WO2016173382A1 - Method for measuring focal length and rotating angle using fabry-perot etalon - Google Patents

Abstract

A method for measuring a focal length and a rotating angle using a Fabry-Perot etalon, comprising: transmitting monochromatic light through a Fabry-Perot etalon (3) to generate a group of standard cone beams with regular and accurate cone angles θ_i, and reflecting the cone beams to a rotating mirror (5) by a half-transmitting and half-reflecting plane mirror (4); transmitting the beams, reflected by the rotating mirror (5), through the half-transmitting and half-reflecting plane mirror (4), passing through an objective lens (6), and forming a group of concentric circular rings (8) on the surface of an area array photoelectric device (7) located on a focal plane of the objective lens (6); selecting a plurality of point fields on each circular ring (8), and applying a photoelectric signal extreme value point location pixel coordinate fine-division method to a one-dimensional pixel in each point field; performing circle regression using a plurality of extreme value point location coordinates on the circular rings (8) to obtain a diameter D_i and standard deviation S_Di of each circle; obtaining f_i/W from D_i＝2(f_i/W)tanθ_i according to a distribution rule of the cone angles θ_i by means of the diameters D_i and standard deviations S_Di of the concentric circular rings (8) of the cone beams, f_i/W being a ratio, calculated by the diameter D_i of a single circle, of a focal length f_i to an average pixel interval W of the area array photoelectric device (7); obtaining a weighted average value (I) of f_i/W so as to obtain a measured focal length f; and rotating, when a rotating angle of the rotating mirror (5) is δθ, central axes of the cone beams, emitted to the objective lens, by an angle of 2δθ so as to make the centers of the concentric circular rings (8) to translate (II), and calculating the rotating angle δθ of the rotating mirror by means of a translation amount, taking W as a relative unit, of centers (x̅₀,y̅₀) of the concentric circular rings (8). The method can improve the measurement accuracy and precision of a focal length and a rotating angle.

Description

Method for measuring focal length and rotation angle by using Buri-Perot etalon Technical field

The present invention relates to the field of optical field and geometric quantity measurement, and more particularly to a method for measuring focal length and rotation angle using a Brib-Perot etalon.

Background technique

At present, in the principle scheme of the self-collimator for measuring small corners, the accuracy index is restricted by two aspects: (1) Most auto-collimators use the formula U _δθ =c ₀ +c ₁ δθ to measure the small rotation angle δθ In the extended uncertainty, the magnification term coefficient c ₁ is restricted by the focal length uncertainty U _f /f. The self-collimator is used to determine the calibration curve by using a small angle generator designed by the tangent relationship of length and length, although it can be used under certain conditions and under certain conditions.

It is less than 0.25% or even less than 1×10 ^-3 , but the variability error of the influence amount such as the stability during the verification period and the temperature during measurement restricts the actual measurement range and the use condition of the angle δθ. (2) The effective resolution and the Class A uncertainty associated with the repeatability standard deviation are limited by the pixel error of the line array (or area array) optoelectronic device. The extended uncertainty of δθ measured by a self-collimator is 0.05′′ (additive component), and the beam distribution pattern with better control is used, and about 40 consecutive pixel signals are used to make the pixel coordinate of the center position of the beam focus. The temperature of a line array (or area array) optoelectronic device pixel spacing W accuracy is high, but the deviation error of the equivalent geometric center of a single pixel and the photoelectric conversion rate error is often significant, such as some lines, The pixel photoelectric conversion rate of the area array optoelectronic device has an error limit of ±5%.

At present, the method or instrument for measuring the focal length f of the objective lens, the relative expansion uncertainty U _f /f is generally only about 0.25%. Although there have been reports in the literature that the U _f /f has reached the order of 10 ^-4 , it is questioned by other professional literatures because of its poor traceability.

The above disclosure of the present invention is only for assisting in understanding the inventive concept and technical solution of the present invention, and it does not necessarily belong to the prior art of the present patent application, and there is no clear evidence that the above content has been disclosed on the filing date of the present patent application. In the event that the above background art should not be used to evaluate the novelty and inventiveness of the present application.

Summary of the invention

SUMMARY OF THE INVENTION A primary object of the present invention is to provide a method for measuring focal length and rotation angle using a Brill-Perot etalon to solve the technical problems of the prior art which are less accurate.

To this end, the present invention provides a method for measuring a focal length using a Buri-Perot etalon, comprising the steps of: first step: transmitting a monochromatic light through a Fabry-Perot etalon to produce a a standard cone beam with a regular cone angle θ _i , the cone beam being reflected by the transflective mirror to the mirror, reflected by the mirror, transmitted through the semi-transparent mirror, and then passed through the objective lens at the objective lens The surface of the planar array optoelectronic device forms a set of concentric rings; the second step: selecting a plurality of dot fields on each ring to subdivide the one-dimensional cells in each dot field; the third step: The concentric annular diameter D _{i of the} cone beam and its standard deviation

Distribution rule by the cone angle θ _{i D i = 2 (f i /} W) tanθ i obtained _{f i / W, f i /} W is a single circle diameter D _i f _i calculated focal plane array and the photoelectric The ratio of the average pixel spacing W of the device, and then the weighted average of f _i /W

To obtain the measured focal length f.

In an embodiment, the second step specifically includes: first finding an approximate center point of the concentric ring

Then, at least three horizontal lines and at least three vertical lines are respectively formed near the approximate center point, so that the horizontal line and the vertical line intersect each ring to form two line segments, and the photoelectric signal extreme value points are obtained on each line segment. The coordinate value of the fractional W, which is divided by the average distance W of the pixels.

The invention also proposes a method for measuring the rotation angle by using the Brie-Perot etalon, comprising the following steps: First step: transmitting the monochromatic light through the Fabry-Perot etalon to generate a set of cone angles θ _i a regularly accurate standard cone beam, which is reflected by a transflective mirror to a rotating mirror, reflected by a rotating mirror, transmitted through a semi-transparent mirror, and then passed through an objective lens at a plane located at a focal plane of the objective lens Forming a set of concentric rings on the surface of the array optoelectronic device; second step: selecting a plurality of dot fields on each ring to subdivide the one-dimensional cells in each dot field; and third step: concentric by the cone beam Ring diameter D _i and its standard deviation

Distribution rule by the cone angle θ _{i D i = 2 (f i /} W) tanθ i obtained _{f i / W, f i /} W is a single circle diameter D _i f _i calculated focal plane array and the photoelectric The ratio of the average pixel spacing W of the device, and then the weighted average of f _i /W

Step 4: After the rotation angle δ0 is generated according to the rotating mirror, the central axis of the cone beam incident on the objective lens will be rotated through the 2δθ angle to make the center circle of the concentric ring

Through the center of the concentric ring

The translation amount is calculated as the rotation angle δθ of the mirror.

In an embodiment, the second step specifically includes: first finding an approximate center point of the concentric ring

Then, at least three horizontal lines and at least three vertical lines are respectively formed near the approximate center point, so that the horizontal line and the vertical line intersect each ring to form two line segments, and the photoelectric signal extreme value points are obtained in each line segment. The coordinate value of the fractional W, which is divided by the average distance W of the pixels.

Advantageous effects of the present invention in comparison with the prior art include: the usage of the Brie-Perot etalon of the present invention, which produces a set of standard cone beams with a regular cone angle as a reference beam, forming a series of concentric rings on the focal plane of the objective lens. Using the pixel subdivision technique of the area array optoelectronic device, multiple rings are acquired, and each circle takes a plurality of dot fields, and each dot field contains information of a plurality of pixels. Statistical calculations are performed on such a large number of large-scale pixel signals, so that the error effects of a single pixel are sufficiently randomized, and the accuracy and precision of the circular radius measurement and the concentric ring associated with the azimuth of the conical axis can be improved. The accuracy and precision of the center coordinates, that is, the accuracy and precision of the focal length and angle measurement.

DRAWINGS

Figure 1 is a structural view of an optical device used in the present invention;

2 is a flow chart of the use of the Buri-Perot etalon of the present invention to measure focal length and corner.

detailed description

The present invention will be further described in detail below in conjunction with the specific embodiments and with reference to the accompanying drawings. It is to be understood that the following description is only illustrative, and is not intended to limit the scope of the invention.

Non-limiting and non-exclusive embodiments will be described with reference to the drawings, wherein like reference numerals refer to the

The symbols, names and units of the quantity in the manual are shown in the table below.

The invention will be further described in detail below. As shown in FIG. 1 and FIG. 2, the light source 1 emits a monochromatic light having a known vacuum wavelength of λ ₀ through a Fabry-Perot etalon having a pitch of d, a spacer of quartz glass material, and a refractive index of n. 3. A set of conical beams (K _i = k ₀ -i, where i = 0, 1, 2, ..., i _max ) of the order of interference K _i are generated, and the half cone angle of the cone beam is θ _i . θ _i is the angle between the conical beam and the conical axis (referred to as the conical axis) perpendicular to the exit surface of the etalon. Here k ₀ is the integer interference order corresponding to the etalon exit beam angle θ _i minimum (i = 0), that is, the integer part of 2dn / λ ₀ = k ₀ + ε, ε is the fractional part of the order, 0 ≤ ε<1. The series of cone beams are reflected by the transflective mirror 4 toward the plane rotating mirror 5, and the object mirror 6 is reflected by the rotating mirror 5 and paralleled by the optical axis and the conical axis, on the focal plane of the objective lens 6 having the focal length f The surface of the array optoelectronic device 7 produces a series of concentric rings 8 of diameter D _i . A combined element 2 comprising a filter and a diffusing sheet can also be arranged between the light source 1 and the Fabry-Perot etalon 3.

When the cone axis is parallel to the optical axis of the objective lens, the relationship between M. Bonn and E. Wolfe's book Optics Principles (Science Press, 1978, P429-444) is available.

D _i ^{2 is} approximated as an order of difference. The approximate simplified linear equation with -i as the dependent variable and D _i ² as the independent variable is

Calculate the intercept by straight line fitting the above model

This is the approximation of ε. will

Substituting into the following formula, taking D _i ² as the dependent variable,

i is the weighted straight line fitting of the independent variable, and the model equation is

The ratio of the intercept b _{0 of the} equation (4) to the slope b ₁ is

Further, the value of the decimal ε can be obtained.

Calculate the standard deviation s _{ε of the} fraction _ε .

The above formula 5 reflects the law of diameter and cone angle distribution when the cone axis is parallel to the optical axis of the objective lens. Set the concentric axis parallel to the optical axis when the center of the concentric ring is

When the angle between the parallel beam of light and the optical axis of the objective lens is θ _l , the element parallel beams converge at the center of the spot (x _l , y _l ) of the focal plane to the center point

Radius

R _{l is} only related to the angle θ _l ,

In the spherical coordinate system centered on the focal plane, the z-axis is perpendicular to the focal plane. When the cone axis has an angle (φ _r , θ _r ) with the optical axis, the center of the concentric ring on the focal plane will translate to

The position of the polar coordinate origin and the polar coordinate is (φ _r , R _r ), R _r = (f / W) tan θ _r . Plane Cartesian coordinates are

The analytic geometry algorithm can be used to find the intersection of the ray and the focal plane parallel to the principal point of the object mirror and parallel to the cone axis.

According to the method of the least squares circle radius in Xiong Youlun's "Mathematical Methods of Precision Measurement" (China Metrology Press, 1989, P30), the circular equation regression can be used to obtain the diameter D _{i of} each circle.

And degrees of freedom v _i . In the regression of concentric rings, the bounds of the center of the circle should be used to find the average of the coordinates of the center of the circle.

And its standard deviation

A single-step formula for finding f _i /W from a single circle diameter D _i can be obtained from equation (1)

Available from (1)

By

Departure to assess the uncertainty of f _i /W. because

Ignore the influence of uncertainty of k ₀ , available

Find the weighted average of each f _i /W

And its standard deviation

The best estimate of the focal length is

The relative expansion uncertainty of f is

U _fad in the above equation is an estimate of the extended uncertainty of focusing. Determining U _fad is usually derived from the decision error limit of the minimum value of the focus point. t in the above formula is the t distribution factor. In the present invention, since the standard deviation of the coordinate after subdivision can be less than 0.1 W in the subdivision of the dot-domain coordinates, the half-width half-width HWHM of the annular stripe distribution line type can also be obtained at the same time, and the effective resolution can generally be less than 0.04. W. Since the objective lens aperture is usually larger than 30mm, W<5μm, it is not difficult to make the objective lens focal length f≥50mm.

When the plane rotation angle (φ _r , δθ) is turned, the cone axis of the cone beam incident on the objective lens is rotated by θ _r = 2δθ in the φ _r direction. The intersection point of the ray and the focal plane passing through the main point of the object mirror and parallel to the conical axis is

This is the center of the quasi-concentric ring after the rotation of the mirror. Set the center of the concentric ring when the cone axis is parallel to the optical axis of the objective lens.

The size and direction of the two-dimensional corner are determined by the two-dimensional coordinate translation of the center of the concentric ring. The displacement value of the center of the concentric ring on the focal plane before and after the rotation

The angle δθ is

The result of (8)

Substituting calculations, essentially using comparative measurement methods, the effects of two factors, focal length error and focus error, are eliminated. The one-dimensional corner of the rotating mirror is

When evaluating the standard uncertainty of the one-dimensional rotation angle δθ _X , only the following two component items need to be calculated:

Standard deviation

Usually |δθ _X |<0.05rad,

The standard deviation is approximately

Because of the independent component standard deviation synthesis

After a slight enlargement, the uncertainty U(δθ _X ) of δθ _X can be written as follows

Where t is the t distribution factor and v is the

The degree of freedom, v _eff is the effective degree of freedom calculated according to the case method in the Measurement Uncertainty Assessment Guide. The one-dimensional corner 0.2c ₀ effective resolution R _e (δθ _X)

R _e (δθ _X )≈0.2c ₀ (14)

The sum of the total corners U(δθ) is

The magnification component coefficient c _{1 is the} same as (13).

The invention will be further illustrated by a specific example. The measuring instrument and the condition parameters are: mercury lamp yellow line wavelength λ ₀₁ = 577.119 84 × 10 ^-6 mm, λ _{01 /} n = 576.959 81 × 10 ^-6 mm. The distance between the etalon d=2.032 056 2mm, the focal length of the objective lens

W≈0.004 70mm, k ₀ = 7044.

The following table lists the nine consecutive concentric annular parameters measured when the conical axis is parallel to the optical axis of the objective lens. Each circle is rounded with 20 points. The focal length and center-weighted average obtained from the last 8 sets of data are also listed in the table.

After adding the temperature measuring component, the error of the substrate temperature estimation of the area array imaging device can reach ±5 °C, and the maximum allowable error of the pixel average spacing W measured at the reference temperature is estimated to be ±3×10 ^-5 , and the relative uncertainty of W is estimated. About U _W / _W ≈ ⁵ × 10 ^-5 , the focus uncertainty is generally not greater than U _fad /f ≤ 1.7 × 10 ^-4

Available from (10)

This example shows that when the focal length f≈70mm is used, the relative expansion uncertainty of the focal length can be made smaller than 3×10 ^-4 .

Calculate the two components of one-dimensional angular measurement uncertainty U(δθ _X ) according to formula (13)

The sum component of U(δθ _X )

Magnification component coefficient

The effective resolution R _e (δθ _X ) ≈ 0.2c ₀ ≈ 0.04′′.

Additive component

It decreases as the focal length increases. It is not difficult to infer: when the embodiment

When increased to 500 mm, the sum component c ₀ will be reduced to below 0.05" and the effective resolution will be below 0.01".

Relative uncertainty of vacuum wavelength

The monochromatic light is transmitted through the Fabry-Perot etalon, producing a set of standard cone beams of interference order of integer K _i , cone angle θ _i . The beam is reflected by the transflective mirror to the plane mirror, reflected by the plane mirror, and then passed through the objective lens with focal length f to produce a set of concentric rings on the surface of the array optoelectronic device located at its focal plane. By the center of the concentric ring

The displacement amount calculates the rotation angle δθ of the mirror.

The stability of the Fabry-Perot etalon of the quartz spacer and the accuracy of the beam angle law ensure the traceability of the measured angle δθ method, and the extended uncertainty of the angle measurement U _δθ = The condition of the magnification component coefficient c ₁ ≤ 2 × 10 ^{-4 in} c ₀ + c ₁ δθ creates a condition. Producing a series of tilt angle laws The known standard beam with high accuracy and high central axis repeatability can reduce the influence of the focal length uncertainty U _f /f on the uncertainty U _δθ of the angle δθ, in order to reduce U _δθ =c The magnitude of the two components in ₀ + c ₁ δθ creates conditions.

Select a plurality of dot fields on each ring according to a certain rule. The specific method is: to find the approximate center point of the concentric ring signal collected by the array photoelectric device.

Then make 3 to 5 or more horizontal lines near the approximate center of the circle, for example

±0.6B, ±B, and then make 3 to 5 or more vertical lines, for example

±0.6B, ±B. Here W is the average pixel spacing. It is required to make B < 2% D ₁₀ , and D ₁₀ is the eleventh ring diameter from the inside to the outside i = 10. Usually there is D ₁₀ >1600W. For example, when B=30, if the center of the circle is at the origin of the coordinate, the coordinate value of the undivided point on the circle is changed from 30W to (30±0.5)W, and the maximum change of the radius of the circle of the inner circle D ₂ ≈720W does not exceed ±0.042W, which is the reason why the one-dimensional photoelectric signal extreme value pixel pixel coordinate subdivision method can be used to simplify the processing of two-dimensional area array information at high speed, because the length of the oblique angle of the acute angle triangle is changed to the length of the short right angle side. Not sensitive.

The subdivision method is divided into three steps for the calculation of a certain dimension of the pixel in each point domain (on the line segment).

(1) Delete too small signals to reduce noise and simplify calculation. For successive pixel signals on the line segment (or the two cell corners on both sides of the ±45 degree line segment coincide with the signal mean of the symmetric pixels on the line segment), the peak value of the pixel signal is I _M , leaving both sides of the peak pixel 8 to 18 consecutive pixels; function of these pixel signals I _i

For the dependent variable, the quadratic regression is performed with the pixel number i (or the corresponding value) and its square i ² as the independent variables; the basic model is Z _i =b ₀ +b ₁ i+b ₂ i ² .

(2) Harmonic weighted regression. Since the standard deviation of the estimate due to the variable Z _i

Large change, the conventional weight factor is

Weighted quadratic regression using harmonics, the relative weight factor of Z _i is taken

Here, α is a number from 0.5 to 1.8, and β is a number from -1 to 0. When the etalon has a small fineness (α, β), the typical value is (1, 0), and when the fineness is large, the typical value is (1, -1), which is between the equal weight factor (0, 0) and the general weighting factor ( Between 2, -1). The regression equation is

(3) Calculate the coordinates of the sub-divided extreme value points from the regression coefficients b ₁ and b ₂

In the dot field parallel to the Y axis, the integer pixel coordinate x _j and the subdivided coordinate y _j ^* are determined in a similar manner. For a plurality of rings (generally not less than 8), the same ring is not less than 24 Coordinate values of points (x _j ^* , y _j ), (x _j , y _j ^* ), and the regression of a circular equation with concentric constraints, and find the diameter D _{i of} each concentric ring and its standard deviation

Simultaneously find the average of the center coordinates

And its standard deviation

The signal processing method in the dot field (on line segment) of ±45 degrees is similar to the above, and can be regarded as new parallel data in the axial direction after the coordinates are rotated by 45 degrees. The distance between adjacent pixels where the diagonal line and the line segment coincide is

If an equivalent pixel of a half-integer number is inserted, the photoelectric signal takes the average of the signal angles of the two symmetric pixels on both sides of the line segment that coincide with the pixel corner, which will make the equivalent image on the line of ±45 degrees. The number of elements is doubled, and the spacing of adjacent equivalent pixels is reduced to

The coordinates of the subdivided peaks on the degree line segment are calculated by the plane geometry, converted into values in the Cartesian coordinate system, and then participate in the circle regression calculation.

Since 50% of the point coordinate values are calculated by subdivision using multiple adjacent pixel magnitudes, the number of original pixels participating in the coordinate subdivision calculation is calculated by using multiple circles and each circle using multiple points for regression calculation. More than 1.5 × 10 ³ , and these pixels are scattered in a large range of area array optoelectronic devices, the geometric error and photoelectric conversion error of a single pixel can be fully randomized, so that the standard deviation of the center coordinates after statistical calculation

Reduced to below 0.02W, also makes the standard deviation of the circle diameter D ²

Reduce to less than 1/3 of the subdivision.

The Buri-Perot etalon of the present invention produces a set of conical beams of a cone angle standard as a reference beam, forming a series of concentric rings on the focal plane of the objective lens. The pixel subdivision technique of the area array optoelectronic device is used to subdivide the extreme value point coordinates of the photoelectric signal, and multiple rings are collected, and each circle takes a plurality of dot fields, and each dot field contains information of a plurality of pixels. Statistical calculations are performed on such a large number of large-scale pixel signals, so that the error effects of a single pixel are sufficiently randomized, and the accuracy and precision of the circular radius measurement and the concentric ring associated with the azimuth of the conical axis can be improved. The accuracy and precision of the center coordinates, that is, the accuracy and precision of the focal length and angle measurement.

The angular magnitude in the present invention is traced back to the spectral lamp monochromatic light wavelength λ ₀ and the etalon interval d, known

It can be conveniently measured and controlled by fractional weight to make U _d /d _≤ 5 × 10 ^-6 , so that the small angle measuring instrument adopting the method of the invention has the advantages of traceability and convenience for calibration or verification.

The uncertainty of the traceable focal length measurement is reduced to less than 40% than the uncertainty U _{f /f} ≈ 2.5 × 10 ^{-3 of the} typical method. The photoelectric signal extreme value point pixel coordinate subdivision technology also creates conditions for reducing the focus error limit and focusing automation.

In the past, the measurement linearity and angle measurement accuracy of most photoelectric autocollimators are limited by the focal length uncertainty of the objective lens. In the present invention, the equations (8) to (9) avoid the difficulty with the comparative measurement method. The coefficient of magnification component in the traceable corner uncertainty is reduced to less than 2/5 compared to conventional instruments. It is also one of the advantages of the present invention to achieve simultaneous measurement of two-dimensional corners with a single optical system and a single area array photo-receiving device.

After using the Brie-Perot etalon and the signal extreme point pixel coordinate subdivision technology to accurately determine the focal length, the one-dimensional linear CCD device is used to measure the deflection angle of the one-dimensional mirror reflected beam, which can achieve nonlinear relative error. Quasi-static or dynamic measurement of high effective resolution limited to a beam deflection angle of less than 0.01%.

Those skilled in the art will recognize that many variations are possible in the above description, and thus the embodiments are only used to describe one or more specific embodiments.

While the invention has been described and described with reference to the embodiments of the embodiments In addition, many modifications may be made to adapt a particular situation to the teachings of the invention, without departing from the inventive concept. Therefore, the invention is not limited to the specific embodiments disclosed herein, but the invention may also include all embodiments and equivalents thereof.

Claims (6)

1. A method for measuring focal length by using a Brie-Perot etalon, comprising: the following steps:

   The first step: using a monochromatic light to transmit through the Fabry-Perot etalon, producing a set of standard cone beams with a regular cone angle θ _i , the cone beam being reflected by the transflective mirror to the mirror, and rotated After mirror reflection, through the half mirror, and then through the objective lens, a set of concentric rings are formed on the surface of the array optoelectronic device located at the focal plane of the objective lens;

   Step 2: Select multiple dot fields on each ring to subdivide the one-dimensional cells in each dot field;

   The third step: the concentric annular diameter D _{i of} the cone beam and its standard deviation

   

   Distribution by the cone angle θ _{i D i = 2 (f i /} W) tanθ i obtained _{f i / W, f i /} W is a single circle diameter D _i f _i calculated focal plane array of the photovoltaic device The ratio of the average pixel spacing W, and then the weighted average of f _i /W

   

   To obtain the measured focal length f.
2. The method of measuring a focal length according to claim 1, wherein the second step comprises: first finding an approximate center point of the concentric ring

   

   At least three horizontal lines, at least three vertical lines, and at least three parallel oblique lines having an azimuth angle of ±45 degrees are respectively formed near the approximate center point, so that each horizontal line, vertical line or ±45 degree line and each The intersecting rings form two line segments, and the photoelectric signal extreme value pixel pixel coordinate subdivision method is used on each line segment to find the average spacing W of the pixels with decimals or

   

   The coordinate value of the unit.
3. The method of measuring a focal length according to claim 2, wherein said photoelectric signal extreme value pixel bit coordinate subdivision method comprises the steps of: successive pixel signals on a line segment, or ±45 degree line segments. The two pixel corner points coincide with the signal mean of the symmetric pixel on the line segment, and the peak value of the pixel signal is I _M , which retains 8 to 18 consecutive pixels on both sides of the peak pixel, including peaks; I _i function

   

   Quadratic regression for the dependent variable, with the cell number i or the corresponding value and its square i ² as the independent variable; due to the standard deviation estimate of Z _i

   

   Large change, using weighted quadratic regression of harmonics, the relative weight factor of Z _i

   

   Here, α is a number from 0.5 to 1.8, and β is a number from -1 to 0. When the etalon has a small fineness (α, β), the typical value is (1, 0), and when the fineness is large, the typical value is (1, -1), which is between the equal weight factor (0, 0) and the general weighting factor ( Between 2, -1). The regression equation is

   

   After the subdivision, the extreme point coordinates are

   
4. A method for measuring a corner by using a Brie-Perot etalon, comprising: the following steps:

   The first step: using a monochromatic light to transmit through the Fabry-Perot etalon, producing a set of standard cone beams with a regular cone angle θ _i , the cone beam being reflected by the transflective mirror to the mirror, and rotated After mirror reflection, through the half mirror, and then through the objective lens, a set of concentric rings are formed on the surface of the array optoelectronic device located at the focal plane of the objective lens;

   Step 2: Select multiple dot fields on each ring to subdivide the one-dimensional cells in each dot field;

   The third step: the concentric annular diameter D _{i of} the cone beam and its standard deviation

   

   Distribution by the cone angle θ _{i D i = 2 (f i /} W) tanθ i obtained _{f i / W, f i /} W is a single circle diameter D _i f _i calculated focal plane array of the photovoltaic device The ratio of the average pixel spacing W, and then the weighted average of f _i /W

   

   Step 4: After the rotation angle δ0 is generated according to the rotating mirror, the central axis of the cone beam incident on the objective lens will be rotated through the 2δ0 angle to make the center circle of the concentric ring

   

   Through the center of the concentric ring

   

   The translation amount is calculated as the rotation angle δθ of the mirror.
5. The method of measuring a corner according to claim 4, wherein the second step comprises: first finding an approximate center point of the concentric ring

   

   At least three horizontal lines, at least three vertical lines, and at least three parallel oblique lines having an azimuth angle of ±45 degrees are respectively formed near the approximate center point, so that each horizontal line, vertical line or ±45 degree line and each The intersecting rings form two line segments, and the photoelectric signal extreme value pixel pixel coordinate subdivision method is used on each line segment to find the average spacing W of the pixels with decimals or

   

   The coordinate value of the unit.
6. The method for measuring a corner according to claim 5, wherein said photoelectric signal extreme point pixel coordinate subdivision method comprises the following steps: a continuous pixel signal on a line segment, or a ±45 degree line segment. The two pixel corner points coincide with the signal mean of the symmetric pixel on the line segment, and the peak value of the pixel signal is I _M , which retains 8 to 18 consecutive pixels on both sides of the peak pixel, including peaks; I _i function

   

   Quadratic regression for the dependent variable, with the cell number i or the corresponding value and its square i ² as independent variables; due to the standard deviation estimate of Z _i

   

   Large change, using weighted quadratic regression of harmonics, the relative weight factor of Z _i

   

   Here, α is a number from 0.5 to 1.8, and β is a number from -1 to 0. When the etalon has a small fineness (α, β), the typical value is (1, 0), and when the fineness is large, the typical value is (1, -1), which is between the equal weight factor (0, 0) and the general weighting factor ( Between 2, -1). The regression equation is

   

   After the subdivision, the extreme point coordinates are

   

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