Stochastic analysis of surface metrology

The design and evaluation of the expected performance of optical systems require sophisticated and reliable information about the surface topography for planned optical elements before they are fabricated. Modern x-ray source facilities are reliant upon the availability of optics with unprecedented quality (surface slope accuracy <0.1 μrad). The problem is especially complex in the case of x-ray optics, particularly for the X-ray Surveyor under development and other missions. The high angular resolution and throughput of future x-ray space observatories requires hundreds of square meters of high-quality optics. The uniqueness of the optics and limited number of proficient vendors makes the fabrication extremely time consuming and expensive, mostly due to the limitations in accuracy and measurement rate of metrology used in fabrication. We discuss improvements in metrology efficacy via comprehensive statistical analysis of a compact volume of metrology data. The data are considered stochastic, and a statistical model called invertible time-invariant linear filter (InTILF) is developed now for two-dimensional (2-D) surface profiles to provide compact description of the 2-D data in addition to one-dimensional data treated so far. The InTILF model captures stochastic patterns in the data and can be used as a quality metric and feedback to polishing processes, avoiding high-resolution metrology measurements over the entire optical surface. The modeling, implemented in our BeatMark™ software, allows simulating metrology data for optics made by the same vendor and technology. The data are vital for reliable specification for optical fabrication, to be exactly adequate for the required system performance

Observation of the thermal Casimir force

Quantum theory predicts the existence of the Casimir force between macroscopic bodies, due to the zero-point energy of electromagnetic field modes around them. This quantum fluctuation-induced force has been experimentally observed for metallic and semiconducting bodies, although the measurements to date have been unable to clearly settle the question of the correct low-frequency form of the dielectric constant dispersion (the Drude model or the plasma model) to be used for calculating the Casimir forces. At finite temperature a thermal Casimir force, due to thermal, rather than quantum, fluctuations of the electromagnetic field, has been theoretically predicted long ago. Here we report the experimental observation of the thermal Casimir force between two gold plates. We measured the attractive force between a flat and a spherical plate for separations between 0.7 $\mu$m and 7 $\mu$m. An electrostatic force caused by potential patches on the plates' surfaces is included in the analysis. The experimental results are in excellent agreement (reduced $\chi^2$ of 1.04) with the Casimir force calculated using the Drude model, including the T=300 K thermal force, which dominates over the quantum fluctuation-induced force at separations greater than 3 $\mu$m. The plasma model result is excluded in the measured separation range.Comment: 6 page

Optical Magnetometry

Some of the most sensitive methods of measuring magnetic fields utilize interactions of resonant light with atomic vapor. Recent developments in this vibrant field are improving magnetometers in many traditional areas such as measurement of geomagnetic anomalies and magnetic fields in space, and are opening the door to new ones, including, dynamical measurements of bio-magnetic fields, detection of nuclear magnetic resonance (NMR), magnetic-resonance imaging (MRI), inertial-rotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of Nature.Comment: 11 pages; 4 figures; submitted to Nature Physic

Characterization of groove density variation of VLS gratings with ALS XROL LTP-II in different operation modes

The long trace profiler, LTP-II, available at the Advanced Light Source (ALS) X-ray Optics Laboratory (XROL), was recently upgraded by replacing a multimode diode laser light source with a single-mode, wavelength-stabilized, fibercoupled diode laser system. The upgrade enables us to reliably characterize the lateral variation of groove density of variable-line-spacing (VLS) x-ray diffraction gratings. Here, we discuss the LTP-II performance with an example of measurements with a VLS grating with the groove density at the grating center of 300 lines/mm. For the measurements, we use the LTP-II in two different operation arrangements, the single Gaussian beam and the pencil beam interferometer arrangements. For each operation arrangement, we apply two data processing algorithms: with calculating the centroid position and with determining the position of a characteristic features of the detected beam intensity distributions. We discuss the observed strong correlation between the LTP-II modes of operation and the resulted (extracted) groove density variations. We also speculate on possible origin of the correlation