the obtained constraints can be achieved due to only a replacement of the plane plate with the sinusoidally corrugated plate. The physical reason for so large strengthening is the same as in Sec. II: when the plate is corrugated the closest separation between the two surfaces is as small as 14.6 nm. This demonstrates that the use of corrugated test bodies is of high promise for obtaining stronger constraints on the Yukawa-type hypothetical interactions from the measurements of the Casimir force. IV. GRADIENT OF THE YUKAWA FORCE BETWEEN A SMOOTH SPHERE AND A CORRUGATED PLATE IN THE DYNAMIC REGIME The most precise experiment in Casimir physics was performed in the dynamic regime by means of micromechanical torsional oscillator [36]. This experiment exploited the con- figuration of a smooth sphere of R = 150 µ m radius above a plane plate which could rotate about a torsional axis. The separation distance between them was varied harmonically with the resonant frequency of the oscillator. This frequency is different in the absence and in the presence of the Casimir force F$_{sp}$ ( a ) between a sphere and a plate. The immediately mea- sured quantity is the frequency shift due to the presence of the sphere which is proportional to the gradient of F$_{sp}$ ( a ). Using the proximity force approximation (PFA), which is valid in the experimental configuration with an accuracy of about 0.1% [21, 22], one obtains P ( a ) = − 1 2 πR ∂F$_{sp}$ ( a ) ∂a , (15) where P ( a ) is the Casimir pressure in the fictitious configuration of two plates having the same layer structure as the plate and the sphere in real experiment. In so doing, the lower plate simply coincides with the real plate. It can be replaced with a semispace if it is sufficiently thick. The upper (fictitious) plate is necessarily infinitely thick, i.e., is always a semispace. Thus, the experiment of Ref. [36] can be considered as an indirect measurement of the Casimir pressure in the configuration of two parallel plates. The constraints on the parameters of Yukawa-type interaction in Ref. [36] were obtained from the condition where P $^{Yu}$( a ) is the Yukawa pressure in the configuration of two parallel plates and [ − Ξ$_{P}$ ( a ) , Ξ$_{P}$ ( a )] is the minimum confidence interval containing all differences between theo- ∣ P $^{Yu}$( a ) ∣ ≤ Ξ$_{P}$ ( a ) , (16) 11