Improving Eye-Tracking Data Quality: A Framework for Reproducible Evaluation of Detection Algorithms.

High-quality eye-tracking data are crucial in behavioral sciences and medicine. Even with a solid understanding of the literature, selecting the most suitable algorithm for a specific research project poses a challenge. Empowering applied researchers to choose the best-fitting detector for their research needs is the primary contribution of this paper. We developed a framework to systematically assess and compare the effectiveness of 13 state-of-the-art algorithms through a unified application interface. Hence, we more than double the number of algorithms that are currently usable within a single software package and allow researchers to identify the best-suited algorithm for a given scientific setup. Our framework validation on retrospective data underscores its suitability for algorithm selection. Through a detailed and reproducible step-by-step workflow, we hope to contribute towards significantly improved data quality in scientific experiments.

Understanding interferometry for micro-cantilever displacement detection.

Interferometric displacement detection in a cantilever-based non-contact atomic force microscope (NC-AFM) operated in ultra-high vacuum is demonstrated for the Michelson and Fabry-Pérot modes of operation. Each mode is addressed by appropriately adjusting the distance between the fiber end delivering and collecting light and a highly reflective micro-cantilever, both together forming the interferometric cavity. For a precise measurement of the cantilever displacement, the relative positioning of fiber and cantilever is of critical importance. We describe a systematic approach for accurate alignment as well as the implications of deficient fiber-cantilever configurations. In the Fabry-Pérot regime, the displacement noise spectral density strongly decreases with decreasing distance between the fiber-end and the cantilever, yielding a noise floor of 24 fm/Hz(0.5) under optimum conditions.

Noise in NC-AFM measurements with significant tip-sample interaction.

The frequency shift noise in non-contact atomic force microscopy (NC-AFM) imaging and spectroscopy consists of thermal noise and detection system noise with an additional contribution from amplitude noise if there are significant tip-sample interactions. The total noise power spectral density DΔf (fm) is, however, not just the sum of these noise contributions. Instead its magnitude and spectral characteristics are determined by the strongly non-linear tip-sample interaction, by the coupling between the amplitude and tip-sample distance control loops of the NC-AFM system as well as by the characteristics of the phase locked loop (PLL) detector used for frequency demodulation. Here, we measure DΔf (fm) for various NC-AFM parameter settings representing realistic measurement conditions and compare experimental data to simulations based on a model of the NC-AFM system that includes the tip-sample interaction. The good agreement between predicted and measured noise spectra confirms that the model covers the relevant noise contributions and interactions. Results yield a general understanding of noise generation and propagation in the NC-AFM and provide a quantitative prediction of noise for given experimental parameters. We derive strategies for noise-optimised imaging and spectroscopy and outline a full optimisation procedure for the instrumentation and control loops.

Determining cantilever stiffness from thermal noise.

We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n , quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy.

The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) consists of cantilever thermal noise, tip-surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density d(z) at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d(Δ) (f) at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip-surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d(z), we predict d(Δ) (f) for specific filter settings, a given level of detection-system noise spectral density d(z) (ds) and the cantilever-thermal-noise spectral density d(z) (th). We find an excellent agreement between the calculated and measured values for d(Δ) (f). Furthermore, we demonstrate that thermal noise in d(Δ) (f), defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.