3d plot with reflected arrows in "planes" using TikZ

Question

I'm trying to reproduce this picture in TikZ, but I don't know how to get those 3D "planes" of arrows shown.

Here is my attempt so far, which isn't remotely close to what I want (and mostly obtained from here anyway):

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
 \draw (-4,0) arc (180:360:4 and 1);
 \draw [dashed] (-4,0) arc (180:0:4 and 1);
 \draw (-4,0) arc (180:0:4 and 4);
 \draw (0,0,0) -- ++(0,-.5,-.5) -- ++(0,.5,0) -- ++(0,.5,.5) -- cycle;
 \draw (0,0) -- ++(-.5,0) -- ++(0,.5) -- ++(.5,0) -- cycle;
 \draw [thick, dashed] (0,0) -- ++(-5,0);
 \draw [thick, {latex}-] (0,0) -- ++(172.5:5cm);
 \draw [thick, dashed] (0,0) -- ++(0,5);
 \draw [thick, dashed] (0,0,0) -- ++(0,-2.5,-2.5);
 \draw [thick, -{latex}] (0,0) -- ++(45:5cm);
 \draw [red, thick, <->] (0,0) ++(172.5:4.5cm) arc (172.5:180:4.5cm) node [midway, left] () {$\gamma_i$};
 \draw [red, thick, <-] (0,0) ++(180:1.5cm) arc (180:532:1.5cm) node [midway, right] () {$\varphi_i$};
\end{tikzpicture}
\end{document}

EDIT: If TikZ isn't good for doing this, any other package will do at this point!

Answer 1

I am uploading the code that done from a friend of mine (@GeorgePapademetriou -not a member, but sure want to share)

\documentclass[svgnames,10pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
%\usepackage{xcolor}
%\usepackage{pgfplots}
\usetikzlibrary{arrows, 3d, decorations.markings}
\usetikzlibrary{calc}
\usepgflibrary{shapes.arrows} 



\begin{document}

%% plane with 
\begin{tikzpicture} % 
\def\R{1.8} % for phi angle
\begin{scope}  [x={(0.9cm,-0.15cm)}, y={(0.25cm,0.435cm)}, z={(0cm,0.8cm)}, scale=2.5]
\begin{scope} [every path/.style={thin}]
\begin{scope} [canvas is xy plane at z=0]
 %the plane
 \draw [fill=green!10] (-2.2,-2)--(-2,2)--(2,2)--(2.2,-2)--cycle; 
\end{scope}
% x,y,z axis
\draw[-latex] (-2.1,0,0) -- (2.5,0,0) node[right]{$x$};
\draw[-latex] (0,-2,0) -- (0,2.5,0) node[right]{$y$};
\draw[-latex] (0,0,0) -- (0,0,2) node [above]{$z$};
\begin{scope}[canvas is xy plane at z=0]
 % phi angle and vectors
 \draw [->, thick, red] (0:\R-0.4) arc[start angle=0,delta angle=310,radius=\R-0.4] node[below] {$\phi_r$};
 \draw [fill=yellow!20, thick] (0,0)--(0:\R-0.8) arc[start angle=0,delta angle=-90, radius=\R-0.8]-- cycle;
 \draw[-latex,black] (0,0)--++(-80:\R-0.8);
 \draw[-latex,black] (0,0)--++(-60:\R-0.8);
 \draw[-latex,black] (0,0)--++(-40:\R-0.8);
 \draw[-latex,black] (0,0)--++(-20:\R-0.8);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
 %theta angle and vectors
 \draw [fill=blue!10, thick] (0,0)-- (90:\R-0.8) arc (90:180:\R-0.8)--cycle;
 \draw [-latex, blue!50!black, thick] (90:\R-0.65) arc (90:141:\R-0.65) node [midway, above] {$\theta_i$};
 \draw[-latex,black] (0,0)--++(110:\R-0.8);
 \draw[-latex,black] (0,0)--++(130:\R-0.8);
 \draw[-latex,black] (0,0)--++(150:\R-0.8);
 \draw[-latex,black] (0,0)--++(170:\R-0.8);
 % node and vector to the theta angle
 \draw[semithick,black,decoration={markings,mark=at position 0.5 with {\arrow{latex}}}, 
postaction=decorate] (0,0)++(141:2.5) node[above,align=center] {Incidence \\ direction} --++ (141:-2.5); 
\end{scope}
% first lobe 
 \draw [fill=blue!5, thick] (0,0,0)--(0,0,1) to [bend left=25] (0.8,0.25, 0.6) to [bend left=20] (2,0.6, 0) 
       to [bend left=20] (1.5,0.4,0)--cycle; 
 \draw[-latex,black] (0,0)--++(95:1.76); 
 \draw[-latex,black] (0,0)--++(80:1.56);
 \draw[-latex,black] (0,0)--++(60:1.5);
 \draw[-latex,black] (0,0)--++(40:1.78);
 \draw[-latex,black] (0,0)--++(25:1.97);
 \draw[-latex,black] (0,0)--++(10:1.5);
 \draw[-latex,black] (0,0)--++(-5:1.5);
\begin{scope}[canvas is xz plane at y=0]
%second lobe
 \draw [fill=blue!18, thick] (0,0)-- (90:\R-0.8) arc(90:40:\R-0.8) to [bend left] (2.2,0.15) to [bend left] (1.5,0) --cycle;
 \draw[-latex,black] (0,0)--++(80:\R-0.8);
 \draw[-latex,black] (0,0)--++(60:\R-0.8);
 \draw[-latex,black] (0,0)--++(40:\R-0.8);
 \draw[-latex,black] (0,0)--++(30:1.32);
 \draw[-latex,black] (0,0)--++(20:1.68);
 \draw[-latex,black] (0,0)--++(10:2);
 \draw[-latex,black] (0,0)--++(4:2.2);
\end{scope}
 %third lobe
 \draw [fill=blue!25, thick] (0,0,0)--(0,0,1) to [bend left] (0.75,-0.25, 0.6) to [bend left=20] (2.1,-0.6, 0.3) 
       to [bend left=20] (1.5,-0.5, 0)--cycle; 
 \draw[-latex,black] (0,0)--++(95:1.6); 
 \draw[-latex,black] (0,0)--++(80:1.23);
 \draw[-latex,black] (0,0)--++(60:0.9);
 \draw[-latex,black] (0,0)--++(40:1.1);
 \draw[-latex,black] (0,0)--++(25:1.33);
 \draw[-latex,black] (0,0)--++(10:1.64);
 \draw[-latex,black] (0,0)--++(-3:1.95);
 %forth lobe
 \draw [fill=blue!30, thick] (0,0,0)--(0,0,1) to [bend left] (0.65,-0.45, 0.5) to [bend left=20] (1.8,-0.6,0,0.5)
       to [bend left=20] (1.2,-0.8,0,0)--cycle;
 \draw[-latex,black] (0,0)--++(100:1.58);
 \draw[-latex,black] (0,0)--++(90:1.28);
 \draw[-latex,black] (0,0)--++(75:0.9);
 \draw[-latex,black] (0,0)--++(50:0.61);
 \draw[-latex,black] (0,0)--++(20:0.8);
 \draw[-latex,black] (0,0)--++(0:1.24);
 \draw[-latex,black] (0,0)--++(-18:1.85);
 \draw[-latex,black] (0,0)--++(-28:1.7);
 %descriptions
 \node at (2.4,-2.2,0) {$q(\phi_r)=q(\phi_r=0)\cos\phi_r$};
 \draw[->, blue!50!black] (2.4,-2,0)--(2.2,-0.2,0);
 \draw[->, blue!50!black] (1.9,-2.1,0)--(1.5,-1,0);
 \node at (-2.6,0,0.5) {Measuring plane};
 \draw[->, blue!50!black] (-2.2,0,0.5)--(-.4,-.2,0.4);
 \node at (-1.6,-1.6,0) {Sample plane};
 \end{scope}
\end{scope}

\end{tikzpicture} 
%


\end{document}

Output:

PS: We have been payed for this graphic, but I suppose that the OP would like to share since he is probably the one that asked and if someone asks for help from a forum we have to believe that he want to help the forum too. PS2: Ok... I mean this... that is not a forum!

Answer 2

This is similar to koleygr's answer but uses tikz-3dplot to obtain the rotated coordinate systems, and \foreach loops to make the code shorter. One reason to post this is that now, i.e. starting from version 3.1 of TikZ, the 3d library treat the xy plane on the same footing as all other planes.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
\tdplotsetmaincoords{70}{20}
\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,%
funky shape/.style={insert path={%
(0,0) -- (2.5,-1) to[bend right] coordinate[pos=0.5] (#1-1) (3.5,0)
coordinate (#1-2) to[bend right] coordinate[pos=1/3] (#1-3) 
coordinate[pos=2/3] (#1-4)(1,1) coordinate (#1-5)
to[bend right] coordinate[pos=0.5] (#1-6) (0,2)}}]
 \draw[fill=yellow!70!gray,canvas is xy plane at z=0] (-5,-5) rectangle (5,5);
 \node[transform shape,canvas is xy plane at z=0,anchor=south west]
 at (-5,-5) {sample plane};
 \draw[-stealth] (-5,0,0) -- (5,0,0) node[pos=1.05]{$x$};
 \draw[-stealth] (0,-5,0) -- (0,5,0) node[pos=1.05]{$y$};
 \draw[-stealth] (0,0,0) -- (0,0,5) node[pos=1.1]{$z$};
 \begin{scope}[canvas is xy plane at z=0]
  \draw[fill=yellow!90!gray] (-90:2.5) arc (-90:0:2.5) -- (0,0);
  \foreach \Z in {-81,-72,...,-9}
   {\draw[thick,-latex] (0,0) -- (\Z:2.5); }
  \draw[-latex] (3.25,0) arc(0:300:3.25) node[below]{$\varphi_r$}; 
 \end{scope}
 \begin{scope}[canvas is xz plane at y=0]
  \draw[fill=blue!20] (90:2.5) arc (90:180:2.5) -- (0,0);
  \foreach \Z in {105,120,...,165}
   {\draw[thick,-latex] (0,0) -- (\Z:2.5); }
  \draw[thick] (135:6.5) node[above,align=center]{incidence\\ direction} -- (135:2.5);
  \draw[thick,-latex] (135:6.5) -- (135:4.5);
  \node[anchor=south east] at (110:3) {$\theta_i$};
  \draw[-latex] (90:3) arc(90:135:3);
 \end{scope}
 \foreach \X [count=\Y,evaluate=\Y as \Col using {int(\Y*20)}] in {30,0,-20,-40}
 {\tdplotsetrotatedcoords{\X}{00}{0}    
 \begin{scope}[tdplot_rotated_coords]
  \begin{scope}[canvas is xz plane at y=0]
   \draw[fill=blue!\Col,funky shape=X-\Y];
   \foreach \Z in {1,...,6}
   {\draw[thick,-latex] (0,0) -- (X-\Y-\Z); }
  \end{scope}
 \end{scope}}
 \node (q) at ([yshift=-2cm]X-2-2) {$q(\varphi_r)=q(\varphi_r=0)\cos\varphi_r$};
 \foreach \Y in {2,3,4}
 {\draw[thick,-latex] (q) -- (X-\Y-2);}
\end{tikzpicture}
\end{document}