## Content review – Lock-in detection

Test and measurement tasks often carry the challenge that sought for signals are buried in noise. The fundamental use of a lock-in amplifier is to recover these signals, but modern digital lock-in amplifiers can do much more than this. To help you take full advantage of the capabilities of your instrument, this blog post gathers content – in the form of videos, application notes and blog posts – dedicated to lock-in measurements, covering from fundamentals to best practices.

For an in-depth overview of the lock-in amplifier’s working scheme, you can refer to our white paper Principles of lock-in detection and its accompanying video. By covering the theoretical aspects and the main elements of lock-in detection, these sources reveal what a modern lock-in amplifier has to offer. In practice, achieving the maximum signal-to-noise ratio and optimal use of the instrument requires careful consideration of each measurement step. The schematic in the figure below depicts these steps, starting from the signal input to the data transfer to the computer. Between these two stages, the input signal is mixed with the reference signal and a low-pass filter is applied. Let’s look more closely at these operations and at what needs to be taken into account for the best performance.

Figure: The schematic of a lock-in measurement as depicted in the Zurich Instruments LabOne user interface. LabOne provides complete user control at each measurement step.

At the signal input stage, the analog signal connected to the instrument’s input channels is converted to the digital domain. The video 6 tips to improve your lock-in measurements provides a practical guide on signal coupling as well as tips on signal conditioning that include how to remove spurious frequencies. You can also find guidance on how to optimize the reference to achieve the best performance, especially when an external signal is required. The take-away message is that the lowest noise figure ($$\small\text{2.5 nV}/\sqrt{\text{Hz}}$$ on the MFLI Lock-in Amplifier) is attainable by choosing the right input range and coupling scheme. Further improvements in the input noise and reduction of the measurement noise floor are made possible by cross-correlation techniques. Performing this kind of measurement requires two nominally identical measurement channels with the ability to sample data simultaneously in real time. The UHFLI Lock-in Amplifier, with its two input channels, can readily perform this task; with the MFLI Lock-in Amplifier, two instruments are needed. The latter configuration requires synchronization of the instrument pair, which is achieved thanks to the multi-device synchronization (MDS) functionality. In both cases, the digitizer software upgrade provides the required spectral resolution and advanced triggering capability. Besides the input noise, and especially for low-temperature physics research, it is crucial to minimize the electrical power dissipated into the system from the input channels of the measurement instrument. Zurich Instruments lock-in amplifiers exhibit the lowest dissipated power at input connectors, thus reducing setup complexity while maintaining performance.

After the optimization of the signal input comes the demodulation performed by numerical mixing of the digitized signal with the reference, applying a low-pass filter (LPF) as shown in the figure. A dual-phase lock-in amplifier performs the mixing at 0 and 90 degrees compared to the reference, so that it provides the in-phase (X) and quadrature (Y) terms simultaneously in Cartesian coordinates. Based on Equation 1 in the white paper, a coordinate transformation to polar coordinates with amplitude (R) and phase ($$\small\Theta$$) is straightforward. For the best measurement performance, it is crucial to configure the LPF settings correctly. The filter setting, defined by its bandwidth and order, makes it possible to find a trade-off between the signal-to-noise ratio and the measurement’s temporal resolution. You can watch the video Low-pass filter settings done right for a deep dive into filter settings or to test your instrument’s response following the measurement strategies explained in the blog posts looking at both frequency and time domain.

Collecting measurement results and saving the data comes as the last step in our schematic. Operating in the digital domain unlocks various strategies, from capturing a single data point to building up images. The Zurich Instruments LabOne software comes with data acquisition tools that make data collection efficient, convenient and correct. The video Choose the right tool to acquire lock-in data and its related blog post provide an overview of the most typical use cases. For a more detailed exploration of the DAQ module in LabOne, you can read the blog post A deep dive into data acquisition with the DAQ tool.

Thanks to the LabOne user interface, Zurich Instruments’ lock-in amplifiers come with an integrated toolset for time- and frequency-domain analysis that includes parametric sweeper, spectrum analyzer, scope, plotter, numeric tool, and data acquisition module. Additional features such as phase-locked loops (PLLs), PID controllers, AM-FM modulation, impedance analysis and digitizer, can be added through software upgrades. These functionalities can work in parallel to capture different aspects of the signal and enable closed-loop control. Let’s take a look at a typical use case: the characterization of a resonator. Starting from a frequency sweep and resonance fitting, the blog post Ring-down method for rapid determination of high Q-factor resonators shows how to use frequency- and time-domain tools to characterize a resonator. Once this is done, the built-in PLL can track its resonance and a PID controller can control its amplitude simultaneously. You can use the modulation transfer function method to measure the closed-loop bandwidth under real experimental conditions. All of the mentioned functionalities are readily available in the application programming interfaces (APIs) for LabVIEW, MATLAB, Python, C, and .Net, so that you can automate your workflow or integrate your instrument into an existing setup.

From the principles of lock-in detection to best practices for setting up the instrument, I hope that the content reviewed in this blog post will prove to be a useful guide for your measurements. If you need support, have questions or ideas for additional content that could help the community, please get in touch!

I thank all the colleagues who generated the content referred to in this blog post, as well as Jelena Trbovic, Paolo Navaretti and Gaia Donati for their input in refining this review.