.. _sphx_glr_auto_gallery_accuracy:

Accuracy and comparisons
------------------------

How well the models are known, and how their predictions depend on the published
formulas, measurement conditions and density conventions.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="The quantity a change of dispersion model moves most visibly in a gas-filled hollow capillary is the zero-dispersion wavelength (ZDW), where the gas&#x27;s normal dispersion balances the waveguide&#x27;s anomalous term. For the fundamental EH11 mode of a capillary of core radius a (Marcatili &amp; Schmeltzer, lossless part)">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_capillary_zdw_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_capillary_zdw`

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      <div class="sphx-glr-thumbnail-title">Capillary zero-dispersion wavelength</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The refractive index of a gas at number density N follows from the per-particle polarizability \alpha through the Lorentz-Lorenz relation. The linear scaling \chi = N\alpha/\varepsilon_0 is its dilute limit. This figure shows the relative error of linear scaling in \chi = n^2 - 1 against pressure, for a polarizability typical of each gas.">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_density_scaling_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_density_scaling`

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      <div class="sphx-glr-thumbnail-title">Linear density scaling against Lorentz-Lorenz</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="How well each fitted model knows the group-velocity dispersion \beta_2 and the third-order dispersion \beta_3: the relative one-sigma uncertainty propagated from the fit&#x27;s covariance (scaled by the reduced chi-squared where it exceeds one; dispersion_sigma_relative), against wavelength over each model&#x27;s range. In the dilute limit these relative uncertainties do not depend on pressure or temperature.">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_dispersion_uncertainty_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_dispersion_uncertainty`

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      <div class="sphx-glr-thumbnail-title">Dispersion uncertainty and sensitivity to dataset selection</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The group-velocity dispersion \beta_2 = (\lambda^3/2\pi c^2)\,\mathrm{d}^2n/\mathrm{d}\lambda^2 of each noble gas at 1 bar and 20 °C, from the fitted model, and the ratio to it of every published, legacy and comparison formula over its stated range. The dispersion of a gas-filled hollow fibre is the gas&#x27;s \beta_2 against the waveguide&#x27;s anomalous term, so these ratios move zero-dispersion wavelengths and phase-matching points directly.">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_gvd_comparison_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_gvd_comparison`

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      <div class="sphx-glr-thumbnail-title">Group-velocity dispersion: the fits against the formulas in use</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A 50/50 helium-argon fill at 294 K, from 1 to 60 bar, at 800 nm. The reference is optmat&#x27;s mixture law (OEP 4): the mixture&#x27;s equation of state for the densities and Lorentz-Lorenz of the whole mixture, with its pair terms. Each curve leaves one piece out and shows the relative change in n - 1 (left) and in the group-velocity dispersion (right):">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_mixture_he_ar_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_mixture_he_ar`

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      <div class="sphx-glr-thumbnail-title">The dispersion of a helium-argon fill against pressure</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Each fit refitted without each of its datasets in turn (``tools/fit/robustness.py``, stored in data/gas/models/robustness): the change of the polarizability at five wavelengths across the model&#x27;s range, in units of the full fit&#x27;s one-sigma uncertainty. A dataset whose removal moves the model by much more than one sigma determines the model there on its own. For the backbones (the ab initio moments of helium, neon and argon, the dielectric static values) that is by design. Two levels rest on one metrology value each: hydrogen&#x27;s on Achtermann&#x27;s (-870 ppm without it) and oxygen&#x27;s on Birch&#x27;s (-840 ppm), where the band understates the uncertainty of the level (TC-101).">

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  .. image:: /auto_gallery/accuracy/images/thumb/sphx_glr_plot_robustness_thumb.png
    :alt:

  :doc:`/auto_gallery/accuracy/plot_robustness`

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      <div class="sphx-glr-thumbnail-title">Robustness: leaving one dataset out</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /auto_gallery/accuracy/plot_capillary_zdw
   /auto_gallery/accuracy/plot_density_scaling
   /auto_gallery/accuracy/plot_dispersion_uncertainty
   /auto_gallery/accuracy/plot_gvd_comparison
   /auto_gallery/accuracy/plot_mixture_he_ar
   /auto_gallery/accuracy/plot_robustness