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

Free surface lens corrugated joining method based on Shack-Hartmann wavefront sensor

Technical field

It is freely bent more particularly to based on Shack-Hartmann wavefront sensor the present invention relates to corrugated splicing field Face eyeglass corrugated joining method.

Background technology

With the development of free form surface technology, using Free-Form Surface Machining technology free surface lens application increasingly Extensively, progressive multi-focus lens occupy critical role as the representative of free surface lens in high-end ophthalmic lens market.At present, in Europe Mei Deng developed countries, progressive lenses have occupied larger market ratio, and the sales volume of Japanese market progressive lenses accounts for glasses The 21% of market, American market this ratio also reaches 60%.

Detection for conventional lenses is ripe already at present, but is directed to the detection of free surface lens, at present in the world Corresponding unified standard is not reached, the industry development to free surface lens produces high resistance.Now, commented with wave front aberration The method of valency free surface lens increasingly attracts attention, but for fear of the instrument Shack-Hartmann wavefront biography of measuring wavefront aberrations Sensor measurement size limitation, it is difficult to realize the measurement to full wafer eyeglass wave front aberration.

The content of the invention

In order to solve the above problems, the invention provides the free surface lens based on Shack-Hartmann wavefront sensor Corrugated joining method.

The present invention is comprised the following steps：

Step one：The W of full wafer free surface lens is obtained using Shack-Hartmann wavefront sensor measurement₁Region, obtains W₁First five term coefficient of region wavefront zernike polynomial, then move a certain distance measurement W₂Region, obtains W₂Region wavefront pool Polynomial first five term coefficient of Buddhist nun gram；Overlap region in point, the zernike polynomial for measuring twice in theory first five Term coefficient 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)、(x₃,y₃), W₁Three points in region Correspondence x, the wavefront slope in y-axis is respectively (c₁,d₁)、(c₂,d₂)、(c₃,d₃), W₂Three points correspondence x in region, in y-axis Wavefront slope difference (c '₁,d₁)、(c’₂,d₂)、(c’₃,d₃).By W₁、W₂The wave front aberration in region is represented with zernike polynomial Out, have (3) formula is write as matrix form：

There can be 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 be by W₁、W₂The wave front aberration in region shows.

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

The form for being expressed as residual error is：

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

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：

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, obtain full wafer freely bent The expression formula of the zernike polynomial of face eyeglass Wave-front phase.

The beneficial effects of the present invention are：Free surface lens corrugated splicing based on Shack-Hartmann wavefront sensor Method, compared to existing technology, the present invention solves the measurement size of limited existing Shack-Hartmann wavefront sensor, it is impossible to real Now to problems such as the measurements of full wafer free surface lens wave front aberration, realize the method spliced using wavefront and obtain full wafer freedom The function of curve lens wave front aberration, with measurement is quick, simple operation and other advantages.

Brief description of the drawings

The present invention is further described with reference to the accompanying drawings and examples.

Fig. 1 is adjacent sub-aperture W of the invention₁、W₂Splicing detects schematic diagram；

Specific embodiment

In order that technological means, creation characteristic, reached purpose and effect that the present invention is realized are easy to understand, tie below Conjunction is specifically illustrating, and the present invention is expanded on further.It should be noted that in the case where not conflicting, embodiment in the application and Feature in embodiment can be combined with each other.

As shown in figure 1, the free surface lens corrugated joining method based on Shack-Hartmann wavefront sensor, including with Lower step：

Step one：Obtain measuring the W of full wafer free surface lens using Shack-Hartmann wavefront sensor measurement₁Region, Obtain W₁First five term coefficient of region wavefront zernike polynomial, then move a certain distance measurement W₂Region, obtains W₂Region ripple First five term coefficient of preceding zernike polynomial；Point in the region for overlapping, the zernike polynomial for measuring twice in theory First five term coefficient 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)、(x₃,y₃), W₁Three points in region Correspondence x, the wavefront slope in y-axis is respectively (c₁,d₁)、(c₂,d₂)、(c₃,d₃), W₂Three points correspondence x in region, in y-axis Wavefront slope difference (c '₁,d₁)、(c’₂,d₂)、(c’₃,d₃).By W₁、W₂The wave front aberration in region is represented with zernike polynomial Out, have (3) formula is write as matrix form：

There can be 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 be by W₁、W₂The wave front aberration in region shows.

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

The form for being expressed as residual error is：

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

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：

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, obtain full wafer freely bent The expression formula of the zernike polynomial of face eyeglass Wave-front phase, i.e. sensor survey the wave front aberration for once obtaining a fritter, pass through Splicing obtains the wave front aberration of whole eyeglass.

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.