A spectroscope can be used to measure the real transmission of a given filter. As one of my project was to perform photometry from my acquired spectra, I needed synthetic filters curves. Some can be found on the web but I wanted my synthetic curves to match the response of the glass filters I have. Usually, such a work is done in laboratory with a stable light source. But I don't have any at hand so I decided to use one free light source, that of the stars themselves. Of course, it would also have been possible to send the filters to someone that can do that job. But by the way, this was also a good exercise in my learning curve of spectroscopy.

To measure the response of a filter from a star, it is best to choose one that have the smoothest continuum spectrum possible, with the fewest absorption bands. The stars that correspond to this description are blue, from late O to early B type, if possible already at a giant phase (class IV to III), since the lower internal pressure of the star leads to less pronounced absorption bands.

When I began that work in December 2018, one interesting star was easily accessible from my site early in the evening: Algenib, Gamma Pegasi, a sub-giant hot blue star (B2IV). Here is the complete spectrum of the star that I have obtained, showing the nice, almost perfect light continuum:


Measuring the response of a filter is simple : you just have to divide one spectrum of the star obtained with the filter, by the spectrum of the same star without the filter. All spectra should be calibrated in wavelengths of course, but no other operation is required than that simple division. Here is a montage of the spectra obtained for my photometric UV, B, and V filters (from Baader):

UBV filter spectra

Trying to measure filters of longer wavelengths poses a problem: with the Star Analyser, the blue end (left) of the second order spectrum begins inside the infrared (right) end of the first order spectrum, from 750 nanometers (or 7500 Angströms). As a result, making a direct division of a red filter spectrum by the whole star spectrum would lead to errors, since the red filter is not going to transmit the blue/red overlap. To solve this problem, the primary spectrum has been obtained through long-pass filters. For the Johnson red filter I used Baader longpass yellow (495 nm cut-on), and for infrared filter I chose Baader red longpass filter (610 nm cuton).

filter spectra R

Here are the raw spectrum of Algenib without filter (in red) and the raw spectrum of Algenib with the Johnson B filter (in blue) algenib_baaderb
And now the result of the division (in red) slightly smoothed in order to eliminate some small irregularities (in blue). The blue curve is saved as the synthetic filter's response, to be used later.

The absolute intensity of a filter's response can be calculated departing from the exposure times of each spectrum but this was not important for my project. I have opened the files in a spreadsheet and modified all values so that the highest intensity match the theoretical maximum value of the filters. I only had one strong problem: the photometric IR filter I have, from an old Schüler Astro-imaging BVRsIs set, was very hard to measure because the transmission of the filter goes far into the infrared, and the end of the spectra proved to be always too much noisy to obtain a valuable profile. Moreover, the current filter's response that is commonly used today is not the same - it is the Johnson-Cousin Ic filter. I have no Ic glass filter on my equipment, but I have built a synthetic curve directly from a spreadsheet.

Here are the synthetic filters I'm using (Is filter is shown only for information, it will not be used for spectro-photometry):

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