WO2003094173A1

WO2003094173A1 - Device for controlling an excitation signal from a resonant mechanical oscillating element, measuring device, method of controlling the excitation signal, method of taking measurements, computer program and storage device

Info

Publication number: WO2003094173A1
Application number: PCT/ES2003/000100
Authority: WO
Inventors: Francisco Javier Tamayo De Miguel; Laura M. LECHUGA GOMÉZ; M. del Mar ÁLVAREZ SÁNCHEZ
Original assignee: Consejo Superior De Investigaciones Científicas
Priority date: 2002-05-03
Filing date: 2003-03-07
Publication date: 2003-11-13
Also published as: AU2003214265A1; ES2194607A1; ES2194607B1

Abstract

The invention relates to a device for controlling an excitation signal from a resonant mechanical oscillating element (3) which is excited by said excitation signal (F). The inventive control device also comprises means for determining a phase difference (?) between a signal that is representative of the oscillation (Z) of the oscillating element and a feedback component (F2) and means for generating the feedback component (F2) which are configured such that the amplitude (GA) of said feedback component (F2) is a function of the aforementioned phase difference (?). The invention also relates to a measuring device, a method of controlling the excitation signal, a method of taking measurements, a computer program and a storage device.

Description

TITLE

A CONTROL DEVICE FOR AN EXCITATION SIGNAL OF A RESONANT MECHANICAL OSCILLATOR ELEMENT, A MEASUREMENT DEVICE, A METHOD FOR CONTROLLING THE EXCITATION SIGNAL, A METHOD FOR PERFORMING MEASUREMENTS, A COMPUTER PROGRAM AND A STORAGE DEVICE.

FIELD OF THE INVENTION

The invention falls within the field of mechanical oscillators and measurements based on the dynamic response of said oscillators.

BACKGROUND OF THE INVENTION

The dynamic response of a mechanical oscillator means the relationship between the oscillator movement and an excitation force with a certain frequency. In a harmonic oscillator, the dynamic response is determined by the resonance frequency, quality factor, damping factor, elastic constant and mass. Examples of relevant mechanical oscillators are cantilevers used in atomic force microscopy (AFM), fiber optic probes used in near field optical microscopy (SNOM), and resonant structures of sensors and mechanical biosensors.

The basic idea of the atomic force microscope (AFM) is to measure the force between a very sharp point (radius of curavature of the order of the nanometer) and a surface that you want to characterize, which can be located at a distance between 0.1 and 100 nm. To measure this force, which is of the order of nN, the tip is attached to the end of a cantilever (micro lever) of micrometric dimensions, so that the force is measured from the cantilever deflection. The cantilever is deflected in response to force following approximately Hooke's law, that is, it behaves like a harmonic oscillator. Deflection is usually measured with sub-nanometric resolution by an optical system illustrated schematically in Figure 1: a laser beam 1 emitted by a laser diode 2 strikes the surface of the cantilever or oscillating element 3 (which is provided with the tip 4) and is reflected in a segmented photodetector 5; the object on which the measurement is carried bears the numerical reference 6. Other optical, capacitive, piezoresistive detection methods etc., can also be used. The images are obtained by sweeping the sample with respect to the tip or vice versa, which have an accuracy of 0.01-0.1 nm. The scanning is usually done using piezoelectric crystals. A feedback system can maintain constant force (constant deflection), vertically moving the sample with respect to the tip or vice versa. The vertical displacement with respect to the horizontal provides the topography of the surface of the sample. Among the characteristics of the AFM, it is worth highlighting its high spatial resolution that is determined by the dimensions of the tip and which allows sub-nanometric resolution to be obtained. On the other hand it allows the topographic visualization of surfaces in different media such as vacuum, air, gases or liquids. It also shows great versatility and allows visualizing magnetic domains, spatial variations of electrical properties or mechanical properties. Currently the AFM has become a fundamental tool in nanotechnology and its use is widespread in the fields of materials physics, physicochemical, biology and biomedicine. The expansion of the atomic forces microscope has led to the commercialization of microfabricated cantilevers with silicon technology. The cantilevers have a length of the order of 100 μm, a width of the order of 10 μm and a thickness of less than approximately 1 μm. The elastic constant (k) is determined by the dimensions of the cantilever, being of the order of 0.1 N / m. The low value of k makes the cantilever very sensitive to measure external forces with high sensitivity, so that the strength of a single bond between a pair of atoms or molecules can be measured. Given the small mass of these devices, the resonance frequency is quite high, f ₀ = 10-1000 kHz.

To detect and measure the force between the tip and the sample in an AFM there are two modes: static mode and dynamic mode.

In static mode, also called contact mode, force is measured from the deflection of the cantilever (z), applying Hooke's law, F = k z. In this mode, the tip is usually in contact with the surface of the sample, with a repulsive force appearing. The minimum detectable force that can be applied to the sample is mainly limited by the thermal noise produced by a fluctuation in cantilever deflection. Using the static method, forces below 0.01 nN can hardly be used.

The dynamic mode allows lower forces to be measured in the air and vacuum media. In this mode the cantilever oscillates with an amplitude of the order of the nanometer, excited by an external sine force with frequency equal to that of the resonance of the Cantilever, or next. The cantilever oscillation changes when the tip is close to the surface of the sample due to the force between the tip and the sample. The oscillation parameters that can be measured are the amplitude and the lag with respect to the exciting force, and its change due to the tip / sample interaction. The change in amplitude or offset is due to the change in the resonant frequency and the change in the damping factor.

The forces exerted in the dynamic mode of an AFM can be analyzed by modeling the cantilever as a forced harmonic oscillator whose equation of motion is:

d ² z dz m— _τ + γ—- + kz = F _Q cos (fi) t) + F _m - _t (z) (1) dt dt

where m is the effective cantilever mass, z is the cantilever deflection, γ is the damping factor, F ₀ cos (ωt) is the excitation force and F¡ _nt is the interaction force between the tip and the sample. The damping factor (γ) depends on the internal friction of the material and the friction of the cantilever with the medium. Another magnitude directly related to the damping factor is the quality factor Q, which is defined as:

Q = ^mω * / _γ (2)

where ω ₀ is the angular resonance frequency. The Q varies depending on the viscosity of the medium, so in vacuum it can reach values of the order of 10,000, in air of the order of 100 and in liquids very low values of 1 to 10.

One way to obtain complete information on the interaction between the tip and the sample is to measure the frequency spectrum of the cantilever, that is, the amplitude and the lag of the oscillation with respect to the frequency of the exciter signal (see Figure 2) . Two magnitudes are measured from the frequency spectrum, the resonance frequency f ₀ and the quality factor Q. The measurement of the offset allows to determine the resonant frequency of the cantilever and its change due to the tip / sample interaction, given that the definition of Resonance frequency is that frequency at which the offset between the cantilever oscillation and the exciter signal is 90 degrees. This frequency is where the maximum amplitude is approximately. However, in the case of low quality factors the Maximum amplitude position differs from the resonant frequency. The quality factor is measured by the width of the amplitude curve as a function of the frequency of the exciter signal by this expression:

Q * 1.74 f ₀ / Δf ₀ . (3)

where Δf ₀ is the width of the curve at which the amplitude has decayed by half.

In the dynamic mode of an AFM, the cantilever is excited at a fixed frequency, equal to or close to that of resonance and the interaction between the tip and the sample can be measured by changing the amplitude of the oscillation. Assume that the interaction between the tip and the sample displaces the resonance frequency and that the system can detect amplitude changes above a certain threshold. The amount that the resonance frequency has to be displaced, that is, the amount of interaction between the tip and the sample, so that a change in amplitude can be detected depends on the quality factor (Q) as illustrated in Figure 3. Thus, it is understood why the dynamic mode of AFM in liquids implies high normal forces. A change in detectable amplitude in liquids only occurs when there are high forces between the tip and the sample (high resonance frequency shift), due to the low Q. Similarly, if the interaction between the tip and the sample were measured by changing the oscillation offset the same would happen; The change in offset due to a change in the resonance frequency is proportional to the quality factor.

One of the main limitations to obtain high resolution in AFM is the mechanical properties of the sample and the adhesion between the sample and the solid support. This limitation is fundamental when you want to visualize biological samples (DNA, proteins, cells, etc.). To visualize the native structure of these samples, visualization is required in an aqueous medium. Under these conditions, the biological samples are soft and weakly adhere to the solid support (mica, graphite, silicon, glass, etc.) as a result of the great screening of the attractive forces between the biological samples and the solid support that is produced in solutions aqueous. In the contact mode, the tip displaces and / or destroys the sample during scanning (lateral forces), and visualization of the sample is prevented or made very difficult. In dynamic mode, the tip usually touches the sample intermittently in each cycle of the oscillation. In this way, the lateral forces that appear in the contact mode are eliminated and the shows. However, normal forces are high (1-10 nN) for the visualization of soft materials. These high forces deform and distort these materials, obtaining low spatial resolution. Researchers have estimated that the undistorted visualization of biological molecules requires the use of forces below 100 pN. However, these forces cannot be reached in the dynamic mode of an AFM in the liquid medium due to the low Q. Simulations have been performed indicating that Qs above 100 are needed to reach forces below 100 pN. These values of Q are 2 orders of magnitude higher than the values found in the cantilever due to hydrodynamic friction between the cantilever and the liquid medium during oscillation.

Currently, resonant structures are microfabricated that can be used as sensors and biosensors. Most sensors based on resonant structures have been developed for the detection of chemical compounds in gaseous media demonstrating very high sensitivity. They also allow real-time detection, require a minimum amount of analyte and the tiny size of these devices makes their miniaturization and integration into chips with low cost feasible. An example is bio / sensors based on cantilevers such as those used in AFM, but in which the tip is not used. An important application of this type of sensors is the biosensors and sensors of chemical substances in liquid media. Biosensors detect biological substances instead of chemical substances. For this reason, the detection must be performed in the liquid medium, in which the biological molecules are functional. From now on, cantilever is understood as any resonant mechanical structure.

In the static detection method, receptor molecules are immobilized on one of the sides of the resonant mechanical structure (EMR), which specifically bind to the substance to be analyzed or detected (analyte). When the substance to be analyzed is introduced into the fluid cell where the EMR is, the analyte binds to the receptor molecules. In this way the surface composition has varied and therefore the surface tension. Since the receptor molecules have been immobilized only on one side of the cantilever, the surface tension on this side changes with respect to that on the other side, and a cantilever curvature occurs. This cantilever curvature can be measured by an optical system such as that used in an AFM and described above, or by other optical, capacitive, piezoresistive methods, etc. An example of cantilevers-based biosensor for detecting DNA hybridization is shown in Figure 4. The device It consists of a cantilevers microarray. Single-stranded DNA with different base sequences has been immobilized on each side of the cantilever. When the microarray is exposed to a liquid solution containing DNA from a chain whose base sequence is complementary to that previously immobilized in one of the cantilevers, this cantilever curves due to the change in surface tension produced by the double strand DNA formation.

In the dynamic detection mode, the receptor molecules are immobilized on one or both sides of the cantilever. The cantilever oscillates with an amplitude of the order of the nanometer and the oscillation is measured in the same way as in a dynamic microscope of forces. When the analyte is bound in the cantilever receptor surface, an increase in the mass that will produce a decrease in the resonance frequency occurs (the resonant frequency can be expressed as f ₀ = 1 / 2π (k / m *) ^{1 2} ). Although this method is basically used to measure mass variations associated with the adsorption of the analyte on the cantilever surface, it has been found that surface tension can cause resonance frequency changes. Until now, the few works in which cantilevers have been used for the detection of biological substances have used the static method. The reason is the low quality factor of the cantilever in the liquid medium due to the strong hydrodynamic friction that the cantilever experiences when it oscillates. Figure 5 shows the effect of the medium change in the cantilever response. In air the quality factor is relatively high (Q = 50-500). When the cantilever is introduced into a liquid medium, two changes in the dynamic response of the cantilever are observed. The resonance frequency decreases a factor between 2 and 3, indicating that the effective mass of the cantilever (m ^* ) has increased. This is due to the associated movement of the liquid near the cantilever when it oscillates. The second and most important change is that the quality factor is very low, on the order of 1. This provides an amplitude vs. curve. Very wide exciter signal frequency, Q «1, 74 f ₀ / Δf.

The sensitivity to measure changes in cantilever oscillation is proportional to the quality factor. In this way, the cantilever resonance frequency is obtained by measuring the oscillation offset with respect to the exciter signal. A change in the resonance frequency produces a offset of the offset with respect to 90 degrees. This deviation is proportional to Q, and therefore, the sensitivity to determine the change in the resonance frequency is proportional to Q. In short, the low sensitivity to measure the dynamic properties of the cantilever in the liquid medium has prevented them from having developed Cantilevers based biosensors using dynamic detection.

Cantilever-based biosensors that use the static measurement method have the disadvantage that the signal being measured, the cantilever deflection, has a large drift, making its use impractical. The origin of this drift is due to turbulence of the liquid, slow chemical reactions between the solution and the cantilever surface, and thermal fluctuations. The latter has a dramatic effect on the measurements. Normally to immobilize the receptor molecules on one side of the cantilever, it is necessary to previously evaporate a thin layer of gold (thickness «10-50 nm). As a consequence, the cantilever not only responds to analyte molecules when they bind to receptor molecules, but is very sensitive to very small variations in temperature. Since the metal has a coefficient of thermal expansion different from that of the cantilever, temperature variations produce an expansion or contraction of the gold layer with respect to the rest of the cantilever, which produces a curvature of the cantilever. This phenomenon is known as bimetallic effect and has been previously used to measure temperature changes as small as 10 ^{~ 5} ° C. Thus, when the analyte is introduced into the fluid cell where the cantilever is located, the change in deflection is due in part to the temperature difference between the solution where the analyte is found and the fluid cell solution, masking the change of the analyte detection signal itself.

The technologies discussed in the above and different related aspects are described in, for example:

Piconewton Regime Dynamic Forcé Microscopy in Liquid (Javier Tamayo, Andrew D.L. Humphris & Mervyn J. Miles; Appl. Phys. Lett. 77, 582 (2000)); Chemical Sensors and Biosensors in Liquid Environment based on

Microcantilevers with the Quality Factor Amplified (J. Tamayo, A.D.L. Humphries, A.R. Malloy & M.J. Miles; Ultramicroscopy 86, 167 (2001));

High Q Dynamic Forced Microscopy in Liquids (J.Tamayo, A.D.L. Humphries, R. Owen & M. Miles; Biophys. J. 81, 526 (2001)); and Active Quality Factor Control in Liquids for Forcé Spectroscopy (A.D.L.

Humphris, J. Tamayo & M.J. Miles, Langmuir, 16, 7891, (2000)).

On the other hand, WO-A-01/81857 (on which the ActivResonance Controller® product marketed by Infinitésima Ltd. is based, describes an arrangement that allows to increase the low quality factor Q of the cantilever in the liquid medium, by means of a system of electronic feedback The applications of WO-A-01/81857 also They are described in the previous publications.

The dynamic response of the cantilever is more sensitive than the static response, as described above. In addition, the dynamic response hardly suffers thermal drift, as with the static response, which requires a long stabilization time. The measurement of the dynamic response of the cantilever in a liquid medium is limited by the very low quality factor Q. This makes the AFM in the liquid medium less sensitive and that the biosensors and chemical sensors that detect substances in liquid media traditionally measure The static answer. The method described in WO-A-01/81857 allows to increase the sensitivity of AFM in liquids up to 3 orders of magnitude, which has a strong impact on the application of AFM in biology. Another area of impact is the field of chemical biosensors and sensors based on resonant mechanical microstructures that need to be measured in the liquid medium. The idea behind the invention described in WO-A-01/81857 is to introduce a cantilever movement control system to increase the quality factor. Let's say that the cantilever reacts to an incident force with frequency ω, F ^ ω) with a transfer function X (ω) that corresponds to a damped harmonic oscillator.

where ω ₀ is the angular resonance frequency, k is the elastic constant and Q is the quality factor of the cantilever. The angular resonance frequency ω ₀ is related to the resonance frequency f ₀ through the expression ω ₀ = 2πf ₀ .

However, the response of the oscillator can be modified by a feedback system with a transfer function C (ω). The scheme is shown in Figure 6. With the inclusion of this system, the cantilever response changes to:

In this way, the cantilever response can be changed as required. The invention described in WO-A-01/81857 is intended to increase the Q of the cantilever, and this can be done by a controller with a function of transfer:

where Q _Θff is the effective quality factor that you want to obtain. Since it is usually operated at frequencies close to that of resonance, and for simplicity of electronics, this function is simplified to:

This feedback system can be easily implemented at the level of analog and digital electronics using a variable phase ^shifter (term e ^{lπ 2} in equation 7) and a variable gain amplifier whose gain G is related to the effective quality factor through the expression G = k (1 / Q-1 / Q _θff ) (equation 7), as illustrated in Figure 7. In this implementation, the cantilever (oscillator element 3) is oscillated by an alternating magnetic field whose frequency is the one of resonance, or next to her. On the cantilever (the oscillating element 3) a thin layer of ferromagnetic material has previously evaporated to respond to the magnetic field. Another excitation method that can be used is the generation of mechanical-acoustic waves in the fluid by means of a piezoelectric crystal.

The other important element of this device is the unit that detects the resonance frequency, which is done by means of a phase-locked loop (PLL) 7 comprising a phase detector 8, a Pl 9 controller and a voltage controlled oscillator ( VCO) 10. The PLL produces an exciter signal of the form F ₀ exp (iωt) and measures the cantilever response, adjusting the exciter frequency, ω = 2πf, to maintain a 90 degree phase difference between the cantilever oscillation and the exciter signal, that is, excites the cantilever at its resonance frequency.

The effect of the feedback system proposed in WO-A-01/81857 can be better understood by analyzing the differential equation of cantilever movement. When the feedback system is not included, the equation of motion is that of a forced damped harmonic oscillator: d ² z dz m ^ X- + γ— + kz = F ₀ e ^mt (8) dt dt

F ₀ e ' ^ωt is the exciting force that makes the cantilever swing. When we include the feedback system, the cantilever is oscillated by the sum of two exciting forces, one is the standard force F ₀ e ' ^ωt , and the other is a force that is proportional to the movement of the cantilever offset 90 degrees, G ze ^{lπ / 2} . Thus the differential equation of this system is:

_m * fl _{+ γ} ^ _{+ kz = F e} >«< _{+ Gze} ^iπ Á (9) dt ² dt °

Since the cantilever movement is sinusoidal, z = Aexp (iωt-φ), the

Cantilever speed can be expressed - = iωAe ' ^{íωl ~ φ)} = ωe' ^πl2 . When entering dt this expression in the differential equation we have

m (10)

Which gives rise to:

which is the equation of a forced harmonic oscillator with a damping factor that can be changed electronically by the gain of the amplifier G,

r _eff = r ~ - (1) ω

The effective quality factor is Q _eff = mωo / γ _eff .

Figure 8 shows the effect of this feedback system on the response of the cantilever immersed in a liquid. The quality factor can be increased up to 3 orders of magnitude, being able to obtain Qs close to 1000. That is a Cantilever in a liquid can present a dynamic response comparable to that found in a vacuum.

In Figure 9, the resonance frequency signal is compared with the deflection signal of the cantilever immersed in aqueous solution. The deflection signal shows great drift due to the thermal drift of the positions of the laser beam, the photodetector, and the cantilever. There are also slow chemical reactions between the cantilever and the solution. However, the resonance frequency signal is immune to these drifts.

The experimental results of applying the system described in WO-A-01/81857 for the detection of biological molecules are shown in Figure 10. On one side of the cantilever, antibodies that are specific to the antigens to be detected were immobilized. The antibodies are immobilized on one side of the cantilever by applying an immobilization protocol that requires the evaporation of a thin layer of gold on that side of the cantilever. The medium is an aqueous buffer solution called PBS. In this experiment, the deflection signal and the real-time resonance frequency were measured. When 5 μl of PBS was introduced into the fluid cell, a change in the deflection signal is observed (the volume in the fluid cell is 50 μl). This change is due to the turbulence caused and the temperature change produced. However, the resonance frequency was immune to this alteration. When the antigen was introduced, a deflection response similar to when the solution was simply introduced without antigen was introduced. This change in the signal is due to the turbulence produced, the effect of local temperature change and the effect of the reaction of the antigen with the antibodies immobilized in the cantilever. By subtracting the signal when only PBS was introduced, the change in deflection associated with the detection of the antigen in the solution is envisioned. However, the signal of the resonance frequency that was immune to the introduction of the PBS shows a marked jump when the antigen is introduced into the solution.

The feedback system, although it does serve to substantially increase the quality factor discussed above, does not always provide optimum sensitivity in the dynamic response of the cantilever or mechanical oscillator element in general.

The feedback system described allows obtaining high quality factors. However, high quality factors involve certain disadvantages due to the presence of transients in the oscillation. The cantilever oscillation is composed of a transitory and a stationary element. The cantilever swing for an excitation force F ₀ e ^lωt can be expressed as ^follows :

z = Ce ^{~ τ} and ^{iiω't + δ)} + Ae ^{i {ωt} - ^φ) (13)

where the first adding is the transitory element and the second the steady state of the oscillation. In AFM, SNOM and bio / sensors based on resonant mechanical structures, the measurement of the amplitude (A) and the offset of the steady state oscillation (φ) requires that the transient oscillation disappears. The magnitude of time that indicates how long it takes for the transient to disappear is the time constant τ,

Obtaining high effective Qs by the feedback system described above implies high time constants (τ), and therefore long times are required for stabilization of the cantilever oscillation. In practice this involves long times in the acquisition of images in AFM, and slow response times in bio / sensors based on resonant mechanical structures.

On the other hand, when profits (G) that give a high effective quality factor are used, situations can be reached in which the effective c damping factor becomes negative, γ _efr = γ, and therefore the constant ^J ω of Transient time (τ) becomes negative, which implies that the transient does not disappear and increases over time until the oscillation exceeds the detection limits and becomes unstable. In general, obtaining high effective Qs, applying the invention described in said publication WO-A-01/81857, implies that the cantilever oscillation is in many cases unstable. The control system gives rise to factors

of small damping, where γ _ñ - γ is close to zero, so that

¹³ ω minimum fluctuations in the damping factor (γ) cause large changes in the effective quality factor (Q _eff = mωo / γ _eff ), which results in large changes in the amplitude and offset of the oscillation, which cannot be controlled giving rise to loud and unstable measures. The damping factor (γ) may change due to changes or fluctuations in the temperature and composition of the liquid. Usually, Obtaining high effective Qs implies noisy and unstable measures.

Another drawback of the control system described above is that the gain value is limited by the maximum voltage or current value that the excitation signal can admit; The sum of the fixed excitation signal and the feedback signal (F ₀ + GA) cannot exceed the voltage or current limit that the exciter device or the system that generates the excitation signal admits. This limits the maximum value of the effective Q that can be achieved.

DESCRIPTION OF THE INVENTION One aspect of the invention relates to a device for controlling an excitation signal of a resonant mechanical oscillating element excited by said excitation signal. The control device comprises: means for receiving a signal representative of the oscillation of the oscillating element; means for generating a feedback component (F ₂ ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z); the excitation signal comprising at least said feedback component (F ₂ ) and the excitation signal having an excitation frequency (ω). The control device further comprises means of determining a lag.

(φ) between the signal representing the oscillation (Z) of the oscillating element and the feedback component (F ₂ ). The means of generating a feedback component (F ₂ ) are configured so that the feedback component (F ₂ ) has an amplitude (GA) that is a function of said offset (φ). In this way, the control system allows changing the dynamic response of the resonant mechanical oscillator element and increasing its sensitivity to measure forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element, or an object that is located in relation to the mechanical element. These mentioned elements produce a change in the oscillation of the mechanical element, which is excited to oscillate. These changes may be the change in amplitude and offset as a result of a change in the resonance frequency and / or the quality factor. The change in amplitude and offset, for a given change in the resonance frequency and / or the quality factor, is greater the greater the quality factor. The control system corresponding to this invention produces a higher apparent quality factor, and therefore increases the sensitivity of mechanical oscillators with a low quality factor.

It is interesting to emphasize the difference between quality factor and the definition that the authors of the present invention make of the concept of "apparent" quality factor. The quality factor of a mechanical oscillator is determined by the energy dissipated during its oscillation due to internal friction of the material of the mechanical element and the friction of the mechanical element with the medium during oscillation. When the amplitude of the oscillation of a mechanical oscillator is measured as a function of the excitation frequency, a peak located approximately at the resonant frequency is observed. The width of this peak is smaller the greater the quality factor Q, that is, the less energy dissipates in the oscillation. Similarly, the offset changes more than 90 degrees when the frequency of the exciter signal deviates from the resonant frequency. The fact that the amplitude and the offset change a greater amount the higher the Q, is what makes the mechanical oscillators with a high quality factor Q more sensitive to external changes. However, if the oscillator dissipates more or less energy, it is indifferent when what is sought is to see changes in the oscillation of the mechanical element due to external changes that are to be measured (forces acting on the mechanical element or changes in the properties physical and / or chemical means of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element). The control system of this invention apparently produces a high Q because it provides very narrow amplitude resonance peaks, but does not necessarily affect the energy dissipation of the system, which is the characteristic that determines the quality factor of a mechanical oscillator. Similarly, the control system of the present invention can cause major phase shifts when the excitation frequency deviates from the resonance frequency.

The control system according to the present invention allows a higher "apparent" quality factor to be obtained but, unlike the system set forth in WO-A-01/81857, it is not intended to increase the actual quality factor. It is intended that when measuring the amplitude of the mechanical oscillator with respect to the excitation frequency, a narrower maximum is obtained than that which the mechanical oscillator would have without this control system and was excited by an excitation force with a fixed amplitude. The maximum is at a frequency close to or equal to that of resonance. Similarly, it can be expected that the feedback system will produce a shift change when the excitation frequency deviates from that of the resonance, which is greater than if there was no control system. The offset is not changed if the excitation force is composed only of the feedback component (F ₂ ). However, if the excitation force is composed of a base component Fi and the feedback component F ₂ in quadrature, the situation is complex, and several feedback loops are required to reach a steady state. This feedback system affects the offset and amplitude.

This control system does not change nor does it necessarily change the energy dissipation of the system. The control system intends that the amplitude curve with respect to the frequency of the excitation signal has a narrow maximum around the resonant frequency or a frequency close to it. It can also be intended to increase the change in the oscillation offset when the frequency of the excitation signal deviates from the resonant frequency or a frequency close to it. This occurs when the quality effect is high, but it can also be obtained with a control system that produces these responses without increasing the quality factor, that is, without changing the energy dissipation of the mechanical oscillator. In this way, changes in the resonance frequency of the mechanical oscillator can be measured with greater sensitivity as a result of forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element. Similarly, changes in the quality factor can also be measured with greater sensitivity as a result of forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is, or of an object which is located in relation to the mechanical element. The control system increases the sensitivity of mechanical oscillators that have a low quality factor because they are made of a material with high internal friction or because measurements are made in a viscous medium such as a liquid. However, the invention does not imply certain problems that the control system described in WO-A-01/81857 has, which it pursues increases the quality factor, see what we have commented in the "background of the invention" section.

According to a preferred embodiment of the invention, the amplitude (GA) has a maximum at a lag (φ _r ) corresponding to a frequency (ω _r ) close to the resonant frequency of the oscillating element. In this way the excitation force acquires a maximum value at a frequency close to that of resonance and an amplitude curve is obtained with respect to the frequency of the exciter signal, which It has a narrow maximum around that frequency. The narrower the maximum of the amplitude (GA) around a predetermined offset (φ _r ), the narrower the maximum of amplitude around the corresponding frequency (ω _r ). Thus, a change in the resonance frequency when the oscillator is being excited at that frequency causes a change in the amplitude (which may be related to the change in the resonance frequency) greater than the change in amplitude produced if excites the mechanical oscillator with an excitation force with a fixed amplitude (the situation is similar to that illustrated in Figure 3). This allows measuring resonance frequency changes caused by forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is located, or of an object that is located in relation to the element mechanical. This is extremely important in mechanical oscillators with a low quality factor in which a change in the resonance frequency results in a too small change in amplitude or offset.

In the case where in addition to F ₂ there is a fixed excitation force Fi 90 degrees out of phase, a very sensitive change of the offset can also be obtained when the resonance frequency and / or the quality factor changes. Initially, this system allows a greater number of possibilities that may be interesting. When the feedback is only F ₂ the answer is easily predictable. It is a harmonic oscillator that instead of being excited by a fixed excitation force, is excited by a force whose amplitude depends on the offset. The resulting amplitude curve is the product of the standard curve by the GA curve. Thus, a narrower GA curve around the resonance frequency implies a narrower amplitude curve. However, the offset response is the same.

According to a preferred embodiment of the invention, the amplitude has a maximum at a offset (φ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element. Thus, the maximum narrow amplitude appears at the resonant frequency. This is ideal, however, very similar results can be obtained if the amplitude (GA) has a maximum at a lag that corresponds to a frequency close to that of resonance.

According to a preferred embodiment of the invention, the amplitude (GA) has a maximum when the offset (φ) is a determined offset. Ideally, the amplitude (GA) has a maximum of a lag that corresponds to the frequency of resonance. Also, if the offset corresponds to a frequency close to that of resonance, the invention works and gives similar results, although not as optimal.

According to a preferred embodiment of the invention, the excitation signal (F) is composed of the feedback component (F ₂ ), that is, it consists exclusively of said feedback component.

According to another preferred embodiment of the invention, the excitation signal (F) comprises the feedback component (F ₂ ) and a base component (Fi). Each of these can be generated by a different device, for example, the base component can be generated by a substantially fixed oscillator and the feedback component can be generated by the control device according to preset parameters and depending on characteristics determined from the signal representative of the oscillation (Z).

As suggested above, the base component (F ^ can be a signal with a fixed excitation frequency (ω) and with a fixed amplitude and the feedback component (F ₂ ) can be a signal with the same excitation frequency (ω) and that is out of phase + 90 ° or -90 ° with respect to the base component

According to a preferred embodiment of the invention, the control device comprises means of modifying the excitation frequency (ω) as a function of the signal representative of the oscillation (Z) so as to maintain a determined offset (φ) between the representative signal of the oscillation (Z) and the feedback component (F ₂ ). Preferably, said determined offset is an offset corresponding to the resonance oscillation of the oscillating element. In this way, it can be achieved that the oscillating element is kept oscillating at resonance or substantially at resonance.

According to a preferred embodiment of the invention, the control device comprises means of modifying the excitation frequency (ω) as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillator element. In this way, it can be achieved that the oscillating element is kept oscillating at resonance or substantially at resonance, since the maximum amplitude occurs at a frequency approximately equal to that of resonance.

According to a preferred embodiment of the invention, the amplitude (GA) of the feedback component (F ₂ ) is a function of both the offset (φ) between the signal representative of the oscillation (Z) and the feedback component (F ₂ ) as of the amplitude of the signal representative of the oscillation (Z). In this way, one more variable is introduced in the dependence of the amplitude GA. It is more complex but the objective is to obtain a higher "apparent" Q. For example, the amplitude GA could have a maximum when the offset is the one that corresponds to the resonance, and in addition the amplitude GA of the feedback component could be greater the greater the amplitude of the signal representative of the oscillation (Z). In this way, the excitation force would have a very pronounced maximum at resonance, since at resonance the offset is the offset for which the amplitude GA has a maximum and in addition to resonance a maximum of amplitude occurs. According to a preferred embodiment of the invention, the means for receiving a signal representative of the oscillation (Z) are associated with a sensor that detects a signal directly related to the oscillation of the oscillating element. For example, the sensor could consist of a laser diode that emits a laser beam that is reflected in the oscillator or cantilever element and that goes to a segmented photodetector. The imbalance between the photocurrents generated in the photodetector segments is due to the deflection and movement of the cantilever. This method is used in most commercial AFMs. Other methods are interferometric, capacitive and piezoresistive optics. In the latter, the cantilever is made of a piezoresisitive material, so that when the cantilever bends the resistance of the cantilever changes.

According to a preferred embodiment of the invention, the device includes a pass-band filter at the excitation frequency (ω) to filter the signal representative of the oscillation (Z). In this way, unwanted frequencies from electrical noise are eliminated in the oscillation detection, mechanical noise affecting the resonant mechanical element, thermal noise of the resonant mechanical element, harmonics caused by external forces acting in the cantilever, etc.

According to a preferred embodiment of the invention, the device is constituted by a processing device with a data acquisition card (TAD), so that: the data acquisition card comprises the means of receiving a signal representative of the oscillation (Z) of the oscillating element; the processor device comprises the means of generating the feedback component (F ₂ ); and the data acquisition card comprises an output for the component of feedback (F ₂ ).

The processor device can be a digital processor device, which allows, for example, the amplitude (GA) and / or the excitation frequency (ω) to be set in a specific way (digitally manipulable) depending on, for example, the characteristics of the signal representative of the oscillation (Z), for example, using conventional computer applications or specifically designed for a specific use or for a certain type of uses.

Another aspect of the invention relates to a measuring device (for example, a biosensor device), comprising: means for generating an excitation signal (F); a resonant mechanical oscillator element; coupling means of the excitation signal to the resonant mechanical oscillator element so that the excitation signal induces an oscillation in said element; a detector device comprising means of generating a signal representative of the oscillation (Z) of the oscillating element; and means for reading and interpreting the signal representative of the oscillation (Z) (for example, of the same type used in the conventional measuring devices discussed in the "background of the invention" section). The means for generating the excitation signal include a control device according to the invention.

The oscillating element can be a micro lever ("cantilever") that can be provided with a tip (for example, as in a microscope of atomic forces).

Another aspect of the invention relates to a method for controlling the excitation signal of a resonant mechanical oscillator element excited by said excitation signal (F). The method comprises the steps of: receiving a signal representative of the oscillation (Z) of the oscillating element; generating a feedback component (F ₂ ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z), the excitation signal comprising at least , said feedback component (F ₂ ) and the excitation signal having an excitation frequency (ω); determine a lag (φ) between the signal representing the oscillation (Z) of the oscillating element and the feedback component (F ₂ ) and generate the feedback component (F ₂ ) so that the feedback component (F ₂ ) has an amplitude (GA) which is a function of said offset (φ). According to a preferred embodiment of the invention, the amplitude has a maximum at a lag (φ) corresponding to a frequency close to the resonant frequency of the oscillating element.

According to a preferred embodiment of the invention, the amplitude has a maximum at a offset (φ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element.

The amplitude (GA) can, for example, have a maximum when the offset (φ) is a certain offset.

The excitation signal (F) may be composed of the feedback component (F ₂ ) (i.e. consist exclusively of said component). There is also the possibility of generating the excitation signal by adding at least the component of feedback (F ₂ ) and a base component (F ^) - As a base component (Fi) a signal with a fixed excitation frequency (ω) and with a fixed amplitude can be chosen and as a feedback component (F ₂ ) You can choose a signal with the same excitation frequency (ω) and that is offset + 90 ° or -90 ° with respect to the base component (Fi).

According to a preferred embodiment of the invention, the excitation frequency (ω) is modified as a function of the signal representative of the oscillation (Z) so as to maintain a certain offset (φ) between the signal representative of the oscillation ( Z) and the feedback component (F ₂ ). Said determined offset may be, for example, a offset corresponding to the oscillation of the oscillating element at its resonance frequency, so that the oscillating element is kept oscillating at resonance.

According to a preferred embodiment of the invention, the excitation frequency (ω) is modified as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillating element.

According to a preferred embodiment of the invention, the amplitude (GA) of the feedback component (F ₂ ) is a function of both the offset (φ) between the signal representative of the oscillation (Z) and the feedback component (F ₂ ) as of the amplitude of the signal representative of the oscillation (Z).

According to a preferred embodiment of the invention, the signal representative of the oscillation (Z) is received through a sensor that detects a signal directly related to the oscillation of the oscillating element. In accordance with a preferred embodiment of the invention, the signal is filtered representative of the oscillation (Z) with a pass-band filter at the excitation frequency (ω).

According to a preferred embodiment of the invention, the feedback component (F ₂ ) is generated with a processor device. Another aspect of the invention relates to a method for carrying out measurements on an object, comprising the steps of: locating the object in relation to the oscillating element of the device described in the foregoing, so that object characteristics affect the oscillation of the object. oscillating element (for example, at the resonant frequency and / or the quality factor of the oscillating element); measure at least one characteristic related to the oscillation of the resonant element; and interpret the result of said measurement.

Depending on the type of object to be studied, the object can be located in the vicinity of the oscillating element (which may be convenient if the object is a substantially solid surface whose surface structure is to be studied) or in direct contact with the oscillating element (which may be convenient if the object is a liquid and if it is desired to detect the presence of a certain component in the liquid; this is applicable to, for example, biosensors). There is also the possibility of having both the object and the oscillating element immersed in a liquid (for example, if the object is a biological structure that must be kept immersed in a liquid).

As suggested above, the method may be suitable for studying very diverse objects, for example, liquids, biological substances, chemicals and / or solid surfaces.

Another aspect of the invention relates to a computer program, characterized in that it comprises program code means for performing all the steps of the control method described above when the program is executed on a computer. Another aspect of the invention relates to a storage device comprising means for storing at least this computer program.

BRIEF DESCRIPTION OF THE DRAWINGS

Next, a series of drawings that help to better understand the invention and some of which are related are described very briefly. expressly with an embodiment of said invention presented as an illustrative and non-limiting example thereof.

Figure 1 is a schematic representation of the detection of the deflection of a micro lever in an AFM system (according to the state of the art). Figure 2 is a spectrum of cantilever frequencies with and without interaction

(according to the state of the art).

Figure 3 illustrates the effect of the resonance frequency shift, due to a possible tip-sample interaction, on the change in amplitude of the cantilever when it is excited to resonance or at a nearby frequency, for a high Q value and a low Q ( according to the state of the art).

Figure 4 schematically illustrates a cantilever-based biosensor for detecting DNA hybridization (according to the state of the art).

Figure 5 illustrates a frequency spectrum of a cantilever in air and in an aqueous medium (according to the state of the art). Figure 6 schematically illustrates a feedback system (according to the state of the art).

Figure 7 schematically illustrates, in more detail, a feedback system used in WO-01/81857 (according to the state of the art).

Figure 8 shows the effect of the feedback system shown in Figure 7 on the response of a cantilever immersed in a liquid (according to the state of the art).

Figure 9 illustrates a comparison of the resonance frequency signal, with the cantilever deflection signal immersed in aqueous solution (according to the state of the art). Figure 10 illustrates results of the feedback system shown in Figure 7 applied to the detection of biological molecules (according to the state of the art).

Figure 11 illustrates a general arrangement according to a preferred embodiment of the invention. Figure 12 is a diagram reflecting the result of a practical test according to a preferred embodiment of the invention.

Figure 13 reflects the results of computer simulations of a preferred embodiment of the invention.

Figure 14 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention. Fig. 15 is a diagram reflecting the result of a practical test according to a preferred embodiment of the invention.

Figure 16 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention. Figure 17 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention.

DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

Figure 11 illustrates a general arrangement that includes the control device according to a preferred embodiment of the invention. This arrangement includes a conventional configuration according to what has been said in the foregoing, based on an oscillating element 3 or cantilever in which oscillation is induced by an excitation signal F applied to an inductor coil 11. On the other hand, obtains a signal representative of the oscillation Z; This signal is obtained by measuring the oscillation with a conventional system comprising a laser diode 2 that emits a laser beam 1 that hits the surface of the cantilever or oscillating element 3 and is reflected in a segmented photodetector 5. The difference between the photocurrents generated in the upper and lower segments is proportional to the cantilever deflection. The cantilever is excited by an oscillating magnetic field generated in the inductor coil 11. For this purpose the cantilever may have been coated with, for example, a thin ferromagnetic layer of cobalt (thickness between 10 and 50 nm).

On the other hand, the illustrated arrangement includes the control device according to the invention, schematically illustrated in Figure 11. Said device comprises a personal computer (PC) 13 and a data acquisition card (TAD) 12 (se These are conventional components, which are not illustrated in more detail). By means of said PC and TAD, a digital control can be applied to increase the "apparent" quality factor of the mechanical oscillator element 3, to increase the sensitivity of the oscillation to forces acting on the mechanical element or changes in the physical properties and / or chemical of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element.

The data acquisition card used has inputs to record the movement of the cantilever, that is to say to record the photocurrents or photovoltaics of each segment of the photodetector 5 as a function of time. amplifier By means of software programmed in, for example, LabView ™, the amplitude and phase of the fundamental harmonic of the oscillation are calculated. Using software, the alternating current that excites the coil and oscillates the cantilever is calculated and generated. Alternatively, the excitation signal is calculated by software and generated in a function generating instrument that is controlled by the computer.

The data acquisition card (TAD) 12 inputs record the oscillator movement, that is, they receive the signal representative of the oscillation Z, whose form is Z = Acos (ωt-φ) + N, where N is a signal which may include thermal noise, measurement induced noise, measurement associated noise, and non-harmonic oscillation elements produced by a non-perfectly harmonic response of the oscillator element or by the effect of introducing the oscillator into a nonlinear force field . The amplitude and offset of the oscillation are determined by software. Through the outputs of the TAD 12 data acquisition card, an excitation force (F) is generated, in this case only by the sinusoidal feedback component F ₂ , whose amplitude is GA and which has a very high maximum to the offset corresponding to the resonant frequency. In this case a function GA = B exp (-C without ² (φ-φ _r )) has been chosen that has a maximum at the resonant frequency where the offset measured by the system is φ _r .

The effect of this control system on the amplitude curve of a cantilever's oscillation with respect to the frequency of the exciter signal is shown in Figure 12.

Figure 13 illustrates the result of a simulation of the effect of this GA function on resonance. As defined in the foregoing, GA is a function that depends on the offset (φ); preferably, GA has a maximum at a lag (φ) corresponding to a frequency close to the resonant frequency of the oscillating element. In an ideal case, said offset would be 90 °, however, in reality and due to imperfections in the measurement, the offset measured at the resonant frequency will not necessarily be exactly 90 °, but may vary substantially. However, the offset corresponding to the resonance frequency can be determined by measuring the amplitude and the offset depending on the excitation frequency. Approximately, the maximum amplitude of the oscillation is found at the resonance frequency, and therefore the offset that is measured at said frequency is the offset corresponding to the resonance frequency.

A simulation of the amplitude curve with respect to the frequency of the excitation signal is shown in Figure 13, using the control system of the signal according to the described embodiment of the invention, for various values of parameter O Specifically, the diagram (a) in Figure 13 reflects a simulation of the amplitude curves and the offset with respect to the frequency of the exciter signal for a harmonic oscillator with low quality factor Q = 2.5, elastic constant k = 0.1 N / m and resonant frequency f ₀ = 10 kHz. Diagram (b) reflects amplitude curves (GA) of the feedback excitation signal (F ₂ = GA eos

(ωt)) depending on the excitation frequency:

GA = B exp (-Csin ² (φ-φ _r )), where φ is the offset measured by the device between the oscillation of the mechanical element and the excitation force, being equal to φ _r when the frequency of the excitation force It is the resonance. In this simulation φ _r = 90 degrees, as shown in the diagram (a). As the value of C is higher, a narrower maximum at the resonant frequency is obtained. B = 1 and its value determines the height of the curve but not its shape.

The diagram (c) of Figure 13 reflects the simulation of the amplitude curves with respect to the frequency of the exciter signal for a mechanical oscillator with a low quality factor, Q = 2.5, excited by a feedback signal F ₂ whose GA amplitude depends on the offset as indicated in (b).

The effect of this feedback system can be analyzed from the differential equation of the movement of the mechanical oscillator, which is approximately that of a harmonic oscillator excited by the excitation signal F ₂ = GA e ^lωt . The equation of motion is that of a forced damped harmonic oscillator:

m * - UZ τ- + γ - QZ + k .z = B _e -Csm ² ( ^κ φ ^ψ -90) lωt dt ² dt

The stationary solution of this differential equation has an amplitude A 'and an offset φ' that depend on the frequency in this way:

A '(ω) = GA A (ω) φ' (ω) = φ (ω)

where A is the amplitude of the mechanical oscillator if it were excited by a standard excitation signal with fixed amplitude equal to one, and φ is the offset if the mechanical oscillator was excited by a standard excitation signal with fixed amplitude. Curves A (ω) and φ (ω) are represented in Figure 13 (a) in the case of a mechanical oscillator with a low quality factor. The effect of the excitation force F ₂ used in this control system can be seen in figure 13 (c). This control system does not change the dependence of the offset. It produces a peak of resonance amplitude as narrow as one wishes, increasing the value of parameter O The curve appears to be a very high quality factor, however, for the purpose of energy dissipation the quality factor remains the same, namely, Q = 2.5. Therefore, the oscillation transients are characteristic of the low quality factor that the mechanical oscillator has, that is to say short, and therefore the response time is also short. In addition the oscillation is very stable, unlike the case of very high quality factors where temperature fluctuations and changes in the composition of the medium make the oscillation very unstable. The system described in WO-A-01/81857 makes it possible to increase the quality factor, and provides amplitude curves with respect to the frequency of the very narrow excitation signal, but suffers from the presence of long transients and oscillation instabilities. An example of a GA (φ) function suitable for the invention is: GA = B exp (-C without ² (φ-φ _r ))

More generally, the function GA = B exp (-C without ⁿ (φ-φ _r )), in which n can be 1, 2, 3, ...

Figure 14 shows the experimental results of the control system represented in Figure 11. The excitation force (F) is composed, in this case, of a sinusoidal feedback component F ₂ whose amplitude is GA, which has a maximum accused approximately at the resonant frequency. In this case, the chosen GA function is the same as in examples 12 and 13 except a constant component. Thus GA = GAo + B exp (-C without ² ((φ-φ _r )). GA has a maximum at approximately the resonant frequency, for which the measured offset is φ _r . The constant component of the amplitude, GA ₀ , it provides a sinusoidal excitation signal of constant amplitude that allows to measure the oscillation offset with low noise.This component is particularly important in cases in which the mechanical oscillator oscillates little with the generated excitation signals. Feedback force (F ₂ ) of Figures 12 and 13 can be very small for frequencies near but not equal to that of resonance, thus the oscillation signal (Z), Z = Acos (ωt-φ) + N , it can have a noise component (N) that prevents the correct measurement of the offset (φ), and therefore the control system may not function properly.With the inclusion of component GA ₀ , the mechanical oscillator can be oscillated with an amplitude that allows the correct measurement of l offset of the swing. In diagram (a) it is represents the amplitude of the cantilever with respect to the frequency of the exciter signal in the absence of control system and for the control system described with values of parameter C = 10 and C = 100. The values of GA ₀ and B are 0.05 and 3 V respectively. The resonance frequency and the elastic constant of the cantilever are approximately 18.93 kHz and 0.06 N / m respectively. Depending on the value of C is higher, a narrower maximum is obtained at the resonant frequency. Diagram (b) shows a very narrow maximum obtained with C = 1000.

Figure 15 shows other experimental results of the amplitude with respect to the excitation frequency, obtained with the experimental system represented in Figure 11, and in which the GA function is the same as that presented in Figure 14. In this example the amplitude is calibrated in angstroms (A °). The mechanical oscillator is a microcantilever for microscopy of atomic forces, which has been coated on both sides with a thin layer of 25 nm thick cobalt by thermal evaporation. This allows it to be excited by a sinusoidal magnetic field over time, which is produced by a coil placed next to the microcantilever. The bandwidth, defined by the frequencies at which the amplitude is half of its maximum value (which is reached at a frequency close to that of resonance) is 560 Hz for when no control is applied (C = 0), and decreases to 84 and 14 Hz for C equal 10 and 300, respectively. This control system allows to reduce the width of the resonance peak without necessarily increasing the amplitude of the oscillation, and therefore it is possible to work with systems in which the amplitude of the oscillator is of the order of 0.1 nm as shown here. The effect of C on bandwidth can be analyzed in a simple way if some simplifications are made. The amplitude of the microcantilever can be approximated as A (f) = X (f) GA, where X (f) is the ratio between amplitude and excitation force of a harmonic oscillator, and f is the excitation frequency. For sufficiently high C values, X (f) is approximately X (f ₀ ), where f ₀ is approximately the resonant frequency. This is because the variation of X as a function of f is approximately negligible with respect to the exponential variation of GA for frequencies close to that of resonance. If we assume that the cosine of the offset is approximately 2Q (ff ₀ ) / fo, for frequencies close to that of resonance, we obtain that the bandwidth is 0.42 f ₀ / (G ^1/2 Q), approximately.

Figure 16 shows the average value and the mean square deviation of the amplitude as a function of the excitation frequency, without active control (a) and with control active (b), using the same experimental system of Figure 15 and described in the previous paragraph, for C values equal to zero (without control), 10 and 300. The mean square deviation of the cantilever amplitude has been calculated at from 50 measurements for each frequency value. As in any active oscillation control system of the mechanical oscillator, the application of the control entails an increase in the noise of the cantilever movement signal, since it is fed back as an excitation force. The amplified noise may come from the device for measuring the cantilever movement, and the Brownian movement due to the thermal coupling between the cantilever and the surrounding environment. Figure 15a shows the amplitude and its noise as a function of the frequency without the active control of the excitation. The noise is mainly distributed around the resonance frequency, indicating that the predominant source of the noise is the Brownian movement of the cantilever. In fact, the cantilever behaves like a harmonic oscillator, which responds to the exciting force and also to the thermal forces of random collision whose spectral density is uniform. Given a measurement bandwidth (B), the magnitude of the thermal force can be approximated as δF _th = (4kk _B T / 2πQ B / f ₀ ) ^1/2 , where k is the cantilever elastic constant, k _B is the Boltsmann constant and T is the temperature. Thus, the average value and the average quadratic value of the amplitude are the product of the oscillator transfer function module (X) and the excitation force and δF _t respectively. The amplitude noise shows a more complex behavior when the control system is applied (fig. 15b). The noise is not significantly increased near the resonance frequency and exhibits two maximums when the amplitude drops around 40% of its maximum value, which reaches an excitation frequency close to that of the resonance. Since the excitation force (when the control system is applied) depends on the offset of the cantilever's oscillation with respect to the excitation force, there are two sources of noise in the amplitude, one is due to the thermal forces (which produced the Brownian movement of the Cantilever without control system), and the other comes from the noise of the oscillation phase. The amplitude is A (f) = X (f) (GA ₀ + Bexp (-C without ² (φ-φ _r ))), thus, the amplitude noise can be separated into two terms, δA = X ( f) δF _th + (dA / dφ) δφ. Since the main source of noise is the Brownian movement of the cantilever, the δφ phase fluctuation is produced by the non-coherent thermal forces δF _lh , which act equally in phase and quadrature with respect to the excitation force. Thus, δφ is approximately equal to the quotient between δF _th and the amplitude of the excitation force. Therefore, amplification of amplitude noise can be approximated as:

δA _m - δA _off 2CJcos φ sin

where δA _on , _off is the amplitude noise with and without oscillation control, respectively. It has been plunged that the resonance offset is 90 degrees. The numerator of this equation is zero at resonance and increases approximately linearly with (ff ₀ ) / foy C near the resonance. However, the denominator shows a minimum in resonance, and grows approximately exponentially with the square of (ff _o ) / fo and C near the resonance. The combination of these dependencies give rise to two symmetrical maximums on both sides of the resonance peak. More interesting, the increase in noise due to feedback of the excitation force is a function of C and GA ₀ / B. Thus, the signal-to-noise ratio can be modified by adjusting GA ₀ and B (for a given value of C that first determines the bandwidth of the response amplitude).

Figure 17 shows the amplitude (a) and its noise (b) as a function of frequency. The experimental system is the same as described for Figures 16 and 17 in the last two paragraphs. To check the noise model described in the last paragraph, the amplitude and its noise are measured for a predetermined value of C = 100, and different values of GA ₀ and B. Specifically, the results in Figure 17 are for GA ₀ / B equal to 0.25 and 2.5, keeping the total excitation force constant (GA ₀ + B). For higher values of the GA ₀ / B ratio there is a significant reduction in noise along with a slight widening of the amplitude peak. The height of the noise peaks on both sides of the resonance frequency decreases about 4.5 times, and its width is also reduced. In another experiment, the amplitude noise approximately does not change for different values of F ₀ and Fn, keeping the ratio between them constant. This is in accordance with the noise model produced with this control system described in the last paragraph. The noise can be reduced by increasing the GA ₀ / B ratio, and the signal-to-noise ratio can be improved by increasing the amount of feedback (B) while maintaining constant the relationship between the two excitation forces. The materials, size, shape and arrangement of the elements will be subject to variation, provided that this does not imply an alteration of the basic concept of the invention.

Throughout the present description and claims the word "comprises" and variations thereof, as "comprising", is not intended to exclude other steps or components.

Claims

1. A control device for an excitation signal of a resonant mechanical oscillator element excited by said excitation signal (F), the control device comprising: means for receiving a signal representative of the oscillation (Z) of the oscillating element (3); means for generating a feedback component (F ₂ ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z); the excitation signal comprising at least said feedback component (F ₂ ) and the excitation signal having an excitation frequency (ω); characterized in that the control device further comprises means for determining a gap (φ) between the signal representative of the oscillation (Z) of the oscillating element and the feedback component (F ₂ ); and because the means of generating a feedback component (F ₂ ) are configured so that the feedback component (F ₂ ) has an amplitude (GA) that is a function of said offset (φ).

2. A device according to claim 1, characterized in that said amplitude has a maximum at a offset (φ) corresponding to a frequency close to the resonant frequency of the oscillating element.

3. A device according to claim 1, characterized in that said amplitude has a maximum at a offset (φ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element.

4. A device according to claim 1, characterized in that said amplitude (GA) has a maximum when the offset (φ) is a determined offset.

5. A device according to any of the preceding claims, characterized in that the excitation signal (F) is composed of the feedback component (F ₂ ).

6. A device according to any of claims 1-4, characterized in that the excitation signal (F) comprises the feedback component (F ₂ ) and a base component (Fi).

7. A device according to claim 6, characterized in that the base component (Fi) is a signal with a fixed excitation frequency (ω) and with a fixed amplitude and because the feedback component (F ₂ ) is a signal with the same excitation frequency (ω) and is out of phase +90 ° or -90 ° with respect to the base component (F ^.

8. A device according to any of the preceding claims, characterized in that it comprises means of modifying the excitation frequency (ω) as a function of the signal representative of the oscillation (Z) so as to maintain a determined offset (φ) between the representative signal of the oscillation (Z) and the feedback component (F ₂ ).

9. A device according to claim 8, characterized in that said determined offset is an offset corresponding to the oscillation at resonance of the oscillating element, so that the oscillating element is kept oscillating at resonance.

10. A device according to any of the preceding claims, characterized in that it comprises means of modifying the excitation frequency (ω) as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillator element.

11. A device according to any of the preceding claims, characterized in that the amplitude (GA) of the feedback component (F ₂ ) is a function of both the offset (φ) between the representative signal of the oscillation (Z) and the component of feedback (F ₂ ) as of the amplitude of the signal representative of the oscillation (Z).

12. A device according to any of the preceding claims, characterized in that the means for receiving a signal representative of the oscillation (Z) are associated with a sensor that detects a signal directly related to the oscillation of the oscillating element.

13. A device according to any of the preceding claims, characterized in that it includes a pass-band filter at the excitation frequency (ω) to filter the signal representative of the oscillation (Z).

14. A device according to any of the preceding claims, characterized in that it is constituted by a processing device with a data acquisition card (12), so that: the data acquisition card comprises the means of receiving a representative signal of the oscillation (Z) of the oscillating element; the processor device comprises the means of generating the feedback component (F ₂ ); and the data acquisition card comprises an output for the feedback component (F ₂ ).

15. A device according to claim 14, characterized in that the processor device is a digital processor device.

16. A measuring device, comprising: means for generating an excitation signal (F); a resonant mechanical oscillator element; coupling means of the excitation signal to the resonant mechanical oscillator element so that the excitation signal induces an oscillation in said element; a detector device comprising means of generating a signal representative of the oscillation (Z) of the oscillating element; means of reading and interpretation of the signal representative of the oscillation

(Z); characterized in that the excitation signal generating means includes a control device according to any of claims 1-15.

17. A device according to claim 16, characterized in that the oscillating element is a micro lever.

18. A device according to claim 17, characterized in that the micro lever is provided with a tip.

19. A method for controlling the excitation signal of a resonant mechanical oscillator element excited by said excitation signal (F), the method comprising the steps of: receiving a signal representative of the oscillation (Z) of the oscillating element; generating a feedback component (F ₂ ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z), the excitation signal comprising at least , said feedback component (F ₂ ) and the excitation signal having an excitation frequency (ω); characterized in that a lag (φ) is determined between the signal representing the oscillation (Z) of the oscillating element and the feedback component (F ₂ ); and because the feedback component (F ₂ ) is generated so that the feedback component (F ₂ ) has an amplitude (GA) that is a function of said offset

(φ).

20. A method according to claim 19, characterized in that said amplitude has a maximum at a offset (φ) corresponding to a frequency close to the resonant frequency of the oscillating element.

21. A method according to claim 19, characterized in that said amplitude has a maximum at a offset (φ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element.

22. A method according to claim 19, characterized in that said amplitude (GA) has a maximum when the offset (φ) is a determined offset.

23. A method according to any of claims 19-22, characterized in that the excitation signal (F) is composed of the feedback component (F ₂ ).

24. A method according to any of claims 19-22, characterized in that the excitation signal (F) is generated by the addition of at least the feedback component (F ₂ ) and a base component (F ^.

25. A method according to claim 24, characterized in that as a base component (F ^ a signal with a fixed excitation frequency (ω) and with a fixed amplitude is chosen and because as a feedback component (F ₂ ) a signal is chosen with the same excitation frequency (ω) and that it is offset + 90 ° or -90 ° with respect to the base component (F ^.

26.- A method according to any of claims 19-25, characterized in that the excitation frequency (ω) is modified as a function of the signal representative of the oscillation (Z) so as to maintain a determined offset (φ) between the representative signal of the oscillation (Z) and the feedback component (F ₂ ).

27. A method according to claim 26, characterized in that said determined offset is an offset corresponding to resonance oscillation of the oscillating element, so that the oscillating element is kept oscillating at resonance.

28. A method according to any of claims 19-27, characterized in that the excitation frequency (ω) is modified as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillator element.

29. A method according to any of claims 19-28, characterized in that the amplitude (GA) of the feedback component (F ₂ ) is a function of both the offset (φ) between the signal representative of the oscillation (Z) and the feedback component (F ₂ ) as of the amplitude of the signal representative of the oscillation (Z).

30. A method according to any of claims 19-29, characterized in that the signal representative of the oscillation (Z) is received through a sensor that detects a signal directly related to the oscillation of the oscillating element.

31. A method according to any of claims 19-30, characterized in that the representative signal of the oscillation (Z) is filtered with a pass-band filter at the excitation frequency (ω).

32. A method according to any of claims 19-31, characterized in that the feedback component (F ₂ ) is generated with a processing device.

33.- A method for carrying out measurements on an object, characterized in that it comprises the steps of: locating the object in relation to the oscillating element of the device according to any of claims 16-18, so that object characteristics affect the oscillation of the object. oscillating element; measure at least one characteristic related to the oscillation of the resonant element; and interpret the result of said measurement.

34. A method according to claim 33, characterized in that the object is located in the vicinity of the oscillating element.

35. A method according to claim 33, characterized in that the object is placed in contact with the oscillating element, so that changes in the constitution of the object affect the resonance frequency of the oscillating element.

36. A method according to any of claims 33-35, characterized in that both the object and the oscillating element are immersed in a liquid.

37. A method according to any of claims 33-35, characterized in that the object is a liquid.

38. A method according to any of claims 33-37, characterized in that the object comprises a biological substance.

39. A method according to any of claims 33-37, characterized in that the object comprises a chemical substance.

40. A method according to any of claims 33-36, characterized in that the object comprises a solid surface.

41. A computer program, characterized in that it comprises program code means for performing all the steps defined in any of claims 19-32, when the program is executed on a computer.

42.- A storage device comprising means for storing at least one computer program, characterized in that it contains a program stored in accordance with claim 41.