Measurement Of Solar Radiation Taking Into Account The Aging Of Optical Interference Filters
It should be noted that in the world photometric practice great attention is paid to the solution of the problem of results correction concerning the influence of temporal and temperature non-stabilities. All possible correction procedures of the photometric measurement results are being developed in order to minimize the influence of degradation of the major characteristics of optical-electronic section elements taking into account the aging of elements. Replacement of the outdated types of interference filters with the new ones is not always possible for a number of objective reasons.
As it is reported in the paper , analogous problems connected with the temporal and temperature drift of the interference filter characteristics also occurred when operating the CIMEL photometer in AERONET World Network of Aerosol Measurements. Authors  considered the optical interference filters as the limiting factor with regard to the long-term stability of calibration coefficients of CIMEL photometer. Degradation of interference filters occurred in the following order: on average for a year characteristics have varied by 1-5% and in two years some models of filters have degraded much more. Results of the experimental study of interference filter parameters drift of different channels of CIMEL photometer are specified in the following table.
As it is outlined in the paper , the replacement of interference filters with ion-precipitated filters (filters No. 11) made it possible to improve considerably the accuracy characteristics of interference filters.
However, as it is seen from the data given in the table, the accuracy characteristics of interference filters of Sun photometers cannot be deemed satisfactory and the special measures must be provided for the compensation of errors caused by the non-stability of interference filter characteristics when developing the new types of Sun photometers.
We suggest considering the new method of the compensation of influence of interference filter characteristics drift in three-wavelength Sun photometer with two-parametric correction based on the principles set forth in the paper .
For the further description of the suggested correction method, let us consider Bouguer-Beer law which has the following form in respect to the monochromatic wavelength
where is the intensity of solar radiation at the Earth level and wavelength ; is the value of solar constant; is the optical air mass; is the optical atmosphere depth.
Taking into account (1) the output signal of hypothetic one-wavelength photometer can be estimated in the following manner:
where is the photometer instrument function estimated as
where is the instrument function of interference filter; is the instrument function of other construction, optical and electronic units of photometer.
In turn, the instrument function of interference filter is estimated as
where is the time decreasing function describing the physical aging of interference filter; is the bell-shaped transmission function with the central wavelength and half-width of transmission wave .
Taking into account (2) and (3) we have the following
It is well known that during two-parametric correction in three-wavelength photometers the parameter (function of intermediate conversion) is introduced for consideration; this function is estimated as
Taking into account (4) and (5) we have the following
It should be noted that when obtaining the formula (6) the following equality was taken into account:
It is clear from the formula (6) that during the following equalities performance the parameter turns out to be the function of only and or in other words the possibility of accurate estimations of triad combinations emerges:
Herewith, the possibility of carrying out the accurate measurements of emerges using the suggested method of the correction of interference photometer degradation which consists in the generation and solution of the combined equations (7) and (8) with regard to the correction coefficients and . Let us show the suggested variant of solution of the combined equations (7) and (8) relative to and . From the expression (8) we detect the following:
Taking into account the expression (9) in (7) we obtain the following:
Taking the logarithm of the expression (10) we obtain the following:
From the expression (11) we obtain the following:
Taking into account the expressions (9) and (12) we obtain the following:
Thus, in three-wavelength photometers two-parametric correction makes it possible to correct such destabilizing factors as the temporal degradation of interference filter and temporal non-stability of atmosphere optical depth.
Obviously, the suggested method does not provide the selective compensation of individual components of atmosphere optical depth. For example, separate compensation of aerosol and ozone in Sun photometer can be provided by the transition to four-wavelength structure of measuring instrument which will undoubtedly and considerably increase the volume of the necessary measuring operations and works concerning the suggested correction.
Therefore, in order to measure the parameters of solar radiation using the multi-wave Sun photometer it is necessary to carry out the correction of all destabilizing factors and two- and multi-parametric method of correction suggested in the paper  for the first time is completely applicable for it.
As a result of carried out study, it is shown that the temporal degradation of major characteristics of interference filters in three-wavelength Sun photometers requires the parametric correction of this factor.
It is also confirmed, that well-known two-parametric method of correction of atmosphere factors in three-wavelength photometers taking into account the degradation of characteristics of interference filters can be transformed to two-parametric correction of filters’ degradation and correction of the results caused by atmospheric non-stability.
The analytical expressions for the calculation of correcting parameters and used in the procedures of measurements of the Sun radiation parameters are obtained.