2.1

Introduction of concepts

To obtain a global overview of the Martian dust, remote sensing of the sunlight, that has been reflected by the Martian surface and scattered by the Martian atmosphere, is required. This light can be described by a vector I as follows:

Where I is the total flux of the light, Q and U represent linearly polarized light and V the circularly polarized light, all with units of W/m². Circularly polarized flux arises typically when light is scattered by optically active or chiral particles. Recent measurements (Sparks et al. (2005)) have shown that the degree of circular polarization averaged over the face of the planet is 0.02 % (detection limit) and that no regions of circular polarization were actually identified. Because of its small value we will ignore circular polarization in the following.

The direction of the light that is incident on a planet is described by elevation angle θ and azimuthal angle ϕ. Figure 1 shows this illumination geometry. Note that the obtainable range of azimuth and elevation angles shown in figure 1 are highly dependent on the orbit parameters of the planet-orbit platform.

Figure 1.

Illumination geometry of a planetary body

The degree of linear polarization P of the light is defined as shown in equation 2:

The direction of linear polarization χ, as mathematically defined in equation 3, is defined with respect to the local meridian plane, i.e. the vertical plane containing the direction to the local nadir and the direction of propagation of the reflected light:

The direction of linear polarization should be in the interval 0 ≤ χ ≤ π and has the same sign as Q. Note that for φ-φ₀ equal to 0 or π and for a horizontally homogeneous surface and atmosphere, χ will always be equal to π/2.

Measuring the flux and the polarisation in combination with the scattering angle dependency proves to be a powerful tool to determine physical properties of the dust.

2.2

Simulated Martian radiances and degrees of linear polarization

Simulated Martian radiances and degrees of linear polarization are needed to establish requirements of-and specifications for the SPEX instrument. We use the adding doubling method (de Haan et al., 1987) which contains a treatment for multiple scattering and takes into account the polarisation state of light. Figure 2 shows an example of a simulation of Martian degree of linear polarisation at 633 nm for a range of sensor geometries, where the sun elevation angle θ₀ was set to 45 degrees (see figure 1). Main inputs for this simulation are:

Figure 2.

simulated reflected degree of linear polarization for a Martian dust storm scenario

It follows from this simulation that a linear degree of polarization in the range from 0.0 to 0.15 at 633 nm is foreseen for a Martian dust storm and that there is a strong angular variance.

3.1

Polarisation measurement concepts

The challenge in the development of SPEX is to find an optimum solution in the choice for- and combination of spectral coverage, polarisation parameters, spatial coverage and phase angle coverage. The data product that SPEX scientists want to obtain in the end is the phase function of the atmospheric flux and polarisation (at as many different locations) as a function of wavelength.

The first challenge is to reduce the 4 dimensions of the observational space (polarisation, wavelength, coverage, phase angle) such that it can be detected with a 2-dimensional detector array. Driven by the vision to ultimately reach a compact few kg instrument we consider only options with a single telescope system, a single detector and no mechanisms, or systems that can be significantly miniaturized. The exclusion of mechanisms rules out any instrument concept such as the POLDER instrument (Leroy et al., 1997) which works with a filterwheel containing different polarisation filters and colour filters. The important advantage of the POLDER concept though, is the impressive daily global coverage capacity from low orbits due to its wide field of view, simultaneously covering an area of ± 43° along track and ± 51° cross track.

The (currently ongoing) trade-off basically boils down to 2 polarisation measurement concepts. Firstly, the conventional concept of splitting up the different polarisation states of the light directly into at least 3 separate beams, by, for example, Wollaston prisms. This method is employed in the Aerosol Polarimetry Sensor (APS) (Mishchenko et al., 2004) to be flown on NASA’s Glory mission (launch currently planned for summer 2009). For a 4 beam system (APS uses 3), the degree of linear polarisation P is determined by equation 2 where follows, after doing some Mueller matrices calculus leads to equation 4 and 5:

And

Where the intensity S_i(λ) is the intensity on each of the 4 beam’s detectors. S_i(λ) is the first element of the vector S_i(λ), where:

Where T_i(λ) is the transmission of the optics chain from telescope to detector, M_i is the Mueller matrix for respectively a horizontal linear polarizer (i=1), a vertical linear polarizer (i=2), a linear polarizer at +45° (i=3) and a linear polarizer at -45° (i=4), and I(λ) is the stokes vector of the incoming light to the instrument.

A novel patent pending concept for measuring the polarization state was invented by Utrecht University (Snik et al., 2008) where the degree and angle of linear polarization of the incoming light is encoded as a sinusoidal modulation of the intensity spectrum. This is achieved by using an achromatic quarter-wave retarder, an athermal multiple-order retarder and a polarizing beamsplitter behind each entrance pupil.

In case there are no spectral features in the incoming light, the degree of linear polarisation P(λ) and the direction of linear polarization χ(λ) can in principle be determined from a single measurement, as shown in equation 7:

Where S(λ) is the measured signal on the detector, I(λ) is the intensity spectrum and δ(λ) is the retardance of the multiple-order retarder.

To be able to determine the degree and direction of linear polarisation P(λ) and χ(λ) with a dedicated algorithm to Eq. 7, it is required that the retardance is chosen such that the modulation is much longer than the wavelength resolution of the spectrometer.

Table 3.1 shows a high level trade-off assessment between the conventional and the modulation concept for polarisation measurement, as described in the former.

Table 3.1.

High level trade-off between the conventional and the modulation concept for polarisation measurement.

The trade-off between the conventional and the modulation concept is ongoing. We foresee to use a Cramér-Rao lower bound (CRLB) analysis to make a proper comparison between the two. It has already been shown by Snik et al. (2008), that the modulation method is able to comply to the science requirements for polarization sensitivity and accuracy (see table 3.2). As such, the current SPEX instrument baseline is the modulation concept for which we will create a breadboard to show system level feasibility.

Table 3.2.

SPEX instrument baseline requirements and specifications

3.2

SPEX instrument baseline specification

Table 3.2 shows the baseline specification / requirement of the SPEX instrument. This set of parameters is derived in an iteration between science and engineering.

The SPEX instrument baseline has 7 nadir looking FOV’s which allow phase angle coverage by overflight of the area of interest. Additional forward and backward limb FOV’s are present to extend the phase angle range for a given area of interest as much as possible. Figure 3 shows the geometry of the SPEX instrument baseline FOV’s.

Figure 3.

SPEX instrument baseline FOV geometry

By using a satellite platform capable of yaw oscillation steering, it proves to be possible to obtain scientific data for all the points in the 7° swath width of the nadir pointed telescope. Without this capability, only part of the scientific data within the 7° swath width is available for the fully achievable scattering range. This is caused by the fact that during overflight of the area of interest, this area rotates away from the orbit plane.

Figure 4 shows a CAD drawing of the optical design of SPEX.

Figure 4.

SPEX instrument baseline optical design

The Martian radiance enters the pre-optics which contains 9 telescope systems which include the polarization modulation optics. Each telescope system contains 2 output beams each having an opposite modulation in its spectrum (see ‘±’ sign in Eq. 7). The advantage of having these 2 opposite modulation spectra is that an un-modulated high resolution spectrum can be obtained by combining them. This spectrum is also foreseen to play an important role in further improving the accuracy of the polarization data products that could already be obtained by any of the 2 modulated spectra.

The 18 output beams from the pre-optics are combined in to a single plane to go through the spectrometer slit. From there on, this plane is imaged onto a 2D detector after dispersion by a transmission grating. The detector we foresee to use is the (space qualified) Cypress Star 250 CMOS detector, with associated control electronics, 512 x 512, 25 μm pitch pixels, reasonable quantum efficiency from 400 to 800 nm and built in 10-bits ADC.

Figure 5 shows a simulated signal for one detector row (i.e. one of the spectra measured within a single SPEX FOV), with an integration time of 3 seconds. The inputs for the radiative transfer model to obtain this simulated signal are as presented in section 2.2. The elevation angle θ for the sensor was set to 0 degrees (i.e. strictly nadir).

Figure 5.

Simulated SPEX signal as a function of wavelength

The features in the signal are a combination of Fraunhofer lines present in the solar irradiance and the modulation introduced by the telescope modulator optics. The latter features are best seen between 700 and 800 nm where the features of the solar irradiance Fraunhofer lines are slightly less pronounced. From the amplitude of the observed modulation, the degree of linear polarisation could be determined and should be in the order of 6 % (with reference to figure 2).