pgf-interference (10jan22)

git-svn-id: svn://tug.org/texlive/trunk@61562 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 460 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/pgf-interference/pgf-interference.sty b/Master/texmf-dist/tex/latex/pgf-interference/pgf-interference.sty
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+% pgf-interference.sty
+% LaTeX package for simulating interference patterns
+% Author: K. Wehr
+% Version 0.1
+% 9th January 2022
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+\ProvidesExplPackage {pgf-interference} {2022-01-09} {0.1} {simulating interference patterns}
+
+\RequirePackage {tikz}
+
+\bool_new:N \g_pgfinterference_draft_bool
+
+\int_new:N \l_pgfinterference_slits_int % Anzahl der Spalte
+
+\fp_new:N \l_pgfinterference_wavelength_fp % Wellenlänge
+\fp_new:N \l_pgfinterference_slit_distance_fp % Spaltabstand (in m)
+\fp_new:N \l_pgfinterference_slit_width_fp % Spaltbreite (in m)
+\fp_new:N \l_pgfinterference_h_fp % Hilfsgröße (in 1/m)
+\fp_new:N \l_pgfinterference_hb_fp % Hilfsgröße (dimensionslos)
+\fp_new:N \l_pgfinterference_hs_fp % Hilfsgröße (dimensionslos)
+\fp_new:N \l_pgfinterference_x_fp % Position auf dem Schirm (in m)
+\fp_new:N \l_pgfinterference_screen_distance_fp % Schirmabstand (in m)
+\fp_new:N \l_pgfinterference_screen_width_fp % Schirmbreite (in m)
+\fp_new:N \l_pgfinterference_screen_height_fp % Schirmhöhe (in m)
+\fp_new:N \l_pgfinterference_screen_scale_fp % Skalierung
+\fp_new:N \l_pgfinterference_i_fp % relative Intensität innerhalb des Musters
+\fp_new:N \l_pgfinterference_i_scale_fp % Skalierung der Intensität
+
+\str_new:N \l_pgfinterference_ruler_type_str
+
+\tl_const:Nn \c_pgfinterference_ruler_unity_tl { \fontsize{9}{9} \upshape \sffamily cm }
+\tl_const:Nn \c_pgfinterference_ruler_tick_format_tl { \fontsize{9}{9} \upshape \sffamily }
+
+\dim_new:N \l_pgfinterference_screen_width_dim % Schirmbreite in der Abbildung
+\dim_new:N \l_pgfinterference_screen_height_dim % Schirmhöhe in der Abbildung
+\dim_new:N \l_pgfinterference_ruler_height_dim % Höhe des Lineals in der Abbildung
+\dim_new:N \l_pgfinterference_ruler_ticklength_i_dim % Länge eines langen Skalenstrichs auf dem Lineal
+\dim_new:N \l_pgfinterference_ruler_ticklength_ii_dim % Länge eines mittleren Skalenstrichs auf dem Lineal
+\dim_new:N \l_pgfinterference_ruler_ticklength_iii_dim % Länge eines kurzen Skalenstrichs auf dem Lineal
+\dim_new:N \l_pgfinterference_ruler_linewidth_dim % Strichstärke der Linealskala in der Abbildung
+\dim_const:Nn \c_pgfinterference_delta_dim {0.2pt} % Größe eines Bildpunkts
+
+\msg_new:nnn {pgf-interference} {non-positive number}
+  {
+    The~value~of~#1~must~be~positive~ \msg_line_context: .
+  }
+
+\msg_new:nnn {pgf-interference} {wavelength too big}
+  {
+    The~wavelength~is~greater~than~1~metre~ \msg_line_context: .~
+    Radio~waves~are~not~supported!
+  }
+
+\msg_new:nnn {pgf-interference} {slit width too big}
+  {
+    The~slit~width~is~greater~than~the~slit~distance~ \msg_line_context: .~
+    This~is~not~possible!
+  }
+
+\int_set:Nn \l_pgfinterference_slits_int {2}
+\fp_set:Nn \l_pgfinterference_wavelength_fp {632.8e-9}
+\fp_set:Nn \l_pgfinterference_slit_width_fp {1e-5}
+\fp_set:Nn \l_pgfinterference_slit_distance_fp {1e-4}
+\fp_set:Nn \l_pgfinterference_screen_distance_fp {1}
+\fp_set:Nn \l_pgfinterference_screen_width_fp {0.1}
+\fp_set:Nn \l_pgfinterference_screen_height_fp {0.03}
+\fp_set:Nn \l_pgfinterference_screen_scale_fp {1}
+\fp_set:Nn \l_pgfinterference_i_scale_fp {1}
+\str_set:Nn \l_pgfinterference_ruler_type_str {none}
+
+\colorlet {pgfinterferencescreencolor} {black}
+
+% Paketoption
+\DeclareOption {draft}
+  {
+    \bool_gset_true:N \g_pgfinterference_draft_bool
+  }
+\ProcessOptions
+
+% Optionen für das Licht
+\keys_define:nn {pgf-interference}
+  {
+    wavelength .value_required:n = true ,
+    wavelength .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_wavelength_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {wavelength}
+          }
+      } ,
+    intensity .value_required:n = true ,
+    intensity .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_i_scale_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {intensity}
+          }
+      }
+  }
+
+% Optionen für das Beugungsobjekt
+\keys_define:nn {pgf-interference}
+  {
+    slits .value_required:n = true ,
+    slits .code:n =
+      {
+        \int_compare:nNnTF {#1} > {0}
+          {
+            \int_set:Nn \l_pgfinterference_slits_int {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {slits}
+          }
+      } ,
+    slit-distance .value_required:n = true ,
+    slit-distance .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_slit_distance_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {slit-distance}
+          }
+      } ,
+    slit-width .value_required:n = true ,
+    slit-width .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_slit_width_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {slit-width}
+          }
+      }
+  }
+
+% Optionen für den Schirm
+\keys_define:nn {pgf-interference}
+  {
+    screen-distance .value_required:n = true ,
+    screen-distance .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_screen_distance_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {screen-distance}
+          }
+      } ,
+    screen-width .value_required:n = true ,
+    screen-width .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_screen_width_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {screen-width}
+          }
+      } ,
+    screen-height .value_required:n = true ,
+    screen-height .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_screen_height_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {screen-height}
+          }
+      } ,
+    screen-color .value_required:n = true ,
+    screen-color .code:n = { \colorlet {pgfinterferencescreencolor} {#1} } ,
+    scale .value_required:n = true ,
+    scale .code:n =
+      {
+        \fp_compare:nNnTF {#1} > {0}
+          {
+            \fp_set:Nn \l_pgfinterference_screen_scale_fp {#1}
+          }
+          {
+            \msg_warning:nnn {pgf-interference} {non-positive number} {scale}
+          }
+      }
+  }
+
+% Optionen für das Lineal
+\keys_define:nn {pgf-interference}
+  {
+    ruler .choices:nn = { above , below , screen , none }
+      {
+        \str_set:Nn \l_pgfinterference_ruler_type_str {#1}
+      } ,
+    ruler .default:n = {below}
+  }
+
+\cs_new:Nn \pgfinterference_prepare_ruler:
+  {
+    \dim_set:Nn \l_pgfinterference_ruler_height_dim
+      {
+        \fp_eval:n { \l_pgfinterference_screen_scale_fp * 1.2 }  cm
+      }
+    \dim_set:Nn \l_pgfinterference_ruler_ticklength_i_dim
+      {
+        \fp_eval:n { \l_pgfinterference_screen_scale_fp * 5 } mm
+      }
+    \dim_set:Nn \l_pgfinterference_ruler_ticklength_ii_dim
+      {
+        \fp_eval:n { \l_pgfinterference_screen_scale_fp * 4 } mm
+      }
+    \dim_set:Nn \l_pgfinterference_ruler_ticklength_iii_dim
+      {
+        \fp_eval:n { \l_pgfinterference_screen_scale_fp * 3 } mm
+      }
+    \dim_set:Nn \l_pgfinterference_ruler_linewidth_dim
+      {
+        \fp_eval:n { \l_pgfinterference_screen_scale_fp * 0.15 } mm
+      }
+  }
+
+\cs_new:Nn \pgfinterference_draw_ruler:
+  {
+    \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {above}
+      {
+        \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+          ( 0.5 \l_pgfinterference_screen_width_dim , 0.5 \l_pgfinterference_screen_height_dim )
+          -- ++ ( - \l_pgfinterference_screen_width_dim , 0 ) -- ++ ( 0 , \l_pgfinterference_ruler_height_dim )
+          node [ below~right , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]  { \c_pgfinterference_ruler_unity_tl }
+          -- ++ ( \l_pgfinterference_screen_width_dim , 0 ) -- cycle ;
+      }
+      {
+        \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {below}
+          {
+            \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+              ( 0.5 \l_pgfinterference_screen_width_dim , -0.5 \l_pgfinterference_screen_height_dim )
+              -- ++ ( - \l_pgfinterference_screen_width_dim , 0 ) -- ++ ( 0 , - \l_pgfinterference_ruler_height_dim )
+              node [ above~right , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]  { \c_pgfinterference_ruler_unity_tl }
+              -- ++ ( \l_pgfinterference_screen_width_dim , 0 ) -- cycle ;
+          }
+          {
+            \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+              ( 0.5 \l_pgfinterference_screen_width_dim , 0.5 \l_pgfinterference_screen_height_dim )
+              -- ++ ( - \l_pgfinterference_screen_width_dim , 0 ) -- ++ ( 0 , - \l_pgfinterference_ruler_height_dim )
+              node [ above~right , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]  { \c_pgfinterference_ruler_unity_tl }
+              -- ++ ( \l_pgfinterference_screen_width_dim , 0 ) -- cycle ;
+          }
+      }
+    \int_set:Nn \l_tmpa_int { \fp_eval:n { floor ( 1000 * \l_pgfinterference_screen_width_fp ) - 1 } }
+    \int_step_inline:nnn {1} { \l_tmpa_int }
+      {
+        \dim_set:Nn \l_tmpa_dim { \fp_eval:n { \l_pgfinterference_screen_scale_fp * ##1 } mm }
+        \dim_sub:Nn \l_tmpa_dim { 0.5 \l_pgfinterference_screen_width_dim }
+        \int_compare:nNnTF { \int_mod:nn {##1} {10} } = {0}
+          {
+            \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {above}
+              {
+                \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                  ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                  -- ++ ( 0 , \l_pgfinterference_ruler_ticklength_i_dim )
+                  node [ above , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]
+                    { \c_pgfinterference_ruler_tick_format_tl \int_eval:n {##1/10} } ;
+              }
+              {
+                \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {below}
+                  {
+                    \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                      ( \l_tmpa_dim , -0.5 \l_pgfinterference_screen_height_dim )
+                      -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_i_dim )
+                      node [ below , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]
+                        { \c_pgfinterference_ruler_tick_format_tl \int_eval:n {##1/10} } ;
+                  }
+                  {
+                    \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                      ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                      -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_i_dim )
+                      node [ below , scale = \fp_use:N \l_pgfinterference_screen_scale_fp ]
+                        { \c_pgfinterference_ruler_tick_format_tl \int_eval:n {##1/10} } ;
+                  }
+              }
+          }
+          {
+            \int_compare:nNnTF { \int_mod:nn {##1} {5} } = {0}
+              {
+                \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {above}
+                  {
+                    \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                      ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                      -- ++ ( 0 , \l_pgfinterference_ruler_ticklength_ii_dim ) ;
+                  }
+                  {
+                    \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {below}
+                      {
+                        \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                          ( \l_tmpa_dim , -0.5 \l_pgfinterference_screen_height_dim )
+                          -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_ii_dim ) ;
+                      }
+                      {
+                        \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                          ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                          -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_ii_dim ) ;
+                      }
+                  }
+              }
+              {
+                \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {above}
+                  {
+                    \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                      ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                      -- ++ ( 0 , \l_pgfinterference_ruler_ticklength_iii_dim ) ;
+                  }
+                  {
+                    \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {below}
+                      {
+                        \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                          ( \l_tmpa_dim , -0.5 \l_pgfinterference_screen_height_dim )
+                          -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_iii_dim ) ;
+                      }
+                      {
+                        \draw [ line~width = \l_pgfinterference_ruler_linewidth_dim ]
+                          ( \l_tmpa_dim , 0.5 \l_pgfinterference_screen_height_dim )
+                          -- ++ ( 0 , - \l_pgfinterference_ruler_ticklength_iii_dim ) ;
+                      }
+                  }
+              }
+          }
+      }
+  }
+
+\cs_new:Nn \pgfinterference_draw_pattern:
+  {
+    \dim_step_inline:nnnn { -0.5 \l_pgfinterference_screen_width_dim + 0.5 \c_pgfinterference_delta_dim }
+      { \c_pgfinterference_delta_dim } { 0.5 \l_pgfinterference_screen_width_dim }
+      {
+        \fp_set:Nn \l_pgfinterference_x_fp { \dim_ratio:nn {##1} {100cm} / \l_pgfinterference_screen_scale_fp }
+        \fp_set:Nn \l_pgfinterference_h_fp
+          {
+            pi / \l_pgfinterference_wavelength_fp
+            / sqrt ( ( \l_pgfinterference_screen_distance_fp / \l_pgfinterference_x_fp ) ^ 2 + 1 )
+          }
+        \fp_set:Nn \l_pgfinterference_hb_fp { \l_pgfinterference_slit_width_fp * \l_pgfinterference_h_fp }
+        \fp_set:Nn \l_pgfinterference_hs_fp { \l_pgfinterference_slit_distance_fp * \l_pgfinterference_h_fp }
+        \fp_set:Nn \l_pgfinterference_i_fp
+          {
+            ( sin ( \l_pgfinterference_hb_fp ) / \l_pgfinterference_hb_fp
+              * sin ( \l_pgfinterference_slits_int * \l_pgfinterference_hs_fp ) / sin ( \l_pgfinterference_hs_fp )
+              / \l_pgfinterference_slits_int ) ^ 2
+          }
+        \int_set:Nn \l_tmpa_int
+          {
+            \fp_eval:n { round ( 100 * \l_pgfinterference_i_fp * \l_pgfinterference_i_scale_fp ) }
+          }
+        \int_compare:nNnTF { \l_tmpa_int } < {100}
+          {
+            \colorlet {pgfinterferencecolor}
+              {
+                pgfinterferencelasercolor
+                ! \int_use:N \l_tmpa_int
+                ! pgfinterferencescreencolor
+              }
+          }
+          {
+            \colorlet {pgfinterferencecolor} {pgfinterferencelasercolor}
+          }
+        \dim_set:Nn \l_tmpa_dim { ##1 - 0.5 \c_pgfinterference_delta_dim }
+        \fill [ pgfinterferencecolor ] ( \l_tmpa_dim , -0.5 \l_pgfinterference_screen_height_dim )
+          rectangle ++ ( \c_pgfinterference_delta_dim , \l_pgfinterference_screen_height_dim ) ;
+      }
+  }
+
+\NewDocumentCommand \pgfinterferenceoptions {m}
+  {
+    \keys_set:nn {pgf-interference} {#1}
+  }
+
+\NewDocumentCommand \pgfinterferencepattern {m}
+  { 
+    \group_begin:
+    \keys_set:nn {pgf-interference} {#1}
+    \selectcolormodel {rgb}
+    \fp_compare:nNnTF { \l_pgfinterference_wavelength_fp * 1e9 } < {1000}
+      {
+        \definecolor {pgfinterferencelasercolor} {wave}
+          {
+            \fp_eval:n { \l_pgfinterference_wavelength_fp * 1e9 }
+          }
+      }
+      {
+        \colorlet {pgfinterferencelasercolor} {black}
+      }
+    \dim_set:Nn \l_pgfinterference_screen_width_dim
+      {
+        \fp_eval:n { 100 * \l_pgfinterference_screen_scale_fp * \l_pgfinterference_screen_width_fp } cm
+      }
+    \str_if_eq:VnF \l_pgfinterference_ruler_type_str {none}
+      {
+        \pgfinterference_prepare_ruler:
+      }
+    \str_if_eq:VnTF \l_pgfinterference_ruler_type_str {screen}
+      {
+        \colorlet {pgfinterferencescreencolor} {white}
+        \dim_set_eq:NN \l_pgfinterference_screen_height_dim \l_pgfinterference_ruler_height_dim
+      }
+      {
+        \dim_set:Nn \l_pgfinterference_screen_height_dim
+          {
+            \fp_eval:n { 100 * \l_pgfinterference_screen_scale_fp * \l_pgfinterference_screen_height_fp }  cm
+          }
+      }
+    \begin {tikzpicture}
+      \extractcolorspec {pgfinterferencescreencolor} \pgfinterference_tmpa:
+      \extractcolorspec {white} \pgfinterference_tmpb:
+      \bool_lazy_and:nnTF { ! \str_if_eq_p:Vn \l_pgfinterference_ruler_type_str {screen} }
+        { \cs_if_eq_p:NN \pgfinterference_tmpa: \pgfinterference_tmpb: }
+        {
+          \draw [ fill = pgfinterferencescreencolor ]
+            ( -0.5 \l_pgfinterference_screen_width_dim , -0.5 \l_pgfinterference_screen_height_dim )
+            rectangle ( 0.5 \l_pgfinterference_screen_width_dim , 0.5 \l_pgfinterference_screen_height_dim ) ;
+        }
+        {
+          \fill [ pgfinterferencescreencolor ]
+            ( -0.5 \l_pgfinterference_screen_width_dim , -0.5 \l_pgfinterference_screen_height_dim )
+            rectangle ( 0.5 \l_pgfinterference_screen_width_dim , 0.5 \l_pgfinterference_screen_height_dim ) ;
+        }
+      \fp_compare:nNnTF { \l_pgfinterference_wavelength_fp } > {1}
+        {
+          \msg_warning:nn {pgf-interference} {wavelength too big}
+        }
+        {
+          \fp_compare:nNnTF { \l_pgfinterference_slit_width_fp } > { \l_pgfinterference_slit_distance_fp }
+            {
+              \msg_warning:nn {pgf-interference} {slit width too big}
+            }
+            {
+              \bool_if:NF \g_pgfinterference_draft_bool {  \pgfinterference_draw_pattern: }
+            }
+        }
+      \str_if_eq:VnF \l_pgfinterference_ruler_type_str {none}
+        {
+          \pgfinterference_draw_ruler:
+        }
+    \end {tikzpicture}
+    \group_end:
+  }