INSTRUMENTATION AND EXPERIMENTATION - Nanoindentation with Biological Applications - page 63

indenters, and therefore exhibit semi-apex angles of ~70° for Berkovich
and Vickers pyramids, with finite apex radii on the order of 100s nm.
3.4 . Experimental approaches
3.4.1. Calibration over appropriate signal range
To convert cantilever deflection to load-depth responses, three
calibration values are key: OLS, cantilever spring constant k , and signal
drift rate. These calibrations assume that the user has already confirmed
the range of linear voltage-displacement response of the laser-photodiode
feedback loop, and is either working within the linear range or has
linearized over a larger operating range as discussed in Section 3.1.1.
These calibrations also assume that the piezoactuator (to move the
cantilever base or the stage) is independently calibrated.
Calibration of the OLS, or conversion of photodiode voltage to actual
cantilever free-end deflection, was noted previously and requires
displacement of the cantilever against a rigid surface such as a glass
slide. Upward deflection of the cantilever free-end will be equivalent to
downward displacement of the cantilever base; as the base displacement
is independently calibrated ( e.g ., it is a piezoactuator), conversion
between the deflection measured as photodiode voltage and the actual
deflection measured in meters is readily obtained as the slope of the free-
end deflection (V) vs base displacement (m) line. Note that, in practice,
there will be a linear region of this relation near the initial contact point,
so it is important to maximize the number of data points within that
region and average over many replicate responses to obtain an average
OLS . This method typically determines OLS with 3% standard error.
This parameter is sufficiently sensitive that it must be repeated for
each use of each cantilever, and can differ for the same cantilever in
different imaging fluids. Cantilever spring constant k can be obtained
subsequently, via collection of the frequencies and amplitudes of the
cantilever oscillation at ambient temperature. Most commercial AFMs
include semi-automated analyses to render the fast Fourier transform of
this oscillation as a power spectral density, from which the spring
constant k can be estimated by analogy to a simple harmonic oscillator: