As a comparison Fig d

As a comparison, Fig. 2d shows the shape of the curve for the probe approaching the measured sample (curve 2) for the case when the standard system for detecting the position of the probe tip is used. This system is based on the principle of registering the position of the laser beam reflected from the probe via the quadrant photodetector (Fig. 1b). The beam reflected from a straight cantilever falls in the center of the photodetector. The deformation of the cantilever results in the displacement of the beam [3]. It should be noted that the optical interferometric systems provide greater measurement accuracy compared with the systems using quadrant photodetectors. For example, the accuracy of measuring the amplitude of probe vibrations in dynamic scanning modes may exceed 160fm/(Hz)1/2[4]. The technique we propose involves using a segment of the approach curve corresponding to the contact interaction between the probe and the surface (Region III in Fig. 2b) for determining Young\'s modulus. The tip of the probe is simulated by a hemisphere with the radius equal to the curvature radius of the probe tip, and the sample is simulated by an infinite half-plane. The tip of the probe is indented into the surface of the sample. The experimentally measured value of the indentation is used for solving the Hertz problem [5]. The solution to the above-described problem defines the relationship between the force F acting on the probe from the sample and the value of the indentation δ of the probe into the sample surface. This relatioship is expressed by the formula where E is Young\'s modulus, R is the curvature radius of the probe tip (R=10nm), and μ is Poisson\'s ratio (for biological objects it is typically assumed that μ=0.5). Correctly using the Hertz model is only possible if the value of probe indentation into the surface of the sample is much smaller than the curvature radius of the probe tip (in our study, it is less than 10nm, and this condition is satisfied). This condition is imposed in elasticity endothelin receptor antagonists in order to prevent the occurrence of plastic deformations in the sample. The main difficulty arising in our measurements of the force F depending on the value of indentation δ (for determining Young\'s modulus) is in finding the point of contact between the probe and the surface of the sample on the approach curve. We have developed the following technique for determining this point. In contact scanning mode, the level of the signal received from the interferometer output is taken for the contact point ; this signal level corresponds to the mean between the maximum and the minimum transmission values of the interferometer =ΔV/2 (see Fig. 2a). In other words, when the probe does not interact with the sample surface, the optical system is adjusted so that the transmission of the interferometer is at its maximum value (Region I in Fig 2b); as the probe approaches the sample surface, the piezoscanner starts moving forwards until the signal from the interferometer falls to . The region near this contact point is linear due to the properties of the Fabry–Pérot interferometer and corresponds to its maximum sensitivity. We approximated this region near the operating point of the contact mode by a line, and defined the point of the contact (CP in Fig. 2b) between the probe and the sample surface the point in which the line of the approach curve diverges from the approximating line. To determine the value of δ, we used the calibration interferogram (see Fig. 2a). The region near the point was approximated by a straight line. A reference set point (SP) was determined from the separation of the straight line from the interferogram, and was then aligned with the contact point (CP) on the approach-retraction curve (Fig. 2c). The value of δ was found from the difference between the dV values for the lines approximating the linear regions (see the plots in Fig. 2a and b), with the dZ values corresponding to the CP and exceeding it. We believe that this technique for determining the value of probe indentation into the surface of the sample is similar to that for systems using the quadrant photodetector (see Fig. 1b). In such systems, the indentation value is calculated as the difference δ between the corresponding values on the approach curves obtained for the test and the study samples (curves 1 and 2 in Fig. 2d, respectively). This procedure can be also used to determine the stiffness of the cantilever. The value of the elastic constant of the test sample by far exceeds that of the corresponding constant of the cantilever. In this case, the probe will not indent the sample surface in contact mode and curve 1 can be used for determining the elastic constant of the cantilever. The difference between the approach curves obtained for the test and the study samples with the dZ values starting from the contact point and higher is taken as the indentation value δ. Similarly, the difference between the linear regions near on the calibration interferogram and the approach curve is taken in the systems with an interferometer as the indentation value δ (see Fig. 2c).