New Method to Calculate the Angular Weighting Function for a Scattering Instrument: Application to a Dust Sensor on Mars

Abstract

Suspended dust above the Martian surface is an important element in Martian climatology. In the frame of the Exomars’22 mission, we developed a dust sensor instrument, designed to provide size parameters of dust particles suspended in Mars surface from the light scattered by the particles. Thus, to interpret the data of the dust sensor, we need a method to calculate the theoretical optical power dispersed by the particles and, therefore, the theoretical signal obtained by the instrument. This signal depends on the suspended particles and on the instrument configuration. In this paper, we present a new method to calculate the angular weighting function (Wf) for scattering sensors. Wf encompasses the scattering angles measured by the sensor and depends only on the instrument and not on the suspended particles. To calculate this Wf, we use fundamental radiometry principles and an appropriate coordinate system, where one coordinate is the scattering angle. The method is applied to the dust sensor instrument and compared with other methods. The comparison highlights the advantages of the proposed method since it avoids using an ideal sampling volume, preserves the radiometric meaning, and avoids instrument calibration. The effectiveness of the method makes it a valuable tool for the design of scattering instruments and also for the interpretation of their data.

Calibration of a Dust Scattering Instrument Using Tomographic Techniques and Its Application to a Dust Sensor Instrument

“…In the previous section, the W f function for the forward configuration of the PbS sensor of the Dust Sensor was obtained experimentally. The results are in good agreement with the values obtained in a previous article [19], where it was found that the scattering angles measured in this configuration range roughly from 30 to 130 degrees.…”

“…In [19], W f was calculated from the measurement of the irradiance pattern of the source and the angular sensitivity of the detector. Both were measured separately and then the detector and the IR source were assembled in the instrument.…”

“…is a function that groups the terms that depend only on the geometry of the instrument and will be called from now on as volume weighting function (VWF). As explained in detail in a previous work [19], there is a specific coordinate system (q 1 , q 2 , θ) that allow us to express the VWF as a one-dimensional function, called angular weighting function (W f ), that only depends on the scattering angle θ. This W f (θ) function can be calculated through integration on the other two coordinates, q 1 and q 2 :…”

“…To obtain W f as defined by Equation ( 7), it is necessary to express VWF(x, y, z) in a coordinate system (q 1 , q 2 , θ), where one of its coordinates is the scattering angle. This coordinate system has been defined in [19]. To numerically calculate the integral in ( 7), an interpolation of VWF(x, y, z) exp is performed on an (equispaced) mesh of the new coordinate system (Figure 6).…”

“…To solve the nonidealities in integrating nephelemoters, some studies include a truncated angular weighting function [16][17][18]. In a previous work [19], the authors proposed a method to solve the problem of the idealization of the volume of interaction by defining an angular weight function, W f (θ), based on the choice of an appropriate coordinate system for the instrument, which depends only on the scattering angle θ and groups all the geometric factors of the instrument, without assuming ideal emission or FoV patterns.…”