We present a scheme of the high-precise three-dimensional (3D) localization by the measurement of the atomic-level population. The scheme is applied to a four-level tripod-type atom coupled by three strong standing waves and a probe running wave. As a result, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength. The upper-level distribution depends crucially on the atom-field coupling and it forms 3D periodic structures composed of spheres, hourglasses, bowls, donuts, or deformed barrels.PACS numbers: 42.50. Gy, 42.50.Nn, 42.50.Wk, 42.50.St The concept of Heisenberg microscope [1] demonstrates that atoms can not be localized using light within the optical half-wavelength unless one takes advantage of the internal structure of atoms. One approach is to obtain spatially changing structures in level populations in a cloud of atoms. Motivated e.g. by possible applications in atomic nanolithography [2], different methods for going beyond this limit have been proposed over the years, including the measurement of the atomic resonance frequency [3][4][5], the phase shift [6][7][8], or the atomic dipole [9]. The highest theoretical localization degrees have been demonstrated in schemes that rely on measuring either spontaneous emission [10][11][12] or a level population [13,14] of an atom moving through a resonant standing wave.In general, as a proof-of-principle, one-dimensional systems have been very popular, see e.g. the recent studies [15][16][17][18][19][20]. Studies of atomic systems in two dimensions have also been numerous recently [21][22][23][24][25][26][27][28][29][30][31][32]. It is important to note that in 2D, one can obtain, in addition to mere subwavelength localization, further spatial structuring of the atomic locations, see e.g. [33]. A key question is whether localization and structuring can be obtained also in 3D, and what kind of structures can appear. Possible applications may include high-precision position-dependent chemistry without a real change in the atomic distribution, combining state-selective localization with state-selective chemical reactions. In addition, 3D structuring produces a wide variety of practical realizations of such chemical reactions, demonstrating the necessity of reliable methods for the prediction of localization structures. For any realistic scheme one needs to carefully consider the atomic structure and to include spontaneous emission. Previously 3D localization has been discussed in a five-level system without taking the geometry of the atomic dipole coupling into account [34]. We show that 3D localization is realistically possible with only four atomic levels in a tripod scheme, and that one obtains interesting structures around points of localization by simple tuning of the parameters of the localizing fields.We consider the 87 Rb D 2 line (the 5 2 S 1/2 → 5 2 P 3/2 transition), which is only thought as a possible example of tripod system with three ground states |F = 1, m F (m F = −1, 0, 1) and upper state |F = 0, m...