1 clc;
 2 clear;
 3 
 4 % Here the Aspheric function parameter.
 5 R = 2.684150;
 6 k = -0.517612;
 7 A4 = -5.980307E-5;
 8 A6 = 1.527613E-5;
 9 A8 = 3.647708E-6; 
10 A10 = -1.381275E-7;
11 A12 = 4.485638E-8;
12 
13 Lens_Aspheric_hRange = 5.1; % This the Aspheric h Range.
14 
15 Slice = 100; % Data Slice number.
16 
17 y = linspace(0,Lens_Aspheric_hRange/2,Slice); % h direction linspace data slice.
18 z=y.^2./R./(1+sqrt(1-(1+k)*y.^2./R^2)) + A4*y.^4 + A6*y.^6 + A8*y.^8 + A10*y.^10 +A12*y.^12; % Caculate the z direction axis value.
19 plot(y,z)
20 axis equal
21 
22 syms Aspheric_Func(x)
23 Aspheric_Func(x) = x^2/R/(1+sqrt(1-(1+k)*x^2/R^2)) + A4*x^4 + A6*x^6 + A8*x^8 + A10*x^10 +A12*x^12; % Aspheric surface description function.
24 diff_Aspheric = diff(Aspheric_Func,x); % The Slope function of the Aspheric surface description function.
25 plot(y,Aspheric_Func(y))
26 hold on
27 
28 Lens_Square_thickness = 1.743; % Square Zone thickness value.
29 Lens_thickness = 3.135; % Totally Lens thickness value.
30 Lens_Aspheric_thickness = Lens_thickness - Lens_Square_thickness; % Aspheric zone thickness.
31 max(double(Aspheric_Func(y)));
32 
33 syms PLANO_Func(x)
34 PLANO_Func(x) = Lens_thickness; % First Seperate 
35 plot(y,PLANO_Func(y))
36 light_O = [0,4.41]; % 5.41 is the Focus position
37 plot(light_O(1),light_O(2),'*') % Plot the Laser Light Point O.
38 
39 light_line_S1_K = (light_O(2) - PLANO_Func(y))./(light_O(1) - y); % Draw the Laser Light line from Point to PLANO.
40 Line_YRange = linspace(light_O(2),Lens_thickness,Slice); % The YRange data slice.
41 Line_Step = 5; % Set the Light Line simulation number.
42 syms x
43 for i=1:Line_Step:Slice
44     Line_XRange = (Line_YRange - light_O(2)) / light_line_S1_K(i); % Calculate the XRange data.
45     % fprintf('%d\n',i)
46     plot(Line_XRange,Line_YRange) % Draw the Light line.
47 end
48 % axis equal
49 Light_iU = pi/2 - abs(double(atan(light_line_S1_K))); % Calculate the First input light theta angle.
50 n1 = 1.0; % The Refractive index of the Air.
51 n2 = 1.583; % The Refractive index of the Lens with the material D-ZK3.
52 theta_out = asin(sin(Light_iU)*n1./n2); % Caculate the First output
53 light_line_S2_K = -cot(theta_out); % Caculate the Slope of the Output Light Line.
54 
55 cross_Point = zeros(2,Slice); % Create the Aspheric and Line Cross-Point Buff array.
56 syms Light_S2_Func(x)
57 for i=1:Line_Step:Slice
58     x_s = (Lens_thickness - light_O(2)) / light_line_S1_K(i); % Calculate the Start Point of the Light on PLANO.
59     Light_S2_Func(x) = (light_line_S2_K(i)*(x-x_s) + Lens_thickness); % Define the Light Line Func.
60     for xt = x_s:0.01:(x_s-Lens_thickness/light_line_S2_K(i)+0.02)
61         % temp = abs(Aspheric_Func(xt) - Light_S2_Func(xt))
62         if abs(Aspheric_Func(xt) - Light_S2_Func(xt)) < 0.1 % Calculate the Cross-Point Value.
63             cross_Point(:,i) = [xt,Aspheric_Func(xt)];
64             x_r = linspace(x_s,xt,100);
65             plot(x_r,Light_S2_Func(x_r)) % Draw the Light-Line Graph.
66             break
67         end
68     end
69 end
70 
71 light_line_S3_K_Reg = zeros(1,Slice); % Alloc a Buffer for Storage the Slope of the Output Light Line.
72 
73 for i=1:Line_Step:Slice
74     slope = diff_Aspheric(cross_Point(1,i)); % Calculate the Slope of the Aspheric surface.
75     % normal_alpha = atan(slope)+pi/2; % 法线角度(Units:rad)
76     Light_iU_S2 = atan(slope) - theta_out(i); % Calculate the input angle on the Aspheric surface.
77     Light_oU_S2 = asin(sin(Light_iU_S2)*n2./n1); % Calculate the output angle of the Aspheric surface.
78     light_line_S3_K_Reg(1,i) = tan(pi/2 - abs(Light_oU_S2) + atan(slope)); % Generate the Output Light line function.
79     y_res = linspace(cross_Point(2,i),-10);
80     x_res = (y_res - cross_Point(2,i)) / light_line_S3_K_Reg(1,i) + cross_Point(1,i);
81     plot(x_res,y_res) % Draw the Output Light Line.
82 end
83 axis equal
84 % plot(y,diff_Aspheric(y))