Quadrature phase interferometer for high resolution force spectroscopy

Abstract

In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10(-15) m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.

Measurements of mechanical thermal noise and energy dissipation in optical dielectric coatings

“…More details about the instrument can be found in reference 19 . This set-up has notably been used previously to characterize mechanical thermal noise and viscoelastic behavior of metallic coatings on micro-cantilevers 20,21 .…”

“…Our measurements of the micro-cantilever deflection rely on a quadrature phase differential interferometer [17][18][19] . The optical path difference is measured between the sensing and reference beams focused respectively on the free end and close to the clamping base of the cantilever (see inset of figure 2).…”

Dynamic stiffness of the contact between a carbon nanotube and a flat substrate in a peeling geometry

“…The shape of the CNT is fixed by an equilibrium between the adhesion of the part in contact and the bending of the free standing part of the nanotube. From the measurement of the AFM cantilever deflection d (using differential interferometry 20 ) and sample position zs, the force F acting on the nanotube and its compression zc can be recorded. (c) The system is modeled by the effective mass m of the cantilever being connected to two springs: the cantilever (spring constant k0) attached to the static reference, and the nanotube in contact with the substrate (effective stiffness kc).…”

Resonance frequency shift of strongly heated micro-cantilevers

“…Both are uncoated tipless AFM silicon cantilevers. Geometrical dimensions were measured using a scanning electron microscope (SEM), with uncertainties around 1% for L and W, and 5% for H. The thermal noise measurements are performed using a quadrature phase differential interferometer, 20 with the sensing laser beam focused on the free end of the cantilever, and the reference beam on the silicon chip where the cantilever is clamped (see inset of Figure 1). We use a stabilized solid state laser from Spectra Physics, with a 100 mW maximum output power at 532 nm.…”

“…[7][8][9][10] The detection of their deflection is usually performed optically: optical lever scheme 11 in most of commercial systems, interferometric measurements in the most precise instruments. 6,[12][13][14][15][16][17][18][19][20] The former approach is very sensitive 21 while remaining simple to set up, and the latter reaches the highest resolution in challenging experiments. The limit to the sensitivity of these optical systems is due to the shot-noise of the photodetectors: this white noise sets the lower limit of detectable deflections.…”