Boxcar Averager Option

The UHF-BOX option adds 2 independent 600 MHz boxcar averager units to the UHFLI Lock-in Amplifier, increasing the measurement speed and signal-to-noise ratio (SNR) for applications that use non-sinusoidal waveforms. Unlike the case of a digitizer or an oscilloscope, the measurement results from a boxcar averager are immediately available in the digital domain and as analog signals with user-defined offset and scaling factors.

A boxcar measurement is easily set up thanks to the LabOne^® user interface: the periodic waveform analyzer (PWA) displays a single period of the waveform, averaged to suppress noise and to highlight the features of interest. The boxcar window can be set graphically by placing the PWA cursors around the relevant part of the waveform; a second averaging window can be set to reduce baseline fluctuations and enable differential measurements. To achieve the best trade-off between measurement speed and SNR, the result can be averaged over consecutive periods between 1 and 1 million times.

Lock-in vs boxcar

Whereas lock-in amplifiers are ideal for analyzing sinusoidal signals and extracting specific components of a frequency spectrum, boxcar averagers are the tool of choice for low-duty-cycle signals (see figure). A typical input signal from a pulsed experiment has a pulse width T_p, repetition period of the pulses T_rep, and duty cycle d. In boxcar averaging, the input signal is multiplied with a boxcar function, also know as rectangular pulse train, with pulse width T_Box. In this way, noise contributions outside of the boxcar window are rejected (see panel c). Inside the boxcar gate, signal integration results in a single value per period later averaged over N periods.

Data extraction from low-duty-cycle signals requires information from the base frequency and many higher harmonics simultaneously. To capture this additional information, boxcar averagers need a signal input bandwidth that is many times larger than the base frequency, so that setting up a boxcar measurement requires careful control of more parameters compared to a lock-in measurement. The payoff usually comes in the form of shorter measurement times and higher SNR, which can make a big difference in areas such as imaging. Therefore, lock-in measurements and boxcar measurements are complementary tools for analyzing periodic signals.

Using only the boxcar window leads to a measurement that includes the DC component of the spectrum. This makes results vulnerable to DC drifts over the course of the measurements. Introducing a reference window shifted by a user-defined amount with respect to the normal boxcar window, and subtracting it from the main boxcar gate results eliminates this DC component. The data are then free from DC drift artifacts and more stable over time.

The reference window can also be used for differential measurements. In pump-probe experiments, for example, the pump pulse that induces the effect to be measured is only present for every second probe pulse. By locking on the pump periodicity, users can display pump and probe pulses in the same period (see figure). It is then possible to use the boxcar window to measure the combined pump-and-probe signal and the reference window to measure the probe-only signal. In the figure, the green time trace indicates the result of the boxcar gate measurement alone - a sine-modulated pulse train - and the red one corresponds to the difference between boxcar and reference windows. The systematic offset introduced by the pump is eliminated and some noise components are suppressed, leading to significantly higher SNR and accuracy.

The periodic waveform analyzer (PWA) takes a continuous stream of samples and links them synchronously to the phase of the reference oscillator. Samples are also averaged with previous samples displaying the same phase. Performing this operation over many periods of the reference frequency leads to a dense set of phase and sample pairs; plotting the averaged values with the phase on the X-axis provides the phase-domain representation of the signal of interest with strong noise suppression.

The PWA places each input sample into one of 1024 bins based on its phase, leading to a waveform plot with a resolution of 2π/1024 or 0.4 degrees. If this resolution is not sufficient, it is possible to zoom into the region of interest and push the phase resolution down to millidegrees.

The combination of high noise rejection through averaging and high temporal resolution thus makes the PWA a powerful tool to set the boxcar and baseline windows accurately and with minimal effort.

The harmonic analyzer visualizes the FFT performed on the PWA data, hence showing the spectral distribution of the signal amplitude over the harmonics of the reference frequency: this corresponds to the energy distribution at DC together with the first harmonics up to the 511th. This capability allows users to identify the most appropriate measurement method – lock-in amplification or boxcar averaging.

Indeed, if the signal spreads out over many harmonic components without any prominent peak (see figure to the left), boxcar detection may be the better choice to achieve the best possible SNR. If one harmonic carries most signal of interest (see figure to the right), however, lock-in detection is likely to be a robust option.

The Arithmetic Unit included in the UHFLI Lock-in Amplifier performs arithmetic operations using the results from the two boxcar units as operands, and it does so inside the instrument. This opens up even more advanced measurement possibilities such as direct normalization to a value on a shot-by-shot basis.

Some applications, for instance the characterization of materials for non-linear absorption, require the precise knowledge of the amount of power delivered to the sample, pulse-by-pulse. Measuring the output power of the laser with a separate photodiode to normalize the power reaching the sample thanks to the Arithmetic Unit yields a much more accurate characterization.

When a low-duty-cycle signal is subject to an additional modulation, the boxcar unit can route the boxcar signal directly to the input of one of the lock-in demodulators. This is achieved without leaving the digital domain, hence the best SNR is extracted with high numerical precision in a minimal amount of time. Typical applications are the additional amplitude modulation of a pulsed laser source (see figure) or a periodic delay change in a pump-probe experiment.