Fourier Helicity Spectra as Quantifiers of Multiscale Chirality

Quantifying the chirality of three-dimensional (3D) objects is crucial for understanding interactions of nanoscale structures, biological molecules, and hierarchical materials. Although chirality is simultaneously present at multiple scales for each case, existing chirality measures rely only on singular scale-specific quantifiers, and some of them yield incorrect chirality assignments for biomolecules. Here we introduce the Fourier Helicity Spectra, a mathematical framework to decompose geometry of chemical and biological structures encompassing the scale dependence of mirror asymmetry. Fourier decomposition of 3D objects into helical harmonics enables one to compute a handedness-resolved characteristics of complex shapes, while reducing computational cost. We show its applicability for a diverse range of chemical systems, from biomacromolecular electron densities to tomographic reconstructions of inorganic nanostructures. Furthermore, inverse transform of isolated spectral components into real space enables visualization of helicity-matched interfaces, identifying how chirality governs biomolecular interactions. We anticipate that this methodology can be generalized with alternative basis sets to encompass a broad range of chiral symmetries governing biological signaling, polarization optics, drug design, and advanced synthesis.