Research supported by the ERC Advanced Grant &#8470; 320773. We thank the Laboratory of Chronology of the Finnish Museum of Natural History for the help with sample characterization.

1. Light scattering measurement
<ol>
	<li>Setting up the scatterometer for measurement (Figure 2)
	<ol>
		<li>To begin, set up the scatterometer by turning on the light source, photo-multiplier tubes (PMTs), and amplifiers. Allow the system to stabilize for 30 min.</li>
		<li>Align and center the incident beam with pinholes. Two pinholes are attached at pre-measured points on the rotating breadboard, 180&#176; apart and at the same radius. Center the beam on the first pinhole and adjust its angle such that the light also enters through the second pinhole.</li>
	</ol>
	</li>
	<li>Setting up the acoustic sample levitator
	<ol>
		<li>Next, set up the acoustic sample levitator by inserting the microphone in the center of the levitator and running the calibration script.</li>
		<li>Calibrate the phased array acoustic levitator by measuring the acoustic pressure for each array element in the intended levitation spot as a function of the driving voltage. Use this calibration to compensate for differences between the array channels. Position the calibration microphone by centering its shadow both in the beam and in a perpendicular beam created with two mirrors.</li>
		<li>Calculate the driving parameters for the array that create an asymmetric acoustic trap and supply them to the signal generation electronics. This is accomplished by minimizing the Gor&#8217;kov potential25 and aligning the pressure gradients in the levitation spot.</li>
		<li>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.</li>
	</ol>
	</li>
	<li>Sample handling, insertion, and measurement
	<ol>
		<li>Once set up, use an acoustically transparent mesh spoon to inject the sample into the acoustic levitator.</li>
		<li>Using a video camera and high-magnification optics, inspect the orientation and the stability of the sample before and after the scattering measurements.</li>
		<li>The strength and asymmetry of the acoustic trap are optimized for maximum sample stability. Consequently, acoustic power is set as low as possible.</li>
		<li>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.</li>
		<li>Next, close the measurement chamber to block out external light.</li>
		<li>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.</li>
		<li>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).</li>
		<li>Repeat each sweep three times to eliminate outliers. For asymmetric samples, repeat the measurement at different sample orientations.</li>
		<li>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 empty levitator to detect any possible drifting due to the ambient light conditions.</li>
		<li>When finished, save the data. Analyze the data to calculate Mueller matrix elements for each angle through linear combination of intensities at different polarizations1</li>
	</ol>
	</li>
</ol>
2. Modeling the mm-sized densely-packed spherical media consisting of spherical particles
<ol>
	<li>To begin modeling, use SSH access to connect into the CSC &#8211; IT Center for Science Limited&#8217;s cluster, Taito.&#160; Download and compile all of the required programs which are preconfigured for Taito by running bash compile.sh.</li>
	<li>Move into the working directory by executing cd $WRKDIR.</li>
	<li>Download sources files with git (git clone git@bitbucket.org:planetarysystemresearch/protocol2.git protocol2).</li>
	<li>Move into the newly created directory cd protocol2.</li>
	<li>Download and compile required programs by running bash compile.sh, which are preconfigured for Taito.</li>
	<li>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.</li>
	<li>Then, run pipeline by executing a command bash run.sh. When finished, write the full Mueller matrix of the sample into the temp folder as final.out.</li>
</ol>
3. Interpreting the reflectance spectra for asteroid (4) Vesta
<ol>
	<li>Deriving the complex refractive indices for howardite.
	<ol>
		<li>Download SIRIS4 (git clone git@bitbucket.org:planetarysystemresearch/siris4.2.git).</li>
		<li>Compile by executing make in the src-folder. Rename the executable siris42 to siris4.</li>
		<li>In mainGo.f90, change line 395 to r0=0.05*rmax*sqrt(ran2). Compile by executing make.</li>
		<li>Download the needed MATLAB scripts by executing &#8220;git clone git@bitbucket.org:planetarysystemresearch/protocol4a.git&#8221;.</li>
		<li>Copy the executable files created in steps 3.1.2. and 3.1.3. to JoVEOptimize-folder.</li>
		<li>Go to folder JoVEOptimize.</li>
		<li>In input1.in file, set the radius to 30 &#181;m for the howardite particle size, and fix the real part of the refractive index to 1.8. In input2.in file, set the radius to 15,000 &#181;m.</li>
		<li>Estimate the upper and lower boundaries for the imaginary part of the refractive indices and save them into two separate files. The code utilizes the bisectioning method and uses these values as the starting point.</li>
		<li>In optimizek.m file, set the file names of the upper and lower boundaries of the imaginary part of the refractive indices and the file name of the measured reflectance spectrum of the howardite powder. Set the wavelength range to 0.4&#8211;2.5 &#181;m with 0.05-&#181;m steps.</li>
		<li>Run optimizek.m in MATLAB to obtain the complex refractive indices for howardite (see Figure 3). First, the code computes scattering properties for 30-&#181;m sized (radius) howardite particles, and then uses these particles as diffuse scatterers inside a 15,000-&#181;m sized (radius) volume. These steps are repeated for each wavelength until the computed reflectance matches with the measured reflectance.</li>
	</ol>
	</li>
	<li>Modeling the reflectance spectrum of Vesta.
	<ol>
		<li>Computing the scattering properties of howardite particles by utilizing SIRIS4
		<ol>
			<li>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.&#160; Then, copy the input_1.in and pmatrix_1.in from the test-folder.</li>
			<li>In input_1.in, set the number of rays to 2 million, the number of sample particles to 1000, the standard deviation of radius to 0.17, and the power-law index of the correlation function to 3. 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.</li>
			<li>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.</li>
			<li>Next, save each computed scattering phase matrix P into a pmatrix_x.in file.&#160; The x in the file name describes the wavelength number and ranges from 1 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.</li>
		</ol>
		</li>
		<li>Average the obtained scattering matrices, single-scattering albedos, and mean-free paths over a power-law size distribution with an index of 3.219,24.
		<ol>
			<li>Move the pmatrix-files into folders so that each folder represents one particle size and contains the computed p-matrices for all the wavelengths. Name the folders fold1, fold2,&#8230;, foldN, where N is the number of particle sizes.</li>
			<li>Write the scattering and extinction efficiencies qsca and qext, as well as the equal-projected-area-sphere radius values rhit from the outputQ-files into one file, Qscas.dat.</li>
			<li>Go to folder JoVEAverage that was downloaded in step 3.1.4.</li>
			<li>Move the folders and Qscas.dat into the same folder with AvgPowerLaw.m.</li>
			<li>Run AvgPowerLaw.m in MATLAB. The code computes averaged scattering matrices, single-scattering albedos, and mean free- path lengths over a power-law size distribution with index 3.2.</li>
		</ol>
		</li>
		<li>Computing the final spectrum of Vesta by utilizing SIRIS4
		<ol>
			<li>Use diffuse scatterers inside a Vesta-sized volume with a refractive index of 1. In the input-file, use the averaged single-scattering albedos and mean free path lengths for internal scatterers.</li>
			<li>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 diffuse scatterers.</li>
			<li>Study the absolute reflectance at a 17.4-degree phase angle.</li>
			<li>Obtain Vesta&#8217;s observed spectra at 17.4-degree phase angle from the NASA Planetary Data System26.</li>
			<li>Scale Vesta&#8217;s observed spectra to a geometric albedo value of 0.42327 at 0.55 microns27. To get to 17.4 degrees, apply a factor of 0.491 on the scaled spectra28. Compare both the modeled and the observed spectra across the whole wavelength range.</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>
4. Photometric and polarimetric modeling of (4) Vesta
<ol>
	<li>Computing scattering properties for volume elements containing Voronoi-shaped howardite particles
	<ol>
		<li>Connect into the CSC &#8211; IT Center for Science Ltd.&#8217;s cluster Taito via SSH access.</li>
		<li>Move into the working directory by executing cd $WRKDIR.</li>
		<li>Download the source files (git clone git@bitbucket.org:planetarysystemresearch/jvie_t_matrix.git).</li>
		<li>Compile by executing make in the -folder.</li>
		<li>Generate volume elements that contain Voronoi-shaped howardite particles by using a MATLAB-code voronoi_element.m. In voronoi_element.m, set the wavelength to 0.45 &#181;m, N_elems&#160;to 128, the size parameter (elem_ka) to 10, power-law index to 3, minimum particle radius to 0.143 &#181;m, maximum particle radius to 0.35 &#181;m, packing density to 30%, and use the derived complex refractive index for howardite.</li>
		<li>Run voronoi_element.m in MATLAB. The code generates 128 mesh-files for volume-elements with different Voronoi-particle realizations using the power-law size distribution.</li>
		<li>Compute T-matrices for the generated volume-elements by using JVIE. In runarray_JVIE_T.sh, set&#160;array=1-128. The paramaters are k = 13.962634, mesh = name of the generated mesh in 4.1.6, T_out = name of the output T-matrix, T_matrix = 1, and elem_ka = 10.</li>
		<li>Run JVIE by executing sbatch runarray_JVIE_T.sh.</li>
		<li>Compute averaged scattering properties from the T-matrices computed with the JVIE code. Execute ./multi_T -N_Tin 128 in the same folder where the computed T-matrices are. The code writes the averaged incoherent Mueller matrix into and the cross-sections and albedo into output.txt.</li>
	</ol>
	</li>
	<li>RT-CB computations
	<ol>
		<li>Start by downloading the sources files with git (git clone git@bitbucket.org:planetarysystemresearch/protocol4b.git protocol4b) and move the files into the downloaded directory protocol4b.</li>
		<li>Next, download and compile all of the required programs by running bash compile.sh.</li>
		<li>When ready, copy the averaged input scattering matrix (step 3.2.2.5) as well as the amplitude scattering matrix (step 4.1.9) into the current working directory.</li>
		<li>Next, open the text editor, nano, and modify the file PARAMS to set the desired parameters.</li>
		<li>Run the pipeline by executing bash run.sh. Then, write the full Mueller matrix into the temp folder as rtcb.out.</li>
	</ol>
	</li>
</ol>
5. Interpreting the observations for Comet 67P/Churyumov-Gerasimenko.
<ol>
	<li>Computing incoherent volume elements with the fast superposition T-matrix method (FaSTMM) for the organic and particle&#160;grains
	<ol>
		<li>Execute ./incoherent_input &#8211;lambda 0.649 -m_r 2.0 -m_i 0.2 -density 0.3 -lowB 0.075 -upB 0.125 -npower 3 -S_out pmatrix_org.dat.</li>
		<li>Execute ./incoherent_input &#8211;lambda 0.649 -m_r 1.6 -m_i 0.0001 -density 0.0375 -lowB 0.6 -upB 1.3 -npower 3 -S_out pmatrix_sil.dat.</li>
	</ol>
	</li>
	<li>Computing the average incoherent Mueller matrix (pmatrix.in), albedo (albedo), mean free path (mfp), and coherent effective refractive index (m_eff) 
	<ol>
		<li>Run matlab. Type commands: 
		Sorg=load(&#39;pmatrix_org.dat&#39;); 
		Ssil=load(&#39;pmatrix_sil.dat&#39;); 
		S = (Sorg+Ssil)/2; save(&#39;pmatrix.in&#39;,&#39;S&#39;,&#39;-ascii&#39;); 
		Csca = (Csca_sil + Csca_org)/2; 
		Cext = (Cext_sil + Cext_org)/2; 
		albedo = Csca/Cext; 
		mfp = Vol/Cext; 
		where Csca_org and Cext_org are the incoherent scattering and extinction cross sections from the step 5.1.2, and Csca_sil and Cext_sil are the incoherent scattering and extinction cross sections from the step 5.1.3.</li>
		<li>Run ./m_eff(Csca, r) in the command line to obtain m_eff where is the radius of the volume element.</li>
	</ol>
	</li>
	<li>Computing scattering properties for the coma particles.
	<ol>
		<li>Set the values from the step 5.2.1 and 5.2.2 (i.e., albedo, mfp, m_eff in the&#160;input.in file).</li>
		<li>Set power-law index for the correlation length to 3.5 in the input.in file.</li>
		<li>Run SIRIS4 solver (./siris4 input.in pmatrix.in) for particle sizes from 5 &#181;m to 100 &#181;m using a step of 5.</li>
		<li>Output the coma phase functions from the SIRIS4 solver.</li>
	</ol>
	</li>
	<li>Computing scattering properties of the nucleus
	<ol>
		<li>Start in MATLAB and run the averaging routine powerlaw_ave.m to average the results over the power-law size distribution of index -3 after calculating the coma phase functions (step 5.3.4) from the SIRIS4 solver. The expected routine outputs are pmatrix2.in, albedo, and the mean free path.</li>
		<li>Next, set the results from the outputs, albedo and the mean free path, into the input.in file.&#160;</li>
		<li>Set the size to 1 billion, and 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.</li>
	</ol>
	</li>
</ol>

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D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=IRAS+Minor+Planet+Survey.+IRAS-A-FPA-3-RDR-IMPS-V6.0.">IRAS Minor Planet Survey. IRAS-A-FPA-3-RDR-IMPS-V6.0.</a> NASA Planetary Data System. , (2004).</li><li>Hicks, M. D., Buratti, B. J., Lawrence, K. J., Hillier, J., Li, J. -. Y., Vishnu Reddy, V., Schr&#246;der, S., Nathues, A., Hoffmann, M., Le Corre, L., Duffard, R., Zhao, H. -. B., Raymond, C., Russell, C., Roatsch, T., Jaumann, R., Rhoades, H., Mayes, D., Barajas, T., Truong, T. -. T., Foster, J., McAuley, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Spectral+diversity+and+photometric+behavior+of+main-belt+and+near-Earth+vestoids+and+(4)+Vesta:+A+study+in+preparation+for+the+Dawn+encounter.">Spectral diversity and photometric behavior of main-belt and near-Earth vestoids and (4) Vesta: A study in preparation for the Dawn encounter.</a> Icarus. 235, 60-74 (2014).</li><li>Weidling, R., G&#252;ttler, C., Blum, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Free+collisions+in+a+micro-gravity+many-particle+experiment.+I.+Dust+aggregate+sticking+at+low+velocities.">Free collisions in a micro-gravity many-particle experiment. I. Dust aggregate sticking at low velocities.</a> Icarus. 218, 688-700 (2012).</li><li>Blum, J., Beitz, E., Bukhari, M., Gundlach, B., Hagemann, J. -. H., Hei&#223;elmann, D., Kothe, S., Schr&#228;pler, R., von Borstel, I., Weidling, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Laboratory+drop+towers+for+the+experimental+simulation+of+dust-aggregate+collisions+in+the+early+solar+system.">Laboratory drop towers for the experimental simulation of dust-aggregate collisions in the early solar system.</a> Journal of Visualized Experiments (JoVE). (88), e51541 (2014).</li><li>Poppe, T., Schr&#228;pler, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Further+experiments+on+collisional+tribocharging+of+cosmic+grains.">Further experiments on collisional tribocharging of cosmic grains.</a> Astronomy &amp; Astrophysics. 438, 1-9 (2005).</li><li>Reddy, V., Sanchez, J. A., Nathues, A., Moskovitz, N. A., Li, J. -. Y., Cloutis, E. A., Archer, K., Tucker, R. A., Gaffey, M. J., Mann, J. P., Sierks, H., Schade, U. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photometric+spectral+phase+and+temperature+effects+on+Vesta+and+HED+meteorites:+Implications+for+Dawn+mission.">Photometric spectral phase and temperature effects on Vesta and HED meteorites: Implications for Dawn mission.</a> Icarus. 217, 153-168 (2012).</li><li>Gehrels, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Minor+planets.+I.+The+rotation+of+Vesta.+Photometric+studies+of+asteroids.">Minor planets. I. The rotation of Vesta. Photometric studies of asteroids.</a> Astronomical Journal. 72, 929-938 (1967).</li><li>Bertini, I., La Forgia, F., Tubiana, C., G&#252;ttler, C., Fulle, M., Moreno, F., Frattin, E., Kovacs, G., Pajola, M., Sierks, H., Barbieri, C., Lamy, P., Rodrigo, R., Koschny, D., Rickman, H., Keller, H. U., Agarwal, J., A&#39;Hearn, M. F., Barucci, M. A., Bertaux, J. -. L., Bodewits, D., Cremonese, G., Da Deppo, V., Davidsson, B., Debei, S., De Cecco, M., Drolshagen, E., Ferrari, S., Ferri, F., Fornasier, S., Gicquel, A., Groussin, O., Gutierrez, P. J., Hasselmann, P. H., Hviid, S. F., Ip, W. -. H., Jorda, L., Knollenberg, J., Kramm, J. R., K&#252;hrt, E., K&#252;ppers, M., Lara, L. M., Lazzarin, M., Lin, Z. -. Y., Lopez Moreno, J. J., Lucchetti, A., Marzari, F., Massironi, M., Mottola, S., Naletto, G., Oklay, N., Ott, T., Penasa, L., Thomas, N., Vincent, J. -. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+scattering+phase+function+of+comet+67P/Churyumov-Gerasimenko+coma+as+seen+from+the+Rosetta/OSIRIS+instrument.">The scattering phase function of comet 67P/Churyumov-Gerasimenko coma as seen from the Rosetta/OSIRIS instrument.</a> Monthly Notices of the Royal Astronomical Society. 469, 404-415 (2017).</li></ol>

The authors have nothing to disclose.

Experimental, theoretical, and computational methods have been presented for light scattering by discrete random media of particles. The experimental methods have been utilized to validate the basic concepts in the theoretical and computational methods. The latter methods have then been successfully applied in the interpretation of astronomical observations of asteroid (4) Vesta and comet 67P/Churyumov-Gerasimenko.
The experimental scatterometer relies on ultrasonically controlled sample levitation that allows for Mueller-matrix measurements for a sample aggregate in a desired orientation. The aggregate can be repeatedly utilized in the measurements, as it is possible to conserve the aggregate after each measurement set. This is the first time that such non-contact, non-destructive scattering measurements are carried out on a sample under full control.
The theoretical and computational methods rely on the so-called incoherent scattering, absorption, and extinction processes in random media. Whereas the exact electromagnetic interactions always occur coherently, within an infinite random medium after configurational averaging, only incoherent interactions remain among volume elements of particles. In the present work, the incoherent interactions among these elements are exactly accounted for by using the Maxwell equations: after subtracting the coherent fields from the fields in free space, it is the incoherent fields within the random medium that remain. The treatment has presently been taken to its complete rigor in that the interactions, as well as the extinction, scattering, and absorption coefficients of the medium, are derived within the framework of incoherent interactions. Furthermore, it has been shown that accounting for the coherent field effects on the interface between the free space and the random medium results in a successful overall treatment for a constrained random medium.
Application of the theoretical and computational methods has been illustrated for experimental measurements of a mm-scale spherical sample aggregate composed of submicron-scale spherical SiO2 particles. The application shows, unequivocally, that the sample aggregate must be composed of a distribution of particles with varying sizes, instead of being composed of equisized spherical particles. There may be far-reaching consequences of this result for the characterization of random media: it is plausible that the media are significantly more complex than what has been deduced earlier using state-of-the-art characterization methods.
The synoptic interpretation of the spectrum for asteroid (4) Vesta across the visible and near-infrared wavelengths as well as Vesta&#8217;s photometric and polarimetric phase curves at the wavelength of 0.45 &#181;m shows that it is practical to utilize the numerical methods in constraining the mineral compositions, particle size distributions, as well as regolith volume density from remote astronomical observations. Such retrievals are further enhanced by the simultaneous interpretation of the photometric phase curves for comet 67P/Churyumov-Gerasimenko concerning its coma and nucleus. Finally, realistic modeling of the polarimetric phase curve of 67P has been obtained20. There are major future prospects in applying the present methods in the interpretation of observations of solar system objects at large.
There are future prospects for the present combined experimental and theoretical approach. As it is extremely difficult to accurately characterize random media composed of sub-wavelength-scale inhomogeneities, controlled Mueller-matrix measurements can offer a tool for retrieving information on the volume density and particle size distribution in the medium. Quantitative inversion of these physical parameters is facilitated by the novel numerical methods.

Asteroids, cometary nuclei, and airless solar system objects at large are covered by planetary regoliths, loose layers of particles of varying size, shape, and composition. For these objects, two ubiquitous astronomical phenomena are observed at small solar phase angles (the Sun-object-observer angle). First, the brightness of the scattered light in the astronomical magnitude scale is observed to increase nonlinearly toward the zero phase angle, commonly called the opposition effect1,2. Second, the scattered light is partially linearly polarized parallel to the scattering plane (the Sun-object-observer plane), commonly called negative polarization3. The phenomena have been lacking quantitative interpretation since late 19th century for the opposition effect and since early 20th century for the negative polarization. Their proper interpretation is a prerequisite for the quantitative interpretation of the photometric, polarimetric, and spectrometric observations of airless objects, as well as radar scattering from their surfaces.
It has been suggested4,5,6,7 that the coherent backscattering mechanism (CBM) in multiple scattering is at least partly responsible for the astronomical phenomena. In the CBM, partial waves, interacting with the same scatterers in opposite order, always interfere constructively in the exact backscattering direction. This is due to the coinciding optical paths of the reciprocal waves. In other directions, the interference varies from destructive to constructive. Configurational averaging within a discrete random medium of particles results in enhanced backscattering. As for the linear polarization, the CBM is selective and results in negative polarization in the case of positively polarizing single scatterers, a common characteristic in single scattering (cf. Rayleigh scattering, Fresnel reflection).
Scattering and absorption of electromagnetic waves (light) in a macroscopic random medium of microscopic particles has constituted an open computational problem in planetary astrophysics8,9. As illustrated above, this has resulted in the absence of quantitative inverse methods to interpret ground-based and space-based observations of solar system objects. In the present manuscript, novel methods are presented for bridging the gap between the observations and their modeling.
Experimental measurements of scattering by a small-particle sample in a controlled position and orientation (six degrees of freedom) has remained open. Scattering characteristics for single particles have been earlier measured as ensemble averages over the size, shape, and orientation distribution10 by introducing a particle flow through the measurement volume. Scattering characteristics for single particles in levitation have been carried out using, for example, electrodynamic levitation11 and optical tweezers12,13,14. In the present manuscript, a novel experimental method based on ultrasonic levitation with full control of the sample position and orientation is offered15.
The present manuscript summarizes the findings of a project funded for five years in 2013-2018 by the European Research Council (ERC): Scattering and Absorption of ElectroMagnetic waves in ParticuLate media (SAEMPL, ERC Advanced Grant). SAEMPL succeeded in meeting its three main goals: first, novel numerical Monte Carlo methods were derived for multiple scattering by discrete random media of densely-packed particles16,17,18; second, novel experimental instrumentation was developed and constructed for controlled laboratory measurements of validation samples in levitation15; third, the numerical and experimental methods were applied to interpret astronomical observations19,20.
In what follows, protocols for utilizing the experimental scattering pipeline for measurements, the corresponding computational pipeline, as well as the application pipelines are described in detail. The computational pipeline consists of software for asymptotically exact computations in the case of finite systems of particles (Superposition T-Matrix Method STMM21 and Volume Integral Equation Method VIEM22) and approximate computations for asymptotically infinite discrete random media of particles using multiple scattering methods (SIRIS23,24, Radiative Transfer with Coherent Backscattering RT-CB8,9, and Radiative Transfer with Reciprocal Transactions R2T2 16,17,18). The experimental pipeline encompasses the preparation, storage, and utilization of the samples, their levitation in the measurement volume, and performing the actual scattering measurement across the range of scattering angles with varying polarizer configurations. The application pipeline concerns the utilization of the computational and experimental pipelines in order to interpret astronomical observations or experimental measurements.

<table>
	<tbody>
		<tr>
			<td>10GL08</td>
			<td>Newport</td>
			<td></td>
			<td>Calcite polarizer</td>
		</tr>
		<tr>
			<td>12X Zoom Body Tube 1-50487AD</td>
			<td>Navitar</td>
			<td></td>
			<td>Microscope objective</td>
		</tr>
		<tr>
			<td>43-412-000</td>
			<td>Edmund optics</td>
			<td></td>
			<td>Optical flat</td>
		</tr>
		<tr>
			<td>8MPR16-1</td>
			<td>Standa</td>
			<td></td>
			<td>Motorized Polarizer Rotator</td>
		</tr>
		<tr>
			<td>8MRB240-152-59D</td>
			<td>Standa</td>
			<td></td>
			<td>Rotation stage</td>
		</tr>
		<tr>
			<td>8SMC5-ETHERNET</td>
			<td>Standa</td>
			<td></td>
			<td>Motor controller</td>
		</tr>
		<tr>
			<td>Digi-pas DWL3500XY</td>
			<td>Digi-pas</td>
			<td></td>
			<td>Digital 2-axis level</td>
		</tr>
		<tr>
			<td>DMT 65-D25-HiDS</td>
			<td>Owis</td>
			<td></td>
			<td>Optics rotation stage</td>
		</tr>
		<tr>
			<td>EQ-99 LDLS</td>
			<td>Energetiq</td>
			<td></td>
			<td>Light source</td>
		</tr>
		<tr>
			<td>FL488-10</td>
			<td>Thorlabs</td>
			<td></td>
			<td>Laser line filter</td>
		</tr>
		<tr>
			<td>IBM 65-D0-35-HiDS</td>
			<td>Owis</td>
			<td></td>
			<td>Motorized iris shutter</td>
		</tr>
		<tr>
			<td>LPVISE100-A</td>
			<td>Thorlabs</td>
			<td></td>
			<td>Film polarizer</td>
		</tr>
		<tr>
			<td>microPMT H12403-01</td>
			<td>Hamamatsu</td>
			<td></td>
			<td>Photomultiplier tube</td>
		</tr>
		<tr>
			<td>NI PXIe-5171R</td>
			<td>National Instruments</td>
			<td></td>
			<td>Digital oscilloscope</td>
		</tr>
		<tr>
			<td>NI PXIe-8880</td>
			<td>National Instruments</td>
			<td></td>
			<td>PXIe chassis</td>
		</tr>
		<tr>
			<td>Phantom v611</td>
			<td>Vision Research</td>
			<td></td>
			<td>High speed camera</td>
		</tr>
		<tr>
			<td>PS 10-32-DC</td>
			<td>Owis</td>
			<td></td>
			<td>Motor controller</td>
		</tr>
		<tr>
			<td>RC08FC-P01</td>
			<td>Thorlabs</td>
			<td></td>
			<td>Fiber collimator</td>
		</tr>
		<tr>
			<td>SET-NDF-D22-G25</td>
			<td>Owis</td>
			<td></td>
			<td>Neutral density filter</td>
		</tr>
		<tr>
			<td>TIA60</td>
			<td>Thorlabs</td>
			<td></td>
			<td>PMT amplifier</td>
		</tr>
	</tbody>
</table>

scattering and absorption of light in planetary regoliths

Theoretical, numerical, and experimental methods are presented for multiple scattering of light in macroscopic discrete random media of densely-packed microscopic particles. The theoretical and numerical methods constitute a framework of Radiative Transfer with Reciprocal Transactions (R2T2). The R2T2 framework entails Monte Carlo order-of-scattering tracing of interactions in the frequency space, assuming that the fundamental scatterers and absorbers are wavelength-scale volume elements composed of large numbers of randomly distributed particles. The discrete random media are fully packed with the volume elements. For spherical and nonspherical particles, the interactions within the volume elements are computed exactly using the Superposition T-Matrix Method (STMM) and the Volume Integral Equation Method (VIEM), respectively. For both particle types, the interactions between different volume elements are computed exactly using the STMM. As the tracing takes place within the discrete random media, incoherent electromagnetic fields are utilized, that is, the coherent field of the volume elements is removed from the interactions. The experimental methods are based on acoustic levitation of the samples for non-contact, non-destructive scattering measurements. The levitation entails full ultrasonic control of the sample position and orientation, that is, six degrees of freedom. The light source is a laser-driven white-light source with a monochromator and polarizer. The detector is a mini-photomultiplier tube on a rotating wheel, equipped with polarizers. The R2T2 is validated using measurements for a mm-scale spherical sample of densely-packed spherical silica particles. After validation, the methods are applied to interpret astronomical observations for asteroid (4) Vesta and comet 67P/Churyumov-Gerasimenko (Figure 1) recently visited by the NASA Dawn mission and the ESA Rosetta mission, respectively.

Watch this Scientific Journal Video about Scattering And Absorption of Light in Planetary Regoliths at JoVE.com

Scattering And Absorption of Light in Planetary Regoliths

Numerical and experimental methods are presented for multiple scattering of light in discrete random media of densely-packed particles. The methods are utilized to interpret the observations of asteroid (4) Vesta and comet 67P/Churyumov-Gerasimenko.

Theoretical, numerical, and experimental methods are presented for multiple scattering of light in macroscopic discrete random media of densely-packed ...

scattering-and-absorption-of-light-in-planetary-regoliths

Research

JoVE Journal

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10.1K Views.  University of Helsinki. Numerical and experimental methods are presented for multiple scattering of light in discrete random media of densely-packed particles. The methods are utilized to interpret the observations of asteroid (4) Vesta and comet 67P/Churyumov-Gerasimenko.

Video: Scattering And Absorption of Light in Planetary Regoliths

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Light interacts with an organism's integument on a variety of spatial scales. For example in an iridescent bird: nano-scale structures produce color; the milli-scale structure of barbs and barbules largely determines the directional pattern of reflected light; and through the macro-scale spatial structure of overlapping, curved feathers, these directional effects create the visual texture. Milli-scale and macro-scale effects determine where on the organism's body, and from what viewpoints and under what illumination, the iridescent colors are seen. Thus, the highly directional flash of brilliant color from the iridescent throat of a hummingbird is inadequately explained by its nano-scale structure alone and questions remain. From a given observation point, which milli-scale elements of the feather are oriented to reflect strongly? Do some species produce broader "windows" for observation of iridescence than others? These and similar questions may be asked about any organisms that have evolved a particular surface appearance for signaling, camouflage, or other reasons.
In order to study the directional patterns of light scattering from feathers, and their relationship to the bird's milli-scale morphology, we developed a protocol for measuring light scattered from biological materials using many high-resolution photographs taken with varying illumination and viewing directions. Since we measure scattered light as a function of direction, we can observe the characteristic features in the directional distribution of light scattered from that particular feather, and because barbs and barbules are resolved in our images, we can clearly attribute the directional features to these different milli-scale structures. Keeping the specimen intact preserves the gross-scale scattering behavior seen in nature. The method described here presents a generalized protocol for analyzing spatially- and directionally-varying light scattering from complex biological materials at multiple structural scales.

We present a non-destructive method for sampling spatial variation in the direction of light scattered from structurally complex materials. By keeping the material intact, we preserve gross-scale scattering behavior, while concurrently capturing fine-scale directional contributions with high-resolution imaging. Results are visualized in software at biologically-relevant positions and scales.

Light interacts with an organism's integument on a variety of spatial scales. For example in an iridescent bird: nano-scale structures produce color; the ...

Simulation of the Planetary Interior Differentiation Processes in the Laboratory

A planetary interior is under high-pressure and high-temperature conditions and it has a layered structure. There are two important processes that led to that layered structure, (1) percolation of liquid metal in a solid silicate matrix by planet differentiation, and (2) inner core crystallization by subsequent planet cooling. We conduct high-pressure and high-temperature experiments to simulate both processes in the laboratory. Formation of percolative planetary core depends on the efficiency of melt percolation, which is controlled by the dihedral (wetting) angle. The percolation simulation includes heating the sample at high pressure to a target temperature at which iron-sulfur alloy is molten while the silicate remains solid, and then determining the true dihedral angle to evaluate the style of liquid migration in a crystalline matrix by 3D visualization. The 3D volume rendering is achieved by slicing the recovered sample with a focused ion beam (FIB) and taking SEM image of each slice with a FIB/SEM crossbeam instrument. The second set of experiments is designed to understand the inner core crystallization and element distribution between the liquid outer core and solid inner core by determining the melting temperature and element partitioning at high pressure. The melting experiments are conducted in the multi-anvil apparatus up to 27 GPa and extended to higher pressure in the diamond-anvil cell with laser-heating. We have developed techniques to recover small heated samples by precision FIB milling and obtain high-resolution images of the laser-heated spot that show melting texture at high pressure. By analyzing the chemical compositions of the coexisting liquid and solid phases, we precisely determine the liquidus curve, providing necessary data to understand the inner core crystallization process.

The high-pressure and high-temperature experiments described here mimic planet interior differentiation processes. The processes are visualized and better understood by high-resolution 3D imaging and quantitative chemical analysis.

A planetary interior is under high-pressure and high-temperature conditions and it has a layered structure. There are two important processes that led to ...

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators

Mechanically underdamped electrostatic fringing-field MEMS actuators are well known for their fast switching operation in response to a unit step input bias voltage. However, the tradeoff for the improved switching performance is a relatively long settling time to reach each gap height in response to various applied voltages. Transient applied bias waveforms are employed to facilitate reduced switching times for electrostatic fringing-field MEMS actuators with high mechanical quality factors. Removing the underlying substrate of the fringing-field actuator creates the low mechanical damping environment necessary to effectively test the concept. The removal of the underlying substrate also a has substantial improvement on the reliability performance of the device in regards to failure due to stiction. Although DC-dynamic biasing is useful in improving settling time, the required slew rates for typical MEMS devices may place aggressive requirements on the charge pumps for fully-integrated on-chip designs. Additionally, there may be challenges integrating the substrate removal step into the back-end-of-line commercial CMOS processing steps. Experimental validation of fabricated actuators demonstrates an improvement of 50x in switching time when compared to conventional step biasing results. Compared to theoretical calculations, the experimental results are in good agreement.

The robust device design of fringing-field electrostatic MEMS actuators results in inherently low squeeze-film damping conditions and long settling times when performing switching operations using conventional step biasing. Real-time switching time improvement with DC-dynamic waveforms reduces the settling time of fringing-field MEMS actuators when transitioning between up-to-down and down-to-up states.

Mechanically underdamped electrostatic fringing-field MEMS actuators are well known for their fast switching operation in response to a unit step input ...

Printing Fabrication of Bulk Heterojunction Solar Cells and In Situ Morphology Characterization

Polymer-based materials hold promise as low-cost, flexible efficient photovoltaic devices. Most laboratory efforts to achieve high performance devices have used devices prepared by spin coating, a process that is not amenable to large-scale fabrication. This mismatch in device fabrication makes it difficult to translate quantitative results obtained in the laboratory to the commercial level, making optimization difficult. Using a mini-slot die coater, this mismatch can be resolved by translating the commercial process to the laboratory and characterizing the structure formation in the active layer of the device in real time and in situ as films are coated onto a substrate. The evolution of the morphology was characterized under different conditions, allowing us to propose a mechanism by which the structures form and grow. This mini-slot die coater offers a simple, convenient, material efficient route by which the morphology in the active layer can be optimized under industrially relevant conditions. The goal of this protocol is to show experimental details of how a solar cell device is fabricated using a mini-slot die coater and technical details of running in situ structure characterization using the mini-slot die coater.

Printing Fabrication of Bulk Heterojunction Solar Cells and In Situ Morphology Characterization

Here, we present a protocol to fabricate organic thin film solar cells using a mini-slot die coater and related in-line structure characterizations using synchrotron scattering techniques.

Polymer-based materials hold promise as low-cost, flexible efficient photovoltaic devices. Most laboratory efforts to achieve high performance devices ...

Free-form Light Actuators &#8212; Fabrication and Control of Actuation in Microscopic Scale

Liquid crystalline elastomers (LCEs) are smart materials capable of reversible shape-change in response to external stimuli, and have attracted researchers&#39; attention in many fields. Most of the studies focused on macroscopic LCE structures (films, fibers) and their miniaturization is still in its infancy. Recently developed lithography techniques, e.g., mask exposure and replica molding, only allow for creating 2D structures on LCE thin films. Direct laser writing (DLW) opens access to truly 3D fabrication in the microscopic scale. However, controlling the actuation topology and dynamics at the same length scale remains a challenge.
In this paper we report on a method to control the liquid crystal (LC) molecular alignment in the LCE microstructures of arbitrary three-dimensional shape. This was made possible by a combination of direct laser writing for both the LCE structures as well as for micrograting patterns inducing local LC alignment. Several types of grating patterns were used to introduce different LC alignments, which can be subsequently patterned into the LCE structures. This protocol allows one to obtain LCE microstructures with engineered alignments able to perform multiple opto-mechanical actuation, thus being capable of multiple functionalities. Applications can be foreseen in the fields of tunable photonics, micro-robotics, lab-on-chip technology and others.

Free-form Light Actuators &amp;#8212; Fabrication and Control of Actuation in Microscopic Scale

Here, we fabricate 3D polymeric micro/nano structures in which both the shape and the molecular alignment can be engineered with nanometer scale accuracy by the use of direct laser writing. Light induced deformation of several types of liquid crystalline elastomer microstructures can be controlled in the microscopic scale.

Liquid crystalline elastomers (LCEs) are smart materials capable of reversible shape-change in response to external stimuli, and have attracted ...

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Dielectric microspheres can confine light and sound for a length of time through high quality factor whispering gallery modes (WGM). Glass microspheres can be thought as a store of energy with a huge variety of applications: compact laser sources, highly sensitive biochemical sensors and nonlinear phenomena. A protocol for the fabrication of both the microspheres and coupling system is given. The couplers described here are tapered fibers. Efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility &#935;(3) interactions in triply resonant silica microspheres is presented in this paper. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS). A proof of the cavity-enhanced phenomenon is given by the lack of correlation among the pump, signal and idler: a resonant mode has to exist in order to obtain the pair of signal and idler. In the case of hyperparametric oscillations (four wave mixing and stimulated anti-stokes Raman scattering), the modes must fulfill the energy and momentum conservation and, last but not least, have a good spatial overlap.

Efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility &#935;(3) interactions in triply resonant silica microspheres is presented in this paper. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS).

Dielectric microspheres can confine light and sound for a length of time through high quality factor whispering gallery modes (WGM). Glass microspheres ...

Dielectric RheoSANS &#8212; Simultaneous Interrogation of Impedance, Rheology and Small Angle Neutron Scattering of Complex Fluids

A procedure for the operation of a new dielectric RheoSANS instrument capable of simultaneous interrogation of the electrical, mechanical and microstructural properties of complex fluids is presented. The instrument consists of a Couette geometry contained within a modified forced convection oven mounted on a commercial rheometer. This instrument is available for use on the small angle neutron scattering (SANS) beamlines at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR). The Couette geometry is machined to be transparent to neutrons and provides for measurement of the electrical properties and microstructural properties of a sample confined between titanium cylinders while the sample undergoes arbitrary deformation. Synchronization of these measurements is enabled through the use of a customizable program that monitors and controls the execution of predetermined experimental protocols. Described here is a protocol to perform a flow sweep experiment where the shear rate is logarithmically stepped from a maximum value to a minimum value holding at each step for a specified period of time while frequency dependent dielectric measurements are made. Representative results are shown from a sample consisting of a gel composed of carbon black aggregates dispersed in propylene carbonate. As the gel undergoes steady shear, the carbon black network is mechanically deformed, which causes an initial decrease in conductivity associated with the breaking of bonds comprising the carbon black network. However, at higher shear rates, the conductivity recovers associated with the onset of shear thickening. Overall, these results demonstrate the utility of the simultaneous measurement of the rheo-electro-microstructural properties of these suspensions using the dielectric RheoSANS geometry.

Dielectric RheoSANS &amp;#8212; Simultaneous Interrogation of Impedance, Rheology and Small Angle Neutron Scattering of Complex Fluids

Here, we present a procedure for the measurement of simultaneous impedance, rheology and neutron scattering from soft matter materials under shear flow.

A procedure for the operation of a new dielectric RheoSANS instrument capable of simultaneous interrogation of the electrical, mechanical and ...

Scanning Light Scattering Profiler (SLPS) Based Methodology to Quantitatively Evaluate Forward and Backward Light Scattering from Intraocular Lenses

The scanning light scattering profiler (SLSP) methodology has been developed for the full-angle quantitative evaluation of forward and backward light scattering from intraocular lenses (IOLs) using goniophotometer principles. This protocol describes the SLSP platform and how it employs a 360&#176; rotational photodetector sensor that is scanned around an IOL sample while recording the intensity and location of scattered light as it passes through the IOL medium. The SLSP platform can be used to predict, non-clinically, the propensity for current and novel IOL designs and materials to induce light scatter. Non-clinical evaluation of light scattering properties of IOLs can significantly reduce the number of patient complaints related to unwanted glare, glistening, optical defects, poor image quality, and other phenomena associated with the unintended light scattering. Future studies should be conducted to correlate SLSP data with clinical results to help identify which measured light scatter is most problematic for patients that have undergone cataract surgery subsequent to IOL implantation.

Scanning Light Scattering Profiler SLPS Based Methodology to Quantitatively Evaluate Forward and Backward Light Scattering from Intraocular Lenses

This protocol describes the scanning light scattering profiler (SLSP) that enables the full-angle quantitative evaluation of forward and backward scattering of light from intraocular lenses (IOLs) using goniophotometer principles.

The scanning light scattering profiler (SLSP) methodology has been developed for the full-angle quantitative evaluation of forward and backward light ...

Characterization of Ultra-fine Grained and Nanocrystalline Materials Using Transmission Kikuchi Diffraction

One of the challenges in microstructure analysis nowadays resides in the reliable and accurate characterization of ultra-fine grained (UFG) and nanocrystalline materials. The traditional techniques associated with scanning electron microscopy (SEM), such as electron backscatter diffraction (EBSD), do not possess the required spatial resolution due to the large interaction volume between the electrons from the beam and the atoms of the material. Transmission electron microscopy (TEM) has the required spatial resolution. However, due to a lack of automation in the analysis system, the rate of data acquisition is slow which limits the area of the specimen that can be characterized. This paper presents a new characterization technique, Transmission Kikuchi Diffraction (TKD), which enables the analysis of the microstructure of UFG and nanocrystalline materials using an SEM equipped with a standard EBSD system. The spatial resolution of this technique can reach 2 nm. This technique can be applied to a large range of materials that would be difficult to analyze using traditional EBSD. After presenting the experimental set up and describing the different steps necessary to realize a TKD analysis, examples of its use on metal alloys and minerals are shown to illustrate the resolution of the technique and its flexibility in term of material to be characterized.

This paper provides a detailed method to characterize the microstructure of ultra-fine grained and nanocrystalline materials using a scanning electron microscope equipped with a standard electron backscatter diffraction system. Metal alloys and minerals presenting refined microstructures are analyzed using this technique, showing the diversity of its possible applications.

One of the challenges in microstructure analysis nowadays resides in the reliable and accurate characterization of ultra-fine grained (UFG) and ...

Synchrotron X-ray Microdiffraction and Fluorescence Imaging of Mineral and Rock Samples

In this report, we describe a detailed procedure for acquiring and processing&#160;x-ray microfluorescence (&#956;XRF), and Laue and powder microdiffraction two-dimensional (2D) maps at beamline 12.3.2 of the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory. Measurements can be performed on any sample that is less than 10 cm x 10 cm x 5 cm, with a flat exposed surface. The experimental geometry is calibrated using standard materials (elemental standards for XRF, and crystalline samples such as Si, quartz, or Al2O3 for diffraction). Samples are aligned to the focal point of the x-ray microbeam, and raster scans are performed, where each pixel of a map corresponds to one measurement, e.g., one XRF spectrum or one diffraction pattern. The data are then processed using the in-house developed software XMAS, which outputs text files, where each row corresponds to a pixel position. Representative data from moissanite and an olive snail shell are presented to demonstrate data quality, collection, and analysis strategies.

We describe a beamline setup meant to carry out rapid two-dimensional x-ray fluorescence and x-ray microdiffraction mapping of single crystal or powder samples using either Laue (polychromatic radiation) or powder (monochromatic radiation) diffraction. The resulting maps give information about strain, orientation, phase distribution, and plastic deformation.