The methods in this protocol can help solve the open computational problem of light scattering by planetary regoliths, densely packed layers of particles on the surfaces of asteroids going through nuclei and other solar system objects. To validate the computations, we introduce unique non-contacting and non-destructive measurements based on ultrasonic sample levitation. We have full control on sample position and orientation.
Here we apply validated computational methods to interpret observations of asteroid 4 Vesta and 67P/Churyumov-Gerasimenko. The computational and the experimental methods are universal and can be applied for example in terrestrial remote sensing, nanoscale material sciences, and biomedical optics. Utilizing these methods requires patience.
However, the effort pays off due to the absolute and quantitative nature of the result. Visual demonstration of the methods is critical. The experimental part shown in this video combines state-of-the-art techniques in both optics and acoustics.
Demonstrating the procedure will be Dr.Antti Penttila, Ms.Julia Martikainen, Mr.Petteri Helander, Mr.Goran Maconi, and Mr.Timo Vaisanen. To begin, set up the scatterometer by turning on the light source, photo multiplier tubes and amplifiers. Allow the system to stabilize for 30 minutes.
Next, set up the acoustic sample levitator by inserting the microphone in the center of the levitator and running the calibration script. Then make a measurement sweep with an empty levitator. The sweep reveals any signals generated by ambient light, reflections from the surroundings or electrical noises.
Once setup, use an acoustically transparent mesh spoon to inject the sample into the acoustic levitator. Using a video camera and high magnification optics, inspect the orientation and the stability of the sample before and after the scattering measurements. The strength and assymetry of the acoustic trap are optimized for maximum sample stability.
Consequently, the acoustic power is set as low as possible. If the sample is asymmetric, rotate it around the vertical axis to gain information about its shape. Perform the rotation by slowly changing the alignment of the acoustic trap.
While imaging, apply additional illumination to improve the image quality. Next, close the measurement chamber to block out external light. Using the computer interface, select the orientation of the sample as well as the angular resolution and range of the measurement.
The incoming and the scattered light are filtered by linear polarizers which are motorized. Run the automated measurement sweep. This will measure four points for each angle with polarizer orientations of horizontal-horizontal, horizontal-vertical, vertical-vertical, and vertical-horizontal.
Recover the sample after the measurement by switching off the acoustic field and letting the sample fall on the acoustically transparent fabric. Then execute another measurement sweep with an empty levitator to detect any possible drifting due to the ambient light conditions. When finished, save the data.
Analyze the data to calculate Mueller matrix elements for each angle through linear combination of intensities at different polarizations. To begin modeling, use SSH access to connect into the CSC IT Center for science limited cluster Taito. Download and compile all of the required programs which are pre-configured for Taito by running bash compile.sh.
Next, open the text editor Nano and set up the parameters for a single scatterer, volume element and the studied sample to match the studied sample by modifying the file PARAMS. Then run the pipeline by executing command bash run.sh. When finished, write the full Mueller matrix of the sample into the temp folder as final.out.
Utilize Siris4 to compute the scattering properties of howardite particles by first moving the Siris4 executable file into the same folder with the input file and P matrix file. Then copy the input_1. in and pmatrix_1.
in from the test folder. In input_1. in, set the number of rays to two million, the number of sample particles to 1, 000, the standard deviation of radius to 0.17, and the power law index of the correlation function to three.
Then set the real part of the refractive index to 1.8 and use the imaginary part of the refractive index n as described in the text protocol. Next, run Siris4 by executing the command shown here for each wavelength from 0.4 to 2.5 microns using a size range of 10 to 200 microns in diameter with a sampling step of 10 microns. Next, save each computed scattering phase matrix p into a pmatrix_x.
in file. The x in the filename describes the wavelength number and ranges from one to 43 for each particle size. The file will contain the scattering angles as well as the scattering matrix elements P11, P12, P22, P33, P34, and P44 for one wavelength and particle size.
Average the obtained scattering matrices, single scattering Albedos, and mean free paths over a power law size distribution with an index of 3.2. Use diffused scatterers inside a Vesta-sized volume with a refractive index of one. In the input file, use the average single scattering Albedos and mean free path lengths for internal scatterers.
Next, run Siris4 at each wavelength by executing the command shown here where x is the wavelength. The code reads the averaged scattering matrices as its input for the internal diffused scatterers. Scale Vesta's observed spectra to a geometric Albedo value of 0.42327 at 0.55 microns.
To get to 17.4 degrees, apply a factor of 0.491 on the scaled spectra. Compare both the modeled and the observed spectra across the whole wavelength range. Start by downloading the source files with Git and move the files into the downloaded directory cd protocol4b.
Next, download and compile all of the required programs by running bash compile.sh. When ready, copy the averaged input scattering matrix as well as the amplitude scattering matrix into the current working directory. Next, open the text editor Nano and modify the file PARAMS to set the desired parameters.
Run the pipeline by executing bash run.sh. Then write the full Mueller matrix into the temp folder as rtcb.out. Start in MATLAB and run the averaging routine powerlaw_ave.
m to average the results over the power law size distribution of index minus three after calculating the coma phase functions from the Siris4 solver. The expected routine outputs are pmatrix2. in, Albedo and the mean free path.
Next, set the results from the outputs Albedo and the mean free path into the input. in file. Set the size to one billion and set the power law index of the correlation function for the shape to 2.5.
Then run Siris4 using the command line shown here to obtain the nucleus phase function. With Siris4, the scattering properties of 100, 000 aggregates were solved and averaged. These results are plotted here showing the experimental measurements and an additional simulation without the effective medium.
Both choices for the particle distribution produced a match to the measured phase function although they result in different polarization characteristics. These differences can be used to identify the underlying distribution of the particles in the sample. The best choice is to use the truncated normal distribution instead of the equisized particles.
If only normalized phase functions are used, the two distributions give indistinguishable results. For the depolarization, the numerical results have features similar to the measured curve but the functions are shifted by 10 degrees to the backscattering direction. The differences in the polarization indicate that the sample has presumably a more complex structure than the homogeneous model.
It is however beyond the existing microscopic methods for sample characterization to retrieve the true structure of the aggregate. Here the photometric phase curve has been accompanied with the linear dependence on the magnitude mimicking the effect of shadowing in a densely packed high Albedo regolith. The model successfully explains the observed photometric and polarimetric phase curves and offers a realistic prediction for the maximum polarization.
It is striking how the minute fraction of the small particle population is capable of completing the explanation of the phase curves. When performing this experiment, the ultrasonic sample levitation is the key to successful scattering measurements. In the computational part, the incoherent treatment of scattering within the medium of particles is essential.
In the future, we plan to extend the experimental methods to both larger and smaller samples reaching into centimeter and micrometer scales. We are currently developing ways to utilize full ultrasonic sample control in microscopes. Take appropriate precautions when performing this protocol as powerful ultrasound and light sources are utilized in these measurements.
