CN106768892A - Free surface lens corrugated joining method based on Hartmann shark wavefront sensor - Google Patents

Abstract

The invention discloses a kind of free surface lens corrugated joining method based on Hartmann shark wavefront sensor.The present invention obtains the W of full wafer free surface lens using Hartmann shark wavefront sensor measurement₁Region, obtains W₁First five term coefficient of region wavefront zernike polynomial, then move a certain distance measurement W₂Region, obtains W₂First five term coefficient of region wavefront zernike polynomial.Selection W₁、W₂Three points of overlapping region, by W₁、W₂The wave front aberration in region is showed with zernike polynomial, and solution obtains splicing parameter, and the Ze Nike expansions that the splicing parameter is substituted into Wave-front phase can be by W₁、W₂The wave front aberration in region shows.The present invention is realized the method spliced using wavefront and obtains the function of full wafer free surface lens wave front aberration, with measurement is quick, simple operation and other advantages.

Description

Wavefront splicing method for free-form lens based on Hartmann-Shack wavefront sensor

technical field

The invention relates to the technical field of wavefront splicing, in particular to a wavefront splicing method for a free-form lens based on a Hartmann-Shack wavefront sensor.

Background technique

With the development of free-form surface technology, the application of free-form surface lenses using free-form surface processing technology is becoming more and more extensive. As a representative of free-form surface lenses, progressive multi-focal lenses occupy an important position in the high-end lens market. At present, in developed countries such as Europe and the United States, progressive lenses have already occupied a relatively large market proportion. The sales volume of progressive lenses in the Japanese market accounts for 21% of the glasses market, and the proportion in the US market has also reached 60%.

The detection of traditional lenses has already matured, but for the detection of free-form lenses, there is currently no corresponding unified standard in the world, which has greatly hindered the development of the free-form lens industry. Nowadays, the method of evaluating the free-form surface lens by wavefront aberration has attracted more and more attention, but due to the limitation of the measurement size of the Hartmann-Shack wavefront sensor of the instrument for measuring wavefront aberration, it is difficult to realize the wavefront aberration of the entire lens. Measurement.

Contents of the invention

In order to solve the above problems, the present invention provides a wave-front splicing method for free-form mirrors based on a Hartmann-Shack wave-front sensor.

The present invention comprises the following steps:

Step 1: Use the Hartmann-Shack wavefront sensor to measure the W ₁ region of the entire free-form surface lens, get the first five coefficients of the wavefront Zernike polynomial in the W ₁ region, and then move a certain distance to measure the W ₂ region to get W _2. The first five coefficients of the wavefront Zernike polynomials; at the point in the overlapping area, the first five coefficients of the Zernike polynomials of the two measurements should be equal in theory, but due to the existence of measurement errors, the measurement results cannot be completely equal.

The usual Zernike expansion for the wavefront phase is:

The first five expansions are:

The phase distribution of the W ₁ region As a reference, the moving distance is x ₀ , y ₀ , and the phase distribution of W ₂ area is Measurements using the Shaker-Hartmann wavefront sensor are:

Formula (2) is derived separately for x and y:

Step 2: Select three points (x ₁ ,y ₁ ), (x ₂ ,y ₂ ), (x ₃ ,y ₃ ) in the overlapping area of W ₁ and W ₂ , and the three points in the area of W ₁ correspond to x, The wavefront slopes on the y-axis are (c ₁ ,d ₁ ), (c ₂ ,d ₂ ), (c ₃ ,d ₃ ), and the three points in the W ₂ area correspond to the wavefronts on the x and y-axes The slopes are (c' ₁ ,d ₁ ), (c' ₂ ,d ₂ ), (c' ₃ ,d ₃ ), respectively. Express the wavefront aberration in the regions W ₁ and W ₂ with Zernike polynomials, and write equation (3) in matrix form:

For the above formula (4), there can be a unique solution (a ₁ , a ₂ , a ₃ , a ₄ , a ₅ ), which is the splicing parameter. Substituting this splicing parameter into the formula (1) can make the W ₁ and W ₂ areas Wavefront aberrations are shown.

Step 3: For n points (x ₁ ,y ₁ )...(x _n ,y _n ) in the overlapping area of W ₁ and W ₂ :

It is expressed in the form of residual error as:

When measuring with equal precision, the matrix form with the smallest sum of squared residual errors is:

in:

When measuring with equal precision, the normal equation in matrix form is:

Obtain the solution of the normal equation according to (6), the matrix expression of the first five coefficients of the Zernike polynomial:

Then, the wavefront aberrations in W ₁ area and W ₂ area are:

By repeating step 1 and step 2, the wavefront splicing of the entire free-form lens can be realized, and the expression of the Zernike polynomial of the wavefront phase of the entire free-form lens can be obtained.

The beneficial effects of the present invention are: based on the Hartmann-Shack wavefront sensor wavefront splicing method for free-form mirrors, compared with the prior art, the present invention solves the limited measurement size of the existing Hartmann-Shack wavefront sensor, which cannot be realized For the measurement of the wavefront aberration of the entire free-form lens, the function of obtaining the wavefront aberration of the entire free-form lens by using the method of wavefront splicing has been realized, which has the advantages of fast measurement and simple operation.

Description of drawings

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

Fig. 1 is a schematic diagram of splicing detection of adjacent sub-apertures W ₁ and W ₂ in the present invention;

detailed description

In order to make the technical means, creative features, goals and effects achieved by the present invention easy to understand, the present invention will be further described below in conjunction with specific illustrations. It should be noted that, in the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

As shown in Figure 1, the wavefront stitching method for free-form mirrors based on the Hartmann-Shack wavefront sensor includes the following steps:

Step 1: Use the Hartmann-Shack wavefront sensor to measure the W _{1 area of the entire free-form surface lens, and obtain the first five coefficients of the wavefront Zernike polynomial in the W 1 area} , and then move a certain distance to measure the W ₂ area to obtain The first five coefficients of the wavefront Zernike polynomial in the W ₂ area; at points in the overlapping area, the first five coefficients of the Zernike polynomials of the two measurements should be equal in theory, but due to the existence of measurement errors, the measurement results are impossible exactly equal.

The usual Zernike expansion for the wavefront phase is:

The first five expansions are:

The phase distribution of the W ₁ region As a reference, the moving distance is x ₀ , y ₀ , and the phase distribution of W ₂ area is Measurements using the Shaker-Hartmann wavefront sensor are:

Formula (2) is derived separately for x and y:

Step 2: Select three points (x ₁ ,y ₁ ), (x ₂ ,y ₂ ), (x ₃ ,y ₃ ) in the overlapping area of W ₁ and W ₂ , and the three points in the area of W ₁ correspond to x, The wavefront slopes on the y-axis are (c ₁ ,d ₁ ), (c ₂ ,d ₂ ), (c ₃ ,d ₃ ), and the three points in the W ₂ area correspond to the wavefronts on the x and y-axes The slopes are (c' ₁ ,d ₁ ), (c' ₂ ,d ₂ ), (c' ₃ ,d ₃ ), respectively. Express the wavefront aberration in the regions W ₁ and W ₂ with Zernike polynomials, and write equation (3) in matrix form:

For the above formula (4), there can be a unique solution (a ₁ , a ₂ , a ₃ , a ₄ , a ₅ ), which is the splicing parameter. Substituting this splicing parameter into the formula (1) can make the W ₁ and W ₂ areas Wavefront aberrations are shown.

Step 3: For n points (x ₁ ,y ₁ )...(x _n ,y _n ) in the overlapping area of W ₁ and W ₂ :

It is expressed in the form of residual error as:

When measuring with equal precision, the matrix form with the smallest sum of squared residual errors is:

in:

When measuring with equal precision, the normal equation in matrix form is:

Obtain the solution of the normal equation according to (6), the matrix expression of the first five coefficients of the Zernike polynomial:

Then, the wavefront aberrations in W ₁ area and W ₂ area are:

Repeat steps 1 and 2 to realize the wavefront splicing of the entire free-form lens, and obtain the expression of the Zernike polynomial of the wavefront phase of the entire free-form lens, that is, a small piece of wavefront aberration can be obtained by the sensor once measured , the wavefront aberration of the entire lens is obtained by splicing.

Claims (1)

1. the free surface lens corrugated joining method of Shack-Hartmann wavefront sensor is based on, it is characterised in that the method bag Include following steps：

Step one：The W of full wafer free surface lens is obtained using Shack-Hartmann wavefront sensor measurement₁Region, obtains W₁Area First five term coefficient of domain wavefront zernike polynomial, then move a certain distance measurement W₂Region, obtains W₂Region wavefront Ze Nike Polynomial first five term coefficient；Point in the region for overlapping, first five term system for the zernike polynomial for measuring twice in theory Number should be equal, but due to the presence of measurement error, measurement result can not possibly be essentially equal；

The conventional Ze Nike expansions of Wave-front phase are：

First five items expansion is：

With W₁The phase distribution in regionOn the basis of, mobile distance is x₀、y₀, W₂The phase distribution in region isHad using Shack Hartmann wave front sensor measurement：

(2) to x, derivation is obtained y formula respectively：

Step 2：Selection W₁、W₂Three point (x of overlapping region₁,y₁)、(x₂,y₂)、(x₂,y₃), W₁Three points correspondence in region X, the wavefront slope in y-axis is respectively (c₁,d₁)、(c₂,d₂)、(c₃,d₃), W₂Three points correspondence x in region, the ripple in y-axis Front slope distinguishes (c '₁,d₁)、(c’₂,d₂)、(c’₃,d₃)；By W₁、W₂The wave front aberration in region is represented with zernike polynomial Come, have (3) formula is write as matrix form：

$\left(\begin{array}{ccccc}1& 0& 4x_1& 2x_1& 2y_1\\ 0& 1& 4y_1& -2y_1& 2x_1\\ 1& 0& 4x_2& 2x_2& 2y_2\\ 0& 1& 4y_2& -2y_2& 2x_2\\ 1& 0& 4x_3& 2x_3& 2y_3\end{array}\right)\left(\begin{array}{c}{a}_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right)=\left(\begin{array}{c}{c_1}^{\′}-c_1\\ {d_1}^{\′}-d_1\\ {c_2}^{\′}-c_2\\ {d_2}^{\′}-d_2\\ {c_3}^{\′}-c_3\end{array}\right)\mathrm{......}\left(4\right)$

There is unique solution (a for above formula (4)₁、a₂、a₃、a₄、a₅), it is splicing parameter, the splicing parameter is substituted into (1) formula can W₁、W₂The wave front aberration in region shows；

Step 3：For W₁、W₂N point (x of overlapping region₁,y₁)…(x_n,y_n) have：

$\left(\begin{array}{ccccc}1& 0& 4x_1& 2x_1& 2y_1\\ 0& 1& 4y_1& -2y_1& 2x_1\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 1& 0& 4x_n& 2x_n& 2y_n\\ 0& 1& 4y_n& -2y_n& 2x_n\end{array}\right)\left(\begin{array}{c}{a}_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right)=\left(\begin{array}{c}{c_1}^{\′}-c_1\\ {d_1}^{\′}-d_1\\ {c_2}^{\′}-c_2\\ {d_2}^{\′}-d_2\\ {c_3}^{\′}-c_3\end{array}\right)\mathrm{......}\left(5\right)$

The form for being expressed as residual error is：

$\left\{\begin{array}{c}{v}_1=l_1-\[a_1+2y_1\·a_5+2x_1\·(2a_3+a_4)\]\\ v_2=l_2-\[a_2+2x_1\·a_5+2y_1\·(2a_3-a_4)\]\\ \mathrm{......}\\ v_{2n}=l_{2n}-\[a_2+2x_n\·a_5+2y_n\·(2a_3-a_4)\]\end{array}\right.$

$\left(\begin{array}{c}{v}_1\\ v_2\\ \mathrm{...}\\ v_{2n}\end{array}\right)=\left(\begin{array}{c}{l}_1\\ l_2\\ \mathrm{...}\\ l_{2n}\end{array}\right)-\left(\begin{array}{ccccc}1& 0& 4x_1& 2x_1& 2y_1\\ 0& 1& 4y_1& -2y_1& 2x_1\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& 1& 4y_n& -2y_1& 2x_n\end{array}\right)\left(\begin{array}{c}{a}_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right)$

During equal precision measurement, the minimum matrix form of residual error quadratic sum is：

$\left(\begin{array}{cccc}{v}_1& v_2& \mathrm{...}& v_{2n}\end{array}\right)\left(\begin{array}{c}{v}_1\\ v_2\\ \mathrm{...}\\ v_{2n}\end{array}\right)=\min ;$

Wherein：

During equal precision measurement, the normal equation of matrix form is：

The solution of normal equation, the matrix expression of first five term coefficient of zernike polynomial are obtained according to (6) formula：

$\widehat{\mathrm{\α}}={\left(A^{T}A\right)}^{-1}{A}^{T}L$

Then, W₁Region, W₂The wave front aberration in region is：

Repeat step one, step 2, you can realize the corrugated splicing to full wafer free surface lens.