Hatch with Shading

Question

I would like to have a rectangle that has some hatch. Furthermore, the hatch should have some shading. But, I am only able to get a transition of the colors in the background. Does anyone know how to only have a color gradient in the hatch with only a white background?

Thanks a lot.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture} 
\fill[left color=blue!40, right color=white, postaction={pattern=north west lines, pattern color=blue!40}] (0,0) rectangle (3,3);
\end{tikzpicture}
\end{document}

Answer 1

Only for fun!

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\def\a{3}
\def\lw{0.2}
\draw[blue, thick] (0,0) rectangle (\a,\a);
\foreach \x [count=\i] in{0,0.1,0.2,...,\a}{
\draw [blue,line width=\lw mm,opacity=\i/45](\x,0)--(0,\x) (\a,\a-\x)--(\a-\x,\a);}
\end{tikzpicture}

\end{document}

Answer 2

This is conceptually the same as Ignasi's nice answer in that the pattern is in the background color, so it determines what should be left unshaded. And in order to customize the pattern I use this answer. And of course you need to dial a shading angle to make the shading follow the north east lines.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{patterns}
% defining the new dimensions and parameters
\newlength{\hatchspread}
\newlength{\hatchthickness}
\newlength{\hatchshift}
\newcommand{\hatchcolor}{}
% declaring the keys in tikz
\tikzset{hatchspread/.code={\setlength{\hatchspread}{#1}},
         hatchthickness/.code={\setlength{\hatchthickness}{#1}},
         hatchshift/.code={\setlength{\hatchshift}{#1}},% must be >= 0
         hatchcolor/.code={\renewcommand{\hatchcolor}{#1}}}
% setting the default values
\tikzset{hatchspread=3pt,
         hatchthickness=0.4pt,
         hatchshift=0pt,% must be >= 0
         hatchcolor=black}
% declaring the pattern
\pgfdeclarepatternformonly[\hatchspread,\hatchthickness,\hatchshift,\hatchcolor]% variables
   {custom north west lines}% name
   {\pgfqpoint{\dimexpr-2\hatchthickness}{\dimexpr-2\hatchthickness}}% lower left corner
   {\pgfqpoint{\dimexpr\hatchspread+2\hatchthickness}{\dimexpr\hatchspread+2\hatchthickness}}% upper right corner
   {\pgfqpoint{\dimexpr\hatchspread}{\dimexpr\hatchspread}}% tile size
   {% shape description
    \pgfsetlinewidth{\hatchthickness}
    \pgfpathmoveto{\pgfqpoint{-1.5\hatchthickness}{\dimexpr1.5\hatchthickness+\hatchspread+\hatchshift}}
    \pgfpathlineto{\pgfqpoint{\dimexpr\hatchspread+1pt+\hatchshift}{-1pt}}
    \ifdim \hatchshift > 0pt
      \pgfpathmoveto{\pgfqpoint{0pt}{\hatchshift}}
      \pgfpathlineto{\pgfqpoint{\dimexpr1pt+\hatchshift}{-1pt}}
    \fi
    \pgfsetstrokecolor{\hatchcolor}
    \pgfusepath{stroke}
   }

\begin{document}
\begin{tikzpicture} 
\fill[left color=blue!40, right color=white,shading angle=45,line width=2pt,
postaction={pattern=custom north west lines, 
hatchthickness=1pt,hatchcolor=white}] (0,0) rectangle (3,3);
\end{tikzpicture}
\end{document}