PhotoShop - Response Curve Comparison of Soft Light Mode and Hard Light Mode

As you can see from the image below, both Soft Light and Hard Light modes enhance the contrast of the midtones when the same source layers are blended;
the difference is that Soft Light does less.




Finally, attach the matlab code for drawing the response curve:

%% Soft light mode response curve when the base color and blend color are the same,
f1=@(x) x.^2.*(3-2*x);
f2=@(x) 2*x.*(1-x)+sqrt(x).*(2*x-1);

x1=linspace(0,0.5,128);
x2=linspace(.5,1,128);

y1=f1(x1);
y1(y1<0)=0;
y2=f2(x2);
y2(y2>1)=1;
plot([x1 x2],[y1,y2],'LineWidth',3,'Color',[0 0 0])
grid on
hold on
%% The response curve of the high light mode when the base color and the mixed color are the same
f1=@(x) 2*x.^2;
f2=@(x)  1-2*(1-x).^2 ;

x1=linspace(0,0.5,128);
x2=linspace(.5,1,128);

y1=f1(x1);
y1(y1<0)=0;
y2=f2(x2);
y2(y2>1)=1;
plot([x1 x2],[y1,y2],'LineWidth',3,'Color',[1 0 0])

%% Normal mode response curve when base color and blend color are the same
plot([x1 x2],[x1 x2],'--','LineWidth',2,'Color',[0 0 1])

%%

fontSize=16;
xlabel('base color and mixed color gray value','FontSize',fontSize)
ylabel('Result color','FontSize',fontSize)
title('Comparison of soft light mode and strong light mode','FontSize',fontSize)


legend('Soft Light Mode','High Light Mode','Normal Mode','Location','SouthEast')
axis equal
xlim ([0 1])
ylim ([0 1])