Calibration of triaxial accelerometers by constant rotation rate in the gravitational field.

We extend the use of the intrinsic properties calibration method for triaxial accelerometers that we reported previously from discrete angular steps to using a constant rotation rate to produce a time varying sinusoidal excitation in the earth's gravitational field. We show that this extension yields the low frequency calibration response of the device under test. Whereas traditional vibration-based methods using shakers generally exhibit an increased measurement uncertainty with decreased excitation frequency, we show that this approach does not. We report results obtained from a commercial triaxial digital accelerometer from DC up to a 0.5 Hz rotation rate. The maximum rotation rate that we report is limited by our rotation stage; but we expect that the method can be extended to higher rotation rates with an upper limit constrained by what can be tolerated as a maximum centripetal acceleration.

Reduction of calibration uncertainty due to mounting of three-axis accelerometers using the intrinsic properties model.

We show that the calibration of tri-axis accelerometers based on the device's intrinsic properties alleviates the uncertainty due to mounting misalignment in comparison to the use of the sensitivity matrix. The intrinsic properties of a tri-axis accelerometer are based on a (u, v, w) coordinate system that represent the direction of maximum sensitivities of each of the three accelerometers (U, V, W) and are assumed not to be perfectly orthogonal to each other. The calibration procedure requires rotation of the device in the gravitational field around each of the Cartesian coordinate (x, y, z) axes. One component in driving down the uncertainty of laboratory comparisons and calibration repeats relates to misalignment in mounting the device onto the calibration instrument. We show that the uncertainty of the cross-axis terms of the sensitivity matrix is a dominating factor affecting uncertainty down to a 0.01° misalignment at a 100 µV noise level. The misalignment component can be exacerbated when calibrating modern microelectromechanical systems (MEMS)-based accelerometers, which are typically a few millimeters in dimension.

Accurate localization microscopy by intrinsic aberration calibration.

A standard paradigm of localization microscopy involves extension from two to three dimensions by engineering information into emitter images, and approximation of errors resulting from the field dependence of optical aberrations. We invert this standard paradigm, introducing the concept of fully exploiting the latent information of intrinsic aberrations by comprehensive calibration of an ordinary microscope, enabling accurate localization of single emitters in three dimensions throughout an ultrawide and deep field. To complete the extraction of spatial information from microscale bodies ranging from imaging substrates to microsystem technologies, we introduce a synergistic concept of the rigid transformation of the positions of multiple emitters in three dimensions, improving precision, testing accuracy, and yielding measurements in six degrees of freedom. Our study illuminates the challenge of aberration effects in localization microscopy, redefines the challenge as an opportunity for accurate, precise, and complete localization, and elucidates the performance and reliability of a complex microelectromechanical system.

Shock Measurements Based on Pendulum Excitation and Laser Doppler Velocimetry: Primary Calibration by SI-Traceable Distance Measurements.

A new method is described to provide a primary calibration of shock measurements produced by a shock measurement system consisting of pendulum excitation and laser Doppler velocimetry. The method uses the laser Doppler velocimeter to determine the total distance traveled by a rigid block that slides along a Teflon (fluorocarbon) channel after being struck by a pendulum head, and the resulting distance is compared to the distance measured by an SI-traceable length measurement. The instantaneous velocity of the block is measured by the velocimeter and is used to calculate the displacement of the block by integrating the velocity data. The result is compared to the displacement measured using calibrated rulers and calipers. The method was applied to an independently calibrated commercial velocimeter for impact accelerations ranging from 2000 to 30,000 m/s2. The results of the independent mechanical displacement measurements agreed with those from the commercial velocimeter to within ±0.3 %, with better agreement above accelerations of order 10,000 m/s2 to within ±0.1 %. A conservative, upper-bound, uncertainty analysis included the effects of noise and other random errors, as well as type B estimates for systematic errors from occasional momentary demodulation failures (dropouts), use of a different number of rulers before and after shock distance measurement, and the relative frequency response of the velocimeter.

Particle Tracking of Microelectromechanical System Performance and Reliability.

Microelectromechanical systems (MEMS) that require contact of moving parts to implement complex functions exhibit limits to their performance and reliability. Here, we advance our particle tracking method to measure MEMS motion in operando at nanometer, microradian, and millisecond scales. We test a torsional ratcheting actuator and observe dynamic behavior ranging from nearly perfect repeatability, to transient feedback and stiction, to terminal failure. This new measurement capability will help to understand and improve MEMS motion.

Subnanometer localization accuracy in widefield optical microscopy.

The common assumption that precision is the limit of accuracy in localization microscopy and the typical absence of comprehensive calibration of optical microscopes lead to a widespread issue-overconfidence in measurement results with nanoscale statistical uncertainties that can be invalid due to microscale systematic errors. In this article, we report a comprehensive solution to this underappreciated problem. We develop arrays of subresolution apertures into the first reference materials that enable localization errors approaching the atomic scale across a submillimeter field. We present novel methods for calibrating our microscope system using aperture arrays and develop aberration corrections that reach the precision limit of our reference materials. We correct and register localization data from multiple colors and test different sources of light emission with equal accuracy, indicating the general applicability of our reference materials and calibration methods. In a first application of our new measurement capability, we introduce the concept of critical-dimension localization microscopy, facilitating tests of nanofabrication processes and quality control of aperture arrays. In a second application, we apply these stable reference materials to answer open questions about the apparent instability of fluorescent nanoparticles that commonly serve as fiducial markers. Our study establishes a foundation for subnanometer localization accuracy in widefield optical microscopy.

Gravity-Based Characterization of Three-Axis Accelerometers in Terms of Intrinsic Accelerometer Parameters.

Cross-sensitivity matrices are used to translate the response of three-axis accelerometers into components of acceleration along the axes of a specified coordinate system. For inertial three-axis accelerometers, this coordinate system is often defined by the axes of a gimbal-based instrument that exposes the device to different acceleration inputs as the gimbal is rotated in the local gravitational field. Therefore, the cross-sensitivity matrix for a given three-axis accelerometer is not unique. Instead, it depends upon the orientation of the device when mounted on the gimbal. We define nine intrinsic parameters of three-axis accelerometers and describe how to measure them directly and how to calculate them from independently determined cross-sensitivity matrices. We propose that comparisons of the intrinsic parameters of three axis accelerometers that were calculated from independently determined cross-sensitivity matrices can be useful for comparisons of the cross-sensitivity-matrix measurement capability of different institutions because the intrinsic parameters will separate the accelerator-gimbal alignment differences among the participating institutions from the purely gimbal-related differences, such as gimbal-axis orthogonality errors, z-axis gravitational-field alignment errors, and angle-setting or angle-measurement errors.

Transfer of motion through a microelectromechanical linkage at nanometer and microradian scales.

Mechanical linkages are fundamentally important for the transfer of motion through assemblies of parts to perform work. Whereas their behavior in macroscale systems is well understood, there are open questions regarding the performance and reliability of linkages with moving parts in contact within microscale systems. Measurement challenges impede experimental studies to answer such questions. In this study, we develop a novel combination of optical microscopy methods that enable the first quantitative measurements at nanometer and microradian scales of the transfer of motion through a microelectromechanical linkage. We track surface features and fluorescent nanoparticles as optical indicators of the motion of the underlying parts of the microsystem. Empirical models allow precise characterization of the electrothermal actuation of the linkage. The transfer of motion between translating and rotating links can be nearly ideal, depending on the operating conditions. The coupling and decoupling of the links agree with an ideal kinematic model to within approximately 5%, and the rotational output is perfectly repeatable to within approximately 20 microradians. However, stiction can result in nonideal kinematics, and input noise on the scale of a few millivolts produces an asymmetric interaction of electrical noise and mechanical play that results in the nondeterministic transfer of motion. Our study establishes a new approach towards testing the performance and reliability of the transfer of motion through assemblies of microscale parts, opening the door to future studies of complex microsystems.

Dimensional reduction of duplex DNA under confinement to nanofluidic slits.

There has been much interest in the dimensional properties of double-stranded DNA (dsDNA) confined to nanoscale environments as a problem of fundamental importance in both biological and technological fields. This has led to a series of measurements by fluorescence microscopy of single dsDNA molecules under confinement to nanofluidic slits. Despite the efforts expended on such experiments and the corresponding theory and simulations of confined polymers, a consistent description of changes of the radius of gyration of dsDNA under strong confinement has not yet emerged. Here, we perform molecular dynamics (MD) simulations to identify relevant factors that might account for this inconsistency. Our simulations indicate a significant amplification of excluded volume interactions under confinement at the nanoscale due to the reduction of the effective dimensionality of the system. Thus, any factor influencing the excluded volume interaction of dsDNA, such as ionic strength, solution chemistry, and even fluorescent labels, can greatly influence the dsDNA size under strong confinement. These factors, which are normally less important in bulk solutions of dsDNA at moderate ionic strengths because of the relative weakness of the excluded volume interaction, must therefore be under tight control to achieve reproducible measurements of dsDNA under conditions of dimensional reduction. By simulating semi-flexible polymers over a range of parameter values relevant to the experimental systems and exploiting past theoretical treatments of the dimensional variation of swelling exponents and prefactors, we have developed a novel predictive relationship for the in-plane radius of gyration of long semi-flexible polymers under slit-like confinement. Importantly, these analytic expressions allow us to estimate the properties of dsDNA for the experimentally and biologically relevant range of contour lengths that is not currently accessible by state-of-the-art MD simulations.

DNA molecules descending a nanofluidic staircase by entropophoresis.

A complex entropy gradient for confined DNA molecules was engineered for the first time. Following the second law of thermodynamics, this enabled the directed self-transport and self-concentration of DNA molecules. This new nanofluidic method is termed entropophoresis. As implemented in experiments, long DNA molecules were dyed with cyanine dimers, dispersed in a high ionic strength buffer, and confined by a nanofluidic channel with a depth profile approximated by a staircase function. The staircase step depths spanned the transition from strong to moderate confinement. The diffusion of DNA molecules across slitlike steps was ratcheted by entropic forces applied at step edges, so that DNA molecules descended and collected at the bottom of the staircase, as observed by fluorescence microscopy. Different DNA morphologies, lengths, and stoichiometric base pair to dye molecule ratios were tested and determined to influence the rate of transport by entropophoresis. A model of ratcheted diffusion was used to interpret a shifting balance of forces applied to linear DNA molecules of standard length in a complex free energy landscape. Related metrics for the overall and optimum performance of entropophoresis were developed. The device and method reported here transcend current limitations in nanofluidics and present new possibilities in polymer physics, biophysics, separation science, and lab-on-a-chip technology.

Separation and metrology of nanoparticles by nanofluidic size exclusion.

A nanofluidic technology for the on-chip size separation and metrology of nanoparticles is demonstrated. A nanofluidic channel was engineered with a depth profile approximated by a staircase function. Numerous stepped reductions in channel depth were used to separate a bimodal mixture of nanoparticles by nanofluidic size exclusion. Epifluorescence microscopy was used to map the size exclusion positions of individual nanoparticles to corresponding channel depths, enabling measurement of the nanoparticle size distributions and validation of the size separation mechanism.

Accurate optical analysis of single-molecule entrapment in nanoscale vesicles.

We present a nondestructive method to accurately characterize low analyte concentrations (0-10 molecules) in nanometer-scale lipid vesicles. Our approach is based on the application of fluorescence fluctuation analysis (FFA) and multiangle laser light scattering (MALLS) in conjunction with asymmetric field flow fractionation (AFFF) to measure the entrapment efficiency (the ratio of the concentration of encapsulated dye to the initial bulk concentration) of an ensemble of liposomes with an average diameter less than 100 nm. Water-soluble sulforhodamine B (SRB) was loaded into the aqueous interior of nanoscale liposomes synthesized in a microfluidic device. A confocal microscope was used to detect a laser-induced fluorescence signal resulting from both encapsulated and unencapsulated SRB molecules. The first two cumulants of this signal along with the autocorrelation function (ACF) were used to quantify liposome entrapment efficiency. Our analysis moves beyond typical, nonphysical assumptions of equal liposome size and brightness. These advances are essential for characterizing liposomes in the single-molecule encapsulation regime. Our work has further analytical impact because it could increase the interrogation time of free-solution molecular analysis by an order of magnitude and form the basis for the development of liposome standard reference materials.

Polyelectrolyte Multilayer-Treated Electrodes for Real-Time Electronic Sensing of Cell Proliferation.

We report on the use of polyelectrolyte multilayer (PEM) coatings as a non-biological surface preparation to facilitate uniform cell attachment and growth on patterned thin-film gold (Au) electrodes on glass for impedance-based measurements. Extracellular matrix (ECM) proteins are commonly utilized as cell adhesion promoters for electrodes; however, they exhibit degradation over time, thereby imposing limitations on the duration of conductance-based biosensor experiments. The motivation for the use of PEM coatings arises from their long-term surface stability as promoters for cell attachment, patterning, and culture. In this work, a cell proliferation monitoring device was fabricated. It consisted of thin-film Au electrodes deposited with a titanium-tungsten (TiW) adhesion layer that were patterned on a glass substrate and passivated to create active electrode areas. The electrode surfaces were then treated with a poly(ethyleneimine) (PEI) anchoring layer and subsequent bilayers of sodium poly(styrene sulfonate) (PSS) and poly(allylamine hydrochloride) (PAH). NIH-3T3 mouse embryonic fibroblast cells were cultured on the device, observed by optical microscopy, and showed uniform growth characteristics similar to those observed on a traditional polystyrene cell culture dish. The optical observations were correlated to electrical measurements on the PEM-treated electrodes, which exhibited a rise in impedance with cell proliferation and stabilized to an approximate 15 % increase as the culture approached confluency. In conclusion, cells proliferate uniformly over gold and glass PEM-treated surfaces, making them useful for continuous impedance-based, real-time monitoring of cell proliferation and for the determination of cell growth rate in cellular assays.

MEMS Young's Modulus and Step Height Measurements With Round Robin Results.

This paper presents the results of a microelectromechanical systems (MEMS) Young's modulus and step height round robin experiment, completed in April 2009, which compares Young's modulus and step height measurement results at a number of laboratories. The purpose of the round robin was to provide data for the precision and bias statements of two \ related Semiconductor Equipment and Materials International (SEMI) standard test methods for MEMS. The technical basis for the test methods on Young's modulus and step height measurements are also provided in this paper. Using the same test method, the goal of the round robin was to assess the repeatability of measurements at one laboratory, by the same operator, with the same equipment, in the shortest practical period of time as well as the reproducibility of measurements with independent data sets from unique combinations of measurement setups and researchers. Both the repeatability and reproducibility measurements were done on random test structures made of the same homogeneous material. The average repeatability Young's modulus value (as obtained from resonating oxide cantilevers) was 64.2 GPa with 95 % limits of ± 10.3 % and an average combined standard uncertainty value of 3.1 GPa. The average reproducibility Young's modulus value was 62.8 GPa with 95 % limits of ± 11.0 % and an average combined standard uncertainty value of 3.0 GPa. The average repeatability step height value (for a metal2-over-poly1 step from active area to field oxide) was 0.477 µm with 95 % limits of 7.9 % and an average combined standard uncertainty value of 0.014 µm. The average reproducibility step height value was 0.481 µm with 95 % limits of ± 6.2 % and an average combined standard uncertainty value of 0.014 µm. In summary, this paper demonstrates that a reliable methodology can be used to measure Young's modulus and step height. Furthermore, a micro and nano technology (MNT) 5-in-1 standard reference material (SRM) can be used by industry to compare their in-house measurements using this methodology with NIST measurements thereby validating their use of the documentary standards.

Generalized temperature measurement equations for Rhodamine B dye solution and its application to microfluidics.

Temperature mapping based on fluorescent signal intensity ratios is a widely used noncontact approach for investigating temperature distributions in various systems. This noninvasive method is especially useful for applications, such as microfluidics, where accurate temperature measurements are difficult with conventional physical probes. However, the application of a calibration equation to relate fluorescence intensity ratio to temperature is not straightforward when the reference temperature in a given application is different than the one used to derive the calibration equation. In this report, we develop and validate generalized calibration equations that can be applied for any value of reference temperature. Our analysis shows that a simple linear correction for a 40 degrees C reference temperature produces errors in measured temperatures between -3 to 8 degrees C for three previously published sets of cubic calibration equations. On the other hand, corrections based on an exact solution of these equations restrict the errors to those inherent in the calibration equations. The methods described here are demonstrated for cubic calibration equations derived by three different groups, but the general method can be applied to other dyes and calibration equations.

Low Cost Digital Vibration Meter.

This report describes the development of a low cost, digital Micro Electro Mechanical System (MEMS) vibration meter that reports an approximation to the RMS acceleration of the vibration to which the vibration meter is subjected. The major mechanical element of this vibration meter is a cantilever beam, which is on the order of 500 µm in length, with a piezoresistor deposited at its base. Vibration of the device in the plane perpendicular to the cantilever beam causes it to bend, which produces a measurable change in the resistance of a piezoresistor. These changes in resistance along with a unique signal-processing scheme are used to determine an approximation to the RMS acceleration sensed by the device.

Microwave Power Absorption in Low-Reflectance, Complex, Lossy Transmission Lines.

Simple sets of equations have been derived to describe the absorption of microwave power in three-region, lossy transmission lines in terms of S-parameter reflection and transmission amplitudes. Each region was assumed to be homogeneous with discontinuities at the region boundaries. Different sets of equations were derived to describe different assumptions about the amplitudes of the reflection coefficients at the different boundaries. These equations, which are useful when interference effects due to multiple reflections are small, were used to analyze S-parameter measurements on a transmission line that had a microfluidic channel in its middle region. The channel was empty for one set of measurements and filled with water for a second set of measurements. Most of the reflection assumptions considered here produced similar results for the fraction of the applied microwave power that was absorbed by a water-filled microchannel. This shows that the absorbed power is relatively insensitive to the reflection details as long as energy is conserved in the analysis. Another important result of this work is that the difference between the power absorbed in a water-filled channel and the power absorbed in the same empty channel can be a poor predictor of the power absorbed in the water in the presence of competing absorption processes such as absorption by the transmission-line metal.

Surface modification of poly(methyl methacrylate) for improved adsorption of wall coating polymers for microchip electrophoresis.

The development of rapid and simple wall coating strategies for high-efficiency electrophoretic separation of DNA is of crucial importance for the successful implementation of miniaturized polymeric DNA analysis systems. In this report, we characterize and compare different methods for the chemical modification of poly(methyl methacrylate) (PMMA) surfaces for the application of wall coating polymers. PMMA surfaces coated with 40 mol% diethylacrylamide and 60 mol% dimethylacrylamide are compared to the PMMA surfaces first oxidized and then coated with hydroxypropylmethyl-cellulose or poly(vinyl alcohol) (PVA). PMMA oxidation was accomplished with UV/ozone or an aqueous solution of HNO(3) to yield hydrogen-bond donors for the spontaneous adsorption of the coating polymers. Contact angle measurements of UV/ozone exposed PMMA surfaces indicate increase in hydrophilicity, and polymer coated surfaces show a strong dependence on the coating polymer and the oxidation method. Fast and repeatable electrophoretic separations of a 10-base and 20-base DNA ladder were performed in PMMA micro CE devices. All analyses were completed in less than 10 min, resulting in the number of theoretical plates as high as 583 000 in a 7.7 cm long separation channel. The duration of UV/ozone treatment was found to have a considerable impact on separation performance. The microchips irradiated with UV for 10 min and coated with PVA as well as the microchips treated with HNO(3) and coated with HPMC were found to have the best separation performance. These results demonstrate facile and robust methods for the surface modification of PMMA enabling low-cost single use devices for electrophoretic DNA separations.

Capillarity induced solvent-actuated bonding of polymeric microfluidic devices.

Rapid, robust, and economical fabrication of fluidic microchannels is of fundamental importance for the successful development of disposable lab-on-a-chip devices. In this work, we present a solvent-actuated bonding method for fabricating polymeric microfluidic devices at room temperature. A PMMA sheet with an imprinted microchannel was clamped to a blank PMMA sheet, and then 80 +/- 5 muL of acetone (bonding solvent) was introduced at one end of the fluidic channel and aspirated out at the other end. As the solvent moved down the channel, capillary forces drew a fraction of the solvent into the interstitial space between the two polymeric substrates. After aspiration, the assembly was incubated in the clamp for 5 min for effective bond formation. The quantity of the bonding solvent, its water content and flow rate, along with residence time in the channel were found to have significant impact on the bond quality and the channel integrity. Microfluidic electrophoretic separations of a 400-base DNA ladder were performed in devices fabricated using this method in less than 8 min with efficiencies routinely between 2 x 10(6) and 3 x 10(6) plates/m. The simplicity and economy of this technique make it amenable for automation and mass production, which could make polymeric substrates more attractive for single-use chemical analysis devices.

Simple Thermal-Efficiency Model for CMOS-Microhotplate Design.

Simple, semi-empirical, first-order, analytic approximations to the current, voltage, and power as a function of microhotplate temperature are derived. To lowest order, the voltage is independent of, and the power and current are inversely proportional to, the length of the microhotplate heater legs. A first-order design strategy based on this result is described.