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Matlab code
- Structure, 2021
- Edge roughness analysis

Kim Lab Data and Code

홈
Matlab code
- Structure, 2021
- Edge roughness analysis
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- 홈
- Matlab code
  - Structure, 2021
  - Edge roughness analysis

Structure, 2021

%% 초기화

clear; clc; close all;

cd(fileparts(matlab.desktop.editor.getActiveFilename));

% addpath('D:\추가\파일\경로'); % 파일 있는 경로 여기에 추가

data = {};

%% 개별 작업

% 이미지 로드 -------------------------------------------------

close all;

SCALE_BAR_LENGTH = 450; % nm

file_name = 'P1100-2.png';

img = imread(file_name);

% 그레이 스케일 ------------------------------------------------

% 확인용

%{

figure

subplot(1,3,1); imshow(img(:,:,1)); title('R');

subplot(1,3,2); imshow(img(:,:,2)); title('G');

subplot(1,3,3); imshow(img(:,:,3)); title('B');

figure

subplot(1,2,1); imshow(rgb2gray(img)); title('rgb2gray()');

subplot(1,2,2); imshow(max(img,[],3)); title('max()');

%}

% img_gray = rgb2gray(img); % Mean

img_gray = max(img,[],3); % Max

% 스케일바 픽셀 길이 측정 -------------------------------------

scale_bar = sum(img(:,:,3) == 255);

scale_bar(scale_bar < max(scale_bar)/2) = 0;

scale_bar_pixel = sum(scale_bar ~= 0);

% 점검

ii = 1;

while scale_bar(ii) == 0

ii = ii + 1;

end % black end

while scale_bar(ii) ~= 0

ii = ii + 1;

end % scale bar end

assert(sum(scale_bar(ii:end) ~= 0) == 0,'스케일바 길이 측정 실패')

pixel_length = SCALE_BAR_LENGTH/scale_bar_pixel;

% 이미지 전처리 -----------------------------------------------

% blur

img_blur = im2double(img_gray);

windowSize = 7; % 윈도우 사이즈

repeat_num = 3; % 반복 횟수

avg3 = ones(windowSize) / windowSize^2;

for ii = 1:repeat_num

img_blur = imfilter(img_blur, avg3, 'conv');

end

% 조도

img_blur = imadjust(img_blur,[0.05,0.7]); % saturation 양 조절

% ---------------------- 경계 검출

edge_method = 'Canny'; % 'Sobel', 'Prewitt', 'Roberts', 'log', 'zerocross', 'Canny', 'approxcanny'

edge_threshold = [];

edge_direction = 'vertical'; % 'both', 'horizontal', 'vertical'

edge_BW = edge(img_blur,edge_method,edge_threshold,edge_direction);

% 가장자리 제거

pad_size = 6; % 두께 설정

edge_BW(1:pad_size,:) = 0; % 상

edge_BW(:,1:pad_size) = 0; % 좌

edge_BW(end-pad_size+1:end,:) = 0; % 하

edge_BW(:,end-pad_size+1:end) = 0; % 우

% figure;

% subplot(2,2,1)

% imshow(img); title('Original')

% subplot(2,2,2)

% imshow(img_gray); title('Gray scale')

% subplot(2,2,3)

% imshow(img_blur); title('Preprocess')

% subplot(2,2,4)

% imshow(edge_BW); title('Edge detection')

% 구간 (라인) 선택 -------------------------------------------------

figure, imshow(edge_BW); title('Edge detection')

disp('그래프에서 영역 선택')

roi = drawrectangle('StripeColor','y');

sel_pos = round(roi.Position);

sel_pos(4) = sel_pos(4)-1;

sel_pos(3) = sel_pos(3)-1;

croped_BW = edge_BW(sel_pos(2):sel_pos(2)+sel_pos(4), sel_pos(1):sel_pos(1)+sel_pos(3));

% figure, imshow(croped_BW)

% 픽셀 좌표 검출 ------------------------------------------------

% % 히스토그램 확인

% hist_x = sum(croped_BW);

% figure, plot(hist_x,'-o','LineWidth',1.5)

% % 좌우 분리선

x_center = mean([1,size(croped_BW,2)]);

% hold on;

% axis_top = get(gca,'ylim'); axis_top = axis_top(2);

% plot([x_center;x_center],[0,axis_top],'-r','LineWidth',1)

% xlabel('Pixel number');

% ylabel('Edge pixel count')

% xlim([1,length(hist_x)]);

% grid on;

x_center_ind = round(x_center);

croped_BW_left = croped_BW(:,1:x_center_ind);

croped_BW_right = croped_BW(:,x_center_ind+1:end);

% figure;

% subplot(1,2,1); imshow(croped_BW_left);

% subplot(1,2,2); imshow(croped_BW_right);

x_coord_left = line_extract(croped_BW_left,pixel_length);

x_coord_right = line_extract(croped_BW_right,pixel_length) + x_center_ind*pixel_length;

y_coord = (0:length(x_coord_left)-1)'*pixel_length;

% figure, plot(y_coord, [x_coord_left, x_coord_right])

% xlabel('Y (nm)');

% ylabel('X (nm)');

% xlim([0,max(y_coord)]);

% grid on;

% FFT PSD ------------------------------------------------------

% left

x_pre_l = x_coord_left-mean(x_coord_left,'omitnan');

not_nan_ind(1) = find(~isnan(x_pre_l),1,"first");

not_nan_ind(2) = find(~isnan(x_pre_l),1,"last");

x_pre_l = x_pre_l(not_nan_ind(1):not_nan_ind(2));

% y_pre_l = y_coord(not_nan_ind(1):not_nan_ind(2));

x_pre_l = interpNan(x_pre_l); % 중간에 들어있는 nan제거

[X_l,freq_l] = ssfft(x_pre_l,1/pixel_length);

xlabel('Frequency (1/nm)');

psd_fft_l = length(x_pre_l)*pixel_length*abs(X_l).^2;

% right

x_pre_r = x_coord_right-mean(x_coord_right,'omitnan');

not_nan_ind(1) = find(~isnan(x_pre_r),1,"first");

not_nan_ind(2) = find(~isnan(x_pre_r),1,"last");

x_pre_r = x_pre_r(not_nan_ind(1):not_nan_ind(2));

% y_pre_r = y_coord(not_nan_ind(1):not_nan_ind(2));

x_pre_r = interpNan(x_pre_r); % 중간에 들어있는 nan제거

[X_r,freq_r] = ssfft(x_pre_r,1/pixel_length);

xlabel('Frequency (1/nm)');

psd_fft_r = length(x_pre_r)*pixel_length*abs(X_r).^2;

% figure, loglog(freq_l,psd_fft_l)

% hold on; loglog(freq_r,psd_fft_r)

% xlabel('Frequency (1/nm)');

% ylabel('PSD (nm^3)')

% legend({'Left PSD','Right PSD'},'Location','best');

% grid on

% correlation length fitting ----------------------------------------

% left -----------------------

freq = freq_l;

psd_fft = psd_fft_l;

H = 0.5;

% objective function

std_dev_l = std(x_coord_left,'omitnan');

objfunc = @(cl) log(PSD(freq,std_dev_l,cl,H)) - log(psd_fft);

bound = [pixel_length*2, pixel_length*2*length(croped_BW_left)];

InitCond = mean(bound);

LowBound = bound(1);

UppBound = bound(2);

options = optimset('TolFun',1e-8,'TolX',1e-8,...

'MaxFunEvals',100000,'MaxIter',10000,'Display','iter');

%'off' 'iter' 'iter-detailed' 'notify' 'notify-detailed' 'final' 'final-detailed'

cl_fit_l = lsqnonlin(objfunc,InitCond,LowBound,UppBound,options);

psd_fit_l = PSD(freq,std_dev_l,cl_fit_l,H);

figure, loglog(freq_l,psd_fft_l);

hold on; loglog(freq, psd_fit_l, 'LineWidth',2);

xlabel('Frequency (1/nm)');

ylabel('PSD (nm^3)')

legend({'Left FFT PSD','Fitted PSD'},'Location','best');

grid on

% right -----------------------

freq = freq_r;

psd_fft = psd_fft_r;

H = 0.5;

% objective function

std_dev_r = std(x_coord_right,'omitnan');

objfunc = @(cl) log(PSD(freq,std_dev_r,cl,H)) - log(psd_fft);

bound = [pixel_length*2, pixel_length*2*length(croped_BW_left)];

InitCond = mean(bound);

LowBound = bound(1);

UppBound = bound(2);

options = optimset('TolFun',1e-8,'TolX',1e-8,...

'MaxFunEvals',100000,'MaxIter',10000,'Display','iter');

%'off' 'iter' 'iter-detailed' 'notify' 'notify-detailed' 'final' 'final-detailed'

cl_fit_r = lsqnonlin(objfunc,InitCond,LowBound,UppBound,options);

psd_fit_r = PSD(freq,std_dev_r,cl_fit_r,H);

figure, loglog(freq_r,psd_fft_r);

hold on; loglog(freq, psd_fit_r, 'LineWidth',2);

xlabel('Frequency (1/nm)');

ylabel('PSD (nm^3)')

legend({'Right FFT PSD','Fitted PSD'},'Location','best');

grid on

% 데이터 수집 --------------------------------------------

this_data = {psd_fft_l, freq_l, std_dev_l, ...

psd_fft_r, freq_r, std_dev_r};

y_n = input('이번 결과를 데이터에 추가 : ','s');

if strcmp(y_n,'y')

data = [data;this_data];

disp('데이터 추가 완료!')

else

disp('데이터 추가 취소')

end

%% data 저장

save backup_data.mat data croped_BW_left

%% 데이터 평균, PSD fitting

% data = {psd_fft_l, freq_l, std_dev_l, ...

% psd_fft_r, freq_r, std_dev_r};

short_ind = min(length(data{1,1}),length(data{1,4}));

psd_fft_mean = log10(data{1,1}(1:short_ind))+log10(data{1,4}(1:short_ind));

for ii = 2:size(data,1)

short_ind = min(length(psd_fft_mean),length(data{ii,1}));

psd_fft_mean = psd_fft_mean(1:short_ind) ...

+ log10(data{ii,1}(1:short_ind));

short_ind = min(length(psd_fft_mean),length(data{ii,4}));

psd_fft_mean = psd_fft_mean(1:short_ind) ...

+ log10(data{ii,4}(1:short_ind));

end

psd_fft_mean = psd_fft_mean./(size(data,1)*2);

psd_fft_mean = 10.^psd_fft_mean;

freq = data{1,2}(1:short_ind);

std_dev = mean([data{:,[3,6]}]);

% correlation length fitting ----------------------------------------

psd_fft = psd_fft_mean;

H = 0.5;

H = 0.9;

std_dev = std_dev*1.5

% -------------------- 가중치

freq(1) = 0.0001; % 임시

segment_num = 20;

weight = zeros(size(freq));

freq_seg = 10.^(linspace(log10(freq(1)),log10(freq(end)),segment_num+1));

freq_seg(1) = 0; freq(1) = 0;

for ii = 1:segment_num

freq_window = freq >= freq_seg(ii) & freq <= freq_seg(ii+1);

weight(freq_window) = 1/sum(freq_window);

end

weight = ones(size(freq)); % 최적화 가중치 무효화

% objective function

objfunc = @(cl) (log10(PSD(freq,std_dev,cl,H)) - log10(psd_fft)).*weight;

bound = [pixel_length*2, pixel_length*2*length(croped_BW_left)];

InitCond = mean(bound);

LowBound = bound(1);

UppBound = bound(2);

options = optimset('TolFun',1e-8,'TolX',1e-8,...

'MaxFunEvals',100000,'MaxIter',10000,'Display','iter');

%'off' 'iter' 'iter-detailed' 'notify' 'notify-detailed' 'final' 'final-detailed'

cl_fit = lsqnonlin(objfunc,InitCond,LowBound,UppBound,options);

psd_fit = PSD(freq,std_dev,cl_fit,H);

figure, loglog(freq,psd_fft);

hold on; loglog(freq, psd_fit, 'LineWidth',2);

xlabel('Frequency (1/nm)');

ylabel('PSD (nm^3)')

legend({'FFT PSD','Fitted PSD'},'Location','best');

grid on

% FFT PSD plot ----------------------------

% freq = linspace(1/(pixel_length*2*length(croped_BW_left)),1,100)';

freq = logspace(log10(1/(pixel_length*2*length(croped_BW_left))),0,100)';

LER_psd = PSD(freq,std_dev,cl_fit,H);

figure, loglog(freq,LER_psd,'LineWidth',1.5)

xlabel('Frequency (1/nm)');

ylabel('PSD (nm^3)');

grid on;

%% 데이터 평균, polynomial fitting

% data = {psd_fft_l, freq_l, std_dev_l, ...

% psd_fft_r, freq_r, std_dev_r};

short_ind = min(length(data{1,1}),length(data{1,4}));

psd_fft_mean = log10(data{1,1}(1:short_ind))+log10(data{1,4}(1:short_ind));

for ii = 2:size(data,1)

short_ind = min(length(psd_fft_mean),length(data{ii,1}));

psd_fft_mean = psd_fft_mean(1:short_ind) ...

+ log10(data{ii,1}(1:short_ind));

short_ind = min(length(psd_fft_mean),length(data{ii,4}));

psd_fft_mean = psd_fft_mean(1:short_ind) ...

+ log10(data{ii,4}(1:short_ind));

end

psd_fft_mean = psd_fft_mean./(size(data,1)*2);

psd_fft_mean = 10.^psd_fft_mean;

freq = data{1,2}(1:short_ind);

std_dev = mean([data{:,[3,6]}]);

crop_ind = 6; % 최고점 잘라낼 위치

freq_log = log10(freq(2:end));

psd_log = log10(psd_fft_mean(2:end));

poly_coef = polyfit(freq_log,psd_log,5);

freq_log_poly_fit = linspace(freq_log(crop_ind),freq_log(end),100)';

psd_log_poly_fit = polyval(poly_coef,freq_log_poly_fit);

freq_poly_fit = 10.^freq_log_poly_fit;

psd_poly_fit = 10.^psd_log_poly_fit;

figure, loglog(freq(crop_ind+1:end),psd_fft_mean(crop_ind+1:end))

hold on; loglog(freq_poly_fit,psd_poly_fit,'LineWidth',2)

xlabel('Frequency (1/nm)');

ylabel('PSD (nm^3)');

legend({'FFT PSD','Polynomial fitting'},'Location','best');

grid on;

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