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Fabry-Perot laser interferometry is a common laboratory technique used to interrogate resonant micro- and nano-electromechanical systems (MEMS/NEMS). This method uses the substrate beneath a vibrating MEMS/NEMS device as a static reference mirror, encoding relative device motion in the reflected laser power. In this work, we present a general approach for calibrating these optical systems based on measurements of large-amplitude motion that exceeds one half of the laser wavelength. Utilizing the intrinsic nonlinearity of the optical transduction, our method enables the direct measurement of the system's transfer function (motion-to-detected-voltage). We experimentally demonstrate the use of this technique to measure vibration amplitudes and changes in the equilibrium position of a MEMS/NEMS device using monolithic silicon nitride and silicon cantilevers as sample systems. By scanning the laser along a cantilever surface, we spatially map static and dynamic deflection profiles simultaneously and then compare the static profile against results from a commercial optical profilometer. We further demonstrate the extension of our calibration technique to measurements taken at small amplitudes, where the optical transduction is linear, and to those taken in the frequency domain by a lock-in amplifier. Our aim is to present a robust calibration scheme that is independent of MEMS/NEMS materials and geometry, to completely negate the effects of nonlinear optical transduction, and to enable the assessment of excitation forces and MEMS/NEMS material properties through the accurate measurement of the MEMS/NEMS vibrational response. [ABSTRACT FROM AUTHOR]

The modulation transfer functions of two types of photostimulable phosphor image plates were determined in the 10 keV to 50 keV x-ray energy range using a resolution test pattern with up to 10 line pairs per mm (LP/mm) and a wavelength dispersive x-ray spectrometer. Techniques were developed for correcting for the partial transmittance of the high energy x rays through the lead bars of the resolution test pattern, and the modulation transfer function (MTF) was determined from the measured change in contrast with LP/mm values. The MTF was convolved with the slit function of the image plate scanner, and the resulting point spread functions (PSFs) were in good agreement with the observed shapes and widths of x-ray spectral lines and with the PSF derived from edge spread functions. The shapes and the full width at half-maximum (FWHM) values of the PSF curves of the Fuji Superior Resolution (SR) and Fuji Maximum Sensitivity (MS) image plate detectors, consisting of the image plate and the scanner, determined by the three methods gave consistent results: The SR PSF is Gaussian with 0.13 mm FWHM, and the MS PSF is Lorentzian with 0.19 mm FWHM. These techniques result in the accurate determination of the spatial resolution achievable using image plate and scanner combinations and enable the optimization of spatial resolution for x-ray spectroscopy and radiography. OCIS codes: 040.7480, 300.6560, 300.3700.

Maintaining high resolving power is a primary challenge in hard x-ray spectroscopy of newly developed bright and transient x-ray sources such as laser-produced plasmas. To address this challenge, the line widths in x-ray spectra with energies in the 17 keV to 70 keV range were recorded by positioning the detectors on and behind the focal circles of Cauchois type transmission-crystal spectrometers. To analyze and understand the observed line widths, we developed a geometrical model that accounts for source broadening and various instrumental broadening mechanisms. The x-ray sources were laboratory Mo or W electron-bombarded anodes, and the spectra were recorded on photostimulable phosphor image plates. For these relatively small x-ray sources, it was found that when the detector was placed on or near the focal circle, the line widths were dominated by the effective spatial resolution of the detector. When the detector was positioned beyond the focal circle, the line widths were determined primarily by source-size broadening. Moreover, the separation between the spectral lines increased with distance behind the focal circle faster than the line widths, resulting in increased resolving power with distance. Contributions to line broadenings caused by the crystal thickness, crystal rocking curve width, geometrical aberrations, and natural widths of the x-ray transitions were in all cases smaller than detector and source broadening, but were significant for some spectrometer geometries. The various contributions to the line widths, calculated using simple analytical expressions, were in good agreement with the measured line widths for a variety of spectrometer and source conditions. These modeling and experimental results enable the design of hard x-ray spectrometers that are optimized for high resolving power and for the measurement of the x-ray source size from the line widths recorded behind the focal circle. OCIS codes: 300.6570, 300.3700.

The responsivity of two types of silicon photodiodes, the AXUV series and the SXUV series was measured using synchrotron and laboratory radiation sources. Depending on the wavelength, the responsivity increased with temperature which was also found to be consistent with the decrease in the silicon bandgap energy causing a decrease in the pair creation energy.

The time-dependent response of a 1-[mm.sup.2] silicon photodiode was characterized by use of pulsed synchrotron radiation in the 4- to 16-nm-wavelength range. Modeling the input radiation pulse and the electrical response of the photodiode allowed the photodiode's capacitance as a function of wavelength and applied bias voltage to be determined. The capacitance was in the 7- to 19-pF range and resulted in response fall times as small as 0.4 ns. The capacitance determined by pulsed x-ray illumination was in good agreement with the capacitance determined by pulsed optical laser illumination. The absolute responsivity was measured by comparison with the responsivity of a calibrated photodiode. OCIS codes: 040.7480, 040.5160, 040.6040, 230.5170.

We have developed an improved x-ray imaging system based on spherically curved crystals. It is designed and used for diagnostics of targets ablatively accelerated by the Nike KrF laser. A spherically curved quartz crystal (2d = 6.687 [Angstrom] R = 200 mm) has been used to produce monochromatic backlit images with the He-like Si resonance line (1865 eV) as the source of radiation. The spatial resolution of the x-ray optical system is 1.7 [[micro]meter] in selected places and 2-3 [[micro]meter] over a larger area. Time-resolved backlit monochromatic images of polystyrene planar targets driven by the Nike facility have been obtained with a spatial resolution of 2.5 [[micro]meter] in selected places and 5 [[micro]meter] over the focal spot of the Nike laser.

A two-mirror normal-incidence microscope with multilayer coatings was used to image the soft-x-ray emissions from planar foils irradiated by OMEGA laser beams. The bandpass of the multilayer coatings was centered at a wavelength of 48.3 [Angstrom] (257-eV energy) and was 0.5 [Angstrom] wide. Five overlapping OMEGA beams, without beam smoothing, were typically incident on the gold foils. The total energy was 1500 J, and the focused intensity was 6 x [10.sup.13] W [cm.sup.-2]. The 5.8x magnified images were recorded by a gated framing camera at various times during the 3-ns laser pulse. A pinhole camera imaged the x-ray emission in the energy range of [greater than] 2 keV. On a spatial scale of 10 [[micro]meter], it was found that the soft-x-ray images at 257 eV were quite uniform and featureless. In contrast, the hard-x-ray images in the energy range of [greater than]2 keV were highly nonuniform with numerous features of size 150 [[micro]meter].

The responsivity of an extreme-ultraviolet transmission grating spectrometer with silicon photodiode detectors was measured with synchrotron radiation. The spectrometer was designed to record the absolute radiation flux in a wavelength bandpass centered at 30 nm. The transmission grating had a period of 200 nm and relatively high efficiencies in the +1 and the -1 diffraction orders that were dispersed on either side of the zero-order beam. Three photodiodes were positioned to measure the signals in the zero order and in the +1 and -1 orders. The photodiodes had aluminum overcoatings that passed the desired wavelength bandpass centered at 30 nm and attenuated higher-order radiation and wavelengths longer than approximately 80 nm. The spectrometer's responsivity, the ratio of the photodiode current to the incident radiation power, was determined as a function of the incident wavelength and the angle of the spectrometer with respect to the incident radiation beam. The spectrometer's responsivity was consistent with the product of the photodiode responsivity and the grating efficiency, both of which were separately measured while removed from the spectrometer. OCIS codes: 120.6200, 040.7480, 050.1950.