The Diffraction Effect and its implications
Diffraction effects in solar radiometry become more and more important once the target uncertainty goes below 0.1%. At the radiometric two aperture system, diffraction occurs at the front aperture, and thus reduces or enhances the amount of solar radiation passing the second aperture and reaching the detector. This strongly wavelength dependent effect has an impact in the order of 0.1% and can increase by up to 50% depending on the spectral conditions. This leads to an error in the measurement that needs to be corrected if high accuracy is needed.
Considering the ISO 9060:2018 criteria for radiometer classification, a major problem is to overcome the spectral error introduced by the diffraction effect. Considering the set of spectra given in ISO 9060:2018, it has been found that PMO6/PMO8 and HF type radiometers have an enhanced sensitivity (up to 400 – 500 ppm) compared to the standard conditions (spectrum G-173) for some of the spectra provided by ISO (see also this post).
The problem of diffraction is also most evident for the Cryogenic Solar Absolute Radiometer (CSAR, described by R. Winkler [2013] ) where ultimate precision is needed. In order to overcome this situation, a software has been developed to calculate a diffraction correction for a given atmospheric situation. This approach has first been used by Davos Instruments and PMOD/WRC to provide diffraction corrections for CSAR in the framework of an EMPIR project. Results have been presented at the IPC-XIII in 2021.
Besides the improvement of the accuracy for CSAR, this approach allows to lower the spectral error, introduced by the diffraction effect to a ISO 9060:2018 AA class compatible level for regular standard radiometers such as the PMO6/PMO8.
Software and Workflow
The software derives the current diffraction correction from a look-up table using atmospheric parameters (integrated water vapor, aerosol optical depth) as well as zenith angle of the sun as input parameters.
The look-up table is generated beforehand using the libRatran code to simulate solar spectra based on the given parameters. These spectra are then used to weight the spectrally dependent diffraction correction in order to derive a single correction factor. The workflow for CSAR and the PMO8 is illustrated in the two graphs.
The software has been written in python. A program with an example look-up table can be downloaded here. The provided look up table is generated for an altitude of 1590 m above sea level (Davos). Other tables can be provided on request.
Uncertainties
The program is able to estimate the uncertainty of the correction factor based on the uncertainty of the input parameters (error propagation). This allows the user to judge if such a correction is reliable for a given situation. In addition to these propagating uncertainties, uncertainties arise from the method itself. The combined overall uncertainty for CSAR in well known conditions has been estimated to 33 ppm (k=1). The uncertainty is dominated by the uncertainty of the input parameters. Therefore the error propagation capability of the program is a very valuable tool to asses uncertainties of the individual diffraction corrections.
A second source of error is the misalignment. If the radiometer is not ideally pointed towards the sun, the centre of the diffraction pattern does not match the centre of the precision aperture. Thus a slightly different part of the pattern will enter the cavity, thus more or less light will enter the cavity. This effect is in the order of 50 ppm at 0.3°.