Amplitude–Frequency Characteristic as a Novel Eye-Tracking Diagnostic Feature: A Pilot Study on an Open ADHD Dataset

The frequency characteristic of biological systems is a sensitive tool for describing physiological dynamics, yet it has been virtually unused in pupillometry. A novel eye-tracking feature is proposed—the amplitude–frequency characteristic (AFC) of the “stimulus–pupil size” system—and evaluated as a candidate diagnostic marker on an open ADHD dataset. After quality control, 61 sessions (18 controls, 27 unmedicated ADHD, 16 on-medication ADHD) were analyzed. The AFC of the raw diameter signal reveals a systematic elevation of AFC amplitude in ADHD across the 0.5–30 Hz range, strongest in the 20–30 Hz band (Cohen’s d = +0.995, p = 0.0034). This is a pilot and methodology- and reproducibility-focused study. At the individual diagnostic level, a normative composite z-score of three bands (10–15, 15–20, 20–30 Hz), computed relative to the control group with fixed weights and no training, reaches an ROC-AUC = 0.788 (Ctrl vs. off-ADHD: p = 0.0012). At the group level, a linear discriminant projection of the eight-band profile reaches an ROC-AUC = 0.854. The inter-individual variability of within-subject AFC stability is reduced by a factor of 2.97 in unmedicated ADHD (p = 0.0085) and normalizes under methylphenidate (paired Wilcoxon p = 0.0067, n = 17). The widely used ratio of high- to low-frequency AFC amplitude yields an inflated ROC-AUC of 0.865 on the pre-filtered signal, but only 0.63 on the raw signal. All diagnostic claims are exploratory. The proposed normative feature is simple, interpretable, requires no training set, and can be computed from a single pupil recording.