This work was partly supported by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. YLY acknowledge support by the Virtual Planetary Laboratory at the University of Washington.

1. Programming setup
<ol>
	<li>Set up the programming environment for the attached code. A computer with Linux operating system is required, as the healpy package is not available on Windows. The code is not computationally expensive, so a normal personal computer can handle the protocol.</li>
	<li>Follow the instruction (https://docs.anaconda.com/anaconda/install/linux/) to install Anaconda with Python 3.7 onto the system, then use the following commands in terminal to set up the programming environment: 
	$ conda create --name myenv python=3.7 
	$ conda activate myenv 
	$ conda install anaconda 
	$ conda install healpy 
	NOTE: These steps may take tens of minutes depending on the hardware and Internet speed. The environment name &#8216;myenv&#8217; in the first two command lines can be changed to any other string.</li>
</ol>
2. Obtaining multi-wavelength light curves and viewing geometry from observations
<ol>
	<li>In the viewing geometry, include the longitude and latitude of the sub-stellar and the sub-observer points for each corresponding time frame. 
	To use the following attached code, ensure that these two files have the same format as LightCurve.csv and Geometry.csv.</li>
	<li>Run PlotTimeSeries.py to visualize the data and check their qualities. Two figures LightCurve.png and Geometry.png will be created (Supplemental Figure 1-2). Parameters in this and following plotting codes may need to be adjusted if applied to different observations. 
	$ python PlotTimeSeries.py LightCurve 
	$ python PlotTimeSeries.py Geometry</li>
</ol>
3. Extract surface information from light curves
<ol>
	<li>Center time-resolved multi-wavelength albedo light curves of an exoplanet and normalize them by corresponding standard deviation at each wavelength. This results in the equal importance of each channel. 
	<img alt="Equation 1" src="/files/ftp_upload/60951/60951equ01.jpg" /> 
	where R&#8217;t,k and Rt,k are the scaled and observed albedo at the t-th time step and the k-th wavelength, respectively; &#956;k and &#963;k are the mean and standard deviation of the albedo time series at the k-th wavelength.
	<ol>
		<li>Run Normalize.py to normalize the light curves, Rt,k. The output is saved in NormalizedLightCurve.csv. 
		$ python Normalize.py</li>
	</ol>
	</li>
	<li>Run PlotTimeSeries.py to visualize the normalized light curves. A figure NormalizedLightCurve.png will be created (Supplemental Figure 3). 
	$ python PlotTimeSeries.py NormalizedLightCurve</li>
	<li>Apply SVD on the scaled albedo light curves to find dominant PCs and their corresponding time series. 
	<img alt="Equation 2" src="/files/ftp_upload/60951/60951equ02.jpg" /> 
	On the left hand side, T and K are the total number of time steps and observation wavelengths; R&#8217; is the matrix of scaled albedo observations, whose (t,k)-th element is R&#8217;t,k. On the right hand side, columns of V are PCs, orthonormal vectors that define the space SVD projects to; &#931; is a diagonal matrix, whose (k,k)-th element is the standard deviation of scaled light curves along the k-th axis defined by the k-th column of V; columns of U are the corresponding time series of each PC in V.
	<ol>
		<li>Run SingularValueDecomposition.py to decompose R&#8217;. The resulting U, &#931;, VT are saved in the output files U.csv, SingularValue.csv and V_T.csv, respectively. 
		$ python SingularValueDecomposition.py</li>
	</ol>
	</li>
	<li>Use PlotTimeSeries.py and PlotSVD.py to visualize the SVD result. Three figures U.png, Sigma.png and V_T.png will be created (Supplemental Figure 4-6). 
	$ python PlotTimeSeries.py U 
	$ python PlotSVD.py</li>
	<li>Analyze contributions and corresponding time series of PCs to determine the one that contains surface information.
	<ol>
		<li>Compare the singular values at the diagonal of &#931;. An Earth-like partially cloudy exoplanet is expected to have two comparable dominant singular values. 
		NOTE: &#931; may contain less or more than two dominant singular values, which is discussed below.</li>
		<li>Compare the time series patterns of the two dominant PCs. The PC that contains surface information tends to have more regular shape than the other. Due to the longitudinal asymmetry and the reappearance of surface with small changes in two consecutive days, the corresponding time series tends to have approximately constant daily variation.</li>
		<li>Compute the periodicities of the two dominant PCs using Lomb-Scargle periodogram9,10 to confirm the selection of PC. The PC that contains surface information tends to have higher peak corresponding to rotation period in the power density spectrum.</li>
		<li>Run Periodogram.py to obtain the power spectra of the time series of each PC. The power spectra are saved in Periodogram.csv. 
		$ python Periodogram.py</li>
		<li>Run PlotPeriodogram.py to visualize these periodograms and confirm the selection of PC. A figure Periodogram.png will be created (Supplemental Figure 7). The current plotting code adds in dashed lines representing annual, semi-annual, diurnal and half-daily cycles for reference, which may need to be changed when applied to other observations. 
		$ python PlotPeriodogram.py</li>
		<li>Select the PC, vj, that contains surface information and its time series, uj. 
		<img alt="Equation 3" src="/files/ftp_upload/60951/60951equ03v2.jpg" /> 
		<img alt="Equation 4" src="/files/ftp_upload/60951/60951equ04v2.jpg" /> 
		where V[:,j] and U[:,j] are the j-th columns of V and U, respectively; j is the index of PC inferred at step 3.3 that contains surface information.</li>
	</ol>
	</li>
</ol>
4. Construct planetary surface map
<ol>
	<li>Use the Hierarchical Equal Area iso-Latitude Pixelization (HEALPix)11 method to pixelate the retrieving map. It divides spherical surface of a planet into pixels with the same area and uniform distribution. Denote the unknown value of the p-th pixel as xp.
	<ol>
		<li>Run HEALPixRandom.py to visualize the pixelization method. A figure HEALPixRandom.png will be created (Supplemental Figure 8). The parameter Nside at line 17 can be changed for different resolutions. This step may take a few seconds to minutes depending on the resolution. 
		$ python HEALPixRandom.py</li>
	</ol>
	</li>
	<li>Compute the weight of the p-th pixel in observations at the t-th time step, wt,p, using viewing geometry. 
	<img alt="Equation 5" src="/files/ftp_upload/60951/60951equ05.jpg" /> 
	where &#945;t,p, &#946;t,p are the solar and the spacecraft zenith angles at the p-th pixel at the t-th time step; ct is a normalization term of the t-th observation so that sum of the total weight at each time step is unity. 
	NOTE: Geometry is assumed to be known at this step, or can be derived from other analysis, which is discussed below.
	<ol>
		<li>Run ComputeWeight.py to compute wt,p. Change the value of Nside at line 23 for other resolutions of the retrieved map. The output is saved as W.npz due to its size. 
		$ python ComputeWeight.py</li>
	</ol>
	</li>
	<li>Use PlotWeight.py to visualize these weights. A number of figures, one at each time step, will be created in a folder Weight. Merging them results in Supplemental Video 1, which shows how the weight of each pixel changes with time. This step may take hours to finish due to the large number of visualizations. 
	$ python PlotWeight.py</li>
	<li>Combine geometry and observations to reach a linear regression problem. 
	<img alt="Equation 6" src="/files/ftp_upload/60951/60951equ06.jpg" /> 
	where P is the total number of retrieving pixels; W is the weight matrix with wt,p as the (t,p)-th element; x consists of xp as the p-th element, which is the quantity to be solved in this problem. 
	Solve the linear regression problem with a regularization of L-2 norm. 
	<img alt="Equation 7" src="/files/ftp_upload/60951/60951equ07.jpg" /> 
	where I is the identity matrix and &#955; is the regularization parameter. 
	NOTE: 10-3 is a good value for &#955; when T~104 and P~3*103. They should be adjusted by comparing the values of the two terms in the regularized square error, e, as shown below. 
	<img alt="Equation 8" src="/files/ftp_upload/60951/60951equ08.jpg" />
	<ol>
		<li>Run LinearRegression.py to solve this linear regression problem. The result of x is saved in the file PixelValue.csv. Change the value of &#955; at line 16 for different strengths of regularization. 
		$ python LinearRegression.py</li>
	</ol>
	</li>
	<li>Convert x to a 2D surface map according to the mapping rule of HEALPix.
	<ol>
		<li>Run PlotMap.py to construct the retrieved maps using different regularization parameters. Three figures Map_-2.png, Map_-3.png and Map_-4.png will be created with the current setting (Supplemental Figure 9). The relationship between the pixel indices and their locations on map is described in the HEALPix document11. This step takes tens of seconds. 
		$ python PolotMap.py</li>
	</ol>
	</li>
</ol>
5. Estimate uncertainty of the retrieved map
<ol>
	<li>Rewrite the linear regression problem at step 4.3 with the &#8220;true value&#8221; of x as z and the observation noise, &#949;. <img alt="Equation 9" src="/files/ftp_upload/60951/60951equ09.jpg" />
	<ol>
		<li>Assume &#949; to follow a Gaussian Distribution N (0, &#963;2I[T*T]) and estimate its covariance. T-P is the degree of freedom of uj from observation when the retrieved map is fixed. 
		<img alt="Equation 10" src="/files/ftp_upload/60951/60951equ10.jpg" /></li>
		<li>Combine equations in step 4.4 and 5.1. It results in a Gaussian vector of x. 
		<img alt="Equation 11" src="/files/ftp_upload/60951/60951equ11.jpg" /></li>
		<li>Compute the expectation and the covariance matrix of x. 
		<img alt="Equation 12" src="/files/ftp_upload/60951/60951equ12.jpg" /></li>
		<li>Obtain the uncertainty of each element in x as the square root of the corresponding element on the diagonal of Cov[x]. 
		<img alt="Equation 13" src="/files/ftp_upload/60951/60951equ13.jpg" /> 
		where ep is the uncertainty of xp; Diag[Cov[x]]p is p-th element on the diagonal of Cov[x].</li>
		<li>Run Covariance.py&#160;to compute the covariance matrix of x. The result is saved in Covariance.npz&#160;due to its size. This step takes tens of seconds to minutes depending on the size of W. 
		$ python Covariance.py</li>
	</ol>
	</li>
	<li>Convert ep to the retrieved 2D map according to the mapping rule of HEALPix.
	<ol>
		<li>Run PlotCovariance.py to visualize Cov[x] and map the uncertainty ep to the retrieved map. Two figures Covariance.png and Uncertainty.png will be created (Supplemental Figure 10-11). 
		$ python PlotCovariance.py</li>
	</ol>
	</li>
</ol>

<ol>
	<li>Schwieterman, E. W., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Exoplanet+Biosignatures:+A+Review+of+Remotely+Detectable+Signs+of+Life.">Exoplanet Biosignatures: A Review of Remotely Detectable Signs of Life.</a> Astrobiology. 18 (6), 663-708 (2018).</li><li>Campbell, B., Walker, G. A. H., Yang, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+Search+for+Substellar+Companions+to+Solar-type+Stars.">A Search for Substellar Companions to Solar-type Stars.</a> The Astrophysical Journal. 331, 902 (1988).</li><li>NASA. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> NASA Exoplanet Archive (2019) Confirmed Planets Table. , (2019).</li><li>Gillon, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Seven+temperate+terrestrial+planets+around+the+nearby+ultracool+dwarf+star+TRAPPIST-1.">Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1.</a> Nature. 542 (7642), 456-460 (2017).</li><li>Kawahara, H., Fujii, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Global+Mapping+of+Earth-like+Exoplanets+from+Scattered+Light+Curves.">Global Mapping of Earth-like Exoplanets from Scattered Light Curves.</a> The Astrophysical Journal. 720 (2), 1333 (2010).</li><li>Fujii, Y., Kawahara, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mapping+Earth+Analogs+from+Photometric+Variability:+Spin-Orbit+Tomography+for+Planets+in+Inclined+Orbits.">Mapping Earth Analogs from Photometric Variability: Spin-Orbit Tomography for Planets in Inclined Orbits.</a> The Astrophysical Journal. 755 (2), 101 (2012).</li><li>Cowan, N. B., Fujii, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mapping+Exoplanets.">Mapping Exoplanets.</a> Handbook of Exoplanets. , (2018).</li><li>Farr, B., Farr, W. M., Cowan, N. B., Haggard, H. M., Robinson, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=exocartographer:+A+Bayesian+Framework+for+Mapping+Exoplanets+in+Reflected+Light.">exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light.</a> The Astronomical Journal. 156 (4), 146 (2018).</li><li>Lomb, N. R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Least-Squares+Frequency+Analysis+of+Unequally+Spaced+Data.">Least-Squares Frequency Analysis of Unequally Spaced Data.</a> Astrophysics and Space Science. 39 (2), 447 (1976).</li><li>Scargle, J. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Studies+in+astronomical+time+series+analysis.+II.+Statistical+aspects+of+spectral+analysis+of+unevenly+spaced+data.">Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data.</a> The Astrophysical Journal. 263, 835 (1982).</li><li>G&#243;rski, K. M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=HEALPix:+A+Framework+for+High-Resolution+Discretization+and+Fast+Analysis+of+Data+Distributed+on+the+Sphere.">HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere.</a> The Astrophysical Journal. 622 (2), 759 (2005).</li><li>Jiang, J. H., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Using+Deep+Space+Climate+Observatory+Measurements+to+Study+the+Earth+as+an+Exoplanet.">Using Deep Space Climate Observatory Measurements to Study the Earth as an Exoplanet.</a> The Astronomical Journal. 156 (1), 26 (2018).</li><li>Fan, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Earth+as+an+Exoplanet:+A+Two-dimensional+Alien+Map.">Earth as an Exoplanet: A Two-dimensional Alien Map.</a> The Astrophysical Journal Letters. 882 (1), 1 (2019).</li><li>Cowan, N. B., Strait, T. E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Determining+Reflectance+Spectra+of+Surfaces+and+Clouds+on+Exoplanets.">Determining Reflectance Spectra of Surfaces and Clouds on Exoplanets.</a> The Astrophysical Journal Letters. 765 (1), 17 (2013).</li><li>Fujii, Y., Lustig-Yaeger, J., Cowan, N. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rotational+Spectral+Unmixing+of+Exoplanets:+Degeneracies+between+Surface+Colors+and+Geography.">Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography.</a> The Astronomical Journal. 154 (5), 189 (2017).</li><li>Kawahara, H., Fujii, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mapping+Clouds+and+Terrain+of+Earth-like+Planets+from+Photomertic+Variability:+Demonstration+with+Planets+in+Face-on+Orbits.">Mapping Clouds and Terrain of Earth-like Planets from Photomertic Variability: Demonstration with Planets in Face-on Orbits.</a> The Astrophysical Journal Letters. 739 (2), 62 (2011).</li><li>Kawahara, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Frequency+Modulation+of+Directly+Imaged+Exoplanets:+Geometric+Effect+as+a+Probe+of+Planetary+Obliquity.">Frequency Modulation of Directly Imaged Exoplanets: Geometric Effect as a Probe of Planetary Obliquity.</a> The Astrophysical Journal. 822 (2), 112 (2016).</li><li>Schwartz, J. C., Sekowski, C., Haggard, H. M., Pall &#769;e, E., Cowan, N. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Inferring+planetary+obliquity+using+rotational+and+orbital+photometry.">Inferring planetary obliquity using rotational and orbital photometry.</a> Monthly Notices of the Royal Astronomical Society. 457 (1), 926-938 (2016).</li></ol>

The authors have nothing to disclose.

One critical requirement of the protocol is the feasibility of extracting surface information from light curves, which depends on the cloud coverage. In step 3.5.1, the relative values of the PCs may be different among exoplanets. In the case of Earth, the first two PCs dominate the light curve variations, and correspond to surface-independent clouds and surface (Fan et al. 2019)13. They have comparable singular values so that the surface information can be separated following steps 3.5.2 and 3.5....

Identifying habitable worlds is one of the ultimate goals in astrobiology1. Since the first detection2, more than 4000 exoplanets have been confirmed to date3 with a number of Earth analogs (e.g., TRAPPIST-1e)4. These planets have orbital and planetary properties similar to those of Earth, and therefore are potentially habitable. Evaluating their habitability from limited observations is essential in this context. Based on the knowledge of life on Earth, geological and climate systems are critical to habitability, which can therefore serve as biosignatures. In principle, features of these systems could be observed from a distance even when a planet could not be spatially resolved better than one single point. In this case, identifying geological features and climate systems from single-point light curves is essential when assessing the habitability of exoplanets. Surface mapping of these exoplanets becomes urgent.
Despite the convolution between viewing geometry and spectral features, information of an exoplanet&#8217;s surface is contained in its time-resolved single-point light curves, which can be obtained from a distance, and derived with sufficient observations. However, two-dimensional (2D) surface mapping of potentially habitable Earth-like exoplanets is challenging due to the influence of clouds. Methods of retrieving 2D maps have been developed and tested using simulated light curves and known spectra5,6,7,8, but they have not been applied to real observations. Moreover, in the analyses of exoplanet observations now and in the near future, assumptions of characteristic spectra may be controversial when the planetary surface compositions are not well-constrained.
In this paper, we demonstrate a surface mapping technique for Earth-like exoplanets. We use SVD to evaluate and separate information from different sources that is contained in multi-wavelength light curves without assumptions of any specific spectra. Combined with viewing geometry, we present the reconstruction of surface maps using timely resolved but spatially convoluted surface information. For the purpose of demonstrating this method, two-year multi-wavelength single-point observations of Earth obtained by the Deep Space Climate Observatory/Earth Polychromatic Imaging Camera (DSCOVR/EPIC; www.nesdis.noaa.gov/DSCOVR/spacecraft.html) are analyzed. We use Earth as a proxy exoplanet to assess this method because currently available observations of exoplanets are not sufficient. We attach the code with the paper as an example. It is developed under python 3.7 with anaconda and healpy packages, but the mathematics of the protocol can also be done in other programming environments (e.g., IDL or MATLAB).

<table><tbody><tr><td>Python 3.7 with anaconda and healpy packages</td><td></td><td></td><td>Other programming environments (e.g., IDL or MATLAB) also work.</td></tr></tbody></table>

surface mapping of earth-like exoplanets using single point light curves

Spatially resolving exoplanet features from single-point observations is essential for evaluating the potential habitability of exoplanets. The ultimate goal of this protocol is to determine whether these planetary worlds harbor geological features and/or climate systems. We present a method of extracting information from multi-wavelength single-point light curves and retrieving surface maps. It uses singular value decomposition (SVD) to separate sources that contribute to light curve variations and infer the existence of partially cloudy climate systems. Through analysis of the time series obtained from SVD, physical attributions of principal components (PCs) could be inferred without assumptions of any spectral properties. Combining with viewing geometry, it is feasible to reconstruct surface maps if one of the PCs are found to contain surface information. Degeneracy originated from convolution of the pixel geometry and spectrum information determines the quality of reconstructed surface maps, which requires the introduction of regularization. For the purpose of demonstrating the protocol, multi-wavelength light curves of Earth, which serves as a proxy exoplanet, are analyzed. Comparison between the results and the ground truth is presented to show the performance and limitation of the protocol. This work provides a benchmark for future generalization of exoplanet applications.

We use multi-wavelength single-point light curves of Earth to demonstrate the protocol, and compare the results with the ground truth to evaluate the quality of surface mapping. Observation used here is obtained by DSCOVR/EPIC, which is a satellite located near the first Lagrangian point (L1) between Earth and Sun taking images at ten wavelengths of the sunlit face of Earth. Two years (2016 and 2017) of observations are used for this demonstration, which are the same as those in Jiang et al. (2018)12</s...

Watch this Scientific Journal Video about Surface Mapping of Earth-like Exoplanets using Single Point Light Curves at JoVE.com

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

The protocol extracts information from light curves of exoplanets and constructs their surface maps. It uses light curves of Earth, which serves as a proxy exoplanet, to demonstrate the approach.

Spatially resolving exoplanet features from single-point observations is essential for evaluating the potential habitability of exoplanets. The ultimate ...

surface-mapping-earth-like-exoplanets-using-single-point-light

Universidad San Sebastian

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JoVE Journal

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3.4K Views.  California Institute of Technology. The protocol extracts information from light curves of exoplanets and constructs their surface maps. It uses light curves of Earth, which serves as a proxy exoplanet, to demonstrate the approach.

Video: Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Bringing the Visible Universe into Focus with Robo-AO

The angular resolution of ground-based optical telescopes is limited by the degrading effects of the turbulent atmosphere. In the absence of an atmosphere, the angular resolution of a typical telescope is limited only by diffraction, i.e., the wavelength of interest, &lambda;, divided by the size of its primary mirror's aperture, D. For example, the Hubble Space Telescope (HST), with a 2.4-m primary mirror, has an angular resolution at visible wavelengths of ~0.04 arc seconds. The atmosphere is composed of air at slightly different temperatures, and therefore different indices of refraction, constantly mixing. Light waves are bent as they pass through the inhomogeneous atmosphere. When a telescope on the ground focuses these light waves, instantaneous images appear fragmented, changing as a function of time. As a result, long-exposure images acquired using ground-based telescopes - even telescopes with four times the diameter of HST - appear blurry and have an angular resolution of roughly 0.5 to 1.5 arc seconds at best.
Astronomical adaptive-optics systems compensate for the effects of atmospheric turbulence. First, the shape of the incoming non-planar wave is determined using measurements of a nearby bright star by a wavefront sensor. Next, an element in the optical system, such as a deformable mirror, is commanded to correct the shape of the incoming light wave. Additional corrections are made at a rate sufficient to keep up with the dynamically changing atmosphere through which the telescope looks, ultimately producing diffraction-limited images.
The fidelity of the wavefront sensor measurement is based upon how well the incoming light is spatially and temporally sampled1. Finer sampling requires brighter reference objects. While the brightest stars can serve as reference objects for imaging targets from several to tens of arc seconds away in the best conditions, most interesting astronomical targets do not have sufficiently bright stars nearby. One solution is to focus a high-power laser beam in the direction of the astronomical target to create an artificial reference of known shape, also known as a 'laser guide star'. The Robo-AO laser adaptive optics system2,3 employs a 10-W ultraviolet laser focused at a distance of 10 km to generate a laser guide star. Wavefront sensor measurements of the laser guide star drive the adaptive optics correction resulting in diffraction-limited images that have an angular resolution of ~0.1 arc seconds on a 1.5-m telescope.

Light from astronomical objects must travel through the earth's turbulent atmosphere before it can be imaged by ground-based telescopes. To enable direct imaging at maximum theoretical angular resolution, advanced techniques such as those employed by the Robo-AO adaptive-optics system must be used.

The angular  resolution of ground-based optical telescopes is limited by the degrading  effects of the turbulent atmosphere. In the absence of an ...

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 ...

Quantifying X-Ray Fluorescence Data Using MAPS

The quantification of X-ray fluorescence (XRF) microscopy maps by fitting the raw spectra to a known standard is crucial for evaluating chemical composition and elemental distribution within a material. Synchrotron-based XRF has become an integral characterization technique for a variety of research topics, particularly due to its non-destructive nature and its high sensitivity. Today, synchrotrons can acquire fluorescence data at spatial resolutions well below a micron, allowing for the evaluation of compositional variations at the nanoscale. Through proper quantification, it is then possible to obtain an in-depth, high-resolution understanding of elemental segregation, stoichiometric relationships, and clustering behavior.
This article explains how to use the MAPS fitting software developed by Argonne National Laboratory for the quantification of full 2-D XRF maps. We use as an example results from a Cu(In,Ga)Se2 solar cell, taken at the Advanced Photon Source beamline 2-ID-D at Argonne National Laboratory. We show the standard procedure for fitting raw data, demonstrate how to evaluate the quality of a fit and present the typical outputs generated by the program. In addition, we discuss in this manuscript certain software limitations and offer suggestions for how to further correct the data to be numerically accurate and representative of spatially resolved, elemental concentrations.

Here, we demonstrate the use of the X-ray fluorescence fitting software, MAPS, created by Argonne National Laboratory for the quantification of fluorescence microscopy data. The quantified data that results is useful for understanding the elemental distribution and stoichiometric ratios within a sample of interest.

The quantification of X-ray fluorescence (XRF) microscopy maps by fitting the raw spectra to a known standard is crucial for evaluating chemical ...

Chemistry

Laser-Induced Fluorescence Emission (L.I.F.E.) as Novel Non-Invasive Tool for In-Situ Measurements of Biomarkers in Cryospheric Habitats

Global warming affects microbial communities in a variety of ecosystems, especially cryospheric habitats. However, little is known about microbial-mediated carbon fluxes in extreme environments. Hence, the methodology of sample acquisition described in the very few studies available implies two major problems: A) high resolution data require a large number of samples, which is difficult to obtain in remote areas; B) unavoidable sample manipulation such as cutting, sawing, and melting of ice cores that leads to a misunderstanding of in situ conditions. In this study, a prototype device that requires neither sample preparation nor sample destruction is presented. The device can be used for in situ measurements with a high spectral and spatial resolution in terrestrial and ice ecosystems and is based on the Laser-Induced Fluorescence Emission (L.I.F.E.) technique. Photoautotrophic supraglacial communities can be identified by the detection of L.I.F.E. signatures in photopigments. The L.I.F.E. instrument calibration for the porphyrin derivates chlorophylla (chla) (405 nm laser excitation) and B-phycoerythrin (B-PE) (532 nm laser excitation) is demonstrated. For the validation of this methodology, L.I.F.E. data were ratified by a conventional method for chla quantification that involved pigment extraction and subsequent absorption spectroscopy. The prototype applicability in the field was proven in extreme polar environments. Further testing on terrestrial habitats took place during Mars analog simulations in the Moroccan dessert and on an Austrian rock glacier. The L.I.F.E. instrument enables high resolution scans of large areas with acceptable operation logistics and contributes to a better understanding of the ecological potential of supraglacial communities in the context of global change.

Laser-Induced Fluorescence Emission L.I.F.E. as Novel Non-Invasive Tool for In-Situ Measurements of Biomarkers in Cryospheric Habitats

Carbon fluxes in the cryosphere are hardly assessed yet but are crucial regarding climate change. Here we show a novel prototype device that captures the phototrophic potential in supraglacial environments based on laser-induced fluorescence emission (L.I.F.E.) technology offering high spectral and spatial resolution data under in situ conditions.

Global warming affects microbial communities in a variety of ecosystems, especially cryospheric habitats. However, little is known about ...

Environment

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

The objective of this video protocol is to discuss how to perform and analyze a three-dimensional fluorescent orbital particle tracking experiment using a modified two-photon microscope1. As opposed to conventional approaches (raster scan or wide field based on a stack of frames), the 3D orbital tracking allows to localize and follow with a high spatial (10 nm accuracy) and temporal resolution (50 Hz frequency response) the 3D displacement of a moving fluorescent particle on length-scales of hundreds of microns2. The method is based on a feedback algorithm that controls the hardware of a two-photon laser scanning microscope in order to perform a circular orbit around the object to be tracked: the feedback mechanism will maintain the fluorescent object in the center by controlling the displacement of the scanning beam3-5. To demonstrate the advantages of this technique, we followed a fast moving organelle, the lysosome, within a living cell6,7. Cells were plated according to standard protocols, and stained using a commercially lysosome dye. We discuss briefly the hardware configuration and in more detail the control software, to perform a 3D orbital tracking experiment inside living cells. We discuss in detail the parameters required in order to control the scanning microscope and enable the motion of the beam in a closed orbit around the particle. We conclude by demonstrating how this method can be effectively used to track the fast motion of a labeled lysosome along microtubules in 3D within a live cell. Lysosomes can move with speeds in the range of 0.4-0.5 &#181;m/sec, typically displaying a directed motion along the microtubule network8.

In this video protocol we track - at high speed and in three dimensions - fluorescently labeled lysosomes within living cells, using the orbital tracking method in a modified two-photon microscope.

The objective of this video protocol is to discuss how to perform and analyze a three-dimensional fluorescent orbital particle tracking experiment using a ...

Bioengineering

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.

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 ...

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

In recent years there has been a renewed interest in returning to the Moon for reasons both scientific and exploratory in nature. The Moon provides the perfect training ground for building large scale bases that one may apply to other planets like Mars. The existence of a radio quiet zone on the lunar far side has promise for early universe studies and exoplanet searches, while the near side provides a stable base that may be used to observe low frequency emissions from Earth&#8217;s magnetosphere that may help gauge its response to incoming space weather. The construction of a large-scale radio array would provide large scientific returns as well as acting as a test of humanity&#8217;s ability to build structures on other planets. This work focuses on simulating the response of small to large-scale radio arrays on the Moon consisting of hundreds or thousands of antennas. The response of the array is dependent on the structure of the emission along with the configuration and sensitivity of the array. A set of locations are selected for the simulated radio receivers, using Digital Elevation Models from the Lunar Orbiter Laser Altimeter instrument on Lunar Reconnaissance Orbiter to characterize the elevation of the receiver locations. A custom Common Astronomy Software Applications code is described and used to process the data from the simulated receivers, aligning the lunar and sky coordinate frames using SPICE to ensure the proper projections are used for imaging. This simulation framework is useful for iterating array design for imaging any given scientific target in a small field of view. This framework does not currently support all sky imaging.

A simulation framework for testing the imaging capabilities of large-scale radio arrays on the lunar surface is presented. Major noise components are discussed, and a software pipeline is walked through with details on how to customize it for novel scientific uses.

In recent years there has been a renewed interest in returning to the Moon for reasons both scientific and exploratory in nature. The Moon provides the ...

High-Throughput Analysis of Optical Mapping Data Using ElectroMap

Optical mapping is an established technique for high spatio-temporal resolution study of cardiac electrophysiology in multi-cellular preparations. Here we present, in a step-by-step guide, the use of ElectroMap for analysis, quantification, and mapping of high-resolution voltage and calcium datasets acquired by optical mapping. ElectroMap analysis options cover a wide variety of key electrophysiological parameters, and the graphical user interface allows straightforward modification of pre-processing and parameter definitions, making ElectroMap applicable to a wide range of experimental models. We show how built-in pacing frequency detection and signal segmentation allows high-throughput analysis of entire experimental recordings, acute responses, and single beat-to-beat variability. Additionally, ElectroMap incorporates automated multi-beat averaging to improve signal quality of noisy datasets, and here we demonstrate how this feature can help elucidate electrophysiological changes that might otherwise go undetected when using single beat analysis. Custom modules are included within the software for detailed investigation of conduction, single file analysis, and alternans, as demonstrated here. This software platform can be used to enable and accelerate the processing, analysis, and mapping of complex cardiac electrophysiology.

This protocol describes the setup and use of ElectroMap, a MATLAB-based open-source software platform for analysis of cardiac optical mapping data. ElectroMap provides a versatile high-throughput tool for analysis of optical mapping voltage and calcium datasets across a wide range of cardiac experimental models.

Optical mapping is an established technique for high spatio-temporal resolution study of cardiac electrophysiology in multi-cellular preparations. Here we ...

Medicine

A Light-Stimulation Grid Approach to Study Cellular Optogenetic Protein

Mapping the Cellular Distribution of an Optogenetic Protein Using a Light-Stimulation Grid

Our goal was to accurately track the cellular distribution of an optogenetic protein and evaluate its functionality within a specific cytoplasmic location. To achieve this, we co-transfected cells with nuclear-targeted cAMP sensors and our laboratory-developed optogenetic protein, bacterial photoactivatable adenylyl cyclase-nanoluciferase (bPAC-nLuc). bPAC-nLuc, when stimulated with 445 nm light or luciferase substrates, generates adenosine 3&#39;,5&#39;-cyclic monophosphate (cAMP). We employed a solid-state laser illuminator connected to a point scanning system that allowed us to create a grid/matrix pattern of small illuminated spots (~1 &#181;m2) throughout the cytoplasm of HC-1 cells. By doing so, we were able to effectively track the distribution of nuclear-targeted bPAC-nLuc and generate a comprehensive cAMP response map. This map accurately represented the cellular distribution of bPAC-nLuc, and its response to light stimulation varied according to the amount of protein in the illuminated spot. This innovative approach contributes to the expanding toolkit of techniques available for investigating cellular optogenetic proteins. The ability to map its distribution and response with high precision has far-reaching potential and could advance various fields of research.

This protocol involves transfecting cAMP sensors and bPAC-nLuc, an optogenetic protein, to accurately track its cellular distribution and response to light stimulation. The innovative approach of creating a cAMP response map using a point scanning system holds the potential for advancing research with optogenetic proteins in different fields.

Our goal was to accurately track the cellular distribution of an optogenetic protein and evaluate its functionality within a specific cytoplasmic ...

Biology

Flame Photometry: Overview

Flame photometry, also known as flame emission spectrometry, is a technique used for the qualitative and quantitative analysis of elements present in a sample using a flame as the source of excitation energy. The concept of flame photometry was realized in the early 1860s by Kirchhoff and Bunsen, who discovered that specific elements emit characteristic radiation when excited in flames. The first instrument developed for this purpose was used to measure sodium (Na) in plant ash using a Bunsen flame. However, the challenge lay in finding the most effective way to introduce the sample into the flame. It wasn&#39;t until 1929, when Lundegardh introduced a nebulizer, that a significant breakthrough was made, allowing a reproducible introduction of the sample into the flame.
In flame emission spectrometry, the nebulizer converts a liquid sample into a fine mist or aerosol. This is achieved by passing a high-pressure gas stream over the end of a capillary tube containing the sample and aspirating it into a spray chamber. The aerosol produced is then passed to the burner, where flame heat desolvates it, forming dry particles that volatilize and produce free atoms for analysis.
Early instruments utilized quartz prism spectrographs and photographic recording to disperse and capture atomic emission lines. However, advancements in optical filters and electrical photodetectors replaced these components, improving precision and convenience.
Flame photometry involves introducing the sample solution into a nebulizer, which converts it into a fine mist or aerosol. The atomized sample then enters the flame, along with air or oxygen and a fuel gas such as propane or acetylene. The flame provides the thermal excitation necessary to energize the atoms in the sample. As these excited atoms relax, their emitted radiation is detected by a photocell or photomultiplier.
Flame photometry is particularly effective in measuring sodium, potassium, lithium, and calcium elements. The flame used in flame photometry is typically a propane-air flame with a temperature range of 1900-2000 &#176;C, although alternative flames like butane-air or natural gas-air can also be used. Flame photometry has some limitations that can be overcome by using higher temperatures and more reducing flames, such as air-acetylene, along with higher-resolution spectrometric detection. However, these approaches are not cost-competitive compared to the more broadly applicable flame atomic absorption spectrometry or AAS technique.

Flame photometry, also known as flame emission spectrometry, is a technique used for the qualitative and quantitative analysis of elements present in a ...