Aperture alignment in autocollimator-based deflectometric profilometers.

During the last ten years, deflectometric profilometers have become indispensable tools for the precision form measurement of optical surfaces. They have proven to be especially suitable for characterizing beam-shaping optical surfaces for x-ray beamline applications at synchrotrons and free electron lasers. Deflectometric profilometers use surface slope (angle) to assess topography and utilize commercial autocollimators for the contactless slope measurement. To this purpose, the autocollimator beam is deflected by a movable optical square (or pentaprism) towards the surface where a co-moving aperture limits and defines the beam footprint. In this paper, we focus on the precise and reproducible alignment of the aperture relative to the autocollimator's optical axis. Its alignment needs to be maintained while it is scanned across the surface under test. The reproducibility of the autocollimator's measuring conditions during calibration and during its use in the profilometer is of crucial importance to providing precise and traceable angle metrology. In the first part of the paper, we present the aperture alignment procedure developed at the Advanced Light Source, Lawrence Berkeley National Laboratory, USA, for the use of their deflectometric profilometers. In the second part, we investigate the topic further by providing extensive ray tracing simulations and calibrations of a commercial autocollimator performed at the Physikalisch-Technische Bundesanstalt, Germany, for evaluating the effects of the positioning of the aperture on the autocollimator's angle response. The investigations which we performed are crucial for reaching fundamental metrological limits in deflectometric profilometry.

Linear chirped slope profile for spatial calibration in slope measuring deflectometry.

Slope measuring deflectometry is commonly used by the X-ray optics community to measure the long-spatial-wavelength surface figure error of optical components dedicated to guide and focus X-rays under grazing incidence condition at synchrotron and free electron laser beamlines. The best performing instruments of this kind are capable of absolute accuracy on the level of 30-50 nrad. However, the exact bandwidth of the measurements, determined at the higher spatial frequencies by the instrument's spatial resolution, or more generally by the instrument's modulation transfer function (MTF) is hard to determine. An MTF calibration method based on application of a test surface with a one-dimensional (1D) chirped height profile of constant amplitude was suggested in the past. In this work, we propose a new approach to designing the test surfaces with a 2D-chirped topography, specially optimized for MTF characterization of slope measuring instruments. The design of the developed MTF test samples based on the proposed linear chirped slope profiles (LCSPs) is free of the major drawback of the 1D chirped height profiles, where in the slope domain, the amplitude strongly increases with the local spatial frequency of the profile. We provide the details of fabrication of the LCSP samples. The results of first application of the developed test samples to measure the spatial resolution of the BESSY-NOM at different experimental arrangements are also presented and discussed.

Binary pseudo-random patterned structures for modulation transfer function calibration and resolution characterization of a full-field transmission soft x-ray microscope.

We present a modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) one-dimensional sequences and two-dimensional arrays as an effective method for spectral characterization in the spatial frequency domain of a broad variety of metrology instrumentation, including interferometric microscopes, scatterometers, phase shifting Fizeau interferometers, scanning and transmission electron microscopes, and at this time, x-ray microscopes. The inherent power spectral density of BPR gratings and arrays, which has a deterministic white-noise-like character, allows a direct determination of the MTF with a uniform sensitivity over the entire spatial frequency range and field of view of an instrument. We demonstrate the MTF calibration and resolution characterization over the full field of a transmission soft x-ray microscope using a BPR multilayer (ML) test sample with 2.8 nm fundamental layer thickness. We show that beyond providing a direct measurement of the microscope's MTF, tests with the BPRML sample can be used to fine tune the instrument's focal distance. Our results confirm the universality of the method that makes it applicable to a large variety of metrology instrumentation with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.

Ultra-high efficiency multilayer blazed gratings through deposition kinetic control.

Diffraction efficiency of multilayer-coated blazed gratings (MBG) strongly depends on the perfection of the sawtooth-shaped layers in the overall composite structure. Growth of multilayers on sawtooth substrates should be carefully optimized to reduce groove profile distortion and, at the same time, to avoid significant roughening of multilayer interfaces. In this work, we report on a way to optimize growth of sputter-deposited Mo/Si multilayers on sawtooth substrates through variation of the sputtering gas pressure. We believe a new record for diffraction efficiency of 44% was achieved for an optimized MBG with groove density of 5250 lines/mm at the wavelength of 13.1 nm.

A 10,000 groove/mm multilayer coated grating for EUV spectroscopy.

Ultra-high spectral resolution in the EUV and soft x-ray energy ranges requires the use of very high line density gratings with optimal design resulting in use of a Blazed Multilayer Grating (BMG) structure. Here we demonstrate the production of near-atomically perfect Si blazed substrates with an ultra-high groove density (10,000 l/mm) together with the measured and theoretical performance of an Al/Zr multilayer coating on the grating. A 1st order absolute efficiency of 13% and 24.6% was achieved at incidence angles of 11° and 36° respectively. Cross-sectional TEM shows the effect of smoothing caused by the surface mobility of deposited atoms and we correlate this effect with a reduction in peak diffraction efficiency. This work shows the high performance that can be achieved with BMGs based on small-period anisotropic etched Si substrates, but also the constraints imposed by the surface mobility of deposited species.

Investigation of antirelaxation coatings for alkali-metal vapor cells using surface science techniques.

Many technologies based on cells containing alkali-metal atomic vapor benefit from the use of antirelaxation surface coatings in order to preserve atomic spin polarization. In particular, paraffin has been used for this purpose for several decades and has been demonstrated to allow an atom to experience up to 10 000 collisions with the walls of its container without depolarizing, but the details of its operation remain poorly understood. We apply modern surface and bulk techniques to the study of paraffin coatings in order to characterize the properties that enable the effective preservation of alkali spin polarization. These methods include Fourier transform infrared spectroscopy, differential scanning calorimetry, atomic force microscopy, near-edge x-ray absorption fine structure spectroscopy, and x-ray photoelectron spectroscopy. We also compare the light-induced atomic desorption yields of several different paraffin materials. Experimental results include the determination that crystallinity of the coating material is unnecessary, and the detection of C[Double Bond]C double bonds present within a particular class of effective paraffin coatings. Further study should lead to the development of more robust paraffin antirelaxation coatings, as well as the design and synthesis of new classes of coating materials.

Spectroscopic test of bose-einstein statistics for photons.

Using Bose-Einstein-statistics-forbidden two-photon excitation in atomic barium, we have limited the rate of statistics-violating transitions, as a fraction ν of an equivalent statistics-allowed transition rate, to ν<4.0×10{-11} at the 90% confidence level. This is an improvement of more than 3 orders of magnitude over the best previous result. Additionally, hyperfine-interaction enabling of the forbidden transition has been observed, to our knowledge, for the first time.

Observation of a large atomic parity violation effect in ytterbium.

Atomic parity violation has been observed in the 6s(2 1)S(0)-->5d6s(3)D(1) 408-nm forbidden transition of ytterbium. The parity-violating amplitude is found to be 2 orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measurements of neutron distributions and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition.

Production and detection of atomic hexadecapole at Earth's magnetic field.

Optical magnetometers measure magnetic fields with extremely high precision and without cryogenics. However, at geomagnetic fields, important for applications from landmine removal to archaeology, they suffer from nonlinear Zeeman splitting, leading to systematic dependence on sensor orientation. We present experimental results on a method of eliminating this systematic error, using the hexadecapole atomic polarization moment. In particular, we demonstrate selective production of the atomic hexadecapole moment at Earth's magnetic field and verify its immunity to nonlinear Zeeman splitting. This technique promises to eliminate directional errors in all-optical atomic magnetometers, potentially improving their measurement accuracy by several orders of magnitude.

Kerr effect in liquid helium at temperatures below the superfluid transition.

The electro-optical Kerr effect induced by a slowly varying electric field in liquid helium at temperatures below the lambda point is investigated. The Kerr constant of liquid helium is measured to be (1.43+/-0.02(stat)+/-0.04(sys)) x 10(-20) (cm/V)(2) at T=1.5 K. Within experimental uncertainty, the Kerr constant is independent of temperature in the range T=1.5 K to 2.17 K, which implies that the Kerr constant of the superfluid component of liquid helium is the same as that of normal liquid helium. Pair and higher correlations of He atoms in the liquid phase account for about 23% of the measured Kerr constant. Liquid nitrogen was used to test the experimental setup; the result for the liquid nitrogen Kerr constant is (4.38+/-0.15) x 10(-18) (cm/V)(2). Kerr effect can be used as a noncontact technique for measuring the magnitude and mapping out the distribution of electric fields inside these cryogenic insulants.

Hyperpolarized xenon nuclear spins detected by optical atomic magnetometry.

We report the use of an atomic magnetometer based on nonlinear magneto-optical rotation with frequency-modulated light to detect nuclear magnetization of xenon gas. The magnetization of a spin-exchange-polarized xenon sample (1.7 c m(3) at a pressure of 5 bars, natural isotopic abundance, polarization 1% ), prepared remotely to the detection apparatus, is measured with an atomic sensor. An average magnetic field of approximately 10 nG induced by the xenon sample on the 10 cm diameter atomic sensor is detected with signal-to-noise ratio approximately 10 , limited by residual noise in the magnetic environment. The possibility of using modern atomic magnetometers as detectors of nuclear magnetic resonance and in magnetic resonance imaging is discussed. Atomic magnetometers appear to be ideally suited for emerging low-field and remote-detection magnetic resonance applications.

Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?

We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as N(-3/4); if strongly squeezed probe light is used, the Heisenberg limit of N-1 scaling can be achieved. However, if the measurement time exceeds tau(rel)/N(1/2) in the former case, or tau(rel)/N in the latter, where tau(rel) is the spin relaxation time, the scaling becomes N(-1/2), as for a standard shot-noise-limited magnetometer.

Selective addressing of high-rank atomic polarization moments.

We describe a method of selective generation and study of polarization moments of up to the highest-rank kappa=2F possible for a quantum state with total angular momentum F. The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultranarrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances supported by a given system has important applications in quantum and nonlinear optics and in magnetometry.