We thank Juan Vasquez for his computational contributions with this project. We are grateful for the support of the Vassar College Undergraduate Research Summer Institute (URSI), the Lucy Maynard Salmon Research Fund and the NSF award No. 1058385.

1. C. elegans Growth and Maintenance
<ol>
	<li>Prepare nematode culture dishes.
	<ol>
		<li>Fill the Petri dishes with an agar solution and leave them to solidify, then seed with an E. coli culture of the OP50 strain9,10.</li>
	</ol>
	</li>
	<li>Prepare a starting population of adult nematodes on each plate by moving several adult worms to fresh agar-filled Petri dishes with an E. coli patch. Maintain the nematode cultures at 20 &#176;C in an incubator. 
	NOTE: Nematode strains can be obtained from the Caenorhabditis elegans Genome Center. For this study, the wild type, N2, strain and the OH7547 (otls199[cat-2::GFP + rgel-1(F25B3.3)::dsRed + rol-6(su1006)]) strain, which exhibits a roller phenotype, were utilized.</li>
	<li>Propagate worms for future cultures.
	<ol>
		<li>Remove the Petri dish containing C. elegans and an unused habitat Petri dish from the temperature-controlled incubator. Place them on the stage of a dissecting microscope.</li>
		<li>Light the Bunsen burner and sterilize the platinum nematode pick by placing the metal into the flame until it glows red. Allow the pick to cool to room temperature. Do not set the pick down or let the pick come into contact with contaminants.</li>
		<li>Gently touch the tip of the pick to the edge of the circle of bacteria. This substance is sticky and will make picking individual adult nematodes easier.</li>
		<li>Transfer up to 4 gravid nematodes to a Nematode Growth Medium (NGM) agar-filled Petri plate and incubate at 20 &#176;C. The worms will lay eggs that will mature in four days.</li>
		<li>Return the remaining nematodes to the incubator after moving four adult nematodes.</li>
	</ol>
	</li>
</ol>
2. Optical Setup (Figure 1)
<ol>
	<li>Secure the helium-neon laser near the back-left corner of the optical workbench and connect it to a power source. 
	NOTE: The laser&#39;s beam must fulfill the requirements for oversampling. The C. elegans are approximately 1 mm long, therefore the laser beam should have a diameter greater than 2 mm while incident on the nematode, but no larger than 5 mm so that the diffraction pattern is not difficult to locate.</li>
	<li>Place a neutral density filter between the helium-neon laser and the sample such that the laser beam travels through the filter before reaching the sample.</li>
	<li>Using two front surface aluminum steering mirrors, build a periscope by securing the first mirror after the neutral density filter. Secure the second mirror about 10 cm below the first mirror to give room to steer the laser beam and insert the cuvette between the mirrors. Align the laser beam and cuvette so that the laser beam travels vertically through the cuvette. 
	NOTE: The distance from the diffracting organism to the photodiode must be much larger than the organism itself to achieve far-field diffraction. In this experiment, the distance from the cuvette to the photodiode is 20 cm.</li>
	<li>Secure the photodiode directly across from the second mirror with its sensor facing the mirror. 
	NOTE: The cuvette containing the nematode will be placed between the two mirrors using chemistry clamps. See sections 4 and 5.</li>
	<li>Place a water-filled cuvette on the stand. Adjust the height of the stand. Adjust the heights and angles of mirror 1 and mirror 2 so that the laser beam travels through the cuvette aimed near but not directly at the photodiode.</li>
	<li>Use a level to ensure the stands form a leveled surface for the cuvette. Adjust the mirrors further if necessary.</li>
	<li>Connect the photodiode to the digital oscilloscope using the USB cable provided with the digital oscilloscope. Connect the digital oscilloscope to the computer that will be used to record and save the data.</li>
</ol>
3. Oscilloscope Setup
<ol>
	<li>Using the software for the oscilloscope on the computer, set the sample rate to at least 8 Hz to resolve the thrashing cycle of the worm sufficiently. 
	NOTE: The sample rate should be more than twice that of the expected thrashing frequencies of the species so that the Nyquist theorem11 is satisfied.</li>
</ol>
4. Preparing the Worm and Cuvette for Data Collection
<ol>
	<li>Transfer four adult nematodes to a fresh NGM10 agar-filled Petri plate using a thin, flattened platinum wire pick (see section 1.3).</li>
	<li>Remove one disposable plastic cuvette from its package, being careful to only touch the cuvette on its ridged sides.</li>
	<li>Use a micropipette to pipette distilled water into the cuvette until the cuvette is approximately 80% filled with distilled water. 
	NOTE: It is important to only use distilled water or ionized buffers such as M910 or phosphate-buffered saline (PBS) when handling the nematodes, as tap water contains microorganism-killing compounds.</li>
	<li>Place the Petri dish containing the C. elegans to be used under a dissecting scope.</li>
	<li>Using the platinum pick, remove one mature C. elegans from the Petri dish and submerge the pick into the cuvette, moving the pick in circles if necessary to dislodge the nematode.</li>
	<li>To prevent bubbles forming in the cuvette, fill the cuvette with water until it slightly bulges over the cuvette&#39;s top. Fill the cuvette&#39;s cap entirely with water then quickly put the cap onto the cuvette.</li>
	<li>Use an optical cleaning cloth to remove water droplets that may have spilled over and optical cleaning paper to clean any small remaining droplets.</li>
</ol>
5. Real Time Data-Acquisition of Diffraction Pattern Intensity Changes
<ol>
	<li>Turn on the helium-neon laser and adjust the frequency/color setting so that it produces a red beam. Turn on the sensor. 
	Caution: Use a low-energy beam at 632 nm, as C. elegans avoid high-frequency (blue) light12.</li>
	<li>Locate the worm in the cuvette. Holding the cuvette on its ridged sides, gently tilt the cuvette until nematode is approximately in the center of the portion of the cuvette. 
	NOTE: Shaking or tilting the cuvette violently causes the worm to collide with the walls of the cuvette. This can damage the nematode.
	<ol>
		<li>Place the cuvette onto the stand in the optical system, centering the worm within the laser&#39;s beam reflected from Mirror 1 to Mirror 2. Be sure to eliminate stray light.</li>
	</ol>
	</li>
	<li>Center the worm in the laser beam.
	<ol>
		<li>Place the photodiode in the diffraction pattern so that the location of the photodiode and the central maximum of the diffraction pattern do not coincide.</li>
		<li>Adjust the neutral density filter to prevent saturation of the photodiode. Rotating the neutral density filter wheel regulates the light intensity.
		<ol>
			<li>Rotate the neutral density filter so that the voltage output from the photodiode increases. 
			NOTE: The voltage output is observed using the software for the digital photodiode. The photodiode is saturated if the voltage does not change. In that case, rotate the neutral density filter until the voltage reduces without flattening out at a minimum reading. Ensure that the voltage signal does not flatten at the peak readings, indicating saturation of the photodiode. Reduce the light intensity by rotating the neutral density filter wheel if saturation is observed.</li>
		</ol>
		</li>
		<li>Once the moving diffraction pattern is visible, collect data with the photodiode by clicking the start button on the software controlling the oscilloscope while monitoring the worm&#39;s movement. Continue taking measurements until the worm moves out of the laser beam and the diffraction pattern disappears, which usually takes about 20 s.
		<ol>
			<li>Stop the data collecting process by clicking the stop button on the software for the oscilloscope. Save each trial&#39;s data in .csv or .txt format.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Repeat steps 5.2 - 5.3 until at least 50 data sets have been collected for each phenotype. Use eight to ten animals per trial.</li>
	<li>If the cuvette is scratched dispose of it and the worm, and repeat step 4. If the worm is harmed in the transfer, dispose of it and rinse the cuvette with distilled water before repeating step 4 using the same cuvette.</li>
	<li>Repeat step 5 using the OH7547 &#34;Roller&#34; strain, being careful to label the data to indicate the worm strain.</li>
</ol>
6. Fourier Spectrum of Data
<ol>
	<li>Import the data acquired into a data analysis program capable of performing Discrete Fourier transforms3.</li>
	<li>Perform Fourier transforms on each data set using the fast Fourier transform (FFT) option of the software.</li>
	<li>Average the frequencies from the FFT results for each amplitude for the N2 wild type worms.</li>
	<li>Repeat step 6.3 using the FFTs from the OH7547 &#34;roller&#34; worms.</li>
</ol>
7. Modeling of the Fourier Spectrum
<ol>
	<li>Program a binary model of the nematode locomotion (see program included in the supplemental materials). 
	NOTE: This model is a rough approximation, which at first displays the prominent characteristics of worm motion. The model can be refined as the outcomes are compared with actual worms. Worm shapes are approximations using microscope images13.
	<ol>
		<li>Create sequential frames of the binary model moving through at least two worm cycles (Figure 2a). See the videos in the supplemental materials; C Worm video (CWorm.avi) and W Worm video (WWorm.avi).</li>
	</ol>
	</li>
	<li>Produce sequential diffraction patterns. See the videos in the supplemental materials. C Worm Diffraction video (CWormDiff.avi) and W Worm video (WWormDiff.avi).
	<ol>
		<li>Fourier transform each binary frame of the worm image. The larger the padding of the frame around the worm, the better the resolution of the diffraction image will be. 
		NOTE: The absolute value of each Fourier transformed frame is proportional to the corresponding diffraction pattern (Figure 2b).</li>
		<li>Tune the contrast of the diffraction pattern by mapping the intensities of the diffraction pattern to a logarithmic scale. 
		NOTE: Cameras and eyes tend to function on a non-linear scale. A logarithmic scale can simulate how a diffraction pattern is typically perceived by the human eye.</li>
	</ol>
	</li>
	<li>Extract the modeled diffraction signal.
	<ol>
		<li>Pick an off-center location that corresponds to the location of the photodiode in the diffraction pattern.</li>
		<li>Add the neighboring matrix elements surrounding the location of the photodiode to simulate the size of the photodiode. The size of the photodiode is typically 0.1% of the modeled diffraction pattern.</li>
		<li>Record and plot the sequence of the magnitude of the diffraction signals. Check that the signal is physically reasonable (i.e., in the case of periodic thrashing, the signal from the photodiode should be periodic as well).</li>
	</ol>
	</li>
	<li>Fourier transform the diffraction signal obtained in 7.3 and compare results with the experimental data.</li>
	<li>Repeat for various worm strains and compare.</li>
</ol>

<ol>
	<li>Magnes, J., 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=Analysis+of+Freely+Swimming+C.+elegans+Using+Laser+Diffraction.">Analysis of Freely Swimming C. elegans Using Laser Diffraction.</a> Open J. Biophys. 2, 101-107 (2012).</li><li>Magnes, J., Raley-Susman, K. M., Eells, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Quantitative+Locomotion+Study+of+Freely+Swimming+Micro-organisms+Using+Laser+Diffraction.">Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction.</a> J. Vis. Exp. (68), (2012).</li><li>James, J. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> A Student's Guide to Fourier Transforms with Applications in Physics and Engineering. , (1995).</li><li>Korta, J., Clark, D. A., Gabel, C. V., Mahadevan, L., Samuel, A. D. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanosensation+and+mechanical+load+modulate+the+locomotory+gait+of+swimming+C.+elegans.">Mechanosensation and mechanical load modulate the locomotory gait of swimming C. elegans.</a> J. Exp. Biol. 210, (2007).</li><li>Martin-Garcia, J. M., Conrad, C. E., Coe, J., Roy-Chowdhury, S., Fromme, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Serial+femtosecond+crystallography:+A+revolution+in+structural+biology.">Serial femtosecond crystallography: A revolution in structural biology.</a> Arch. Biochem. Biophys. 602, 32-47 (2016).</li><li>Thibault, P., Rankenburg, I. C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optical+diffraction+microscopy+in+a+teaching+laboratory.">Optical diffraction microscopy in a teaching laboratory.</a> Amer. J. Phys. 75 (9), 827-832 (2007).</li><li>Miao, J., Ishikawa, T., Anderson, E. H., Hodgson, K. O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phase+retrieval+of+diffraction+patterns+from+non+crystalline+samples+using+the+oversampling+method.">Phase retrieval of diffraction patterns from non crystalline samples using the oversampling method.</a> Phys. Rev. B. 67, 174104 (2003).</li><li>Zhang, Y. P., Zhang, J. Q., Xu, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Method+for+eliminating+zero-order+diffraction+in+lensless+Fourier+transform+digital+holography.">Method for eliminating zero-order diffraction in lensless Fourier transform digital holography.</a> Optik - International Journal for Light and Electron Optics. 124 (21), 4873-4875 (2013).</li><li>Brody, A. H., Chou, E., Gray, J. M., Pokrywka, N. J., Raley-Susman, K. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mancozeb-induced+behavioral+deficits+precede+structural+neural+degeneration.">Mancozeb-induced behavioral deficits precede structural neural degeneration.</a> NeuroToxicology. 34, 74-81 (2013).</li><li>Stiernagle, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Maintenance+of+C.+elegans.">Maintenance of C. elegans.</a> WormBook. , (2006).</li><li>Dasalukunte, D., &#214;wall, V., Rusek, F., Anderson, 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=.">.</a> Faster than Nyquist Signaling. Algorithms to Silicon. , (2014).</li><li>Edwards, S. L., 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=A+novel+molecular+solution+for+ultraviolet+light+detection+in+Caenorhabditis+elegans.">A novel molecular solution for ultraviolet light detection in Caenorhabditis elegans.</a> PLoS Biol. 6 (8), e198 (2008).</li><li>Bilbao, A., Wajnryb, E., Vanapalli, S. A., Blawzdziewicz, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nematode+Locomotion+in+Confined+and+Unconfined+Fluids.">Nematode Locomotion in Confined and Unconfined Fluids.</a> Phys. Fluids. 25, 081902 (2013).</li></ol>

The authors have nothing to disclose.

Including stretches of data with inactivity will skew the results since artificial lower frequencies will be averaged into the results. Saturating the photodiode can be recognized by flat peaks or &#34;cut off&#34; peaks in the raw data. Dividing each raw data set by peak intensities will help with accounting for fluctuations in the laser intensity.
The peak frequencies are an indicator of the overall thrashing frequency; however, complicated motion causes interference at beat frequencies in the diffraction pattern and need to be examined carefully.
This method can be used to investigate the locomotion of other nematodes. The environment can be changed to another medium. Wavelengths may be changed as well. Working in the visible range of the electromagnetic spectrum is easiest and safest.
A more refined model will simulate the diffraction spectra more realistically in the future. A future model may include a worm that can change orientations, which would not affect frequency locations but relative peak heights. A more realistic model would allow for a probabilistic distribution of thrashing frequencies, which would broaden the peaks as in the experimental data. A spread in frequencies would account for variations in thrashing frequencies.
The current worm shape is crude, especially in the head and tail region, which should be more tapered than in the current model. It may be interesting to conduct a detailed analysis of the time series of the signal since it could give clues about the complexity of the locomotion in different mutants.
It is worth considering the practicality of expanding this technique into characterizing multiple nematodes simultaneously. This method should be understood as a complementary method to existing methods using traditional microscopes. This method has an advantage in not requiring a microscope during the data-acquisition so that the worm may move out of the focal plane. The averaged frequency spectra show clear differences in worm motion and can be quantified by the prevalent frequency peaks, which is a novel method in quantifying worm locomotion. Data analysis of the diffraction signatures is in further development and will hopefully lead to an automated identification process of multiple mutants and individuals.

This method compares experimental and modeled frequency spectra of the locomotion of C. elegans using two strains with very different locomotory patterns. The results show that the frequency spectrum depends on temporal changes as the nematode swims in a water column so that clear microscopic images are not needed for analysis. This method allows for quantitative real-time analysis and provides complementary information to images/videos obtained with traditional microscopes. Fraunhofer diffraction, also called far-field diffraction, provides the basis for obtaining live diffraction data1,2. The light intensity at any single point in the diffraction pattern is the result of superimposing light from every point in the outline of the nematode3. As a result, the light intensity collected over time carries information about the locomotion of the nematode. Analyzing the time-dependent diffraction signal can identify the characteristic motion of the corresponding mutant since analyzing all the frequencies involved in the locomotion complements the traditional video analysis. In this case, the characteristic differences between the locomotion of the &#34;roller&#34; and wild type C. elegans are confirmed by comparing the frequency spectra of the two different strains of nematode.
Some previous characteristics have been confirmed using frequency analysis of diffraction signals such as swimming frequencies2,4. More importantly, this method can be used as a complementary method to traditional microscopy to observe locomotion in real time on a computer screen as the data are being collected. The frequency spectrum of worms with distinct locomotory patterns can be quantified by considering the Fourier transformed signal of the diffraction signal.
The multidisciplinary nature of Fourier-based diffraction in this work involves the fields of biology and physics. Diffraction by under sampling has long been used to investigate crystal structures in biology5 and other fields. In this experiment, however, oversampling6,7 creates the far-field diffraction pattern so that the organism is centered in the laser beam. Oversampling is typically used for lens-less imaging8 in conjunction with a phase retrieval algorithm that reconstructs an image of the original object. Phase retrieval is difficult to achieve when scatterers are present as is the case with a nematode. The temporal diffraction signature is enough to evaluate key frequencies of the worm motion. This method is less computationally taxing and provides an optical way to quantify locomotion. This technique could readily be adapted for analysis of mutations or environmental conditions that alter behavior.

<table>
	<tbody>
		<tr>
			<td>Tunable Helium-Neon laser</td>
			<td>Research Electro-Optics</td>
			<td>30602</td>
			<td>Four wavelengths can be selected between 543 nm and 633 nm.</td>
		</tr>
		<tr>
			<td>2 Front Surface Aluminum Mirrors</td>
			<td>Thorlabs</td>
			<td>PF10-03-F01</td>
			<td></td>
		</tr>
		<tr>
			<td>Photodiode: SI Amplified Detector</td>
			<td>Thorlabs</td>
			<td>PDA 100A</td>
			<td></td>
		</tr>
		<tr>
			<td>Quartz Cuvette</td>
			<td>Starna Cells</td>
			<td>21/G/5</td>
			<td>Plastic cells may be used as well.</td>
		</tr>
		<tr>
			<td>MatLab (Software)</td>
			<td>MathWorks</td>
			<td>R2016b (9.1.0.441655)</td>
			<td>Use the fft command to simulate diffraction</td>
		</tr>
		<tr>
			<td>Excel</td>
			<td>Microsoft</td>
			<td>14.7.1</td>
			<td>Used for data analysis of Fig. 4</td>
		</tr>
		<tr>
			<td>Caenorhabditis elegans Roller</td>
			<td>University of Minnesota Caenorhabditis elegans Center (CGC)</td>
			<td>Strain: OH7547 
			Genotype: otIs199.</td>
			<td>https://cbs.umn.edu/cgc/home</td>
		</tr>
		<tr>
			<td>Caenorhabditis elegans Wild Type</td>
			<td>University of Minnesota Caenorhabditis elegans Center (CGC)</td>
			<td>Strain:N2 Genotype: C. elegans wild isolate</td>
			<td>https://cbs.umn.edu/cgc/home</td>
		</tr>
	</tbody>
</table>

fourier-based diffraction analysis of live caenorhabditis elegans

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 &#34;roller&#34; C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The &#34;roller&#34; worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the &#34;roller&#34; C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

The optical experimental setup shown in Figure 1 allows for the study of microorganisms without being tied to a focal plane. The thrashing signal from the photodiode can be observed in real time on the computer screen as the data is collected. Unusual patterns will be visible immediately without having to analyze a video in detail.
Examples of modeled sequential worm movement and corresponding diffraction patterns are shown in Figure 2. The modeled diffraction patterns qualitatively resemble experimental patterns1 and are an initial indication that the simulations successfully model the nematode.
A sample temporal diffraction signature of the two types of C. elegans studied here is shown in Figure 3. It can be seen qualitatively that each nematode thrashes at different rates and amplitudes. Some of the differences can be quantified through curve fitting as was done in a previous publication1. The discrete Fourier transform, however, reveals more details regarding embedded frequencies:
<img alt="Equation 1" src="/files/ftp_upload/56154/56154eq1.jpg" />, (1)
where Fk is the digital Fourier transform (FT) and fn is the time-dependent raw diffraction signal with the discrete time variable n and the discrete frequency variable k. N is the total number of data points. The average digital Fourier transform allows for the nematode to be identified by amplitude of its diffraction frequency spectrum (Figure 4). The wild type spectrum is dominated by lower frequencies than the roller motion spectrum.
A model that approximates the wild type versus the roller C. elegans notes the wild type tends to thrash in a wavelike (W or S shape) motion (Figure 2a) while the roller tends to favor one side that roughly resembles an oscillating C shape (Figure 5). This offers some explanation for the different spectra. The roller will mostly form a C to one side while the W oscillation can be thought of as two opposing C motions. For this reason, the W motion is more complex revealing more secondary low frequencies than the C motion. This result is confirmed in the computational model. The W shape has a much higher frequency density than the C shape (Figure 6). This is confirmed in the FFT in Figure 4 where the roller frequencies are more clustered while not completely discrete. The statistics of the roller are skewed since the roller can revert to wild type locomotion temporarily.
The smoothed power spectra of roller type C. elegans shows a broad peak at ~1.5 Hz, while the swimming wild type C. elegans exhibits a multimodal spectrum (including peaks at ~1.0 Hz and 1.75 Hz). The photodiode (PD) has a finite size spreading over several matrix elements. Individual matrix elements or points on the diffraction pattern vary in intensity since constructive and destructive interference varies; nevertheless, the frequencies at which the intensities vary are the same for all matrix elements, as can be seen in Figure 7. Considering the time derivative Eq. 1, it can be seen that the frequency fluctuations do not depend on the phase matrix but only on the original object&#39;s fluctuations:
<img alt="Equation 2" src="/files/ftp_upload/56154/56154eq2.jpg" />, (2)
As the PD spreads over several matrix elements, the peak locations average to a consistent frequency profile. Some variation can be expected and can give clues about the orientation of the worm. The frequency distribution will change as the gait of the worm changes. The current model is a simple model that only allows for the evaluation of peak locations rather than relative peak heights. Different locomotory patterns will average to different peak locations.

<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/56154/56154fig1.jpg" /> 
Figure 1. Experimental Setup. The low power laser beam travels through the neutral density filter, is reflected by mirror M1 down through the cuvette containing the worm onto mirror M2, and travels towards the photodiode. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/56154/56154fig2.jpg" /> 
Figure 2. Sequential Worm Shapes and Corresponding Diffraction Patterns. (a) Some select sequential binary images of modeled W shape nematodes and the (b) corresponding sequential diffraction patterns. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/56154/56154fig3.jpg" /> 
Figure 3. Experimental Sample Diffraction Signatures. Diffraction signatures collected for (a) OH7547 &#34;roller&#34; and (b) N2 wild type C. elegans using a single photodiode in the diffraction pattern. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/56154/56154fig4.jpg" /> 
Figure 4. Experimental Averaged Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series. The spectra show the frequencies present in averaged Fourier transform of the time series recorded with the photodiode. A Gaussian filter of standard deviation 0.075 Hz, truncated at 3 standard deviations, is used for smoothing. Note the broad spectral peak at ~1.5 Hz in the smoothed roller spectrum, compared with the multimodal smoothed wild type spectrum (including peaks at ~1.0 and 1.75 Hz). <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/56154/56154fig5.jpg" /> 
Figure 5. Diffraction Formation Illustration. Diffraction patterns can be modeled by thinking of each line segment as an infinitesimally small straight line (left). Superimposing these lines (right) demonstrates the construction of far-field diffraction patterns generated by a C shaped nematode. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/56154/56154fig6.jpg" /> 
Figure 6. Simulated Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series. (a) C shape and (b) W shape worms with the photodiode centered at the matrix elements 200 (vertical) and 175 (horizontal). The W shape shows a higher density of frequencies due to the more complex locomotion. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/56154/56154fig7.jpg" /> 
Figure 7. Simulated Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series at Different Photodiode Locations. (a) W shape worm and the (b) C shape worm for single matrix elements at various locations simulating various locations of the photodiode. Peak heights vary for various locations; however, peak locations remain the same for specific shapes. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans at JoVE.com

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to distinguish different nematodes using far-field diffraction signatures. We compare the locomotion of 139 wild type and 108 &#34;Roller&#34; C. elegans by averaging frequencies associated with the temporal Fraunhofer diffraction signature at a single location using a continuous wave laser.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column ...

fourier-based-diffraction-analysis-of-live-caenorhabditis-elegans

Research

Education

JoVE Core

JoVE Journal

Electrical Engineering

Engineering

Unit 1

Fourier Series

SCIENTISTS IN ACTION

7.9K 조회수.  Vassar College. This manuscript describes how to distinguish different nematodes using far-field diffraction signatures. We compare the locomotion of 139 wild type and 108 "Roller" C. elegans by averaging frequencies associated with the temporal Fraunhofer diffraction signature at a single location using a continuous wave laser.

비디오: Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Analysis of Contact Interfaces for Single GaN Nanowire Devices

Single GaN nanowire (NW) devices fabricated on SiO2 can exhibit a strong degradation after annealing due to the occurrence of void formation at the contact/SiO2 interface. This void formation can cause cracking and delamination of the metal film, which can increase the resistance or lead to a complete failure of the NW device. In order to address issues associated with void formation, a technique was developed that removes Ni/Au contact metal films from the substrates to allow for the examination and characterization of the contact/substrate and contact/NW interfaces of single GaN NW devices. This procedure determines the degree of adhesion of the contact films to the substrate and NWs and allows for the characterization of the morphology and composition of the contact interface with the substrate and nanowires. This technique is also useful for assessing the amount of residual contamination that remains from the NW suspension and from photolithographic processes on the NW-SiO2 surface prior to metal deposition. The detailed steps of this procedure are presented for the removal of annealed Ni/Au contacts to Mg-doped GaN NWs on a SiO2 substrate.

A technique was developed that removes Ni/Au contact metal films from their substrate to allow for the examination and characterization of the contact/substrate and contact/NW interfaces of single GaN nanowire devices.

단 하나의 GaN 나노 와이어 장치에 대한 문의 인터페이스의 분석

Single GaN nanowire (NW) devices fabricated on SiO2 can exhibit  a strong degradation after annealing due to the  occurrence of void formation at the ...

연구

공학

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, acceleration and forces involved in the locomotory behavior of nematodes suspended in a column of water in response to single wavelengths of light. We demonstrate how to evaluate the locomotion of a microscopic organism using Single Wavelength Shadow Imaging (SWSI) using two different examples.
The first example is a systematic and statistically viable study of the average descent of C. elegans in a column of water. For this study, we used living and dead wildtype C. elegans. When we compared the velocity and direction of nematode active movement with the passive descent of dead worms within the gravitational field, this study showed no difference in descent-times. The average descent was 1.5 mm/sec &#177; 0.1 mm/sec for both the live and dead worms using 633 nm coherent light.
The second example is a case study of select individual C. elegans changing direction during the descent in a vertical water column. Acceleration and force are analyzed in this example. This case study demonstrates the scope of other physical properties that can be evaluated using SWSI while evaluating the behavior using single wavelengths in an environment that is not accessible with traditional microscopes. Using this analysis we estimated an individual nematode is capable of thrusting with a force in excess of 28 nN.
Our findings indicate that living nematodes exert 28 nN when turning, or moving against the gravitational field. The findings further suggest that nematodes passively descend in a column of water, but can actively resist the force of gravity primarily by turning direction.

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

The technique presented here measures the path of freely swimming microscopic species using single wavelength exposure. C. elegans are used to demonstrate shadow imaging as an inexpensive alternative to costly microscopes. This technique can be adapted to accommodate various orientations, environments and species to measure direction, speed, acceleration and forces.

단일 파장 그림자 영상<em&gt; 예쁜 꼬마 선충</em&gt; 로코 모션을 포함하여 강제 추정

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, ...

In Situ Neutron Powder Diffraction Using Custom-made Lithium-ion Batteries

Li-ion batteries are widely used in portable electronic devices and are considered as promising candidates for higher-energy applications such as electric vehicles.1,2 However, many challenges, such as energy density and battery lifetimes, need to be overcome before this particular battery technology can be widely implemented in such applications.3 This research is challenging, and we outline a method to address these challenges using in situ NPD to probe the crystal structure of electrodes undergoing electrochemical cycling (charge/discharge) in a battery. NPD data help determine the underlying structural mechanism responsible for a range of electrode properties, and this information can direct the development of better electrodes and batteries.
We briefly review six types of battery designs custom-made for NPD experiments and detail the method to construct the &#8216;roll-over&#8217; cell that we have successfully used on the high-intensity NPD instrument, WOMBAT, at the Australian Nuclear Science and Technology Organisation (ANSTO). The design considerations and materials used for cell construction are discussed in conjunction with aspects of the actual in situ NPD experiment and initial directions are presented on how to analyze such complex in situ data.

In Situ Neutron Powder Diffraction Using Custom-made Lithium-ion Batteries

We describe the design and construction of an electrochemical cell for the examination of electrode materials using in situ neutron powder diffraction (NPD). We briefly comment on alternate in situ NPD cell designs and discuss methods for the analysis of the corresponding in situ NPD data produced using this cell.

제자리 중성자 분말 회절에서 사용자 정의 - 만든 리튬 이온 배터리를 사용하여

Li-ion batteries are widely used in portable electronic devices and are considered as promising candidates for higher-energy applications such as electric ...

Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

Nuclear reaction analysis (NRA) via the resonant 1H(15N,&#945;&#947;)12C reaction is a highly effective method of depth profiling that quantitatively and non-destructively reveals the hydrogen density distribution at surfaces, at interfaces, and in the volume of solid materials with high depth resolution. The technique applies a 15N ion beam of 6.385 MeV provided by an electrostatic accelerator and specifically detects the 1H isotope in depths up to about 2 &#956;m from the target surface. Surface H coverages are measured with a sensitivity in the order of ~1013 cm-2 (~1% of a typical atomic monolayer density) and H volume concentrations with a detection limit of ~1018 cm-3 (~100 at. ppm). The near-surface depth resolution is 2-5 nm for surface-normal 15N ion incidence onto the target and can be enhanced to values below 1 nm for very flat targets by adopting a surface-grazing incidence geometry. The method is versatile and readily applied to any high vacuum compatible homogeneous material with a smooth surface (no pores). Electrically conductive targets usually tolerate the ion beam irradiation with negligible degradation. Hydrogen quantitation and correct depth analysis require knowledge of the elementary composition (besides hydrogen) and mass density of the target material. Especially in combination with ultra-high vacuum methods for in-situ target preparation and characterization, 1H(15N,&#945;&#947;)12C NRA is ideally suited for hydrogen analysis at atomically controlled surfaces and nanostructured interfaces. We exemplarily demonstrate here the application of 15N NRA at the MALT Tandem accelerator facility of the University of Tokyo to (1) quantitatively measure the surface coverage and the bulk concentration of hydrogen in the near-surface region of a H2 exposed Pd(110) single crystal, and (2) to determine the depth location and layer density of hydrogen near the interfaces of thin SiO2 films on Si(100).

We illustrate the application of 1H(15N,&#945;&#947;)12C resonant nuclear reaction analysis (NRA) to quantitatively evaluate the density of hydrogen atoms on the surface, in the volume, and at an interfacial layer of solid materials. The near-surface hydrogen depth profiling of a Pd(110) single crystal and of SiO2/Si(100) stacks is described.

핵 반응 분석과 깊이 프로파일 링을 통해 표면 및 인터페이스 레이어 및 대량 재료의 수소 농도의 정량화

Nuclear reaction analysis (NRA) via the resonant 1H(15N,&#945;&#947;)12C reaction is a highly effective method of depth profiling that quantitatively and ...

Using Synchrotron Radiation Microtomography to Investigate Multi-scale Three-dimensional Microelectronic Packages

Synchrotron radiation micro-tomography (SR&#181;T) is a non-destructive three-dimensional (3D) imaging technique that offers high flux for fast data acquisition times with high spatial resolution. In the electronics industry there is serious interest in performing failure analysis on 3D microelectronic packages, many which contain multiple levels of high-density interconnections. Often in tomography there is a trade-off between image resolution and the volume of a sample that can be imaged. This inverse relationship limits the usefulness of conventional computed tomography (CT) systems since a microelectronic package is often large in cross sectional area 100-3,600 mm2, but has important features on the micron scale. The micro-tomography beamline at the Advanced Light Source (ALS), in Berkeley, CA USA, has a setup which is adaptable and can be tailored to a sample&#39;s properties, i.e., density, thickness, etc., with a maximum allowable cross-section of 36 x 36 mm. This setup also has the option of being either monochromatic in the energy range ~7-43 keV or operating with maximum flux in white light mode using a polychromatic beam. Presented here are details of the experimental steps taken to image an entire 16 x 16 mm system within a package, in order to obtain 3D images of the system with a spatial resolution of 8.7 &#181;m all within a scan time of less than 3 min. Also shown are results from packages scanned in different orientations and a sectioned package for higher resolution imaging. In contrast a conventional CT system would take hours to record data with potentially poorer resolution. Indeed, the ratio of field-of-view to throughput time is much higher when using the synchrotron radiation tomography setup. The description below of the experimental setup can be implemented and adapted for use with many other multi-materials.

For this study synchrotron radiation micro-tomography, a non-destructive three-dimensional imaging technique, is employed to investigate an entire microelectronic package with a cross-sectional area of 16 x 16 mm. Due to the synchrotron&#39;s high flux and brightness the sample was imaged in just 3 min&#160;with an 8.7 &#181;m spatial resolution.

멀티 스케일 3 차원 마이크로 전자 패키지를 조사하는 방사광 Microtomography 사용

Synchrotron radiation micro-tomography (SR&#181;T) is a non-destructive three-dimensional (3D) imaging technique that offers high flux for fast data ...

Measuring Spray Droplet Size from Agricultural Nozzles Using Laser Diffraction

When making an application of any crop protection material such as an herbicide or pesticide, the applicator uses a variety of skills and information to make an application so that the material reaches the target site (i.e., plant). Information critical in this process is the droplet size that a particular spray nozzle, spray pressure, and spray solution combination generates, as droplet size greatly influences product efficacy and how the spray moves through the environment. Researchers and product manufacturers commonly use laser diffraction equipment to measure the spray droplet size in laboratory wind tunnels. The work presented here describes methods used in making spray droplet size measurements with laser diffraction equipment for both ground and aerial application scenarios that can be used to ensure inter- and intra-laboratory precision while minimizing sampling bias associated with laser diffraction systems. Maintaining critical measurement distances and concurrent airflow throughout the testing process is key to this precision. Real time data quality analysis is also critical to preventing excess variation in the data or extraneous inclusion of erroneous data. Some limitations of this method include atypical spray nozzles, spray solutions or application conditions that result in spray streams that do not fully atomize within the measurement distances discussed. Successful adaption of this method can provide a highly efficient method for evaluation of the performance of agrochemical spray application nozzles under a variety of operational settings. Also discussed are potential experimental design considerations that can be included to enhance functionality of the data collected.

We present protocols to be used in the measurement of spray droplet size from agricultural nozzles used in both aerial and ground based agrochemical applications. These methods presented were developed to provide consistent and repeatable droplet size data both inter- and intra-laboratory, when using laser diffraction systems.

레이저 회절을 사용하여 농업 노즐에서 측정 스프레이 물방울 크기

When making an application of any crop protection material such as an herbicide or pesticide, the applicator uses a variety of skills and information to ...

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.

전송 키쿠치 회절을 사용하여 울트라 미세 그레인과 나노 결정 재료의 특성

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

Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing

Probing remote matter with laser light is a ubiquitous technique used in circumstances as diverse as laser-induced breakdown spectroscopy and barcode scanners. In classical optics, the intensity that can be brought to bear on a remote target is limited by the spot size of the laser at the distance of the target. This spot size has a lower bound determined by the diffraction limit of classical optics. However, amplified femtosecond laser pulses generate intensity sufficient to modify the refractive index of the ambient air and undergo self-focusing. This self-focusing effect leads to the generation of highly intense laser filaments which maintain their intensity and small sub-millimeter diameter size at distances well beyond the classical Rayleigh length. Such intensity provides the capability of remote scanning, imaging, sensing, and spectroscopy with enhanced spatial resolution. We describe a technique for generating filaments with a femtosecond regenerative chirped-pulse amplifier, and for using the resulting filament to conduct imaging and spectroscopic measurements at remote distances of at least several meters.

High-intensity femtosecond pulses of laser light can undergo cycles of Kerr self-focusing and plasma defocusing, propagating an intense sub-millimeter-diameter beam over long distances. We describe a technique for generating and using these filaments to perform remote imaging and sensing beyond the classical diffraction limits of linear optics.

하위 Diffraction 제한 이미징 및 원격 탐사에 사용 하기 위해 펨 레이저 필 라 멘 트

Probing remote matter with laser light is a ubiquitous technique used in circumstances as diverse as laser-induced breakdown spectroscopy and barcode ...

Quantitative Analysis by Thermogravimetry-Mass Spectrum Analysis for Reactions with Evolved Gases

During energy conversion, material production, and metallurgy processes, reactions often have the features of unsteadiness, multistep, and multi-intermediates. Thermogravimetry-mass spectrum (TG-MS) is seen as a powerful tool to study reaction features. However, reaction details and reaction mechanics have not been effectively obtained directly from the ion current of TG-MS. Here, we provide a method of an equivalent characteristic spectrum analysis (ECSA) for analyzing the mass spectrum and giving the mass flow rate of reaction gases as precise as possible. The ECSA can effectively separate overlapping ion peaks and then eliminate the mass discrimination and temperature-dependent effect. Two example experiments are presented: (1) the decomposition of CaCO3 with evolved gas of CO2 and the decomposition of hydromagnesite with evolved gas of CO2 and H2O, to evaluate the ECSA on single-component system measurement and (2) the thermal pyrolysis of Zhundong coal with evolved gases of inorganic gases CO, H2, and CO2, and organic gases C2H4, C2H6, C3H8, C6H14, etc., to evaluate the ECSA on multi-component system measurement. Based on the successful calibration of the characteristic spectrum and relative sensitivity of specific gas and the ECSA on mass spectrum, we demonstrate that the ECSA accurately gives the mass flow rates of each evolved gas, including organic or inorganic gases, for not only single but multi-component reactions, which cannot be implemented by the traditional measurements.

Precise determination of the evolved gases&#39; flow rate is key to study the details of reactions. We provide a novel quantitative analysis method of equivalent characteristic spectrum analysis for thermogravimetry-mass spectrum analysis by establishing the calibration system of the characteristic spectrum and relative sensitivity, for obtaining the flow rate.

Thermogravimetry 질량 스펙트럼 분석 진화 가스와 반응에 대 한 정량 분석

During energy conversion, material production, and metallurgy processes, reactions often have the features of unsteadiness, multistep, and ...

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation

A procedure using digital image correlation (DIC) to detect cracks on welded specimens during fatigue tests on resonance testing machines is presented. It is intended as a practical and reproducible procedure to identify macroscopic cracks at an early stage and monitor crack propagation during fatigue tests. It consists of strain field measurements at the weld using DIC. Images are taken at fixed load cycle intervals. Cracks become visible in the computed strain field as elevated strains. This way, the whole width of a small-scale specimen can be monitored to detect where and when a crack initiates. Subsequently, it is possible to monitor the development of the crack length. Because the resulting images are saved, the results are verifiable and comparable. The procedure is limited to cracks initiating at the surface and is intended for fatigue tests under laboratory conditions. By visualizing the crack, the presented procedure allows direct observation of macrocracks from their formation until rupture of the specimen.

Digital image correlation is used in fatigue tests on a resonance testing machine to detect macroscopic cracks and monitor crack propagation in welded specimens. Cracks on the specimen surface become visible as increased strains.

디지털 이미지 상관 관계를 사용하여 용접된 시편의 공진 피로 테스트에서 균열 모니터링

A procedure using digital image correlation (DIC) to detect cracks on welded specimens during fatigue tests on resonance testing machines is presented. It ...