT drives the reference plane mirror for phase shifting, and obtains the phase shifting interferogram formed by the interference between the back surface of the plane mirror to be measured and the back surface _of the reference plane mirror at the wavelength λ1.

Move the switching mirror into the third optical axis, and the laser emitted by the second laser passes through the switching mirror and is reflected to the beam expander to realize the expansion of the beam. , to become a collimated wide beam, part of the collimated beam is reflected by the back surface of the reference plane mirror and becomes the reference beam, and the other part is transmitted through the reference plane into the plane mirror to be tested, reflected by the back surface of the plane mirror to be tested to become a test beam, and reflected to the reference plane mirror The reference beam and the test beam combine on the rear surface of the reference plane mirror, return to the folding reflector along the optical path, reflect to the beam splitting prism through the bending mirror, reflect and focus on the aperture diaphragm through the beam splitting prism, and then pass through the imaging lens group to form an image _On the target surface of the CCD detector, the interference image corresponding to the wavelength λ2 is obtained, and the PZT drives the reference plane mirror for phase shifting to obtain the phase _- shifting interferogram formed by interference between the back surface of the plane mirror to be measured and the back surface of the reference plane mirror at the wavelength λ2.

Step 5, according to the second phase shift interferogram corresponding to wavelength λ ₁ and λ ₂ , adopt corresponding phase shifting algorithm, obtain the phase information corresponding to wavelength λ ₁ and λ ₂ respectively, and carry out elimination constant to the phase information of two wavelengths Term, de-tilt term processing, obtain the wavefront aberration ΔW ₁₂ (x, y) at any point on the front surface of the plane mirror to be measured corresponding to the wavelength λ ₁ , and the wavefront at any point on the front surface of the plane mirror to be measured corresponding to λ ₂ Aberration ΔW ₂₂ (x, y):

ΔW ₁₂ (x,y)=2(n _a -n ₁₀ )A(x,y)+2n ₁₀ B(x,y)+2Δ(x,y)+2S(x,y)

ΔW ₂₂ (x,y)=2(n _a -n ₂₀ )A(x,y)+2n ₂₀ B(x,y)+2Δ(x,y)+2S(x,y)

In the formula, ΔW ₁₂ (x, y) is the wavefront aberration corresponding to the wavelength λ ₁ measured in the second step, ΔW ₂₂ (x, y) is the wavefront aberration corresponding to the wavelength λ ₂ measured in the second step, B(x , y) is the surface deviation of the rear surface of the plane mirror to be tested, n ₁₀ and n ₂₀ are the average refractive index of the plane mirror to be tested at wavelengths λ ₁ and λ ₂ respectively, and Δ(x, y) is due to the optical Wavefront deviation introduced by non-uniformity.

in,

Δ(x,y)=d ₀ ·Δn(x,y)

In the formula, d ₀ is the average thickness of the plane mirror to be tested, and Δn(x, y) is the optical non-uniformity to be measured.

Step 6. Obtain the optical non-uniformity distribution of the plane mirror to be tested

6-1) Solve the wavefront aberration difference ΔW ₁ (x, y) corresponding to the wavelength λ ₁ of the first and second measurement

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

6-2) Solve the wavefront aberration difference ΔW ₂ (x, y) corresponding to the first and second measurement wavelength λ ₂

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

in,

Δd(x,y)=B(x,y)-A(x,y)

The thickness d(x, y) of the plane mirror to be tested can be expressed as:

d(x,y)=d ₀ +Δd(x,y)

In the formula, d0 is the average thickness of the plane mirror to be tested, and Δd( _x , y) is the thickness variation caused by the shape change of the plane mirror to be tested.

The refractive index n ₁ (x, y) of the plane mirror to be measured for the wavelength λ ₁ and the refractive index n ₂ (x, y) for the wavelength λ ₂ can be expressed as:

n ₁ (x, y)=n ₁₀ +Δn ₁ (x,y)=n ₁₀ +Δn(x,y)

n ₂ (x,y)=n ₂₀ +Δn ₂ (x,y)=n ₂₀ +Δn(x,y)

In the formula, Δn ₁ (x, y) represents the optical non-uniformity of the plane mirror under test at wavelength λ ₁ , and Δn ₂ (x, y) represents the optical non-uniformity of the plane mirror under test at wavelength λ ₂ .

According to Lorentz's dispersion model, the Lorentz-Lorentz equation is obtained:

$\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; N\&alpha;</span>}$

In the formula, n is the refractive index of the material; N is the molecular or atomic number density inside the material; α is the average polarizability, which is related to the angular frequency of the incident light wave.

From the above formula, the relationship between the material refractive index n and its non-uniformity Δn and N can be analyzed and sorted out:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}}$

After derivation, we can get:

$\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 36</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

Further sorting can be obtained:

$\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

so:

$\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$

It can be concluded that the difference of optical non-uniformity in a certain wavelength range is much smaller than the optical non-uniformity itself, and the optical non-uniformity of optical materials or components can be approximately considered as Δn in a certain wavelength range using light waves of different wavelengths. =Δn ₁ =Δn ₂ .

Therefore, Δn(x, y) is the optical non-uniformity of the plane mirror to be measured.

6-3) Determine the optical non-uniformity Δn(x, y) of the plane mirror to be tested:

$\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

Compared with the prior art, the present invention has the advantages of: (1) the optical non-uniformity of the plane mirror to be tested is detected by the two-step measurement method of the dual-wavelength phase-shifting interferometer, and the standard reflector is not required to be introduced, and the standard reflector is completely eliminated. (2) The measurement steps are simple, which makes up for the shortcomings of the traditional absolute measurement method, which is cumbersome and susceptible to air disturbance; at the same time, it also has the advantages of the traditional absolute measurement, thereby reducing the impact on the measured plane mirror. And the accuracy requirements of the surface shape of the interferometer system.

Description of drawings

Fig. 1 is a schematic diagram of an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer.

Fig. 2 is a flow chart of a measurement method of an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer.

Fig. 3 is the corresponding wavefront aberration diagram under two wavelengths of the plane mirror front surface to be measured measured in the embodiment of the present invention, wherein (a) is the wavefront aberration diagram of the plane mirror front surface corresponding to be measured under the wavelength λ ₁ , (b) is the wavefront aberration diagram of the front surface of the plane mirror to be measured corresponding to the wavelength λ ₂ .

Fig. 4 is the corresponding wavefront aberration figure under two wavelengths of the plane mirror back surface to be measured measured in the embodiment of the present invention, wherein (a) is the wavefront aberration figure of the plane mirror back surface corresponding under the wavelength λ ₁ , (b) is the wavefront aberration figure of the corresponding plane mirror back surface to be measured under wavelength λ ₂ .

Fig. 5 is the optical non-uniformity distribution of the plane mirror to be tested measured in the embodiment of the present invention.

Fig. 6 is the optical non-uniformity distribution measured by the ZYGO interferometer of the plane mirror to be tested in the embodiment of the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

1, an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer includes a first laser 1, a second laser 2, a folding mirror 3, a switching mirror 4, a beam expander 5, and a beam splitting prism 6 , refracting mirror 7, collimating objective lens 8, reference plane mirror 9, aperture stop 10, imaging lens group 11, CCD detector 12, plane mirror 13 to be measured; common optical axis arranges refracting mirror 7, collimating objective lens in sequence 8. Reference plane mirror 9, plane mirror 13 to be measured, and the optical axis where the above-mentioned parts are located is the first optical axis; the common optical axis is provided with a dichroic prism 6, an aperture stop 10, an imaging lens group 11, and a CCD detector 12 in sequence, and The optical axis where the above-mentioned components are located is the second optical axis, and the first optical axis is parallel to the second optical axis; the common optical axis is sequentially provided with a folding mirror 3, a switching mirror 4, a beam expander mirror 5, a beam splitting prism 6, and a refracting mirror. Turn the mirror 7, and the optical axis where the above-mentioned components are located is the third optical axis, the third optical axis is perpendicular to the first optical axis, and the switching mirror 4 moves along a direction parallel to the first optical axis; all optical elements are relative to the base Coaxial contour, that is, the coaxial contour relative to the optical table or instrument base.

Wherein, deflection reflector 7, collimating objective lens 8, reference plane mirror 9, plane mirror 13 to be tested are arranged successively along the optical path direction, constitute the test optical path; , forming a reference optical path; the wavelength of the first laser 1 is λ ₁ , and the wavelength of the second laser 2 is λ ₂ .

Move the switching mirror 4 out of the third optical axis, and the laser light emitted by the first laser 1 passes through the deflection mirror 3 and is reflected to the beam expander mirror 5 to realize beam expansion. The mirror 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the rear surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 into the plane mirror 13 to be measured, and passed through the plane mirror 13 to be measured The reflection becomes the test beam, and is reflected to the reference plane mirror 9; the reference beam and the test beam combine on the rear surface of the reference plane mirror 9, return to the folding mirror 7 along the optical path, reflect to the beam splitting prism 6 through the folding mirror 7, and pass through the beam splitting prism 6 is reflected and focused at the aperture stop 10, then passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector 12 to obtain _an interference image corresponding to the wavelength λ1.

Move the switching mirror 4 into the third optical axis, and the laser light emitted by the second laser 2 passes through the switching mirror 4 and is reflected to the beam expander 5 to realize beam expansion. 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the rear surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 into the plane mirror 13 to be measured, and reflected by the plane mirror 13 to be measured Become the test beam, and reflect to the reference flat mirror 9; The reflection is focused at the aperture stop 10, then passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector ₁₂ to obtain an interference image corresponding to the wavelength λ2.

The optical non-uniformity measurement device based on the dual-wavelength Fizeau interferometer, the reference plane mirror 9 is connected with the PZT to realize the phase shift measurement.

In the optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer, the center wavelength of the first laser 1 is λ ₁ , the center wavelength of the second laser 2 is λ ₂ , and λ ₁ ≠ λ ₂ .

A method for measuring an optical non-uniformity measuring device based on a dual-wavelength Fizeau interferometer, the steps are as follows:

Step 1. Build an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer:

An optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer, including a first laser 1, a second laser 2, a folding mirror 3, a switching mirror 4, a beam expander 5, a beam splitting prism 6, and a folding mirror 7. Collimating objective lens 8, reference plane mirror 9, aperture stop 10, imaging lens group 11, CCD detector 12, plane mirror 13 to be measured; common optical axis is provided with folding reflector 7), collimating objective lens 8, reference plane mirror in sequence 9. The plane mirror 13 to be tested, and the optical axis where the above-mentioned components are located is the first optical axis; the common optical axis is sequentially arranged with a dichroic prism 6, an aperture stop 10, an imaging lens group 11, and a CCD detector 12, and the above-mentioned components are located The optical axis of the optical axis is the second optical axis, and the first optical axis is parallel to the second optical axis; the common optical axis is provided with a folding mirror 3, a switching mirror 4, a beam expander 5, a dichroic prism 6, and a folding mirror 7 in sequence , and the optical axis where the above-mentioned components are located is the third optical axis, the third optical axis is perpendicular to the first optical axis, and the switching mirror 4 moves in a direction parallel to the first optical axis; all optical elements are of the same height relative to the base , that is, the coaxial height relative to the optical table or the instrument base;

Adjusting the position of the plane mirror 13 to be measured so that the front surface of the plane mirror 13 to be measured is perpendicular to the first optical axis, so as to realize the interference of the reflected light waves from the front surface of the plane mirror 13 to be measured and the reflected light waves from the reference plane mirror 9;

Step 2, obtain the first phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ respectively:

Move the switching mirror 4 out of the third optical axis, and the laser light emitted by the first laser 1 passes through the deflection mirror 3 and is reflected to the beam expander mirror 5 to realize beam expansion. The mirror 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the rear surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 into the plane mirror 13 to be measured, and passed through the plane mirror 13 to be measured The front surface is reflected to become the test beam, and is reflected to the reference plane mirror 9; the reference beam and the test beam combine at the rear surface of the reference plane mirror 9, return to the folding reflector 7 along the optical path, reflect to the dichroic prism 6 through the folding mirror 7, and pass through The dichroic prism 6 is reflectively focused at the aperture stop 10, passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector 12 to obtain _an interference image corresponding to the wavelength λ1, and the PZT drives the reference plane mirror 9 to shift phase to obtain the wavelength The phase-shifting interferogram formed by the interference of the front surface of the flat mirror 13 to be measured and the rear surface of the reference flat mirror 9 under λ ₁ ;

Move the switching mirror 4 into the third optical axis, and the laser light emitted by the second laser 2 passes through the switching mirror 4 and is reflected to the beam expander 5 to realize beam expansion. 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the back surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 and enters the plane mirror 13 to be measured, and passes through the front of the plane mirror 13 to be measured The surface reflection becomes the test beam, and is reflected to the reference plane mirror 9; the reference beam and the test beam combine on the rear surface of the reference plane mirror 9, return to the folding mirror 7 along the optical path, reflect to the beam splitting prism 6 through the folding mirror 7, and pass through the beam splitting The prism 6 is reflected and focused at the aperture stop 10, then passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector 12 to obtain the interference image corresponding to the wavelength λ2, and the PZT drives the reference plane mirror ₉ to shift phase to obtain the wavelength λ _2. A phase-shifting interferogram formed by interference between the front surface of the plane mirror 13 to be measured and the rear surface of the reference plane mirror 9;

Step 3, according to the first phase shift interferogram corresponding to the wavelength λ ₁ and λ ₂ , adopt the corresponding phase shift algorithm to obtain the phase information corresponding to the wavelength λ ₁ and λ ₂ respectively, and eliminate the phase information under the two wavelengths Constant term, de-tilt term processing, obtain the wavefront aberration at any point on the front surface of the plane mirror 13 to be measured corresponding to wavelength λ ₁ and λ ₂

ΔW ₁₁ (x, y)=2n _a A(x, y)+2S(x, y)

ΔW ₂₁ (x, y)=2n _a A(x, y)+2S(x, y)

In the formula, ΔW ₁₁ (x, y) is the wavefront aberration corresponding to the first measurement wavelength λ ₁ , ΔW ₂₁ (x, y) is the wavefront aberration corresponding to the first measurement wavelength λ ₂ , A(x, y) is the surface deviation of the front surface of the plane mirror 13 to be measured, S (x, y) is the systematic error of the interferometric system, n _a is the air refractive index;

Step 4, obtain the phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ for the second time respectively:

Adjust the angle of the plane mirror 13 to be measured so that the back surface of the plane mirror 13 to be measured is perpendicular to the first optical axis, so that the light wave reflected by the plane mirror 13 to be measured and reflected by the plane mirror 13 back surface to be measured interferes with the light wave reflected by the plane mirror 9 to be measured;

Move the switching mirror 4 out of the third optical axis, and the laser light emitted by the first laser 1 passes through the deflection mirror 3 and is reflected to the beam expander mirror 5 to realize beam expansion. The mirror 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the rear surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 into the plane mirror 13 to be measured, and passed through the plane mirror 13 to be measured The back surface is reflected to become the test beam, and is reflected to the reference flat mirror 9; the reference beam and the test beam combine at the back surface of the reference flat mirror 9, return to the folding reflector 7 along the optical path, and are reflected to the dichroic prism 6 through the folding reflector 7, and pass through The dichroic prism 6 is reflectively focused at the aperture stop 10, passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector 12 to obtain _an interference image corresponding to the wavelength λ1, and the PZT drives the reference plane mirror 9 to shift phase to obtain the wavelength The phase-shifting interferogram formed by the interference of the back surface of the flat mirror 13 to be measured and the back surface of the reference flat mirror 9 at λ ₁ ;

Move the switching mirror 4 into the third optical axis, and the laser light emitted by the second laser 2 passes through the switching mirror 4 and is reflected to the beam expander 5 to realize beam expansion. 7 is reflected to the collimating objective lens 8 to become a collimated wide beam, part of the collimated beam becomes a reference beam after being reflected by the rear surface of the reference plane mirror 9, and the other part is transmitted through the reference plane mirror 9 into the plane mirror 13 to be measured, and after passing through the plane mirror 13 to be measured The surface reflection becomes the test beam, and is reflected to the reference plane mirror 9; the reference beam and the test beam combine on the rear surface of the reference plane mirror 9, return to the folding mirror 7 along the optical path, reflect to the beam splitting prism 6 through the folding mirror 7, and pass through the beam splitting The prism 6 is reflected and focused at the aperture stop 10, then passes through the imaging lens group 11, and is imaged on the target surface of the CCD detector 12 to obtain the interference image corresponding to the wavelength λ2, and the PZT drives the reference plane mirror ₉ to shift phase to obtain the wavelength λ _2. A phase-shifting interferogram formed by interference between the back surface of the plane mirror 13 to be measured and the back surface of the reference plane mirror 9;

Step 5, according to the second phase shift interferogram corresponding to wavelength λ ₁ and λ ₂ , adopt corresponding phase shifting algorithm, obtain the phase information corresponding to wavelength λ ₁ and λ ₂ respectively, and carry out elimination constant to the phase information of two wavelengths Term, de-tilt term processing, obtain wavelength λ ₁ and λ ₂ corresponding to the wavefront aberration at any point on the front surface of the plane mirror 13 to be measured:

ΔW ₁₂ (x,y)=2(n _a -n ₁₀ )A(x,y)+2n ₁₀ B(x,y)+2Δ(x,y)+2S(x,y)

ΔW ₂₂ (x,y)=2(n _a -n ₂₀ )A(x,y)+2n ₂₀ B(x,y)+2Δ(x,y)+2S(x,y)

In the formula, ΔW ₁₂ (x, y) is the wavefront aberration corresponding to the wavelength λ ₁ measured in the second step, ΔW ₂₂ (x, y) is the wavefront aberration corresponding to the wavelength λ ₂ measured in the second step, B(x , y) is the surface deviation of the rear surface of the plane mirror 13 to be measured, n ₁₀ and n ₂₀ are respectively the average refractive index of the plane mirror 13 to be measured at wavelengths λ ₁ and λ ₂ , and Δ(x, y) is due to the plane mirror to be measured The wavefront deviation introduced by the optical inhomogeneity of 13.

in,

Δ(x,y)=d ₀ ·Δn(x,y)

In the formula, d ₀ is the average thickness of the plane mirror 13 to be measured, and Δn(x, y) is the optical non-uniformity to be measured.

Step 6, obtain the optical non-uniformity distribution of the plane mirror 13 to be tested:

6-1) Solve the wavefront aberration difference ΔW ₁ (x, y) corresponding to the wavelength λ ₁ of the first and second measurement

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>$

6-2) Solve the wavefront aberration difference ΔW ₂ (x, y) corresponding to the first and second measurement wavelength λ ₂

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

in,

Δd(x,y)=B(x,y)-A(x,y)

The thickness d(x, y) of the plane mirror 13 to be measured can be expressed as:

d(x,y)=d ₀ +Δd(x,y)

In the formula, d ₀ is the average thickness of the plane mirror 13 to be tested, and Δd(x, y) is the thickness variation caused by the surface shape change of the plane mirror 13 to be tested.

The refractive index n ₁ (x, y) of the plane mirror 13 to be measured for the wavelength λ ₁ and the refractive index n ₂ (x, y) for the wavelength λ ₂ are respectively expressed as:

n ₁ (x, y)=n ₁₀ +Δn ₁ (x,y)=n ₁₀ +Δn(x,y)

n ₂ (x,y)=n ₂₀ +Δn ₂ (x,y)=n ₂₀ +Δn(x,y)

In the formula, Δn ₁ (x, y) represents the optical non-uniformity of the plane mirror 13 to be tested at the wavelength λ ₁ , and Δn ₂ (x, y) represents the optical non-uniformity of the plane mirror 13 to be tested at the wavelength λ ₂ .

According to Lorentz's dispersion model, the Lorentz-Lorentz equation is obtained:

$\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; N\&alpha;</span>}$

In the formula, n is the refractive index of the material; N is the molecular or atomic number density inside the material; α is the average polarizability, which is related to the angular frequency of the incident light wave;

From the above formula, the relationship between the material refractive index n and its non-uniformity Δn and N can be analyzed and sorted out:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}}$

After derivation, we can get:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 36</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

Further sorting can be obtained:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

so:

$\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$

It can be concluded that the difference of optical non-uniformity in a certain wavelength range is much smaller than the optical non-uniformity itself, and the optical non-uniformity of optical materials or components can be approximately considered as Δn in a certain wavelength range using light waves of different wavelengths. =Δn ₁ =Δn ₂ ; therefore Δn(x,y) is the optical non-uniformity of the plane mirror 13 to be measured.

6-3) Determine the optical non-uniformity Δn(x, y) of the plane mirror 13 to be tested:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

Embodiment one

An optical non-uniformity measuring device based on a dual-wavelength Fizeau interferometer, using a frequency-stabilized polarized helium-neon laser with a central wavelength of the first laser 1 of λ ₁ =632.8nm, an output power of 1.5mw, and an output spot diameter of φ1mm; The second laser 2 has a central wavelength of λ ₂ =532nm, a frequency-stabilized polarization semiconductor laser, a power of 1.5mw, and an output spot diameter of φ1mm. The plane mirror 13 to be tested is a quartz crystal, the diameter of the quartz crystal is D=110mm, the thickness d=21.70mm, and the wedge angle is 11'49''. The refractive index of the plane mirror 13 to be tested is n ₁ =1.4570 at the wavelength λ ₁ =632.8nm, and the refractive index at the wavelength λ ₂ =532nm is n ₂ =1.4607. The light beam is reflected by the deflection mirror 3, and the beam spot diameter is φ8mm after the laser beam expander 5, and then reflected by the deflection mirror 7, collimated by the collimating objective lens 8 to form a beam of parallel light, and passes through the reference plane mirror 9 The reference plane wavefront is obtained by reflection; the reference light wave is respectively reflected by the front and rear surfaces of the plane mirror 13 to be tested to obtain test wavefront data. After the reference beam interferes with the test beam, it is reflected by the folding mirror 7 and then reflected by the half-mirror 6 to converge at the pinhole 10, and is imaged on the CCD detector 12 through the imaging objective lens 11 to obtain an interference pattern.

The common optical axis is sequentially provided with a refracting mirror 7, a collimating objective lens 8, a reference plane mirror 9, and a plane mirror to be measured 13, and the optical axis where the above-mentioned components are located is the first optical axis; Diaphragm 10, imaging lens group 11, CCD detector 12, and the optical axis where the above-mentioned parts are located is the second optical axis, and the first optical axis is parallel to the second optical axis; Reflector 4, beam expander 5, dichroic prism 6, folding reflector 7, and the optical axis where the above-mentioned components are located is the third optical axis, the third optical axis is perpendicular to the first optical axis, and the switching reflector 4 is parallel to Move in the direction of the first optical axis; all optical components are coaxially and equally high relative to the base, that is, coaxially and equiheightly relative to the optical platform or the instrument base.

Wherein, deflection reflector 7, collimating objective lens 8, reference plane mirror 9, plane mirror 13 to be tested are arranged successively along the optical path direction, constitute the test optical path; , forming a reference optical path; the wavelength of the first laser 1 is λ ₁ , and the wavelength of the second laser 2 is λ ₂ .

In conjunction with Figure 2, a measurement method for an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer, the steps are as follows:

Step 1. Build an optical non-uniformity measurement device based on a dual-wavelength Fizeau interferometer.

Step 2, obtain the first phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ respectively:

Put the plane mirror 13 to be tested, adjust the plane mirror 13 to be tested so that the front surface of the plane mirror 13 to be tested is perpendicular to the first optical axis, and realize the interference of the reflected light waves from the front surface of the plane mirror 13 to be tested and the reflected light waves from the reference plane. Move the switching mirror 4 into the third optical axis, realize eight-step phase shift measurement by controlling the displacement of the PZT driving reference plane, and measure the phase shift interferogram corresponding to the wavelength λ ₂ =532nm; move the switching mirror 4 out of the third optical axis, Eight-step phase-shift measurement is realized by controlling the displacement of the reference plane driven by the PZT, and the phase-shift interferogram corresponding to the wavelength λ ₁ =632.8nm is measured.

Step 3, adopt eight-step phase-shifting algorithm and phase unwrapping technique, and carry out elimination constant term, elimination oblique term processing to phase information, thereby obtain the wave surface information ΔW ₁₁ (x, y) corresponding to wavelength λ ₁ and wavelength λ ₂ corresponding Wavefront information ΔW ₂₁ (x, y). The wavefront information includes surface shape information and systematic errors of the front surface of the plane mirror 13 to be measured. The wavefront information ΔW ₁₁ (x, y) corresponding to λ ₁ and the wavefront information ΔW ₂₁ (x, y) corresponding to λ ₂ are shown in FIG. 3 .

Step 4, obtain the phase-shifting interference image corresponding to wavelength λ ₁ and λ ₂ for the second time respectively:

The plane mirror 13 to be tested is adjusted so that the back surface of the plane mirror 13 to be tested is perpendicular to the first optical axis, so as to realize the interference of the reflected light waves from the back surface of the plane mirror 13 to be tested and the reflected light waves from the reference plane. Move the switching mirror 4 into the third optical axis, realize eight-step phase shift measurement by controlling the displacement of the PZT driving reference plane, and measure the phase shift interferogram corresponding to the wavelength λ ₂ =532nm; move the switching mirror 4 out of the third optical axis, The eight-step phase-shift measurement is realized by controlling the displacement of the reference plane driven by the PZT, and the phase-shift interferogram corresponding to the wavelength λ ₁ =632.8nm is measured.

Step 5, adopt eight-step phase-shifting algorithm and phase unwrapping technology, and carry out elimination constant term, elimination oblique term processing to phase information, thereby obtain the wavefront information ΔW ₁₂ (x, y) corresponding to wavelength λ ₁ and wavelength λ ₂ corresponding Wavefront information ΔW ₂₂ (x, y). The wavefront information includes the surface shape information of the rear surface of the plane mirror 13 to be measured, internal non-uniformity distribution and systematic error. The wavefront information ΔW ₁₂ (x, y) corresponding to λ ₁ and the wavefront information ΔW ₂₂ (x, y) corresponding to λ ₂ are shown in FIG. 4 .

Step 6: Obtain the optical non-uniformity distribution of the plane mirror to be tested:

6-1) Calculate the difference between the wavefront aberration corresponding to the wavelength λ ₁ of the first measurement and the second measurement:

ΔW ₁ (x, y) = (ΔW ₁₂ (x, y) - ΔW ₁₁ (x, y)) ÷ 2

=n ₁₀ [B(x,y)-A(x,y)]+d ₀ ·Δn(x,y)

=n ₁₀ Δd(x,y)+d ₀ ·Δn(x,y)

6-2) Calculate the difference between the wavefront aberration corresponding to the wavelength λ2 of the first measurement and the _second measurement:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}$

in,

Δd(x,y)=B(x,y)-A(x,y)

Then the thickness d(x, y) of the plane mirror 13 to be measured can be expressed as:

d(x,y)=d ₀ +Δd(x,y)

In the formula, d ₀ is the average thickness of the plane mirror 13 to be tested, and Δd(x, y) is the thickness change caused by the change of the surface shape of the plane mirror 13 to be tested.

According to Lorentz's dispersion model, the Lorentz-Lorentz equation is obtained:

$\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; N\&alpha;</span>}$

In the formula, n is the refractive index of the material; N is the molecular or atomic number density inside the material; α is the average polarizability, which is related to the angular frequency of the incident light wave;

From the above formula, the relationship between the material refractive index n and its non-uniformity Δn and N can be analyzed and sorted out:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}}$

After derivation, we can get:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 36</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N\&alpha;\&pi;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

Further sorting can be obtained:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;N</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}$

so:

$\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$

It can be concluded that the difference of optical non-uniformity in a certain wavelength range is much smaller than the optical non-uniformity itself, and the optical non-uniformity of optical materials or components can be approximately considered as Δn in a certain wavelength range using light waves of different wavelengths. =Δn ₁ =Δn ₂ ; therefore Δn(x,y) is the optical non-uniformity of the plane mirror 13 to be measured.

6-3) The optical non-uniformity Δn(x, y) of the plane mirror 13 to be measured can be calculated and obtained from the first measurement and the second measurement wavelength λ ₁ , λ ₂ corresponding to the wavefront aberration difference:

$\mathrm{<span\; class="notranslate">\; \&Delta;\; n</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; )</span>}$

The optical non-uniformity distribution of the recovered flat mirror 13 to be tested is shown in FIG. 5 .

The results of the optical non-uniformity of the quartz crystal measured by this method are compared with the results of the optical non-uniformity of the quartz crystal recovered by the ZYGO interferometer (as shown in Figure 6), and the distribution of optical non-uniformity is basically the same, which verifies the correctness of the algorithm performance and feasibility.

The invention adopts a two-step measurement method of a dual-wavelength phase-shifting interferometer to detect the optical non-uniformity of the plane mirror to be measured, without introducing a standard reflector, and completely eliminates the influence of the surface shape of the standard reflector on the measurement result; It overcomes the shortcomings of the traditional absolute measurement method, which are cumbersome and susceptible to air disturbance; at the same time, it also has the advantages of traditional absolute measurement, thereby reducing the accuracy requirements for the surface shape of the measured plane mirror and interferometer system.

Claims (4)

1. An optical non-uniformity measuring device based on a dual-wavelength Fizeau interferometer is characterized by comprising a first laser (1), a second laser (2), a turning reflector (3), a switching reflector (4), a beam expander (5), a beam splitter prism (6), a turning reflector (7), a collimating objective lens (8), a reference plane mirror (9), an aperture diaphragm (10), an imaging lens group (11), a CCD detector (12) and a plane mirror (13) to be measured; a deflection reflector (7), a collimating objective (8), a reference plane mirror (9) and a plane mirror (13) to be measured are sequentially arranged on a common optical axis, and the optical axis of the components is a first optical axis; a beam splitter prism (6), an aperture diaphragm (10), an imaging lens group (11) and a CCD detector (12) are sequentially arranged on a common optical axis, the optical axis of the components is a second optical axis, and the first optical axis is parallel to the second optical axis; the common optical axis is sequentially provided with a turning reflector (3), a switching reflector (4), a beam expander (5), a beam splitter prism (6) and a turning reflector (7), the optical axis of the components is a third optical axis, the third optical axis is vertical to the first optical axis, and the switching reflector (4) moves along the direction parallel to the first optical axis; all optical elements are coaxial and equal in height relative to the substrate, namely relative to the optical platform or the instrument base;

wherein, the turning reflector (7), the collimating objective (8), the reference plane mirror (9) and the plane mirror (13) to be tested are arranged in sequence along the direction of the light path to form a testing light path; the turning reflector (7), the collimating objective (8) and the reference plane mirror (9) are sequentially arranged along the direction of the light path to form a reference light path;

moving the switching reflector (4) out of a third optical axis, reflecting laser emitted by the first laser (1) to a beam expander (5) through a turning reflector (3) to expand beams, transmitting the laser through a beam splitter prism (6), reflecting the laser to a collimating objective lens (8) through a turning reflector (7) to form a collimated wide beam, reflecting part of the collimated beam to the rear surface of a reference plane mirror (9) to form a reference beam, transmitting the other part of the collimated beam to a plane mirror (13) to be tested through the reference plane mirror (9), reflecting the other part of the collimated beam to the reference plane mirror (9) to form a test beam, and reflecting the test beam to the reference plane mirror (9); the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₁A corresponding interference image;

the switching reflector (4) is shifted into a third optical axis, laser emitted by the second laser (2) is reflected to the beam expander (5) through the switching reflector (4) to realize beam expansion of the light beam, the light beam is transmitted by the beam splitter prism (6) and then reflected to the collimating objective lens (8) through the turning reflector (7) to form a collimated wide light beam, a part of the collimated light beam is reflected by the rear surface of the reference plane mirror (9) to form a reference light beam, and the other part of the collimated light beam is transmitted into the collimating objective lens (8) through the reference plane mirror (9)Entering a plane mirror (13) to be tested, reflecting the plane mirror (13) to be tested into a test beam and reflecting the test beam to a reference plane mirror (9); the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₂The corresponding interference image.

2. The dual wavelength fizeau interferometer based optical non-uniformity measurement device of claim 1, wherein: the reference plane mirror (9) is connected with PZT to realize phase shift measurement.

3. The dual wavelength fizeau interferometer based optical non-uniformity measurement device of claim 1 wherein: the first laser (1) has a central wavelength of λ₁The central wavelength of the second laser (2) is lambda₂And λ₁≠λ₂。

4. The method of claim 1 for measuring a dual wavelength fizeau interferometer based optical non-uniformity measurement, comprising the steps of:

step 1, building an optical non-uniformity measuring device based on a dual-wavelength Fizeau interferometer:

the optical non-uniformity measuring device based on the dual-wavelength Fizeau interferometer comprises a first laser (1), a second laser (2), a turning reflector (3), a switching reflector (4), a beam expander (5), a beam splitter prism (6), a turning reflector (7), a collimating objective (8), a reference plane mirror (9), an aperture diaphragm (10), an imaging lens group (11), a CCD detector (12) and a plane mirror (13) to be measured; a deflection reflector (7), a collimating objective (8), a reference plane mirror (9) and a plane mirror (13) to be measured are sequentially arranged on a common optical axis, and the optical axis of the components is a first optical axis; a beam splitter prism (6), an aperture diaphragm (10), an imaging lens group (11) and a CCD detector (12) are sequentially arranged on a common optical axis, the optical axis of the components is a second optical axis, and the first optical axis is parallel to the second optical axis; the common optical axis is sequentially provided with a turning reflector (3), a switching reflector (4), a beam expander (5), a beam splitter prism (6) and a turning reflector (7), the optical axis of the components is a third optical axis, the third optical axis is vertical to the first optical axis, and the switching reflector (4) moves along the direction parallel to the first optical axis; all optical elements are coaxial and equal in height relative to the substrate, namely relative to the optical platform or the instrument base;

adjusting the position of the plane mirror (13) to be measured to ensure that the front surface of the plane mirror (13) to be measured is vertical to the first optical axis, so as to realize the interference of the reflected light wave of the front surface of the plane mirror (13) to be measured and the reflected light wave of the reference plane mirror (9);

step 2, respectively obtaining the wavelength lambda₁And λ₂Corresponding first dephasing interference image:

moving the switching reflector (4) out of a third optical axis, reflecting laser emitted by the first laser (1) to a beam expander (5) through a turning reflector (3) to expand beams, transmitting the laser through a beam splitter prism (6), reflecting the laser to a collimating objective lens (8) through a turning reflector (7) to form a collimated wide beam, reflecting part of the collimated beam to the rear surface of a reference plane mirror (9) to form a reference beam, transmitting the other part of the collimated beam to a plane mirror (13) to be tested through the reference plane mirror (9), reflecting the other part of the collimated beam to the front surface of the plane mirror (13) to be tested to form a test beam, and reflecting the test beam to the reference plane mirror (9); the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₁Corresponding interference image, PZT drives the reference plane mirror (9) to shift the phase to obtain the wavelength lambda₁The front surface of the lower plane mirror (13) to be measured interferes with the back surface of the reference plane mirror (9) to form a phase-shifting interference pattern;

the switching reflector (4) is shifted into a third optical axis, laser emitted by the second laser (2) is reflected to the beam expander (5) through the switching reflector (4) to realize beam expansion of the light beam, and the light beam is transmitted by the beam splitter prism (6) and then reflected to the collimating objective lens (8) through the turning reflector (7)The collimated wide beam is formed, part of the collimated beam is reflected by the rear surface of the reference plane mirror (9) to form a reference beam, the other part of the collimated beam is transmitted into the plane mirror (13) to be tested through the reference plane mirror (9), and is reflected by the front surface of the plane mirror (13) to be tested to form a test beam and is reflected to the reference plane mirror (9); the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₂Corresponding interference image, PZT drives the reference plane mirror (9) to shift the phase to obtain the wavelength lambda₂The front surface of the lower plane mirror (13) to be measured interferes with the back surface of the reference plane mirror (9) to form a phase-shifting interference pattern;

step 3, according to the wavelength lambda₁And λ₂The corresponding first phase shift interferogram adopts the corresponding phase shift algorithm to obtain the wavelength lambda₁And λ₂Respectively corresponding phase information, and respectively performing constant term elimination and tilt term elimination on the phase information under two wavelengths to obtain wavelength lambda₁And λ₂Wave front aberration at any point of the front surface of the corresponding plane mirror (13) to be measured

ΔW₁₁(x,y)＝2n_aA(x,y)+2S(x,y)

ΔW₂₁(x,y)＝2n_aA(x,y)+2S(x,y)

In the formula,. DELTA.W₁₁(x, y) is the first measurement wavelength λ₁Corresponding wave front aberration, AW₂₁(x, y) is the first measurement wavelength λ₂Corresponding wavefront aberration, A (x, y) is the surface shape deviation of the front surface of the plane mirror (13) to be measured, S (x, y) is the system error of the interference measurement system, n_aThe refractive index of air is shown, and (x, y) are coordinates of any point on the front surface of the plane mirror (13) to be measured;

step 4, respectively obtaining the wavelength lambda₁And λ₂Corresponding second phase-shifting interference image:

adjusting the angle of the plane mirror (13) to be measured to ensure that the rear surface of the plane mirror (13) to be measured is perpendicular to the first optical axis, so that the light wave which penetrates through the plane mirror (13) to be measured and is reflected by the rear surface of the plane mirror (13) to be measured is interfered with the light wave reflected by the reference plane mirror (9);

moving the switching reflector (4) out of a third optical axis, reflecting laser emitted by the first laser (1) to a beam expander (5) through a turning reflector (3) to expand beams, transmitting the laser through a beam splitter prism (6), reflecting the laser to a collimating objective lens (8) through a turning reflector (7) to form a collimated wide beam, reflecting part of the collimated beam to the rear surface of a reference plane mirror (9) to form a reference beam, transmitting the other part of the collimated beam to a plane mirror (13) to be tested through the reference plane mirror (9), reflecting the other part of the collimated beam to the rear surface of the plane mirror (13) to be tested to form a test beam, and reflecting the test beam to the reference plane mirror (9); the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₁Corresponding interference image, PZT drives the reference plane mirror (9) to shift the phase to obtain the wavelength lambda₁The back surface of the lower plane mirror (13) to be measured interferes with the back surface of the reference plane mirror (9) to form a phase-shifting interference pattern;

the switching reflector (4) is moved into a third optical axis, laser emitted by the second laser (2) is reflected to a beam expanding mirror (5) through the switching reflector (4) to realize beam expanding of the light beam, the laser is transmitted by a light splitting prism (6) and then reflected to a collimating objective lens (8) through a turning reflector (7) to form a collimated wide light beam, a part of the collimated light beam is reflected by the rear surface of a reference plane mirror (9) to form a reference light beam, the other part of the collimated light beam is transmitted by the reference plane mirror (9) to enter a plane mirror (13) to be tested, is reflected by the rear surface of the plane mirror (13) to be tested to form a test light beam, and is reflected to the reference plane mirror (; the reference beam and the test beam are combined on the rear surface of a reference plane mirror (9), return to a turning reflector (7) along a light path, are reflected to a beam splitter prism (6) through the turning reflector (7), are reflected and focused at an aperture diaphragm (10) through the beam splitter prism (6), pass through an imaging lens group (11), and are imaged on a target surface of a CCD detector (12) to obtain a wavelength lambda₂Corresponding interference image, PZT drives the reference plane mirror (9) to shift the phase to obtain the wavelength lambda₂The back surface of the lower plane mirror (13) to be measured and the referenceA phase-shifting interference pattern formed by the interference of the rear surface of the plane mirror (9);

step 5, according to the wavelength lambda₁And λ₂The corresponding second phase shift interferogram adopts the corresponding phase shift algorithm to obtain the wavelength lambda₁And λ₂Respectively corresponding phase information, and performing constant term eliminating and tilt term eliminating treatment on the phase information of the two wavelengths to obtain wavelength lambda₁And λ₂Wave front aberration at any point of the front surface of the corresponding plane mirror (13) to be measured:

ΔW₁₂(x,y)＝2(n_a-n₁₀)A(x,y)+2n₁₀B(x,y)+2Δ(x,y)+2S(x,y)

ΔW₂₂(x,y)＝2(n_a-n₂₀)A(x,y)+2n₂₀B(x,y)+2Δ(x,y)+2S(x,y)

in the formula,. DELTA.W₁₂(x, y) is the second measurement wavelength λ₁Corresponding wave front aberration, AW₂₂(x, y) is the second measurement wavelength λ₂Corresponding wave front aberration, B (x, y) is the surface shape deviation of the back surface of the plane mirror (13) to be measured, n₁₀For the plane mirror (13) to be measured at the wavelength lambda₁Average refractive index of₂₀For the plane mirror (13) to be measured at the wavelength lambda₂The lower average refractive index, delta (x, y), is the wavefront deviation introduced by the optical non-uniformity of the plane mirror (13) to be measured;

wherein,

Δ(x,y)＝d₀·Δn(x,y)

in the formula (d)₀The average thickness of the plane mirror (13) to be measured, and the delta n (x, y) is the optical nonuniformity to be measured;

step 6, obtaining the optical non-uniformity distribution of the plane mirror (13) to be measured:

6-1) determining the first and second measurement wavelengths lambda₁Corresponding wave front aberration difference value DeltaW₁(x,y)

$\begin{array}{c}{\mathrm{\&Delta;W}}_1(x,y)=\frac{({\mathrm{\&Delta;W}}_{12}(x,y)-{\mathrm{\&Delta;W}}_{11}(x,y))}{2}\\ =n_{10}[B(x,y)-A(x,y)]+d_0\&CenterDot;\mathrm{\&Delta;n}(x,y)\\ =n_{10}\mathrm{\&Delta;d}(x,y)+d_0\&CenterDot;\mathrm{\&Delta;n}(x,y)\end{array}$

6-2) determining the first and second measurement wavelengths lambda₂Corresponding wave front aberration difference value DeltaW₂(x,y)

$\begin{array}{c}{\mathrm{\&Delta;W}}_2(x,y)=\frac{{\mathrm{\&Delta;W}}_{22}(x,y)-{\mathrm{\&Delta;W}}_{21}(x,y)}{2}\\ =n_{20}[B(x,y)-A(x,y)]+d_0\&CenterDot;\mathrm{\&Delta;n}(x,y)\\ =n_{20}\mathrm{\&Delta;d}(x,y)+d_0\&CenterDot;\mathrm{\&Delta;n}(x,y)\end{array}$

Wherein,

Δd(x,y)＝B(x,y)-A(x,y)

delta d (x, y) is the thickness variation caused by the deformation of the plane mirror surface (13) to be measured;

6-3) determining the optical nonuniformity delta n (x, y) of the plane mirror (13) to be measured:

$\mathrm{\&Delta;n}(x,y)=\frac{n_{20}\&CenterDot;{\mathrm{\&Delta;W}}_1(x,y)-n_{10}\&CenterDot;{\mathrm{\&Delta;W}}_2(x,y)}{d_0(n_{10}-n_{20})}.$