Use of the Advanced Photon Source and Center for Nanoscale Materials, Office of Science User Facilities operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. We acknowledge Dr. Han Wen, NHLBI / National Institutes of Health, Bethesda, MD 20892, USA, for many helpful suggestions during the data processing.

1. Planning of the Experiment
<ol>
	<li>Identify the synchrotron beamline. Contact beamline scientist to find the appropriateness of the experiment at that beamline. 
	NOTE: Experiments reported in this manuscript were performed at the 1-BM-B beamline, which is dedicated to optics and detectors testing, under XSD of APS.</li>
	<li>Submit a user proposal and beam time request.</li>
	<li>Work out the details of the experiment with the beamline scientist and specify the required instruments including motorized stages for the grating and detector alignment, 2-dimensional detector (CCD or CMOS), long translation stage covering the least and farthest distances needed between the detector and the phase grating.</li>
	<li>Prepare for the beam time by following the instructions provided in the relevant website. Complete the safety trainings and necessary experimental safety assessment form.</li>
</ol>
2. Preparation of the 2-D Checkerboard Phase Grating
<ol>
	<li>Determine the period of the grating, p, which is related to the period of the interferogram pattern, p&#952;, along different transverse direction angle &#952;. The visibility values, V&#952;(d), of the interferogram along different &#952; angle oscillate as a function of the grating-to-detector distance, d. 
	For a 2-D checkerboard &#960;/2 phase grating, V&#952;(d) peaks at distances, 
	<img alt="Equation 1" src="/files/ftp_upload/53025/53025eq1.jpg" /> 
	with n = 1, 2, 3&#8230; and &#955; the photon wavelength. The interferogram pattern has a characteristic period of p&#952; = p/&#8730;2 along the diagonal direction of the square blocks and a period of p&#952; = p/2 along the edge of the square blocks. The choice of p thus relies on the following criteria.</li>
	<li>Make sure at least several V&#952;(d) peaks are within the largest grating-to-detector distance, or the space limit of the experimental station, dmax. To satisfy dn,&#952; &#60; dmax, it follows 
	<img alt="Equation 2" src="/files/ftp_upload/53025/53025eq2.jpg" /> 
	For n = 5, dmax = 1 m, &#955; = 0.06888 nm (18 keV), it gives p&#952; &#60; 3.9 &#181;m.</li>
	<li>Within dmax, make sure that the height of the V&#952;(d) peak at the largest distance dn,&#952; is less than a factor &#947; of that of the first V&#952;(d) peak at d1,&#952; in order to have an accurate Gaussian decay function fitting. Hence, &#947; = V&#952;,n(d) / V&#952;,1(d) which is the ratio of the nth peak visibility to the first peak. For an X-ray source following Gaussian intensity distribution with the coherence length, &#958;&#952;, the period of a &#960;/2 phase grating needs to satisfy 
	<img alt="Equation 3" src="/files/ftp_upload/53025/53025eq3.jpg" /> 
	for instance, with &#947; = 10%, &#958;&#952; = 5 &#181;m and parameters above, it gives p&#952; &#62; 2.4 &#181;m.</li>
	<li>Ensure that the period of the interferogram pattern, p&#952;, is a few times larger than the spatial resolution of the detector by choosing the correct detector systems.</li>
	<li>Determine the thickness, T, of the grating required for a phase shift of, &#966;, at the X-ray photon wavelength, &#955;, using 
	<img alt="Equation 4" src="/files/ftp_upload/53025/53025eq4.jpg" /> 
	where &#948; is the refractive index decrement of the phase shifting material. For example, the refractive index decrement for Au is 9.7&#215;10-6 for 18 keV. The Au thickness for &#966; = &#960;/2 phase grating is thus 1.8 &#181;m.</li>
	<li>Fabricate the phase grating by electroplating Au into a patterned polymer mold on a silicon nitride (Si3N4) window. 
	NOTE: The procedure for preparation of silicon nitride (Si3N4) window substrate and fabrication of the grating structure are presented below.
	<ol>
		<li>Prepare the substrate by first releasing the Si3N4 membrane to form the X-ray transparent window.</li>
		<li>Acquire silicon (Si) wafers with low stress (&#60;250 MPa) Si3N4 deposited on both sides of the wafer from a vendor.</li>
		<li>Load the wafer into a magnetron sputtering deposition system to deposit Cr and Au to act as an electroplating base.</li>
		<li>Deposit 5 nm of Cr then 30 nm of Au on one side of the wafer, following manufacturer&#39;s directions. 
		NOTE: The deposition processes from the system manufacturer will include information such as deposition rate.</li>
		<li>Unload wafer from deposition tool. Use the side of the wafer deposited with Cr and Au for grating fabrication.</li>
		<li>Determine the total size of the grating and then design a photolithography mask to pattern membranes slightly larger. Use the design to acquire a photolithography mask by purchasing from a vendor or fabricate the photolithography mask.</li>
		<li>Spin a 3-&#181;m thick layer of photoresist on the back side of the wafer where there is no Cr and Au coating. Expose the resist with a UV lithography tool for 20 sec using the designed photolithography mask. Develop the exposed resist in aqueous alkaline developer solution for 30 sec then rinse with deionized water and dry with flowing N2.</li>
		<li>Load the wafer into a reactive ion etching (RIE) tool with patterned photoresist facing the chamber. Use CF4 plasma to etch the exposed Si3N4 following tool instructions.</li>
		<li>Evacuate the etching chamber and input etch recipe into RIE tool. Run the recipe until the Si3N4 layer is etched completely and the Si layer is exposed in the pattern.</li>
		<li>Etch the exposed Si on the wafer backside by submerging into 30% KOH solution heated to 80 &#176;C for about 8 hr. Etch rate is approximately 75 &#181;m/hr using the stated recipe.</li>
		<li>After Si etch is finished, rinse with deionized water and dry with flowing N2. The sample is ready for grating fabrication.</li>
	</ol>
	</li>
	<li>Fabricate the electroplating mold for the phase grating using the following steps.
	<ol>
		<li>Design the square checkerboard grating pattern and compensate for pattern biasing by reducing the exposed square pattern size by 100-250 nm. Include a &#62;50-&#181;m wide frame around the grating pattern for thickness confirmation later in the process.</li>
		<li>Load the sample into a resist spin coater and deposit poly (methyl methacrylate) (PMMA) positive resist solution on the grating side of the sample. Run the resist spin coater to form a 2 to 3.5-&#181;m thick resist film depending on desired final grating thickness. 
		NOTE: Spin curves with information on spin speed versus film thickness are provided by the PMMA solution vendor or can be determined empirically.</li>
		<li>Load the wafer into a 100 keV electron beam lithography system.</li>
		<li>Calibrate tool for exposure with a large exposure current greater than 10 nA.</li>
		<li>Expose the PMMA resist using a 100 keV e-beam lithography tool to create the grating pattern, where areas exposed will be removed in the development step. Use an exposure dose range of 1,100-1,250 &#181;C/cm2 depending on resist thickness.</li>
		<li>Unload the sample from the tool.</li>
		<li>Develop the exposed resist by submerging in a 7:3 (by volume) isopropyl alcohol (IPA): deionized water solution for 30-40 sec with gentle swirling. Rinse with IPA, and then dry with flowing N2. Ensure the PMMA was fully developed by looking at exposed area with an optical microscope.</li>
		<li>Load the sample into a RIE tool with PMMA pattern facing the chamber.</li>
		<li>Evacuate the etching chamber and input descum etch recipe into RIE tool. The descum process is a short (&#60;30 sec) O2 plasma based etch to remove any residual PMMA from the exposed grating area.</li>
	</ol>
	</li>
	<li>Finish the Au grating by electroplating into the fabricated mold using the following steps.
	<ol>
		<li>Make sure the electroplating mold thickness by scanning the probe of a profilometer across the frame included for thickness confirmation.</li>
		<li>Submerge the sample into the Au-sulfite electroplating solution heated to 40 &#176;C. The electroplating setup is composed of a beaker filled with the electroplating solution, a constant current DC power supply, and a Pt mesh anode.</li>
		<li>Determine the plating area of the sample by calculating the exposed Au in the exposed pattern, then calculate current for the desired current density, which is the primary variable used to set the deposition rate.</li>
		<li>Calculate plating time to reach desired grating thickness using the plating rate determined by the applied current density.</li>
		<li>Turn on the DC power supply to apply the determined current on the sample, acting as a cathode, and plate for approximately half the total plating time.</li>
		<li>Measure the plating thickness using the same method used in step 2.8.1.</li>
		<li>Turn on the DC power supply to electroplate Au into the PMMA mold and electroplate to the desired grating thickness, taking into account the plated height measured in step 2.8.6.</li>
	</ol>
	</li>
	<li>Remove the polymer mold using a heated solvent by submerging the sample. Then inspect with an optical microscope and a scanning electron microscope (SEM) to confirm grating period, duty cycle, and grating thickness. 
	NOTE: Have two 2-D checkerboard phase gratings (one for the experiment and one as a spare) ready, a few days before the experiment begins.</li>
</ol>
3. Experiment Setup and Alignment at the Synchrotron Facility
<ol>
	<li>Request the beamline scientist to set the X-ray beam energy or wavelength to the desired value that matches the phase grating. Routinely used X-ray energies at the APS 1-BM beamline are between 6&#160;and 28&#160;keV. In this case, tune the photon energy to 18 keV.</li>
	<li>Select the desired objective lens for the detector system. Here, use a Coolsnap HQ2 CCD detector with 1,392 &#215; 1,040 imaging pixels of 6.45 &#215; 6.45 &#181;m2 pixel size. To resolve the smallest interference pattern, use an EC plan Neofluar 10&#215; objective. The effective pixel size of the detector system including the magnification effect of microscopic objective is thus 0.64 &#181;m. The estimated spatial resolution is about 2 &#181;m, which is mainly due to the point spread function of the detector system.</li>
	<li>To set the rough focusing of the detector system, place the scintillator (lutetium-yttrium oxyorthosilicate, 150-&#181;m thick) at the &#39;working distance&#39; from the lens (~5.2 mm for the used system). At first, set the focus under ambient light by monitoring the images acquired under &#39;continuous mode&#39; as the scintillator position is adjusted using a pico-motor.</li>
	<li>Move the 2-D detector into the X-ray beam, by using vertical and horizontal stages align the center of the detector to the beam center.</li>
	<li>Place a &#39;phase sample&#39;, for example a piece of Styrofoam, into the X-ray beam. Perform the fine focusing of the detector system by observing the scattering pattern from the phase sample and adjusting the scintillator position until the highest image sharpness.</li>
</ol>
4. Performing Coherence Measurements
<ol>
	<li>Place the 2-D checkerboard grating into the X-ray beam where the coherence of the beam is to be measured. In this case it is at 34 meters from the bending magnet source.</li>
	<li>Adjust the plane of the 2-D checkerboard phase grating to be perpendicular to the direction of the X-ray beam propagation.</li>
	<li>Center the grating to the X-ray beam by using the motorized stages and looking at the images acquired under detector continuous mode.</li>
	<li>Rotate the grating around the X-ray beam propagation direction (y) so that the diagonal direction of the checkerboard pattern is along the desired transverse beam direction. In this case, align the diagonal directions of the checkerboard (preferred measuring directions) in the horizontal and vertical directions of the beam. Fine tune the grating rotations around the other two axes (x and z) to ensure its perpendicularity to the X-ray beam, which is achieved by maximizing the interferogram periods in both the horizontal and vertical directions.</li>
	<li>Move the detector system as close as physically possible to the phase grating along the beam propagation direction. In this study, use a distance of 43 mm.</li>
	<li>Calculate the smallest period in the interference pattern. The &#960;/2 checkerboard grating with period p = 4.8 &#181;m will generate an interference pattern with p&#952; = 3.4 &#181;m and p&#952; = 2.4 &#181;m (smallest period) along the diagonal and the non-diagonal directions of the checkerboard pattern, respectively. Estimate the number of data points needed in-between V&#952;(d) peak positions given by Equation (1) to obtain a smooth curve.</li>
	<li>Select the appropriate exposure time for each interferogram, four seconds in this case.</li>
	<li>Record interferograms with the same exposure time (e.g., 4 sec) at different grating-to-detector distances. Choose the exposure time based on the beam intensity level. Starting from the minimum grating-to-detector distance (43 mm), move the detector downstream of the X-ray by small intervals (10 mm determined based on step 4.6) and record an interferogram at each detector position until the maximum possible grating-to-detector distance (750 mm).</li>
	<li>Acquire dark-frame images with the same exposure time (4 sec) but turn off the X-ray beam and keep all other experimental conditions the same.</li>
</ol>
5. Data Analysis
NOTE: There is currently no standard software available for the data analysis.
<ol>
	<li>Using the selected image processing program, read in the dark-frame image(s) and the data image. Correct the data image by subtracting the (averaged) dark-frame image.</li>
	<li>Fourier transform the dark-frame corrected image, which produces visible harmonic peaks in the horizontal (&#952; = 0&#186;), vertical (&#952; = 90&#186;) as well as &#952; = 45&#176; and &#952; = 135&#176; directions.</li>
	<li>Crop the 0th order harmonic image centered at the 0th order peak. The length and width of the image equal to the distances between the 0th and 1st order peaks along the horizontal and vertical directions, respectively. Similarly, obtain the 1st order harmonic images of the same length and width along the transverse direction of interest.</li>
	<li>Inverse Fourier Transform (IFT) the cropped harmonic images. Ratio of the mean of the amplitudes of the IFT image from the 1st order harmonic image along any transverse direction to that of the IFT image from the 0th order harmonic image gives the visibility along that direction. 
	Note that this process is valid if few high-frequency components exist in the measured interferogram. Otherwise, one can use the corresponding harmonic peak intensities of the Fourier transform images from step 5.4 instead. Due to the beam divergence, the harmonic peak positions will change gradually at different grating-to-detector distances. Therefore, a correction to p&#39;&#952; at each distance or a peak finding process is needed.</li>
	<li>Repeat step 5.1-5.4 for all the measured images at different grating-to-detector distances and save the visibility value of each image.</li>
	<li>Plot the visibility V&#952;(d) as a function of the grating-to-detector distance. Identify data points at V&#952;(d) peaks. Note that the full curve was measured just to better identify the peak positions given by Equation (1). Manually select peak data points as well as adjacent data points on either side of each peak.</li>
	<li>Draw Gaussian fitting function for the selected data points. Extract standard deviation, &#963;&#952;, of the Gaussian fitting function.</li>
	<li>Obtain the transverse coherence length, &#958;&#952;, using 
	<img alt="Equation 5" src="/files/ftp_upload/53025/53025eq5.jpg" /></li>
</ol>

<ol>
	<li>Als-Nielsen, J., McMorrow, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Elements of Modern X-ray Physics. , (2011).</li><li>Born, M., Wolf, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Principle of Optics. , (1999).</li><li>Lin, J. J. A., 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=Measurement+of+the+Spatial+Coherence+Function+of+Undulator+Radiation+using+a+Phase+Mask.">Measurement of the Spatial Coherence Function of Undulator Radiation using a Phase Mask.</a> Phys. Rev. Lett. 90 (7), 074801 (2003).</li><li>Cloetens, P., Guigay, J. P., De Martino, C., Baruchel, J., Schlenker, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Fractional+Talbot+imaging+of+phase+gratings+with+hard+X-rays.">Fractional Talbot imaging of phase gratings with hard X-rays.</a> Opt. Lett. 22 (14), 1059-1061 (1997).</li><li>Guigay, J. P., 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=The+partial+Talbot+effect+and+its+use+in+measuring+the+coherence+of+synchrotron+X-rays.">The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays.</a> J. Synchrotron Rad. 11, 476-482 (2004).</li><li>Kluender, R., Masiello, F., Vaerenbergh, P. V., H&#228;rtwig, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Measurement+of+the+spatial+coherence+of+synchrotron+beams+using+the+Talbot+effect.">Measurement of the spatial coherence of synchrotron beams using the Talbot effect.</a> Phys. Status Solidi A. 206 (8), 1842-1845 (2009).</li><li>Pfeiffer, F., 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=Shearing+Interferometer+for+Quantifying+the+Coherence+of+Hard+X-Ray+Beams.">Shearing Interferometer for Quantifying the Coherence of Hard X-Ray Beams.</a> Phys. Rev. Lett. 94 (1-4), 164801 (2005).</li><li>Marathe, 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=Probing+transverse+coherence+of+x-ray+beam+with+2-D+phase+grating+interferometer.">Probing transverse coherence of x-ray beam with 2-D phase grating interferometer.</a> Opt. Express. 22 (12), 14041-14053 (2014).</li><li>Shi, X., 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=Circular+grating+interferometer+for+mapping+transverse+coherence+area+of+X-ray+beams.">Circular grating interferometer for mapping transverse coherence area of X-ray beams.</a> Appl. Phys. Lett. 105 (1-6), 041116 (2014).</li><li>Zanette, I., David, C., Rutishauser, S., Weitkamp, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=2D+grating+simulation+for+X-ray+phase-contrast+and+dark-field+imaging+with+a+Talbot+interferometer.">2D grating simulation for X-ray phase-contrast and dark-field imaging with a Talbot interferometer.</a> , 73-79 (2010).</li></ol>

The authors have nothing to disclose.

Figure 5 shows the estimated transverse coherence length along all four directions. Clearly, the 90&#176; direction has higher &#958;&#952; compared to 0&#176; direction. Since the beamline optics has negligible effect on the beam coherence at the grating relative location, the measured coherence area is inversely proportional to the source size area. The presented X-ray beam coherence measurement technique maps this accurately which can be shown as an ellipse with its major axis alon...

The third-generation hard X-ray synchrotron radiation sources, such as the APS at ANL, Lemont, IL, USA (http://www.aps.anl.gov), have had tremendous impacts on the development of X-ray sciences. A synchrotron radiation source generates a spectrum of electromagnetic radiations, from infrared to X-ray wavelengths, when charged particles, such as electrons, are made to move near the speed of light in a circular orbit. These sources have very unique properties such as high brightness, pulsed and pico-second timing structure, and large spatial and temporal coherence. X-ray beam spatial coherence is an important parameter of the third and fourth generation synchrotron sources and the number of experiments making use of this property has dramatically increased over the past two decades1. The future upgrades of these sources, such as the planned Multi-bend achromat (MBA) lattice for the APS storage ring, will dramatically increase the beam coherent flux (http://www.aps.anl.gov/Upgrade/). The X-ray beam can be tuned using a crystal monochromator to achieve higher temporal coherence. The transverse coherence of synchrotron sources is significantly higher than that of laboratory based X-ray sources because of the low electron-beam emittance and long propagation distance from the source to the experimental station.
Normally, Young&#39;s double-pinhole or double-slit experiment is used to measure the spatial coherence of the beam through the inspection of the visibility of the interference fringes2. To obtain the complete Complex Coherence Function (CCF), systematic measurements are needed with the two slits placed at different positions with various separations, which is, especially for hard X-rays, cumbersome and impractical. Uniformly Redundant Array (URA) can also be used for beam coherence measurement by employing it as a phase shifting mask3. Although the technique can provide the full CCF, it is not model-free. More recently, interferometric techniques based on Talbot effect were developed using the self-imaging property of periodic objects. These interferometers make use of the interferogram visibility measured at a few self-imaging distances downstream of the grating for obtaining the beam transverse coherence4-9. Measurements of transverse coherence using two grating system is also reported7.
Mapping the transverse beam coherence, simultaneously along vertical and horizontal directions was first reported by J. P. Guigay et al.5. Recently, scientists in the Optics Group, X-ray Science Division (XSD), of APS have reported two new techniques to measure beam transverses coherence along more than two directions simultaneously using two methods: one with a checkerboard phase grating8, and the other with a circular phase grating9.
In this paper the measurement and data analysis procedures are described for obtaining the transverse coherence of the beam along the 0&#176;, 45&#176;, 90&#176;, and 135&#176; directions relative to the horizontal direction, simultaneously. The measurements were carried out at the 1-BM beamline of APS with a checkerboard &#960;/2 phase grating. The details of this technique listed in the protocol sections include: 1) planning of the experiment; 2) preparation of the 2-d checkerboard phase grating; 3) experiment setup and alignment at the synchrotron facility; 4) performing coherence measurements; 5) data analysis. In addition, the representative results are shown to illustrate the technique. These procedures can be carried out at many synchrotron beamlines with minimum changes on the grating design.

<table><tbody><tr><td>1-BM-B bending magnet X-ray source</td><td>Advanced photon Source/ Argonne National Lab</td><td></td><td>&lt;a href=&quot;http://www.aps.anl.gov/Xray_Science_Division/Optics/Beamline/&quot;&gt;http://www.aps.anl.gov/Xray_Science_Division/Optics/Beamline/&lt;/a&gt;</td></tr><tr><td>LYSO Scintillator</td><td>Proteus Inc</td><td></td><td>&lt;a href=&quot;http://www.apace-science.com/proteus/lyso.htm#top&quot;&gt;http://www.apace-science.com/proteus/lyso.htm#top&lt;/a&gt;</td></tr><tr><td>Coolsnap HQ2 CCD detector</td><td>Photometrics</td><td></td><td>&lt;a href=&quot;http://www.photometrics.com/products/ccdcams/coolsnap_hq2.php&quot;&gt;http://www.photometrics.com/products/ccdcams/coolsnap_hq2.php&lt;/a&gt;</td></tr><tr><td>ATC 2000 UHV sputtering deposition system</td><td>AJA International Inc</td><td></td><td>&lt;a href=&quot;http://www.ajaint.com/systems_atc.htm&quot;&gt;http://www.ajaint.com/systems_atc.htm&lt;/a&gt;</td></tr><tr><td>MICROPOSIT S1800 photoresist</td><td>Dow&amp;nbsp;</td><td></td><td></td></tr><tr><td>MICROPOSIT 351 developer</td><td>Dow&amp;nbsp;</td><td></td><td></td></tr><tr><td>MA/BA6 lithography system</td><td>SUSS MicroTec</td><td></td><td>&lt;a href=&quot;http://www.suss.com/en/products-solutions/products/mask-aligner/maba6/overview.html&quot;&gt;http://www.suss.com/en/products-solutions/products/mask-aligner/maba6/overview.html&lt;/a&gt;</td></tr><tr><td>Spin coater WS-400-6NPPB</td><td>Laurell Technologies Corporation</td><td></td><td>&lt;a href=&quot;http://www.laurell.com/spin-coater/?model=WS-400-6NPP-LITE&quot;&gt;http://www.laurell.com/spin-coater/?model=WS-400-6NPP-LITE&lt;/a&gt;</td></tr><tr><td>JBX-9300FS electron beam lithography system</td><td>JEOL</td><td></td><td>&lt;a href=&quot;http://www.jeolusa.com/PRODUCTS/PhotomaskDirectWriteLithography/ElectronBeamLithography/JBX-9500FS/tabid/245/Default.aspx&quot;&gt;http://www.jeolusa.com/PRODUCTS/PhotomaskDirectWriteLithography/ElectronBeamLithography/JBX-9500FS/tabid/245/Default.aspx&lt;/a&gt;</td></tr><tr><td>CS-1701 RIE system</td><td>Nordson March</td><td></td><td>&lt;a href=&quot;http://www.nordson.com/EN-US/DIVISIONS/MARCH/PRODUCTS/LEGACY/Pages/CS-1701-Anisotropic-RIE-Plasma-System.aspx&quot;&gt;http://www.nordson.com/EN-US/DIVISIONS/MARCH/PRODUCTS/LEGACY/Pages/CS-1701-Anisotropic-RIE-Plasma-System.aspx&lt;/a&gt;</td></tr><tr><td>Techni Gold 25E</td><td>Technic</td><td></td><td>&lt;a href=&quot;http://www.technic.com/eu/applications/industrial/industrial-chemistry/plating-chemistry&quot;&gt;http://www.technic.com/eu/applications/industrial/industrial-chemistry/plating-chemistry&lt;/a&gt;</td></tr><tr><td>Dektak-8 surface profiler</td><td>Bruker</td><td></td><td>&lt;a href=&quot;http://brukersupport.com/ProductDetail/1136&quot;&gt;http://brukersupport.com/ProductDetail/1136&lt;/a&gt;</td></tr><tr><td>MICROPOSIT 1165 remover</td><td>Dow&amp;nbsp;</td><td></td><td></td></tr></tbody></table>

measurement of x-ray beam coherence along multiple directions using 2-d checkerboard phase grating

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is reported. The measurements were demonstrated at the 1-BM bending magnet beamline of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). By using a 2-D checkerboard &#960;/2 phase-shift grating, transverse coherence lengths were obtained along the vertical and horizontal directions as well as along the 45&#176; and 135&#176; directions to the horizontal direction. Following the technical details specified in this paper, interferograms were measured at different positions downstream of the phase grating along the beam propagation direction. Visibility values of each interferogram were extracted from analyzing harmonic peaks in its Fourier Transformed image. Consequently, the coherence length along each direction can be extracted from the evolution of visibility as a function of the grating-to-detector distance. The simultaneous measurement of coherence lengths in four directions helped identify the elliptical shape of the coherence area of the Gaussian-shaped X-ray source. The reported technique for multiple-direction coherence characterization is important for selecting the appropriate sample size and orientation as well as for correcting the partial coherence effects in coherence scattering experiments. This technique can also be applied for assessing coherence preserving capabilities of X-ray optics.

While detailed experimental and simulation results could be found elsewhere8, this section only shows selected results to illustrate the above measurement and data analysis procedures. Figure 1 represents the experiment setup at the APS 1-BM-B beamline. The beam size is defined by a 1&#215;1 mm2 slit placed upstream of the Double Crystal Monochromator (DCM) and 25 m from the bending magnet source. The DCM is tuned to output photon energy of 18 keV. The X-ray beam passes through seve...

Watch this Scientific Journal Video about Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating at JoVE.com

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

The measurement protocol and data analysis procedure are given for obtaining transverse coherence of a synchrotron radiation X-ray source along four directions simultaneously using a single 2-D checkerboard phase grating. This simple technique can be applied for complete transverse coherence characterization of X-ray sources and X-ray optics.

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is ...

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JoVE Journal

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9.5K Views.  Argonne National Laboratory. The measurement protocol and data analysis procedure are given for obtaining transverse coherence of a synchrotron radiation X-ray source along four directions simultaneously using a single 2-D checkerboard phase grating. This simple technique can be applied for complete transverse coherence characterization of X-ray sources and X-ray optics.

Video: Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, spin-flip scattering) is described, using experiments on GaMnAs as a prototype III-Mn-V system.&#160; Spectrally-resolved and time-resolved experimental configurations are described, including the use of zero-background autocorrelation techniques for pulse optimization.&#160; The etching process used to prepare GaMnAs samples for four-wave mixing experiments is also highlighted.&#160; The high temporal resolution of this technique, afforded by the use of short (20 fsec) optical pulses, permits the rapid spin-flip scattering process in this system to be studied directly in the time domain, providing new insight into the strong exchange coupling responsible for carrier-mediated ferromagnetism.&#160; We also show that spectral resolution of the four-wave mixing signal allows one to extract clear signatures of (s,p)-d hybridization in this system, unlike linear spectroscopy techniques.&#160;&#160; This increased sensitivity is due to the nonlinearity of the technique, which suppresses defect-related contributions to the optical response. This method may be used to measure the time scale for coherence decay (tied to the fastest scattering processes) in a wide variety of semiconductor systems of interest for next generation electronics and optoelectronics.

The technique of femtosecond four-wave mixing is described, including spectrally-resolved and time-resolved configurations. We illustrate the utility of this technique for the investigation of crucial physical properties in the III-V diluted magnetic semiconductors, afforded by its nonlinearity and high temporal resolution.

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, ...

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this work, we use single particle tracking of fluorescently labeled PNIPAM microgels as a showcase for tuning microgel size by a rapid non-stirred precipitation polymerization procedure. This approach is well suited for prototyping new reaction compositions and conditions or for applications that do not require large amounts of product. Microgel synthesis, particle size and structure determination by dynamic and static light scattering are detailed in the protocol. It is shown that the addition of functional comonomers can have a large influence on the particle nucleation and structure. Single particle tracking by wide-field fluorescence microscopy allows for an investigation of the diffusion of labeled tracer microgels in a concentrated matrix of non-labeled microgels, a system not easily investigated by other methods such as dynamic light scattering.

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Non-stirred precipitation polymerization provides a rapid, reproducible prototyping approach to the synthesis of stimuli-sensitive poly(N-isopropylacrylamide) microgels of narrow size distribution. In this protocol synthesis, light scattering characterization and single particle fluorescence tracking of these microgels in a wide-field microscopy setup are demonstrated.

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this ...

Chemistry

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis

Recent years have witnessed a significant increase in the use of spontaneous Brillouin spectrometers for non-contact analysis of soft matter, such as aqueous solutions and biomaterials, with fast acquisition times. Here, we discuss the assembly and operation of a Brillouin spectrometer that uses stimulated Brillouin scattering (SBS) to measure stimulated Brillouin gain (SBG) spectra of water and lipid emulsion-based tissue-like samples in transmission mode with &lt;10 MHz spectral-resolution and &lt;35 MHz Brillouin-shift measurement precision at &lt;100 ms. The spectrometer consists of two nearly counter-propagating continuous-wave (CW) narrow-linewidth lasers at 780 nm whose frequency detuning is scanned through the material Brillouin shift. By using an ultra-narrowband hot rubidium-85 vapor notch filter and a phase-sensitive detector, the signal-to-noise-ratio of the SBG signal is significantly enhanced compared to that obtained with existing CW-SBS spectrometers. This improvement enables measurement of SBG spectra with up to 100-fold faster acquisition times, thereby facilitating high spectral-resolution and high-precision Brillouin analysis of soft materials at high speed.

We describe the construction of a rapid continuous-wave-stimulated-Brillouin-scattering (CW-SBS) spectrometer. The spectrometer employs single-frequency diode-lasers and an atomic vapor notch-filter to acquire transmission spectra of turbid/non-turbid samples with high spectral-resolution at speeds up to 100-fold faster than those of existing CW-SBS spectrometers. This improvement enables high-speed Brillouin material analysis.

Recent years have witnessed a significant increase in the use of spontaneous Brillouin spectrometers for non-contact analysis of soft matter, such as ...

Generation and Coherent Control of Pulsed Quantum Frequency Combs

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

A protocol is presented for the practical generation and coherent manipulation of high-dimensional frequency-bin entangled photon states using integrated micro-cavities and standard telecommunications components, respectively.

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional ...

Highly Resolved Intravital Striped-illumination Microscopy of Germinal Centers

Monitoring cellular communication by intravital deep-tissue multi-photon microscopy is the key for understanding the fate of immune cells within thick tissue samples and organs in health and disease. By controlling the scanning pattern in multi-photon microscopy and applying appropriate numerical algorithms, we developed a striped-illumination approach, which enabled us to achieve 3-fold better axial resolution and improved signal-to-noise ratio, i.e. contrast, in more than 100 &#181;m tissue depth within highly scattering tissue of lymphoid organs as compared to standard multi-photon microscopy. The acquisition speed as well as photobleaching and photodamage effects were similar to standard photo-multiplier-based technique, whereas the imaging depth was slightly lower due to the use of field detectors. By using the striped-illumination approach, we are able to observe the dynamics of immune complex deposits on secondary follicular dendritic cells &#8211; on the level of a few protein molecules in germinal centers.

High-resolution intravital imaging with enhanced contrast up to 120 &#181;m depth in lymph nodes of adult mice is achieved by spatially modulating the excitation pattern of a multi-focal two-photon microscope. In 100 &#181;m depth we measured resolutions of 487 nm (lateral) and 551 nm (axial), thus circumventing scattering and diffraction limits.

Monitoring cellular communication by intravital deep-tissue multi-photon microscopy is the key for understanding the fate of immune cells within thick ...

Immunology and Infection

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser radiation. The method is based on the coherent sum of two uniform waves, previously encoded into a phase-only spatial light modulator (SLM) by spatial multiplexing of their phases. Here, the interference process is carried out by spatial filtering of light frequencies at the Fourier plane of certain imaging system. The correct implementation of this method allows arbitrary phase and amplitude information to be retrieved at the output of the optical system.
It is an on-axis, rather than off-axis encoding technique, with a direct processing algorithm (not an iterative loop), and free from coherent noise (speckle). The complex field can be exactly retrieved at the output of the optical system, except for some loss of resolution due to the frequency filtering process. The main limitation of the method might come from the inability to operate at frequency rates higher than the refresh rate of the SLM. Applications include, but are not limited to, linear and non-linear microscopy, beam shaping, or laser micro-processing of material surfaces.

We show how to encode the complex field of laser beams by using a single phase element. A common-path interferometer is employed to mix the phase information displayed into a phase-only spatial light modulator to finally retrieve the desired complex field pattern at the output of an optical imaging system.

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser ...

X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells

X-ray beam induced current (XBIC) measurements allow mapping of&#160;the nanoscale performance of electronic devices such as solar cells. Ideally, XBIC is employed simultaneously with other techniques within a multi-modal X-ray microscopy approach. An example is given herein combining XBIC with X-ray fluorescence to enable point-by-point correlations of the electrical performance with chemical composition. For the highest signal-to-noise ratio in XBIC measurements, lock-in amplification plays a crucial role. By this approach, the X-ray beam is modulated by an optical chopper upstream of the sample. The modulated X-ray beam induced electrical signal is amplified and demodulated to the chopper frequency using a lock-in amplifier. By optimizing low-pass filter settings, modulation frequency, and amplification amplitudes, noise can efficiently be suppressed for the extraction of a clear XBIC signal. A similar setup can be used to measure the X-ray beam induced voltage (XBIV). Beyond standard XBIC/XBIV measurements, XBIC can be measured with bias light or bias voltage applied such that outdoor working conditions of solar cells can be reproduced during in-situ and operando measurements. Ultimately, the multi-modal and multi-dimensional evaluation of electronic devices at the nanoscale enables new insights into the complex dependencies between composition, structure, and performance, which is an important step towards solving the materials&#39; paradigm.

A setup for X-ray beam induced current measurements at synchrotron beamlines is described. It unveils the nanoscale performance of solar cells and extends the suite of techniques for multi-modal X-ray microscopy. From wiring to signal-to-noise optimization, it is shown how to perform state-of-the-art XBIC measurements at a hard X-ray microprobe.

X-ray beam induced current (XBIC) measurements allow mapping of&#160;the nanoscale performance of electronic devices such as solar cells. Ideally, XBIC is ...

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Photonic band structure enables understanding how confined electromagnetic modes propagate within a photonic crystal. In photonic crystals that incorporate magnetic elements, such confined and resonant optical modes are accompanied by enhanced and modified magneto-optical activity. We describe a measurement procedure to extract the magneto-optical band structure by Fourier space microscopy.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by ...

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for moving mechanical parts. This technology is particularly useful for beam steering applications. Here, we focus on OPAs integrated into SiN photonic circuits for a wavelength in the near infrared. A characterization method of such circuits is presented, which allows the output beam of integrated OPAs to be shaped and steered. Furthermore, using a wafer-scale characterization setup, several devices can easily be tested across multiple dies on a wafer. In this way, fabrication variations can be studied, and high-performance devices identified. Typical images of OPA beams are shown, including beams emitted from OPAs with and without a uniform waveguide length, and with varying numbers of channels. In addition, the evolution of output beams during the phase optimization process and beam steering in two dimensions is presented. Finally, a study of the variation in the beam divergence of identical devices is performed with respect to their position on the wafer.

Here, we describe the operation of a SiN integrated photonic circuit containing optical phased arrays. The circuits are used to emit low divergence laser beams in the near infrared and steer them in two dimensions.

Optical phased arrays (OPAs) can produce low-divergence laser beams and can be used to control the emission angle electronically without the need for ...