CN102289146B - Method for optimizing two-phase phase shift mask based on generalized wavelet penalty function - Google Patents

Abstract

The invention provides a method for optimizing a phase shift mask based on a generalized wavelet function. In the method, by separating figures MO and M180 corresponding to opening parts of two-phase PSM 0DEG and 180DEG phases, and using wavelet penalty function of RO and R180 that corresponds to M0 and M180, a generalized wavelet penalty function R of two-phase PSM is obtained; two-phase PSM is optimized by using R; and the complexity and the manufacturing cost of the mask are reduced. and using wavelet penalty function of RO and R180 that corresponds to M0 and M180, a generalized wavelet penalty function R of two-phase PSM is obtained; two-phase PSM is optimized by using R; and the complexity and the manufacturing cost of the mask are reduced. Simultaneously, opening figures of 0DEG and 180DEG phases are independently processed and tokened respectively by a generalized wavelet penalty function method; and therefore, openings of 0DEG and 180DEG phases in the optimized mask are not mutually away from each other so that the advantage of phase modulation of two-phase PSM is reserved.

Description

Optimize the method for two phase phase-shift mask based on broad sense small echo penalty function

Technical field

The present invention relates to a kind of method, belong to photoetching resolution enhancement techniques field based on broad sense small echo penalty function optimization two phase phase-shift mask.

Background technology

Current large scale integrated circuit generally adopts etching system manufacturing.Etching system mainly is divided into: four parts such as illuminator (comprising light source and condenser), mask, optical projection system and wafer.Photo etched mask adopts light transmission medium and resistance light medium to process, and the light transmission part is equivalent to opening to light.The light that light source sends is incident to mask, the opening portion printing opacity of mask after focusing on through condenser; Through behind the mask, light is incident on the wafer that scribbles photoresist via optical projection system, so just mask pattern is replicated on the wafer.

The etching system of main flow is the ArF degree of depth ultraviolet photolithographic system of 193nm at present; Along with the photoetching technique node gets into 45nm-22nm; The critical size of circuit has been far smaller than the wavelength of light source, so interference of light and diffraction phenomena are more remarkable, causes optical patterning to produce distortion and fuzzy.Etching system must adopt RET for this reason, in order to improve image quality.(phase-shifting mask PSM) is a kind of important photoetching resolution enhancement techniques to phase-shift mask.PSM adopts light transmission medium and resistance light medium to process, and the light transmission part is equivalent to opening to light.PSM is through change the topological structure and the etch depth of mask light transmission part (being opening) in advance, and the amplitude and the phase place of modulation mask exit facet electric field intensity are to reach the purpose that improves imaging resolution.

But, the mask behind the employing PSM technical optimization, its manufacturing cost is higher, thereby causes great scale integrated circuit to make the raising of whole cost.The raising of mask manufacturing cost and difficulty mainly comes from following two aspects: the first, the PSM technology is added tiny auxiliary pattern on mask, thereby has increased the complexity of mask pattern.The second, in order to introduce the phase differential of transmitted light, PSM needs the etching depth of some opening is adjusted, thereby has increased the manufacture difficulty of mask.In order to design practical photo etched mask, must in the mask optimizing process, adopt and reduce the mask cost techniques.

Pertinent literature (Optics Express, 2007,15:15066～15079) has proposed a kind of small echo penalty function method of the PSM of reduction complexity.Through utilizing wavelet function R and gradient matrix thereof

that PSM is optimized, thereby effectively reduce the complexity of four phase PSM; Concrete principle is: in the mask optimizing process, make the neighbor pixel on the mask have identical transmissivity as far as possible, thereby make the opening and the resistance light zone that have same phase on the mask concentrated relatively, finally reach the purpose that reduces the mask complexity.But for two phase PSM (like alternative expression PSM), it is made up of 0 ° of phase place opening, 180 ° of phase place openings and light-blocking part.Utilize existing small echo penalty function method that two phase PSM is optimized, can make 0 ° and 180 ° of phase place openings mutually away from; But the advantage of two phase PSM just is to make 0 ° and 180 ° of phase place openings approaching each other, utilizes the negative function Enhanced Imaging resolution of out of phase light; Therefore existing small echo penalty function method is not suitable for two phase PSM.

Summary of the invention

The purpose of this invention is to provide a kind of method of optimizing two phase PSM based on broad sense small echo penalty function; This method can effectively reduce the complexity of two phase PSM under the prerequisite that guarantees two phase PSM advantage, thereby reduces the manufacturing cost of two phase PSM.

Realize that technical scheme of the present invention is following:

A kind of method based on broad sense wavelet function optimization phase-shift mask, concrete steps are:

Step 101,0 ° and 180 ° phase place opening portion graphs of a correspondence of separation two phase PSM; Wherein 0 ° of phase place opening portion graph of a correspondence is expressed as the matrix M of N * N ₀, M ₀The element value of corresponding 0 ° of phase place opening portion is 1, and the remainder element value is 0; 180 ° of phase place opening portion graphs of a correspondence are expressed as the matrix M of N * N ₁₈₀, M ₁₈₀The element value of corresponding 180 ° of phase place opening portions is 1, and the remainder element value is 0;

Step 102, utilize sigmoid curve sigmoid approximation to function M ₀And M ₁₈₀, obtain and have the M that can lead characteristic ₀And M ₁₈₀

Step 103, find the solution M ₀And M ₁₈₀The high fdrequency component of single order Ha Er Haar wavelet transformation, and according to M ₀It is R that corresponding high fdrequency component is found the solution the small echo penalty function ₀, according to M ₁₈₀It is R that corresponding high fdrequency component is found the solution the small echo penalty function ₁₈₀

Step 104, the broad sense small echo penalty function of two phase PSM is defined as R ₀And R ₁₈₀Linear combination, i.e. R=γ ₀R ₀+ γ ₁₈₀R ₁₈₀, γ wherein ₀And γ ₁₈₀Be respectively R ₀And R ₁₈₀Weight coefficient, and ask for the gradient matrix of broad sense small echo penalty function R

Step 105, utilization

and R; Based on existing mask optimization aim function, PSM is optimized to two phase.

The transmissivity that the present invention sets 0 ° of phase place opening of two phase PSM is that the transmissivity of 1,180 ° of phase place opening is-1, and the transmissivity of light-blocking part is 0; With two phase PSM diagrammatic representation is the matrix M of N * N, and the element value of matrix M is the corresponding transmissivity of each pixel on the two phase PSM figure;

Said matrix M ₀Be expressed as:

M ₀＝Γ{M} (1)

Said matrix M ₁₈₀Be expressed as:

M ₁₈₀＝Γ{-1×M} (2)

Wherein, Γ x} is the hard decision function,

$\mathrm{\Γ}\left\{x\right\}=\left\{\begin{array}{cc}1,& x>0\\ 0,& x\≤0\end{array}\right.$

The sigmoid approximation to function M that utilizes according to the invention ₀And M ₁₈₀For: order

$\mathrm{\Γ}\left\{x\right\}\≈\mathrm{sigmoid}\left\{x\right\}=\frac{1}{\exp (-\mathrm{ax}+{\mathrm{at}}_r)}$

Get t _r=0, then (1) formula is approximately respectively with (2) formula:

$M_0\≈\mathrm{sig}\left\{M\right\}=\frac{1}{\exp (-\mathrm{aM})}---\left(3\right)$

${\mathrm{<figure-callout\; id="180"\; label="M"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_{180}\&ap;\mathrm{sig}\{-1\&times;M\}=\frac{1}{\exp \left(\mathrm{aM}\right)}---\left(4\right)$

Beneficial effect

The present invention is through separating 0 ° and 180 ° phase place opening portion graphs of a correspondence of two phase PSM M ₀And M ₁₈₀And utilize M ₀And M ₁₈₀Pairing small echo penalty function R ₀And R ₁₈₀Obtain the broad sense small echo penalty function R of two phase PSM, utilize R that two phase PSM is optimized, effectively reduce the complexity and the manufacturing cost of mask.The present invention simultaneously utilizes broad sense small echo penalty function method that 0 ° and 180 ° of phase place opening figure are carried out independent processing and sign respectively; Therefore can not make 0 ° of optimizing in the mask of back and 180 ° of phase place openings each other away from, thereby kept the phase modulation (PM) advantage of two phase PSM.

Description of drawings

Fig. 1 the present invention is based on the process flow diagram that broad sense small echo penalty function is optimized the method for two phase PSM.

The synoptic diagram that forms images in the photoresist of Fig. 2 for initial two phase PSM and correspondence thereof.

Fig. 3 is under the situation of not using broad sense small echo penalty function method, the synoptic diagram that forms images in the photoresist of the two phase PSM of optimization and correspondence thereof.

The synoptic diagram of Fig. 4 for forming images in the two phase PSM that uses the optimization of broad sense small echo penalty function method and the corresponding photoresist thereof.

Embodiment

Further the present invention is elaborated below in conjunction with accompanying drawing.

Inventive concept is: 0 ° of two phase PSM and 180 ° of phase place opening portion graphs of a correspondence are separated; Calculate the high fdrequency component of 0 ° and the 180 ° pairing single order Haar of phase place opening figure wavelet transformation respectively; Set up broad sense small echo penalty function R according to the high fdrequency component of above calculating; Utilize R to combine with existing optimization aim function, PSM is optimized to two phase.

As shown in Figure 1, based on the method for broad sense small echo penalty function optimization two phase phase-shift mask, concrete steps are:

Step 101,0 ° and 180 ° phase place opening portion graphs of a correspondence of separation two phase PSM; Wherein 0 ° of phase place opening portion graph of a correspondence is expressed as the matrix M of N * N ₀, M ₀The element value of corresponding 0 ° of phase place opening portion is 1, and the remainder element value is 0; 180 ° of phase place opening portion graphs of a correspondence are expressed as the matrix M of N * N ₁₈₀, M ₁₈₀The element value of corresponding 180 ° of phase place opening portions is 1, and the remainder element value is 0.

M in the present embodiment ₀And M ₁₈₀Can specifically be expressed as:

Setting the corresponding transmissivity of PSM0 ° of phase place opening of two phase is that the corresponding transmissivity of 1,180 ° of phase place opening is-1, and the transmissivity that light-blocking part is corresponding is 0.

With two phase PSM diagrammatic representation is the matrix M of N * N; The element value of matrix M is the corresponding transmissivity of each pixel on the two phase PSM figure; The element value that is the corresponding 0 ° of phase place opening of M is 1, and the element value of the corresponding 180 ° of phase place openings of M is-1, and the element value of the corresponding light-blocking part of M is 0.

Matrix M then ₀Can be expressed as:

M ₀＝Γ{M} (1)

Matrix M ₁₈₀Can be expressed as:

M ₁₈₀＝Γ{-1×M} (2)

Wherein, Γ x} is the hard decision function,

$\mathrm{\&Gamma;}\left\{x\right\}=\left\{\begin{array}{cc}1,& x>0\\ 0,& x\&le;0\end{array}\right.$

Wherein, the element of x representing matrix M;

Step 102, { x} is can not derived function, can lead for the broad sense small echo penalty function that makes structure, utilizes sigmoid curve function (sigmoid function) to be similar to M because Γ ₀And M ₁₈₀, obtain and have the M that can lead characteristic ₀And M ₁₈₀

Concrete process is:

Order

$\mathrm{\&Gamma;}\left\{x\right\}\&ap;\mathrm{sigmoid}\left\{x\right\}=\frac{1}{\exp (-\mathrm{ax}+{\mathrm{at}}_r)}$

Wherein a representes slope, is used for controlling according to its different value the degree of tilt of curve; t _rThe expression threshold value.

{ x} is 0 to be the hard decision function of threshold value, therefore gets t because Γ _r=0, then (1) formula is approximately respectively with (2) formula

$M_0\&ap;\mathrm{sigmoid}\left\{M\right\}=\frac{1}{\exp (-\mathrm{aM})}---\left(3\right)$

${\mathrm{<figure-callout\; id="180"\; label="M"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">M</figure-callout>}}_{180}\&ap;\mathrm{sigmoid}\{-1\&times;M\}=\frac{1}{\exp \left(\mathrm{aM}\right)}---\left(4\right)$

Step 103, find the solution M ₀And M ₁₈₀The high fdrequency component of single order Ha Er (Haar) wavelet transformation, wherein said high fdrequency component comprises horizontal high fdrequency component, vertical high frequency component and oblique line high fdrequency component; And according to M ₀Corresponding high fdrequency component is found the solution small echo penalty function R ₀, according to M ₁₈₀Corresponding high fdrequency component is found the solution small echo penalty function R ₁₈₀

The detailed process of this step is:

M ₀Horizontal high fdrequency component, vertical high frequency component and the oblique line high fdrequency component of single order Haar wavelet transformation be respectively

Matrix H ₀, V ₀And D ₀, H ₀(i, j), V ₀(i, j) and D ₀(i j) is respectively matrix element,

H ₀(i，j)＝M ₀(2i-1，2j-1)-M ₀(2i-1，2j)+M ₀(2i，2j-1)-M ₀(2i，2j)

V ₀(i，j)＝M ₀(2i-1，2j-1)+M ₀(2i-1，2j)-M ₀(2i，2j-1)-M ₀(2i，2j)

D ₀(i，j)＝M ₀(2i-1，2j-1)-M ₀(2i-1，2j)-M ₀(2i，2j-1)+M ₀(2i，2j)

I wherein; J=1; 2, K,

M ₁₈₀Horizontal high fdrequency component, vertical high frequency component and the oblique line high fdrequency component of single order Haar wavelet transformation be respectively

Matrix H ₁₈₀, V ₁₈₀And D ₁₈₀, H ₁₈₀(i, j), V ₁₈₀(i, j) and D ₁₈₀(i j) is respectively matrix element,

H ₁₈₀(i，j)＝M ₁₈₀(2i-1，2j-1)-M ₁₈₀(2i-1，2j)+M ₁₈₀(2i，2j-1)-M ₁₈₀(2i，2j)

V ₁₈₀(i，j)＝M ₁₈₀(2i-1，2j-1)+M ₁₈₀(2i-1，2j)-M ₁₈₀(2i，2j-1)-M ₁₈₀(2i，2j)

D ₁₈₀(i，j)＝M ₁₈₀(2i-1，2j-1)-M ₁₈₀(2i-1，2j)-M ₁₈₀(2i，2j-1)+M ₁₈₀(2i，2j)

I wherein; J=1; 2, K,

With small echo penalty function R ₀Be defined as M ₀Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component, promptly

$R_0=\underset{i=1}{\overset{N/2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N/2}{\mathrm{\&Sigma;}}}{H}_0^2(i,j)+V_0^2(i,j)+D_0^2(i,j)$

With small echo penalty function R ₁₈₀Be defined as M ₁₈₀Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component, promptly

${\mathrm{<figure-callout\; id="180"\; label="R"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">R</figure-callout>}}_{180}=\underset{i=1}{\overset{N/2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N/2}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="180"\; label="H"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">H</figure-callout>}}_{180}^2(i,j)+{\mathrm{<figure-callout\; id="180"\; label="V"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">V</figure-callout>}}_{180}^2(i,j)+{\mathrm{<figure-callout\; id="180"\; label="D"\; filenames="HDA0000091236070000011.png"\; state="\{\{state\}\}">D</figure-callout>}}_{180}^2(i,j)$

Step 104, the broad sense small echo penalty function of two phase PSM is defined as R ₀And R ₁₈₀Linear combination, i.e. R=γ ₀R ₀+ γ ₁₈₀R ₁₈₀, γ wherein ₀And γ ₁₈₀Be respectively R ₀And R ₁₈₀Weight coefficient.If think more to limit the complexity of 0 ° of phase place opening figure, then can be with γ ₀Be made as big positive number, and with γ ₁₈₀Be made as less positive number; Otherwise can be with γ ₁₈₀Be made as big positive number, and with γ ₀Be made as less positive number; If think to limit simultaneously the complexity of 0 ° of phase place and 180 ° of phase place opening figure, then can be with γ ₀And γ ₁₈₀The positive number that is set to equate.Ask for the gradient matrix

of broad sense small echo penalty function R

Among the present invention;

is the matrix of N * N, and each element is:

$\&dtri;R(2(i-1)+p,2(j-1)+q)=[3M_0(2(i-1)+p,2(j-1)+q)-M_0(2(i-1)+p^{\&prime;},2(j-1)+q)$

$-M_0(2(i-1)+p,2(j-1)+q^{\&prime;})+M_0(2(i-1)+p^{\&prime;},2(j-1)+q^{\&prime;})]\&times;\mathrm{aT}\{M_0\}$

$+[3M_{180}(2(I-1)+p,2(j-1)+q)-M_{180}(2(i-1)+p^{\&prime;},2(j-1)+q)$

$-M_{180}(2(i-1)+p,2(j-1)+q^{\&prime;})+M_{180}(2(i-1)+p^{\&prime;},2(j-1)+q^{\&prime;})]\&times;\mathrm{aT}\{M_{180}\}$

Wherein, i, j=1; 2, K,

p=1; 2, q=1,2; The mod 2 of p '=(p+1); The mod 2 of q '=(q+1),

comprised 4 kinds of situation: the first, p=1, q=1; The second, p=1, q=2;

Three, p=2, q=1; Four, p=2, q=2.

$T\left\{M_0\right\}=\frac{1}{\exp [-a{M}_0(2(i-1)+p,2(j-1)+q)]}\&times;\{1-\frac{1}{\exp [-a{M}_0(2(i-1)+p,2(j-1)+q)]}\},$

$T\left\{M_{180}\right\}=\frac{1}{\exp [-a{M}_{180}(2(i-1)+p,2(j-1)+q)]}\&times;\{1-\frac{1}{\exp [-a{M}_{180}(2(i-1)+p,2(j-1)+q)]}\}.$

Step 105, utilization

and R; Based on existing mask optimization aim function, PSM is optimized to two phase.

Euler's distance of the difference that pertinent literature (Optics Express, 2007,15:15066～15079) is configured to the optimization aim function D of mask to form images in the targeted graphical photoresist corresponding with mask square; Size like targeted graphical is N * N; Then

is the pixel value of each point in the targeted graphical; Z (x; Y) pixel value for forming images in the corresponding photoresist of mask; (x, y) value with

is 0 or 1 to Z.With the broad sense small echo penalty function R structure fresh target function J that combines with D be:

J＝D+R。

The gradient matrix of fresh target function J may be calculated:

adopt optimized Algorithm based on gradient, the VJ that can utilize J that R obtains and utilization

to obtain carries out iteration optimization to mask pattern.

Embodiment of the present invention:

The synoptic diagram that forms images in the photoresist of Fig. 2 for initial two phase PSM and correspondence thereof.201 is initial two phase PSM figure, and its shape is consistent with targeted graphical, and white is represented 0 ° of phase place opening portion, and black is represented 180 ° of phase place opening portions, and grey is represented light-blocking part, and its critical size is 45nm.202 for adopting 201 as behind the mask; Form images in the photoresist of etching system; Image error is 1526 (image error is defined as the value of objective function here), and the CD error is 20nm, and wherein the CD error is the critical size that forms images in the actual photoresist in horizontal median axis place and the difference of desirable critical size.

Fig. 3 is under the situation of not using broad sense small echo penalty function method, the synoptic diagram that forms images in the photoresist of the two phase PSM of optimization and correspondence thereof.Under the situation of not using broad sense small echo penalty function method, adopt steepest prompt drop method that mask is optimized.301 are the two phase PSM figure after optimizing.302 for adopting 301 as behind the mask, forms images in the photoresist of etching system, and image error is 277, and the CD error is 0.

The synoptic diagram of Fig. 4 for forming images in the two phase PSM that uses the optimization of broad sense small echo penalty function method and the corresponding photoresist thereof.Under the situation of using broad sense small echo penalty function method, adopt steepest prompt drop method that mask is optimized.401 are the two phase PSM figure after optimizing.402 for adopting 401 as behind the mask, forms images in the photoresist of etching system, and image error is 321, and the CD error is 0.

Comparison diagram 2,3,4 can be known; Though the broad sense small echo penalty function method among employing the present invention is optimized two phase PSM; The image error of two phase PSM is slightly larger than the situation of not using broad sense small echo penalty function method, but the opening figure of the two phase PSM after it is optimized more approaches regular rectangular shape or regular polygon.Therefore broad sense small echo penalty function method can effectively be controlled mask complexity and manufacturing cost thereof when being lowered into picture sum of errors CD error.

Only consider the situation of alternative expression PSM among the present invention, alternative expression PSM is: the opening portion transmissivity is 1 or-1, between various openings, hinders the light zone simultaneously in addition; But on behalf of the present invention, this only be confined to the situation of alternative expression PSM, and the present invention also is applicable to various ways such as attenuation type PSM.

Though in conjunction with accompanying drawing embodiment of the present invention has been described; But to those skilled in the art; Under the prerequisite that does not break away from the principle of the invention, can also make some distortion, replacement and improvement, these also should be regarded as belonging to protection scope of the present invention.

Claims (1)

1. optimize the method for two phase phase-shift mask based on broad sense small echo penalty function for one kind, it is characterized in that concrete steps are:

Step 101,0 ° and 180 ° phase place opening portion graphs of a correspondence of separation two phase phase-shift mask PSM; Wherein 0 ° of phase place opening portion graph of a correspondence is expressed as the matrix M of N * N ₀, M ₀The element value of corresponding 0 ° of phase place opening portion is 1, and the remainder element value is 0; 180 ° of phase place opening portion graphs of a correspondence are expressed as the matrix M of N * N ₁₈₀, M ₁₈₀The element value of corresponding 180 ° of phase place opening portions is 1, and the remainder element value is 0;

Above-mentioned M ₀And M ₁₈₀Obtain through following process:

Setting the corresponding transmissivity of PSM0 ° of phase place opening of two phase is that the corresponding transmissivity of 1,180 ° of phase place opening is-1, and the transmissivity that light-blocking part is corresponding is 0; With two phase PSM diagrammatic representation is the matrix M of N * N, and the element value of matrix M is the corresponding transmissivity of each pixel on the two phase PSM figure;

Said matrix M ₀Be expressed as:

M ₀＝Γ{M} （1）

Said matrix M ₁₈₀Be expressed as:

M ₁₈₀＝Γ{-1×M} （2）

Wherein, Γ x} is the hard decision function,

$\mathrm{\&Gamma;}\left\{x\right\}=\left\{\begin{array}{cc}1,& x>0\\ 0,& x\&le;0\end{array}\right.$

Step 102, utilize sigmoid curve sigmoid approximation to function M ₀And M ₁₈₀, obtain and have the M that can lead characteristic ₀And M ₁₈₀

The said sigmoid approximation to function M that utilizes ₀And M ₁₈₀For: order

$\mathrm{\&Gamma;}\left\{x\right\}\&ap;\mathrm{sigmoid}\left\{x\right\}=\frac{1}{\exp (-\mathrm{ax}+{\mathrm{at}}_r)}$

Wherein a representes slope, is used for controlling according to its different value the degree of tilt of curve; t _rThe expression threshold value; Get t _r=0, then (1) formula is approximately respectively with (2) formula:

$M_0\&ap;\mathrm{sig}\left\{M\right\}=\frac{1}{\exp (-\mathrm{aM})}---\left(3\right)$

$M_{180}\&ap;\mathrm{sig}\{-1\&times;M\}=\frac{1}{\exp \left(\mathrm{aM}\right)}---\left(4\right)$

Step 103, find the solution M ₀And M ₁₈₀The high fdrequency component of single order Ha Er Haar wavelet transformation,

According to M ₀It is R that corresponding high fdrequency component is found the solution the small echo penalty function ₀, be about to small echo penalty function R ₀Be defined as M ₀Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component,

$R_0=\underset{i=1}{\overset{N/2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N/2}{\mathrm{\&Sigma;}}}{H}_0^2(i,j)+V_0^2(i,j)+D_0^2(i,j)$

H wherein ₀, V ₀And D ₀Be M ₀Horizontal high fdrequency component, vertical high frequency component and the oblique line high fdrequency component of single order Haar wavelet transformation, H ₀(i, j), V ₀(i, j) and D ₀(i j) is respectively H ₀, V ₀And D ₀Matrix element;

According to M ₁₈₀It is R that corresponding high fdrequency component is found the solution the small echo penalty function ₁₈₀Be about to small echo penalty function R ₁₈₀Be defined as M ₁₈₀Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component,

$R_{180}=\underset{i=1}{\overset{N/2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N/2}{\mathrm{\&Sigma;}}}{H}_{180}^2(i,j)+V_{180}^2(i,j)+D_{180}^2(i,j)$

H wherein ₁₈₀, V ₁₈₀And D ₁₈₀Be M ₁₈₀The horizontal high fdrequency component of single order Haar wavelet transformation, vertical high frequency component and oblique line high fdrequency component, H ₁₈₀(i, j), V ₁₈₀(i, j) and D ₁₈₀(i j) is respectively H ₁₈₀, V ₁₈₀And D ₁₈₀Matrix element;

Step 104, the broad sense small echo penalty function of two phase PSM is defined as R ₀And R ₁₈₀Linear combination, i.e. R=γ ₀R ₀+ γ ₁₈₀R ₁₈₀, γ wherein ₀And γ ₁₈₀Be respectively R ₀And R ₁₈₀Weight coefficient, and ask for the gradient matrix of broad sense small echo penalty function R

Step 105, utilization

and R; Based on existing mask optimization aim function, PSM is optimized to two phase.

Images