  We compare theory and experiment in the Casimir force measurement between
gold surfaces performed with the atomic force microscope. Both random and
systematic experimental errors are found leading to a total absolute error
equal to 8.5 pN at 95% confidence. In terms of the relative errors,
experimental precision of 1.75% is obtained at the shortest separation of 62 nm
at 95% confidence level (at 60% confidence the experimental precision of 1% is
confirmed at the shortest separation). An independent determination of the
accuracy of the theoretical calculations of the Casimir force and its
application to the experimental configuration is carefully made. Special
attention is paid to the sample-dependent variations of the optical tabulated
data due to the presence of grains, contribution of surface plasmons, and
errors introduced by the use of the proximity force theorem. Nonmultiplicative
and diffraction-type contributions to the surface roughness corrections are
examined. The electric forces due to patch potentials resulting from the
polycrystalline nature of the gold films are estimated. The finite size and
thermal effects are found to be negligible. The theoretical accuracy of about
1.69% and 1.1% are found at a separation 62 nm and 200 nm, respectively. Within
the limits of experimental and theoretical errors very good agreement between
experiment and theory is confirmed characterized by the root mean square
deviation of about 3.5 pN within all measurement range. The conclusion is made
that the Casimir force is stable relative to variations of the sample-dependent
optical and electric properties, which opens new opportunities to use the
Casimir effect for diagnostic purposes.
