Discovery of a big void in Khufu's Pyramid by observation of cosmic-ray muons

The Great Pyramid, or Khufu's Pyramid, was built on the Giza plateau in Egypt during the fourth dynasty by the pharaoh Khufu (Cheops), who reigned from 2509 bc to 2483 bc. Despite being one of the oldest and largest monuments on Earth, there is no consensus about how it was built. To understand its internal structure better, we imaged the pyramid using muons, which are by-products of cosmic rays that are only partially absorbed by stone. The resulting cosmic-ray muon radiography allows us to visualize the known and any unknown voids in the pyramid in a non-invasive way. Here we report the discovery of a large void (with a cross-section similar to that of the Grand Gallery and a minimum length of 30 metres) situated above the Grand Gallery. This constitutes the first major inner structure found in the Great Pyramid since the nineteenth century. The void, named ScanPyramids' Big Void, was first observed with nuclear emulsion films installed in the Queen's chamber, then confirmed with scintillator hodoscopes set up in the same chamber and finally re-confirmed with gas detectors outside the pyramid. This large void has therefore been detected with high confidence by three different muon detection technologies and three independent analyses. These results constitute a breakthrough for the understanding of the internal structure of Khufu's Pyramid. Although there is currently no information about the intended purpose of this void, these findings show how modern particle physics can shed new light on the world's archaeological heritage.

Ray tracing method in phase space for two-dimensional optical systems

Ray tracing is a forward method to calculate the photometric variables at the target of a non-imaging optical system. In this paper, a new ray tracing technique is presented to improve the accuracy and to reduce the computational time of the classical ray tracing approach. The method is based on the phase space representation of the source and the target of the optical system, and it is applied to a two-dimensional TIR-collimator. The strength of the method lies in tracing fewer rays through the system. Only rays that lie in the meridional plane are considered. A procedure that disregards rays in smooth regions in phase space, where the luminance is continuous, is implemented and only the rays close to discontinuities are traced. The efficiency of the method is demonstrated by numerical simulations that compare the new method with Monte Carlo ray tracing. The results show that the phase space approach is faster and more accurate than the already existing ray tracing method; moreover the phase space method converges as one over the number of rays traced unlike Monte Carlo ray tracing in which the speed of convergence is proportional to one over the square root of the number of rays.