Optical modelling in the mid- and far- infrared
After some discussion with M.Theiss Hard- and Software we agree with the following explanation for the wrong mid-infrared spectra of Float A: The optical constants of Float A have been determined in the range 200 ... 2500 nm only, analyzing R and T spectra recorded with our spectrometer system S1. For the computation of the mid- and far-infrared spectra the program needs to extrapolate the optical constants which is done in the most simple way: The values of n and k at the last available data point (2500 nm wavelength in this case) are used for the whole extrapolation range.
The best solution would be to record spectra in the whole required wavelength range up to 50000 nm. However, we are not going to buy a mid- and far-infrared spectrometer yet. So we need a satisfying extrapolation of the optical constants. Fortunately, for float glass the following solution can be used: We take the infrared optical constants of microscope slide glass from the database delivered with CODE and combine them with our data for the NIR/Vis/UV. This way we get a data set for the required wide spectral range.
M.Theiss Hard- and Software sent us an optical constant object that we can use to elegantly merge the data: The main object computes the optical constants in the range 200 ... 50000 1/cm with 1000 data points. In wavelengths, this is the range 200 ... 50000 nm. Wavenumbers are used because the spacing of the data points is more appropriate in this case (Note that the objects in CODE can have individual spectral ranges and units). The data are composed adding up three susceptibility objects:
The first object contains the infrared optical constants of microscope slide glass from the CODE database:
The second one called 'subtract' adds a constant and negative value which exactly compensates the real part of the dielectric function (which is the square of the complex refractive index) of the mid-infrared data. Adding our NIR/Vis/UV data (third susceptibility term) the final dataset smoothly extends from the far infrared to the UV without any significant jump in the real part of the optical constants:
The absorption coefficient of the combined dataset is shown below:
We test the proposed optical constant model using the window_design.wcd configuration. The optical spectra look fine now:
A layer stack representing a double pane window is made and we compute its technical data:
Using Ar (100%) as filling gas between the two Float A panes a U-value of 2.7 is obtained which matches our expectations.
Opening the list of integral quantities in CODE we have access to the details of the computation of U and g. In particular, we can check if the value of the computed emissivity of the glass is correct. The emissivity is calculated using our far infrared extrapolation. The configuration for the computation of U is this:
The computed value of 0.8363 is very close to the proposed value of 0.837 in EN 673. Being satisfied with this agreement, we add the 'wide range' optical constants of Float A to the database, using the name 'Float A (wide range)'.
Since we are going to work with the extended optical constants of Float A in the future all the time, we replace the current substrate definitions involving Float A by corresponding ones using 'Float A (wide range)'.
For proper emissivity calculations (needed for g and U) the optical constants of all materials in the stack should be extended to the far infrared, in particular the ones for silver. Since we use a Drude model for the electrons, the extrapolation is simple. We just have to evaluate n and k in the wider spectral range. Like in the case of Float A, we use the range 200 ... 50000 1/cm with 1000 points. In order to modify the silver in the database we have to proceed the following way:
| · | Load the object from the database into the material list of CODE
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| · | Delete the object in the database (It might save typing effort if you copy the comment of the old object before you delete it)
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| · | Modify the object in the wanted way
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| · | Enter the modified object as a new object to the database
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The optical constants of the new Ag version are the following:
An update of the oxides to the far infrared is not required - the constant extrapolation that CODE does works fine for these materials.