Understanding interferometry for micro-cantilever displacement detection

• Alexander von Schmidsfeld,
• Tobias Nörenberg,
• Matthias Temmen and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 841–851, doi:10.3762/bjnano.7.76

• displacement noise spectral density strongly decreases with decreasing distance between the fiber-end and the cantilever, yielding a noise floor of 24 fm/Hz0.5 under optimum conditions. Keywords: displacement noise spectral density; interferometer; non-contact atomic force microscope (NC-AFM); opto-mechanic

• density into the displacement noise spectral density . The corresponding results are shown in Figure 9. For d = 18 μm, we additionally determine the noise floor as a function of P with the results being shown in the inset. For the Fabry–Pérot regime (d ≤ 200 μm), we find an exponential increase of the

• noise level with distance from a minimum equivalent displacement noise spectral density of for d = 6 μm to over at 200 μm. Hence, the interferometer exhibits excellent noise figures when operated in the Fabry–Pérot regime with high . The dramatic increase of the noise level can be explained by the

Determining cantilever stiffness from thermal noise

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• realised that the cantilever properties fn, kn and Qn appear as linearly independent parameters in Equation 1. This allows their independent determination from a single measurement of the displacement noise spectral density over a limited spectral range around the resonance for a cantilever kept at a

• to cover a broad range of eigenfrequencies f0 ranging from 50 kHz to 2 MHz, static stiffness k [16] ranging from 3 to 120 N/m, and Q-factors Q0 [12] covering the range of 20,000 to 120,000; details are provided in Table 1. Measurements of the total displacement noise spectral density (f) are

• thermal frequency-shift noise spectral density (fm) [6]. Results and Discussion Stiffness from displacement thermal noise In a displacement noise measurement of a cantilever with a high Q-factor, the spectrum analyser measures the total displacement noise spectral density (f) for the nth cantilever

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• ) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density dz at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density dΔf

• usable bandwidth Bmax is defined by the total displacement-noise spectral density as schematically illustrated in Figure 2. In this figure, we show the displacement spectral density dz(f) present at the input of the frequency demodulator with contributions of the measurement signal and noise (see Figure

• the noise can be described in the frequency domain by the displacement-noise spectral density . This is the square root of the displacement-noise power spectral density , which is proportional to the unwanted energy per frequency interval stored in the oscillating system. A cantilever that is not