Background: Noncontact atomic force microscopy (NC-AFM) now regularly produces atomic-resolution images on a wide range of surfaces, and has demonstrated the capability for atomic manipulation solely using chemical forces. Nonetheless, the role of the tip apex in both imaging and manipulation remains poorly understood and is an active area of research both experimentally and theoretically. Recent work employing specially functionalised tips has provided additional impetus to elucidating the role of the tip apex in the observed contrast.
Results: We present an analysis of the influence of the tip apex during imaging of the Si(100) substrate in ultra-high vacuum (UHV) at 5 K using a qPlus sensor for noncontact atomic force microscopy (NC-AFM). Data demonstrating stable imaging with a range of tip apexes, each with a characteristic imaging signature, have been acquired. By imaging at close to zero applied bias we eliminate the influence of tunnel current on the force between tip and surface, and also the tunnel-current-induced excitation of silicon dimers, which is a key issue in scanning probe studies of Si(100).
Conclusion: A wide range of novel imaging mechanisms are demonstrated on the Si(100) surface, which can only be explained by variations in the precise structural configuration at the apex of the tip. Such images provide a valuable resource for theoreticians working on the development of realistic tip structures for NC-AFM simulations. Force spectroscopy measurements show that the tip termination critically affects both the short-range force and dissipated energy.
force spectroscopy; image contrast; noncontact AFM; qPlus; Si(001); Si(100); tip (apex) structure
Noncontact atomic force microscopy (NC-AFM) is being increasingly used to measure the interaction force between an atomically sharp probe tip and surfaces of interest, as a function of the three spatial dimensions, with picometer and piconewton accuracy. Since the results of such measurements may be affected by piezo nonlinearities, thermal and electronic drift, tip asymmetries, and elastic deformation of the tip apex, these effects need to be considered during image interpretation.
In this paper, we analyze their impact on the acquired data, compare different methods to record atomic-resolution surface force fields, and determine the approaches that suffer the least from the associated artifacts. The related discussion underscores the idea that since force fields recorded by using NC-AFM always reflect the properties of both the sample and the probe tip, efforts to reduce unwanted effects of the tip on recorded data are indispensable for the extraction of detailed information about the atomic-scale properties of the surface.
atomic force microscopy; force spectroscopy; NC-AFM; three-dimensional atomic force microscopy; tip asymmetry; tip elasticity
Measurements of the frequency shift versus distance in noncontact atomic force microscopy (NC-AFM) allow measurements of the force gradient between the oscillating tip and a surface (force-spectroscopy measurements). When nonconservative forces act between the tip apex and the surface the oscillation amplitude is damped. The dissipation is caused by bistabilities in the potential energy surface of the tip–sample system, and the process can be understood as a hysteresis of forces between approach and retraction of the tip. In this paper, we present the direct measurement of the whole hysteresis loop in force-spectroscopy curves at 77 K on the PTCDA/Ag/Si(111) √3 × √3 surface by means of a tuning-fork-based NC-AFM with an oscillation amplitude smaller than the distance range of the hysteresis loop. The hysteresis effect is caused by the making and breaking of a bond between PTCDA molecules on the surface and a PTCDA molecule at the tip. The corresponding energy loss was determined to be 0.57 eV by evaluation of the force–distance curves upon approach and retraction. Furthermore, a second dissipation process was identified through the damping of the oscillation while the molecule on the tip is in contact with the surface. This dissipation process occurs mainly during the retraction of the tip. It reaches a maximum value of about 0.22 eV/cycle.
atomic force microscopy; energy dissipation; force spectroscopy; hysteresis loop; PTCDA/Ag/Si(111) √3 × √3
Key developments in NC-AFM have generally involved atomically flat crystalline surfaces. However, many surfaces of technological interest are not atomically flat. We discuss the experimental difficulties in obtaining high-resolution images of rough surfaces, with amorphous SiO2 as a specific case. We develop a quasi-1-D minimal model for noncontact atomic force microscopy, based on van der Waals interactions between a spherical tip and the surface, explicitly accounting for the corrugated substrate (modeled as a sinusoid). The model results show an attenuation of the topographic contours by ~30% for tip distances within 5 Å of the surface. Results also indicate a deviation from the Hamaker force law for a sphere interacting with a flat surface.
graphene; model; noncontact atomic force microscopy; SiO2; van der Waals
The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett.
2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip–sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.
atomic force microscopy; dAFM; high-resolution; liquids
Noncontact atomic force microscopy provides access to several complementary signals, such as topography, damping, and contact potential. The traditional presentation of such data sets in adjacent figures or in colour-coded pseudo-three-dimensional plots gives only a qualitative impression. We introduce two-dimensional histograms for the representation of multichannel NC-AFM data sets in a quantitative fashion. Presentation and analysis are exemplified for topography and contact-potential data for graphene grown epitaxially on 6H-SiC(0001), as recorded by Kelvin probe force microscopy in ultrahigh vacuum. Sample preparations by thermal decomposition in ultrahigh vacuum and in an argon atmosphere are compared and the respective growth mechanisms discussed.
FM-AFM; graphene; 6H-SiC(0001); KPFM; SPM
The adsorption on KBr(001) of a specially designed molecule, consisting of a flat aromatic triphenylene core equipped with six flexible propyl chains ending with polar cyano groups, is investigated by using atomic force microscopy in the noncontact mode (NC-AFM) coupled to Kelvin probe force microscopy (KPFM) in ultrahigh vacuum at room temperature. Two types of monolayers are identified, one in which the molecules lie flat on the surface (MLh) and another in which they stand approximately upright (MLv). The Kelvin voltage on these two structures is negatively shifted relative to that of the clean KBr surface, revealing the presence of surface dipoles with a component pointing along the normal to the surface. These findings are interpreted with the help of numerical simulations. It is shown that the surface–molecule interaction is dominated by the electrostatic interaction of the cyano groups with the K+ ions of the substrate. The molecule is strongly adsorbed in the MLh structure with an adsorption energy of 1.8 eV. In the MLv layer, the molecules form π-stacked rows aligned along the polar directions of the KBr surface. In these rows, the molecules are less strongly bound to the substrate, but the structure is stabilized by the strong intermolecular interaction due to π-stacking.
atomic force microscopy; insulating surfaces; Kelvin force probe microscopy; molecular adsorption
We introduce drive-amplitude-modulation atomic force microscopy as a dynamic mode with outstanding performance in all environments from vacuum to liquids. As with frequency modulation, the new mode follows a feedback scheme with two nested loops: The first keeps the cantilever oscillation amplitude constant by regulating the driving force, and the second uses the driving force as the feedback variable for topography. Additionally, a phase-locked loop can be used as a parallel feedback allowing separation of the conservative and nonconservative interactions. We describe the basis of this mode and present some examples of its performance in three different environments. Drive-amplutide modulation is a very stable, intuitive and easy to use mode that is free of the feedback instability associated with the noncontact-to-contact transition that occurs in the frequency-modulation mode.
atomic force microscopy; control systems; dissipation; frequency modulation; noncontact
Based on high-resolution noncontact atomic force microscopy (NC-AFM) experiments we reveal a detailed structural model of the polar (111) surface of the insulating ternary metal oxide, MgAl2O4 (spinel). NC-AFM images reveal a 6√3×6√3R30° superstructure on the surface consisting of patches with the original oxygen-terminated MgAl2O4(111) surface interrupted by oxygen-deficient areas. These observations are in accordance with previous theoretical studies, which predict that the polarity of the surface can be compensated by removal of a certain fraction of oxygen atoms. However, instead of isolated O vacancies, it is observed that O is removed in a distinct pattern of line vacancies reflected by the underlying lattice structure. Consequently, by the creation of triangular patches in a 6√3×6√3R30° superstructure, the polar-stabilization requirements are met.
aluminium oxide; metal oxide surfaces; noncontact atomic force microscopy (NC-AFM); polar surfaces; reconstructions; spinel
Packaging DNA into condensed structures is integral to the transmission of genomes. The mammalian mitochondrial genome (mtDNA) is a high copy, maternally inherited genome in which mutations cause a variety of multisystem disorders. In all eukaryotic cells, multiple mtDNAs are packaged with protein into spheroid bodies called nucleoids, which are the fundamental units of mtDNA segregation. The mechanism of nucleoid formation, however, remains unknown. Here, we show that the mitochondrial transcription factor TFAM, an abundant and highly conserved High Mobility Group box protein, binds DNA cooperatively with nanomolar affinity as a homodimer and that it is capable of coordinating and fully compacting several DNA molecules together to form spheroid structures. We use noncontact atomic force microscopy, which achieves near cryo-electron microscope resolution, to reveal the structural details of protein–DNA compaction intermediates. The formation of these complexes involves the bending of the DNA backbone, and DNA loop formation, followed by the filling in of proximal available DNA sites until the DNA is compacted. These results indicate that TFAM alone is sufficient to organize mitochondrial chromatin and provide a mechanism for nucleoid formation.
Locally anodic oxidation has been performed to fabricate the nanoscale oxide structures onp-GaAs(100) surface, by using an atomic force microscopy (AFM) with the conventional and carbon nanotube (CNT)-attached probes. The results can be utilized to fabricate the oxide nanodots under ambient conditions in noncontact mode. To investigate the conversion of GaAs to oxides, micro-Auger analysis was employed to analyze the chemical compositions. The growth kinetics and the associated mechanism of the oxide nanodots were studied under DC voltages. With the CNT-attached probe the initial growth rate of oxide nanodots is in the order of ~300 nm/s, which is ~15 times larger than that obtained by using the conventional one. The oxide nanodots cease to grow practically as the electric field strength is reduced to the threshold value of ~2 × 107 V cm−1. In addition, results indicate that the height of oxide nanodots is significantly enhanced with an AC voltage for both types of probes. The influence of the AC voltages on controlling the dynamics of the AFM-induced nanooxidation is discussed.
Atomic force microscopy; p-GaAs(100); Nanooxidation; Multi-walled carbon nanotube; Auger electron spectroscopy
We investigated the adsorption of 4-methoxy-4′-(3-sulfonatopropyl)stilbazolium (MSPS) on different ionic (001) crystal surfaces by means of noncontact atomic force microscopy. MSPS is a zwitterionic molecule with a strong electric dipole moment. When deposited onto the substrates at room temperature, MSPS diffuses to step edges and defect sites and forms disordered assemblies of molecules. Subsequent annealing induces two different processes: First, at high coverage, the molecules assemble into a well-organized quadratic lattice, which is perfectly aligned with the <110> directions of the substrate surface (i.e., rows of equal charges) and which produces a Moiré pattern due to coincidences with the substrate lattice constant. Second, at low coverage, we observe step edges decorated with MSPS molecules that run along the <110> direction. These polar steps most probably minimize the surface energy as they counterbalance the molecular dipole by presenting oppositely charged ions on the rearranged step edge.
alkali halide surface; noncontact atomic force microscopy; organic molecule; self-organization; zwitterion
The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) 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 d
z at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d
f at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d
z, we predict d
f for specific filter settings, a given level of detection-system noise spectral density d
ds and the cantilever-thermal-noise spectral density d
th. We find an excellent agreement between the calculated and measured values for d
f. Furthermore, we demonstrate that thermal noise in d
f, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.
Cantilever; feedback loop; filter; noncontact atomic force microscopy (NC-AFM); noise
We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f
n, quality factor Q
n and specifically the stiffness k
n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k
n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.
AFM; cantilever; noncontact atomic force microscopy (NC-AFM); Q-factor; thermal excitation; resonance; spectral analysis; stiffness
Significant advances have recently been made in understanding the mechanisms involved in noncontact anterior cruciate ligament (ACL) injury. Most ACL injuries involve minimal to no contact. Female athletes sustain a two- to eightfold greater rate of injury than do their male counterparts. Recent videotape analyses demonstrate significant differences in average leg and trunk positions during injury compared with control subjects. These findings as well as those of cadaveric and MRI studies indicate that axial compressive forces are a critical component in noncontact ACL injury. A complete understanding of the forces and risk factors associated with noncontact ACL injury should lead to the development of improved preventive strategiess for this devastating injury.
A novel noncontact indentation system with the combination of an air jet and optical coherence tomography (OCT) was presented in this paper for the quantitative measurement of the mechanical properties of soft tissues. The key idea of this method is to use a pressure-controlled air jet as an indenter to compress the soft tissue in a noncontact way and utilize the OCT signals to extract the deformation induced. This indentation system provides measurement and mapping of tissue elasticity for small specimens with high scanning speed. Experiments were performed on 27 silicone tissue-mimicking phantoms with different Young’s moduli, which were also measured by uniaxial compression tests. The regression coefficient of the indentation force to the indentation depth (N mm−1) was used as an indicator of the stiffness of tissue under air jet indentation. Results showed that the stiffness coefficients measured by the current system correlated well with the corresponding Young’s moduli obtained by conventional mechanical testing (r = 0.89, p < 0.001). Preliminary in vivo tests also showed that the change of soft tissue stiffness with and without the contraction of the underlying muscles in the hand could be differentiated by the current measurement. This system may have broad applications in tissue assessment and characterization where alterations of mechanical properties are involved, in particular with the potential of noncontact micro-indentation for tissues.
indentation; ultrasound indentation; soft tissue; elasticity; air jet; optical coherence tomography
A simple noncontact force sensor based on an optical fiber Bragg grating attached to a small magnet has been proposed and built. The sensor measures the force between the magnet and any ferromagnetic material placed within a few millimeters of the sensor. Maintaining the sensor at a constant standoff distance, material loss due to corrosion increases the distance between the magnet and the corroded surface, which decreases the magnetic force. This will decrease the strain in the optical fiber shifting the reflected Bragg wavelength. The measured shift for the optical fiber used was 1.36 nm per Newton. Models were developed to optimize the magnet geometry for a specific sensor standoff distance and for particular corrosion pit depths. The sensor was able to detect corrosion pits on a fuel storage tank bottom with depths in the sub-millimeter range.
fiber Bragg grating; magnetic force sensor; photonic force sensor; internal corrosion
OCT is able to safely, rapidly, and effectively image the palisades of Vogt without direct contact to the eye. This ability will greatly enhance our understanding of this stem cell niche and will allow development of new clinical and research techniques.
This study explored the efficacy of optical coherence tomography (OCT) as a high-resolution, noncontact method for imaging the palisades of Vogt by correlating OCT and confocal microscopy images.
Human limbal rims were acquired and imaged with OCT and confocal microscopy. The area of the epithelial basement membrane in each of these sets was digitally reconstructed, and the models were compared.
OCT identified the palisades within the limbus and exhibited excellent structural correlation with immunostained tissue imaged by confocal microscopy.
OCT successfully identified the limbal palisades of Vogt that constitute the corneal epithelial stem cell niche. These findings offer the exciting potential to characterize the architecture of the palisades in vivo, to harvest stem cells for transplantation more accurately, to track palisade structure for better diagnosis, follow-up and staging of treatment, and to assess and intervene in the progression of stem cell depletion by monitoring changes in the structure of the palisades.
Muscle strains are one of the most common complaints treated by physicians. High-force lengthening contractions can produce very high forces resulting in pain and tissue damage; such strains are the most common cause of muscle injuries. The hamstring muscles are particularly susceptible as they cross two joints and regularly perform lengthening contractions during running. We describe a patient with return to full function after a large hamstring tear.
We report the case of a 26-year-old man who presented 1 year after a noncontact, left-sided proximal hamstring tear incurred while sprinting. He received no medical treatment or formal rehabilitation. He was able to return to all sports and activities 1 to 2 months after injury, but noted a persistent deformity of the proximal thigh, which led him to seek evaluation. Physical examination, MRI functional tests, and specific muscle tests 1 year after his injury documented a major hamstring tear at the musculotendinous junction with muscle retraction, but no avulsion of the proximal tendon attachment.
Surgery often is recommended for major proximal hamstring tendon tears, especially when more than one tendon of origin is ruptured from the ischial tuberosity. Myotendinous tears are treated nonoperatively, but may be associated with decreased strength, prolonged recovery, and recurrence.
Purpose and Clinical Relevance
We describe the case of a young man who sustained a hamstring tear, with retraction, at the proximal myotendinous junction, where the biceps femoris and semitendinosus arise from the conjoint tendon. He achieved full functional recovery without medical attention, but had a persistent cosmetic deformity and slight hamstring tightness. This case suggests a benign natural history for this injury and the appropriateness of noninvasive treatment.
In principle, non-contact atomic force microscopy (NC-AFM) now readily allows for the measurement of forces with sub-nanonewton precision on the atomic scale. In practice, however, the extraction of the often desired ‘short-range’ force from the experimental observable (frequency shift) is often far from trivial. In most cases there is a significant contribution to the total tip–sample force due to non-site-specific van der Waals and electrostatic forces. Typically, the contribution from these forces must be removed before the results of the experiment can be successfully interpreted, often by comparison to density functional theory calculations. In this paper we compare the ‘on-minus-off’ method for extracting site-specific forces to a commonly used extrapolation method modelling the long-range forces using a simple power law. By examining the behaviour of the fitting method in the case of two radically different interaction potentials we show that significant uncertainties in the final extracted forces may result from use of the extrapolation method.
background subtraction; DFM; F(z); force; atomic resolution; NC-AFM; Si(111); STM; van der Waals
Aims: To compare central corneal thickness measurements of three pachymetry devices in eyes after laser in situ keratomileusis (LASIK).
Methods: Central corneal thickness was measured in 203 eyes after myopic LASIK. Orbscan II scanning slit topography (Bausch & Lomb), SP-2000P non-contact specular microscopy (Topcon), and ultrasonic pachymetry (Tomey) were used in this sequence.
Results: Three devices gave significantly different corneal thickness readings (p<0.0001, repeated measure analysis of variance). The measurements of Orbscan II (445.6 (SD 60.0) μm) were significantly smaller than those of noncontact specular microscopy (467.9 (SD 40.2) μm; p<0.0001, Tukey multiple comparison) and ultrasonic pachymetry (478.8 (SD 41.9) μm; p<0.0001). The value obtained with SP-2000P non-contact specular microscopy was significantly smaller than that taken with ultrasonic pachymetry (p<0.001). There were significant linear correlations between scanning slit topography and non-contact specular microscopy (Pearson’s correlation coefficient r = 0.912, p<0.0001), non-contact specular microscopy and ultrasonic pachymetry (r = 0.968, p<0.0001), and ultrasonic pachymetry and scanning slit topography (r = 0.933, p<0.0001).
Conclusion: In post-LASIK eyes, Orbscan II scanning slit topography significantly underestimated corneal thickness. Non-contact specular microscopy gave smaller thickness readings than ultrasonic pachymetry, but these two units showed an excellent linear correlation.
pachymetry; corneal thickness; scanning slit topography; laser in situ keratomileusi; non-contact specular microscopy
This article describes the novel application of Brillouin optical microscopy for 3D mechanical imaging of the cornea in situ with high spatial resolution. Brillouin images reveal a depth-dependent variation of the elastic modulus across the cornea and marked changes on collagen cross-linking.
The mechanical properties of corneal tissue are linked to prevalent ocular diseases and therapeutic procedures. Brillouin microscopy is a novel optical technology that enables three-dimensional mechanical imaging. In this study, the feasibility of this noncontact technique was tested for in situ quantitative assessment of the biomechanical properties of the cornea.
Brillouin light-scattering involves a spectral shift proportional to the longitudinal modulus of elasticity of the tissue. A 532-nm single-frequency laser and a custom-developed ultrahigh-resolution spectrometer were used to measure the Brillouin frequency. Confocal scanning was used to perform Brillouin elasticity imaging of the corneas of whole bovine eyes. The longitudinal modulus of the bovine corneas was compared before and after riboflavin corneal collagen photo-cross-linking. The Brillouin measurements were then compared with conventional stress–strain mechanical test results.
High-resolution Brillouin images of the cornea were obtained, revealing a striking depth-dependent variation of the elastic modulus across the cornea. Along the central axis, the Brillouin frequency shift varied gradually from 8.2 GHz in the epithelium to 7.5 GHz near the endothelium. The coefficients of the down slope were measured to be approximately 1.09, 0.32, and 2.94 GHz/mm in the anterior, posterior, and innermost stroma, respectively. On riboflavin collagen cross-linking, marked changes in the axial Brillouin profiles (P < 0.001) were noted before and after cross-linking.
Brillouin imaging can assess the biomechanical properties of cornea in situ with high spatial resolution. This novel technique has the potential for use in clinical diagnostics and treatment monitoring.
One of the applications of Molecular Dynamics (MD) simulations is to explore the energetic barriers to mechanical unfolding of proteins such as occurs in response to the mechanical pulling of single molecules in Atomic Force Microscopy (AFM) experiments. Although Steered Molecular Dynamics simulations have provided microscopic details of the unfolding process during the pulling, the simulated forces required for unfolding are typically far in excess of the measured values. To rectify this, we have developed the Pulsed Unconstrained Fluctuating Forces (PUFF) method, which induces constant-momentum motions by applying forces directly to the instantaneous velocity of selected atoms in a protein system. The driving forces are applied in pulses, which allows the system to relax between pulses, resulting in more accurate unfolding force estimations than in previous methods. In the cases of titin, ubiquitin and e2lip3, the PUFF trajectories produce force fluctuations that agree quantitatively with AFM experiments. Another useful property of PUFF is that simulations get trapped if the target momentum is too low, simplifying the discovery and analysis of unfolding intermediates.
Magnetic force microscopy (MFM) allows one to image the domain structure of ferromagnetic samples by probing the dipole forces between a magnetic probe tip and a magnetic sample. The magnetic domain structure of the sample depends on the alignment of the individual atomic magnetic moments. It is desirable to be able to image both individual atoms and domain structures with a single probe. However, the force gradients of the interactions responsible for atomic contrast and those causing domain contrast are orders of magnitude apart, ranging from up to 100 Nm−1 for atomic interactions down to 0.0001 Nm−1 for magnetic dipole interactions. Here, we show that this gap can be bridged with a qPlus sensor, with a stiffness of 1800 Nm−1 (optimized for atomic interaction), which is sensitive enough to measure millihertz frequency contrast caused by magnetic dipole–dipole interactions. Thus we have succeeded in establishing a sensing technique that performs scanning tunneling microscopy, atomic force microscopy and MFM with a single probe.
hard disc; high-stiffness cantilever; magnetic force microscopy; qPlus
Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip–surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip–surface force that are in-phase with the tip motion (F
I) and quadrature to the motion (F
Q). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F
I and F
Q actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F
I and F
Q from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F
I and F
Q, providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.
atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency