Many problems in time-dependent metrology can be phrased mathematically as a deconvolution problem. In such a problem, measured data is modeled as the convolution of a known system response function with an unknown source signal. The goal of deconvolution is to estimate the unknown source signal given knowledge about the system response function. A well-studied method for calculating this estimate is Tikhonov regularized deconvolution which attempts to balance the average difference between the estimated solution and true source signal with the variance in the estimated solution. In this article we study this so-called bias-variance tradeoff in the context of estimating a source measured by a high speed oscilloscope. By assuming we have bounds on the true source’s Fourier coefficients and a structural model for the uncertainties in the system response function, we derive pointwise-in-time confidence intervals on the true signal based on the estimated signal. We demonstrate the new technique with simulations relevant to the high speed measurement context.

Instruments for measuring high-speed waveforms typically require calibration to obtain accurate results. The national metrology institutes of the United States of America, the United Kingdom, and Germany offer measurement services based on electro-optic sampling that can be used to establish a traceable calibration chain between high-speed waveform measurements and the SI. These services are increasingly switching to a full waveform metrology paradigm, obtaining an estimate of the central value and associated uncertainty of the entire waveform as a function of time.

We describe a straightforward method of separately characterizing up- and down-conversion in microwave mixers using a sampling oscilloscope. The method mismatch-corrects the results, determines both magnitude and phase, and uses a novel time-base correction scheme to improve the accuracy of the measurements. We estimate our measurement accuracy to be on the order of a tenth of a decibel in magnitude and a few degrees in phase. We use the method to characterize the magnitude and phase reciprocity of a microwave mixer.

We develop a covariance matrix describing the uncertainty of mismatch-corrected measurements performed on the National Institute of Standards and Technology's electrooptic sampling system. This formulation offers a general way of describing the uncertainties of the measurement system in both the temporal and frequency domains. We illustrate the utility of the approach with several examples, including determining the uncertainty in the temporal voltage generated by the photodiode

We develop a method for mismatch-correcting temporal waveforms measured with a high-speed electrooptic sampling system to 200 GHz. The new calibration determines a complete equivalent-circuit model describing the source in both the time and frequency domains with uncertainties, and accounts for all impedances and multiple reflections in the measurement system.

We describe current measurement capabilities as well as research focused on two areas: improving temporal and frequency response characterization of detectors and instrumentation using electro-optic sampling, and improving wavelength metrology using frequency combs.

The proliferation of wireless devices and the availability of new wireless applications and services raise new privacy and security concerns. Although network-layer anonymity protects the identities of the communication endpoints, the physical layer of many wireless communication protocols offers no such guarantee. The electromagnetic signal transmitted over an open communication medium can be monitored, captured, and analyzed in an effort to trace and identify users of wireless devices. In this paper we present preliminary results on the feasibility of identifying wireless nodes in a network by measuring distinctive electromagnetic characteristics or "signatures" of wireless local area network (WLAN) cards

This paper discusses the typical uncertainties associated with characterizing high-speed photodiodes to 65 GHz when using a vector network analyzer (VNA) measurement technique. We analyzed the accuracy of the technique by comparing measurements of two reference standards that had previously been calibrated using electro-optic sampling (EOS) and heterodyne methods. The results of the comparison show very good correlation to the direct characterizations. Typical uncertainties were less than 1.0 dB at frequencies up to 50 GHz and less than 2 dB at 65 GHz. The dominant sources of uncertainty come from the noise floor in the VNA above 50 GHz (depending upon signal level) and the base uncertainty in the reference-standard calibration.

Describes the most straightforward method for accurately measuring the frequency response of optoelectronic devices. The method uses a calibrated optical reference receiver, a modulated optical source, and a calibrated electrical vector network analyzer.

We estimate the root-mean-square (RMS) value of timing jitter noise in simulated signals similar to measured highspeed sampled signals. The simulated signals are contaminated by additive noise, timing jitter noise, and time shift errors. Before estimating the RMS value of the jitter noise, we align the signals (unless there are no time shift errors) based on estimates of the relative shifts from cross-correlation analysis. We compute the mean and sample variance of the aligned signals based on repeated measurements at each time sample. We estimate the derivative of the noise-free signal based, in part, on a regression spline fit to the average of the aligned signals. Our initial estimate of the RMS value of the jitter noise depends on estimated derivatives and sample variances at time samples where the magnitude of the estimated derivative exceeds a selected threshold. This initial estimate is generally biased. Using a parametric bootstrap approach, we adaptively adjust this initial estimate of the RMS value of the jitter noise based on an estimate of this bias. We apply our method to real data collected at NIST. We study how results depend on the derivative threshold.

We have measured the magnitude and phase responses of a photoreceiver to 110 GHz using a calibrated electro-optic sampling system. The frequency range of the calibration is limited only by our 1 mm coaxial connectors.

We study several problems related to the characterization of the timebase in high-speed sampling oscilloscopes. First, we examine the bias of using the method of the first-order approximation to estimate the additive and time jitter noises, and present a procedure to adjust for the bias in the estimates. We then study the bias and variance of a least-squares timebase distortion estimate that uses multiple sets of waveforms. Based on simulations, a method for calculating the uncertainty of the timebase distortion estimate is proposed. We also study the effects of amplitude and phase drifts, as well as jitter error on the estimation of timebase distortion. Results are shown using simulations with parameters that are closely related to those we observe in our laboratory.

Increased data rates require improved measurements. We give specific guidance to avoid measurement pitfalls in two critical high data rate areas: Polarization-mode dispersion and transmitter/receiver frequency response. For audiences familiar (not expert) with either field.

We describe a calibration and measurement procedure for determining the intrinsic frequency response of gigabit chip photodiodes embedded in simple test fixtures. The procedure is unique because we make the measurements in the time domain using a calibrated oscilloscope, and we then apply frequency-domain mismatch corrections to remove the effects of the fixture, bias T, and cables from the measurements. We demonstrate the procedure on photodiodes with an active region of approximately 150-/spl mu/m diameter excited by short 800-nm wavelength optical pulses.

We use "standard" optical sources along with microwave calibration methods to accurately calibrate optical receivers to 50 GHz and beyond. The calibrated receivers can be used to characterize sources and receivers using common electrical instrumentation.

We apply frequency-domain impedance mismatch corrections to a temporal electro-optic sampling system and use it to characterize the magnitude and phase response of a photoreceiver that is physically far removed from the point where the voltage waveforms are measured.We identify and evaluate additional sources of measurement uncertainty.

We describe estimation of the magnitude and phase response of a sampling oscilloscope with 50 GHz bandwidth using the nose-to-nose method. The measurements are corrected for the non-ideal properties of the oscilloscope and calibration apparatus, including mismatch and time-base distortion, drift, and jitter. The mean and standard deviation of repeated measurements of an ensemble of three oscilloscope samplers are reported, along with attempts to verify the magnitude calibration using a swept sine-wave method.

We develop and apply frequency-domain mismatch corrections to a temporal electro-optic sampling system. We use these corrections to characterize the magnitude and phase of electrical sources that are physically far removed from the point at which the electro-optic sampling system measures voltage waveforms. We demonstrate the technique by determining the power spectrum of a photoreceiver¿s optical impulse response.

We present an efficient least-squares algorithm for estimating the time-base distortion of sampling oscilloscopes. The method requires measurements of signals at multiple phases and frequencies. The method can accurately estimate the order of the harmonic model that is used to account for the amplitude nonlinearity of the sampling channel. We study several practical problems related to the time-base distortion estimation, such as the effect of averaging and sample size requirements. We also compare the relative performance of various methods for estimating time-base distortion using simulated and measured data.