a sinusoidally corrugated grating of size 5 × 5 mm 2 vertically mounted on the piezotube of an AFM (see Fig. 1). Here, the corrugations have an average period Λ = 574 . 7 nm (i.e., more than two times smaller than in Refs. [37, 38] in order to achieve the regime where the PFA becomes inappropriate for the calculation of the lateral Casimir force between the corrugated surfaces). The amplitude of corrugations on the grating A$_{1}$ = 85 . 4 ± 0 . 3 nm was a factor of 1.45 larger than in Refs. [37, 38]. A 320 µ m long V-shaped silicon nitride cantilever of the AFM was first uniformly coated with 40 nm of Al. This modification of cantilever was performed to improve its thermal and electric conductivity and prevent deformation due to differential thermal expansion in vacuum. A polystyrene sphere of a 200 ± 4 µ m diameter was placed at the end of the cantilever with conductive Ag epoxy. Next, a freshly cleaved mica sheet of 400 µ m length, 200 µ m width, and a few micrometer thickness was attached to the bottom of the sphere also with Ag epoxy. Then a second polystyrene sphere with a nominal diameter 2 R = 200 ± 4 µ m was attached to the bottom free end of the mica sheet (see Fig. 1). After imprint of corrugations on its surface (see below), this last sphere was used as the second test body in the measurement of the lateral Casimir force. We emphasize that the silver epoxy is rigid at all attachments. The first sphere and mica sheet are needed to isolate the laser reflection spot on the cantilever tip from the interaction region between the two corrugated surfaces. As a result, the effect of scattered light from the top and sides of the corrugated plate is substantially reduced. The resulting system (cantilever, mica sheet and the attached two spheres) was uniformly coated with a 10 nm layer of Cr and then with a more than 50 nm layer of Au in a thermal evaporator. Uniformity of coating was ensured through rotation of the cantilever [42]. The Cr layer was used to improve the adhesion of the Au coating and prevent its peeling during the imprint of the corrugations on the sphere. The lateral Casimir force arises when the uniaxial corrugations on the two test bodies are perfectly aligned and have the same period Λ [20–23, 37, 38]. To ensure that these conditions are satisfied, we have imprinted corrugations on the second sphere using the grating as a template. In order to obtain deeper corrugations than in Refs. [37, 38], a more sophisticated procedure was implemented. Here, the template grating had a 300 nm Au coating applied by the manufacturer on top of sinusoidal corrugations made of hard epoxy on a 3-mm-thick Pyrex substrate. Note that hard epoxy does not require the use of the oxide of Al layer which was coated on the soft plastic grating in Refs. [37, 38]. The 7