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<h1>Source code for optifik.scheludko</h1><div class="highlight"><pre>
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<span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.optimize</span><span class="w"> </span><span class="kn">import</span> <span class="n">curve_fit</span>
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<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">.io</span><span class="w"> </span><span class="kn">import</span> <span class="n">load_spectrum</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">OptimizeResult</span><span class="p">,</span> <span class="n">setup_matplotlib</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">.analysis</span><span class="w"> </span><span class="kn">import</span> <span class="n">finds_peak</span>
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<span class="k">def</span><span class="w"> </span><span class="nf">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
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<span class="n">intensities</span><span class="p">,</span>
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<span class="n">interference_order</span><span class="p">,</span>
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<span class="n">refractive_index</span><span class="p">,</span>
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<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> Compute thicknesses vs wavelength for a given interference order.</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> wavelengths : array</span>
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<span class="sd"> Wavelength values in nm.</span>
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<span class="sd"> intensities : array</span>
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<span class="sd"> Intensity values.</span>
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<span class="sd"> interference_order : int</span>
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<span class="sd"> Interference order.</span>
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<span class="sd"> refractive_index : array_like (or float)</span>
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<span class="sd"> Refractive index.</span>
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<span class="sd"> intensities_void : array, optional</span>
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<span class="sd"> Intensities of void.</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> thicknesses : array</span>
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<span class="sd"> """</span>
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<span class="k">if</span> <span class="n">intensities_void</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
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<span class="n">Imin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">Imin</span> <span class="o">=</span> <span class="n">intensities_void</span>
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<span class="n">n</span> <span class="o">=</span> <span class="n">refractive_index</span>
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<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
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<span class="n">I_norm</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities</span><span class="p">)</span> <span class="o">-</span> <span class="n">Imin</span><span class="p">)</span>
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<span class="n">prefactor</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span>
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<span class="n">argument</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">I_norm</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">I_norm</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)))</span>
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<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="n">term1</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">term1</span> <span class="o">=</span> <span class="p">((</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
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<span class="n">term2</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arcsin</span><span class="p">(</span><span class="n">argument</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">prefactor</span> <span class="o">*</span> <span class="p">(</span><span class="n">term1</span> <span class="o">+</span> <span class="n">term2</span><span class="p">)</span>
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<span class="k">def</span><span class="w"> </span><span class="nf">_Delta</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">refractive_index</span><span class="p">):</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> Compute the Delta values.</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> wavelengths : array</span>
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<span class="sd"> Wavelength values in nm.</span>
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<span class="sd"> thickness : array_like (or float)</span>
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<span class="sd"> Film thickness.</span>
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<span class="sd"> interference_order : int</span>
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<span class="sd"> Interference order.</span>
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<span class="sd"> refractive_index : array_like (or float)</span>
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<span class="sd"> Refractive index.</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> ndarray</span>
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<span class="sd"> Delta values.</span>
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<span class="sd"> """</span>
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<span class="c1"># ensure that the entries are numpy arrays</span>
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<span class="n">wavelengths</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">)</span>
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<span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">thickness</span><span class="p">)</span>
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<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">refractive_index</span><span class="p">)</span>
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<span class="n">m</span> <span class="o">=</span> <span class="n">interference_order</span>
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<span class="c1"># Calculation of p as a function of the parity of m</span>
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<span class="k">if</span> <span class="n">m</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="n">p</span> <span class="o">=</span> <span class="n">m</span> <span class="o">/</span> <span class="mi">2</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">p</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
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<span class="c1"># Calculation of alpha</span>
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<span class="n">alpha</span> <span class="o">=</span> <span class="p">((</span><span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
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<span class="c1"># Argument of sinus</span>
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<span class="n">angle</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">h</span> <span class="o">/</span> <span class="n">wavelengths</span><span class="p">)</span> <span class="o">-</span> <span class="n">p</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
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<span class="c1"># A = sin²(argument)</span>
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<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
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<span class="c1"># Final calcuation of Delta</span>
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<span class="k">return</span> <span class="p">(</span><span class="n">A</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">alpha</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">A</span> <span class="o">*</span> <span class="n">alpha</span><span class="p">)</span>
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<span class="k">def</span><span class="w"> </span><span class="nf">_Delta_fit</span><span class="p">(</span><span class="n">xdata</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">):</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> Wrapper on Delta() for curve_fit.</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> xdata : tuple</span>
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<span class="sd"> (wavelengths, refractive_index)</span>
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<span class="sd"> thickness : array_like (or float)</span>
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<span class="sd"> Film thickness.</span>
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<span class="sd"> interference_order : int</span>
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<span class="sd"> Interference order.</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> ndarray</span>
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<span class="sd"> Delta values.</span>
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<span class="sd"> """</span>
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<span class="n">lambdas</span><span class="p">,</span> <span class="n">r_index</span> <span class="o">=</span> <span class="n">xdata</span>
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<span class="k">return</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">lambdas</span><span class="p">,</span> <span class="n">thickness</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index</span><span class="p">)</span>
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<div class="viewcode-block" id="get_default_start_stop_wavelengths">
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<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.get_default_start_stop_wavelengths">[docs]</a>
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<span class="k">def</span><span class="w"> </span><span class="nf">get_default_start_stop_wavelengths</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
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<span class="n">intensities</span><span class="p">,</span>
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<span class="n">refractive_index</span><span class="p">,</span>
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<span class="n">min_peak_prominence</span><span class="p">,</span>
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<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> Returns the start and stop wavelength values of the last monotonic branch.</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> wavelengths : array</span>
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<span class="sd"> Wavelength values in nm.</span>
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<span class="sd"> intensities : array</span>
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<span class="sd"> Intensity values.</span>
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<span class="sd"> refractive_index : scalar, optional</span>
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<span class="sd"> Value of the refractive index of the medium.</span>
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<span class="sd"> min_peak_prominence : scalar</span>
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<span class="sd"> Required prominence of peaks.</span>
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<span class="sd"> plot : bool, optional</span>
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<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
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<span class="sd"> Raises</span>
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<span class="sd"> ------</span>
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<span class="sd"> RuntimeError</span>
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<span class="sd"> if at least one maximum and one minimum are not detected.</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> wavelength_start : scalar</span>
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<span class="sd"> wavelength_stop : scalar</span>
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<span class="sd"> """</span>
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<span class="c1"># idx_min idx max</span>
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<span class="n">idx_peaks_min</span><span class="p">,</span> <span class="n">idx_peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
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<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
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<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
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<span class="n">failure</span><span class="p">,</span> <span class="n">message</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="s1">''</span>
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<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_min</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="n">message</span> <span class="o">+=</span> <span class="s1">'Failed to detect at least one minimum. '</span>
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<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
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<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx_peaks_max</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="n">message</span> <span class="o">+=</span> <span class="s1">'Failed to detect at least one maximum. '</span>
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<span class="n">failure</span> <span class="o">=</span> <span class="kc">True</span>
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<span class="k">if</span> <span class="n">failure</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="n">message</span><span class="p">)</span>
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<span class="c1"># Get the last oscillation peaks</span>
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<span class="n">lambda_min</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_min</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
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<span class="n">lambda_max</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">idx_peaks_max</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
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<span class="c1"># Order them</span>
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<span class="n">wavelength_start</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
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<span class="n">wavelength_stop</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">lambda_min</span><span class="p">,</span> <span class="n">lambda_max</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">wavelength_start</span><span class="p">,</span> <span class="n">wavelength_stop</span></div>
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<div class="viewcode-block" id="thickness_from_scheludko">
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<a class="viewcode-back" href="../../api_reference.html#optifik.scheludko.thickness_from_scheludko">[docs]</a>
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<span class="k">def</span><span class="w"> </span><span class="nf">thickness_from_scheludko</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span>
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<span class="n">intensities</span><span class="p">,</span>
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<span class="n">refractive_index</span><span class="p">,</span>
|
|
<span class="n">wavelength_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
|
<span class="n">wavelength_stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
|
<span class="n">interference_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
|
<span class="n">intensities_void</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
|
|
<span class="n">plot</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
|
<span class="w"> </span><span class="sd">"""</span>
|
|
<span class="sd"> Compute the film thickness based on Scheludko method.</span>
|
|
|
|
<span class="sd"> Parameters</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> wavelengths : array</span>
|
|
<span class="sd"> Wavelength values in nm.</span>
|
|
<span class="sd"> intensities : array</span>
|
|
<span class="sd"> Intensity values.</span>
|
|
<span class="sd"> refractive_index : scalar, optional</span>
|
|
<span class="sd"> Value of the refractive index of the medium.</span>
|
|
<span class="sd"> wavelength_start : scalar, optional</span>
|
|
<span class="sd"> Starting value of a monotonic branch.</span>
|
|
<span class="sd"> Mandatory if interference_order != 0.</span>
|
|
<span class="sd"> wavelength_stop : scalar, optional</span>
|
|
<span class="sd"> Stoping value of a monotonic branch.</span>
|
|
<span class="sd"> Mandatory if interference_order != 0.</span>
|
|
<span class="sd"> interference_order : scalar, optional</span>
|
|
<span class="sd"> Interference order, zero or positive integer.</span>
|
|
<span class="sd"> If set to None, the value is guessed.</span>
|
|
<span class="sd"> intensities_void : array, optional</span>
|
|
<span class="sd"> Intensity in absence of a film.</span>
|
|
<span class="sd"> Mandatory if interference_order == 0.</span>
|
|
<span class="sd"> plot : bool, optional</span>
|
|
<span class="sd"> Display a curve, useful for checking or debuging. The default is None.</span>
|
|
|
|
<span class="sd"> Returns</span>
|
|
<span class="sd"> -------</span>
|
|
<span class="sd"> results : Instance of `OptimizeResult` class.</span>
|
|
<span class="sd"> The attribute `thickness` gives the thickness value in nm.</span>
|
|
|
|
<span class="sd"> """</span>
|
|
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
|
|
<span class="n">setup_matplotlib</span><span class="p">()</span>
|
|
|
|
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">interference_order</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
<span class="k">if</span> <span class="n">wavelength_stop</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">wavelength_start</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'wavelength_start and wavelength_stop must be passed for interference_order != 0.'</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">if</span> <span class="n">wavelength_start</span> <span class="o">></span> <span class="n">wavelength_stop</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'wavelength_start and wavelength_stop are swapped.'</span><span class="p">)</span>
|
|
|
|
<span class="n">r_index</span> <span class="o">=</span> <span class="n">refractive_index</span>
|
|
|
|
<span class="c1"># Handle the interference order</span>
|
|
<span class="k">if</span> <span class="n">interference_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="c1"># A bit extreme...</span>
|
|
<span class="n">max_tested_order</span> <span class="o">=</span> <span class="mi">12</span>
|
|
|
|
<span class="c1"># mask input data</span>
|
|
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o">>=</span> <span class="n">wavelength_start</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">wavelengths</span> <span class="o"><=</span> <span class="n">wavelength_stop</span><span class="p">)</span>
|
|
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
|
|
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
|
|
<span class="n">thickness_values</span> <span class="o">=</span> <span class="kc">None</span>
|
|
|
|
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$h$ ($\mathrm{{nm}}$)'</span><span class="p">)</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)'</span><span class="p">)</span>
|
|
|
|
<span class="k">for</span> <span class="n">_order</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_tested_order</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
|
|
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
|
|
<span class="n">intensities_masked</span><span class="p">,</span>
|
|
<span class="n">_order</span><span class="p">,</span>
|
|
<span class="n">r_index_masked</span><span class="p">)</span>
|
|
|
|
<span class="n">difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">h_values</span><span class="p">)</span>
|
|
|
|
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"h-difference for m=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">difference</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2"> nm"</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">difference</span> <span class="o"><</span> <span class="n">min_difference</span><span class="p">:</span>
|
|
<span class="n">min_difference</span> <span class="o">=</span> <span class="n">difference</span>
|
|
<span class="n">interference_order</span> <span class="o">=</span> <span class="n">_order</span>
|
|
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
|
|
|
|
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">h_values</span><span class="p">,</span> <span class="s1">'.'</span><span class="p">,</span>
|
|
<span class="n">markersize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s2">"Order=</span><span class="si">{</span><span class="n">_order</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
|
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
|
|
|
<span class="n">min_peak_prominence</span> <span class="o">=</span> <span class="mf">0.02</span>
|
|
<span class="n">peaks_min</span><span class="p">,</span> <span class="n">peaks_max</span> <span class="o">=</span> <span class="n">finds_peak</span><span class="p">(</span><span class="n">wavelengths</span><span class="p">,</span> <span class="n">intensities</span><span class="p">,</span>
|
|
<span class="n">min_peak_prominence</span><span class="o">=</span><span class="n">min_peak_prominence</span><span class="p">,</span>
|
|
<span class="n">plot</span><span class="o">=</span><span class="n">plot</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">peaks_max</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s1">'Failed to detect a single maximum peak.'</span><span class="p">)</span>
|
|
|
|
<span class="n">lambda_unique</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">peaks_max</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
|
|
|
|
<span class="c1"># keep rhs from the maximum</span>
|
|
<span class="n">mask</span> <span class="o">=</span> <span class="n">wavelengths</span> <span class="o">>=</span> <span class="n">lambda_unique</span>
|
|
<span class="n">wavelengths_masked</span> <span class="o">=</span> <span class="n">wavelengths</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
<span class="n">r_index_masked</span> <span class="o">=</span> <span class="n">r_index</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
<span class="n">intensities_masked</span> <span class="o">=</span> <span class="n">intensities</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
<span class="n">intensities_void_masked</span> <span class="o">=</span> <span class="n">intensities_void</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
|
|
|
|
<span class="n">interference_order</span> <span class="o">=</span> <span class="mi">0</span>
|
|
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
|
|
<span class="n">intensities_masked</span><span class="p">,</span>
|
|
<span class="n">interference_order</span><span class="p">,</span>
|
|
<span class="n">r_index_masked</span><span class="p">,</span>
|
|
<span class="n">intensities_void</span><span class="o">=</span><span class="n">intensities_void_masked</span><span class="p">)</span>
|
|
|
|
<span class="k">elif</span> <span class="n">interference_order</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
<span class="n">h_values</span> <span class="o">=</span> <span class="n">_thicknesses_scheludko_at_order</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
|
|
<span class="n">intensities_masked</span><span class="p">,</span>
|
|
<span class="n">interference_order</span><span class="p">,</span>
|
|
<span class="n">r_index_masked</span><span class="p">)</span>
|
|
<span class="n">thickness_values</span> <span class="o">=</span> <span class="n">h_values</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'interference_order must be >= 0.'</span><span class="p">)</span>
|
|
|
|
|
|
|
|
<span class="c1"># Compute the thickness for the selected order</span>
|
|
|
|
<span class="c1"># Delta</span>
|
|
<span class="k">if</span> <span class="n">interference_order</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
|
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
|
|
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_void_masked</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">num</span> <span class="o">=</span> <span class="n">intensities_masked</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
|
|
<span class="n">denom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">intensities_masked</span><span class="p">)</span>
|
|
<span class="n">Delta_from_data</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">denom</span>
|
|
|
|
|
|
|
|
<span class="c1"># Delta_from_data = (intensities_masked -np.min(intensities_masked))/(np.max(intensities_masked) -np.min(intensities_masked))</span>
|
|
<span class="c1"># Delta_from_data = (intensities_raw_masked -np.min(intensities_raw_masked))/(np.max(intensities_raw_masked) -np.min(intensities_raw_masked))</span>
|
|
|
|
<span class="n">DeltaScheludko</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span>
|
|
<span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">),</span>
|
|
<span class="n">interference_order</span><span class="p">,</span>
|
|
<span class="n">r_index_masked</span><span class="p">)</span>
|
|
|
|
|
|
<span class="n">xdata</span> <span class="o">=</span> <span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
|
|
<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">_Delta_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">),</span> <span class="n">xdata</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span> <span class="n">p0</span><span class="o">=</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)])</span>
|
|
<span class="n">fitted_h</span> <span class="o">=</span> <span class="n">popt</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
|
<span class="n">std_err</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">pcov</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span>
|
|
|
|
<span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
|
|
<span class="n">Delta_values</span> <span class="o">=</span> <span class="n">_Delta</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">fitted_h</span><span class="p">,</span> <span class="n">interference_order</span><span class="p">,</span> <span class="n">r_index_masked</span><span class="p">)</span>
|
|
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_from_data</span><span class="p">,</span>
|
|
<span class="s1">'bo-'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
|
|
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">'$\mathrm{{Smoothed}}\ \mathrm{{Data}}$'</span><span class="p">)</span>
|
|
|
|
<span class="c1"># Scheludko</span>
|
|
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">'$\mathrm</span><span class="se">{{</span><span class="s1">Scheludko</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \pm </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">thickness_values</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$'</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">DeltaScheludko</span><span class="p">,</span>
|
|
<span class="s1">'go-'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
|
|
<span class="c1"># Fit</span>
|
|
<span class="n">label</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">'$\mathrm</span><span class="se">{{</span><span class="s1">Fit</span><span class="se">}}</span><span class="s1">\ (h = </span><span class="si">{</span><span class="n">fitted_h</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">\pm </span><span class="si">{</span><span class="n">std_err</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> \ \mathrm</span><span class="se">{{</span><span class="s1">nm</span><span class="se">}}</span><span class="s1">)$'</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">wavelengths_masked</span><span class="p">,</span> <span class="n">Delta_values</span><span class="p">,</span>
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<span class="s1">'ro-'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
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<span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\Delta$'</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\lambda$ ($ \mathrm</span><span class="si">{nm}</span><span class="s1"> $)'</span><span class="p">)</span>
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<span class="kn">import</span><span class="w"> </span><span class="nn">inspect</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">currentframe</span><span class="p">()</span><span class="o">.</span><span class="n">f_code</span><span class="o">.</span><span class="n">co_name</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">OptimizeResult</span><span class="p">(</span><span class="n">thickness</span><span class="o">=</span><span class="n">fitted_h</span><span class="p">,</span> <span class="n">stderr</span><span class="o">=</span><span class="n">std_err</span><span class="p">)</span></div>
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</pre></div>
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