Self-calibration strategies for reducing systematic slope measurement errors of autocollimators in deflectometric profilometry.

Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change - all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.

A clock directly linking time to a particle's mass.

Historically, time measurements have been based on oscillation frequencies in systems of particles, from the motion of celestial bodies to atomic transitions. Relativity and quantum mechanics show that even a single particle of mass m determines a Compton frequency ω(0) = mc(2)/[formula: see text] where c is the speed of light and [formula: see text] is Planck's constant h divided by 2π. A clock referenced to ω(0) would enable high-precision mass measurements and a fundamental definition of the second. We demonstrate such a clock using an optical frequency comb to self-reference a Ramsey-Bordé atom interferometer and synchronize an oscillator at a subharmonic of ω(0.) This directly demonstrates the connection between time and mass. It allows measurement of microscopic masses with 4 × 10(-9) accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms.