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We present a constraint on the abundance of supergiant (SG) stars at redshift z approx. 1, based on recent observations of a strongly lensed arc at this redshift. First we derive a free-form model of MACS J0416.1-2403 using data from the BUFFALO program. The new lens model is based on 72 multiply lensed galaxies that produce 214 multiple images, making it the largest sample of spectroscopically confirmed lensed galaxies on this cluster. The larger coverage in BUFFALO allows us to measure the shear up to the outskirts of the cluster, and extend the range of lensing constraints up to ~ 1 Mpc from the central region, providing a mass estimate up to this radius. As an application, we make predictions for the number of high-redshift multiply-lensed galaxies detected in future observations with JWST. Then we focus on a previously known lensed galaxy at z=1.0054, nicknamed Spock, which contains four previously reported transients. We interpret these transients as microcaustic crossings of SG stars and compute the probability of such events. Based on simplifications regarding the stellar evolution, we find that microlensing (by stars in the intracluster medium) of SG stars at z=1.0054 can fully explain these events. The inferred abundance of SG stars is consistent with either (1) a number density of stars with bolometric luminosities beyond the Humphreys-Davidson (HD) limit (L ~ $6\times10^5 L_{\odot}$) that is below 400 stars per sq. kpc, or (2) the absence of stars beyond the HD limit but with a SG number density of ~ 9000 per sq. kpc for stars with luminosities between $10^5$ and $6\times10^5$. This is equivalent to one SG star per 10x10 pc$^2$. We finally make predictions for future observations with JWST's NIRcam. We find that in observations made with the F200W filter that reach 29 mag AB, if cool red SG stars exist at z~1 beyond the HD limit, they should be easily detected in this arc, Comment: 24 pages & 18 figures

One-dimensional single-wire chamber was developed to provide high position resolution for powder diffraction experiments with synchrotron radiation. A diffraction test using the sample of SiO2 has been accomplished at 1W2B laboratory of Beijing Synchrotron Radiation Source. The data of beam test were analyzed and some diffraction angles were obtained. The experimental results were in good agreement with standard data from ICDD powder diffraction file. The precision of diffraction angles was 1% to 4.7%. Most of relative errors between measured values of diffraction angles and existing data were less than 1%. As for the detector, the best position resolution in the test was 138 um (sigma value) with an X-ray tube. Finally, discussions of the results were given. The major factor that affected the precision of measurement was deviation from the flat structure of detector. The effect was analyzed and it came to a conclusion that it would be the optimal measurement scheme when the distance between the powder sample and detector was from 400 mm to 600 mm.