A force measurement apparatus and method

Abstract

According to an example aspect of the present invention, there is provided an apparatus comprising: an elastic element having a spring constant; and a confocal chromatic sensor configured to optically connect to a surface of the elastic element in order to measure the displacement of the surface caused by a force.

Description

A FORCE MEASUREMENT APPARATUS AND METHODFIELD

[0001] The present disclosure relates to force measurements as well as devices and methods related thereto.BACKGROUND

[0002] Measuring forces is needed in many applications in research and industry, for example. For small forces, such as forces in the micro-newton range, the techniques are usually based on micro-electromechanical system (MEMS) based sensors or laser interferometry. Atomic force microscopy (AFM) may be used, for example, to detect surface contours using a cantilever. However, due to the working principle of AFM, a calibration of the AFM cantilever orientation and / or position is needed, and the lateral surface area for measurement is rather small, for example, 1 mm by 1 mm, millimeters. Moreover, due to their small-size, such devices might not necessarily be durable. As such, there is a need for a robust, and durable devices and methods for measuring forces, such as microscopic forces in the micro-newton range or in the nano-newton range.SUMMARY OF THE INVENTION

[0003] The invention is defined by the features of the independent claims. Some specific embodiments are defined in the dependent claims.

[0004] According to a first aspect of the present invention, there is provided an apparatus comprising: an elastic element having a spring constant; and a confocal chromatic sensor configured to optically connect to a surface of the elastic element in order to measure the displacement of the surface caused by a force.

[0005] According to an aspect, the elastic element is a cantilever. In a further aspect, the cantilever comprises a first end portion being non-fixed and a second end portion being fixed to a mount. In a further aspect the first end portion and the second end portion are connected via a first strip and a second strip, wherein the first end portion, the second end portion, the first strip and the second strip delimit an elongated hole between the first end portion and the second end portion

[0006] According to a second aspect of the present invention, there is provided a method comprising: providing an elastic element having a spring constant; directing a confocal chromatic beam of light on a surface of the elastic element; and measuring, based on at least one wavelength of reflected light, displacement of the surface caused by a force.

[0007] According to a third aspect of the present invention, there is provided a method for obtaining a spring constant, the method comprising: providing an elastic element; applying a pre-defined force on the elastic element, thereby causing a displacement of a surface of the elastic element; detecting, with a confocal chromatic sensor, the displacement of the surface of the elastic element; and calculating, based on the pre-defined force and the displacement of the surface of the elastic element, the spring constant of the elastic element.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1A, IB, 2A, 2B, 3A, 3B, 4A & 4B illustrate apparatuses according to at least some embodiments;

[0009] FIG. 5A & 5B illustrate an example of an elastic element according to at least some embodiments;

[0010] FIG. 6A & 6B illustrate an example of an elastic element according to at least some embodiments;

[0011] FIG. 7 illustrates an example measurement capable of supporting at least some embodiments;

[0012] FIG. 8A, 8B & 8C illustrate example measurements with apparatuses according to at least some embodiments;

[0013] FIG. 9A & 9B illustrates a mount capable of supporting at least some embodiments;

[0014] FIG. 10A, 10B & 10C illustrate a method according to at least some embodiments;

[0015] FIG. 11, 12 & 13 illustrate graphs capable of supporting at least some embodiments; and

[0016] FIG. 14A & 14B illustrates examples of an elastic elements capable of supporting at least some embodiments.EMBODIMENTS

[0017] Confocal chromatic sensing provides distance information based on dispersion of light, the dispersed light having a plurality of wavelengths having different focal planes from one another. The reflection of a wavelength of the plurality of wavelengths is therefore dependent on the focal plane of the wavelength. In other words, distance of an object is determined based on the spectral information of a reflected wavelength or plurality thereof. A confocal chromatic sensor is configured to emit light at different wavelengths, said wavelengths having a different focal plane and / or focus point from one another. Moreover, the confocal chromatic sensor is configured to measure reflected wavelengths of light, reflected from a surface, providing, based on wavelength information, distance between the confocal chromatic sensor and said surface.

[0018] The term “displacement” is to be understood as an action of moving or relocating an object from its place or position, and / or the amount by which an object is moved from its place or position. Such a displacement may be depicted as a distance, for example in millimeters. The direction to which a displacement occurs may be included in the displacement. Thus, displacement may be a real number or a vector, for example. The term “deflection” is to be understood as a change in direction or course of an object, such as a displacement of a cantilever or part thereof. In at least some embodiments, displacement is denoted by “Ax” or “5”.

[0019] As used in the context of the present disclosure, the term “hole” is to be understood as an absence of material delimited by a surface of a material object or plurality thereof. For example, a material object, such as a cantilever or parts thereof, may have a hole such that said cantilever and structures thereof define said hole. A hole may also be known as a “cut-out”. A “cut-out” is to be understood as a hole not necessarily limited by method of manufacture thereof. In other words, in at least some embodiments, a cut-out is obtained in other means than “cutting out” a part of a material object, for example, using additive manufacturing. In at least some other embodiments, the cut-out is obtained, for example, by cutting, such as laser-cutting.

[0020] The embodiments of the present disclosure provide several advantages. The wavelength-dependent distance measurements provide results without the need for a preliminary calibration of, for example, positioning dependent on intensity or wavelength of light. For example, atomic force microscope, AFM, utilizes a laser -based detection and therefore a baseline for AFM cantilever detection is needed in order to deduce deflections of the AFM cantilever and the reflected laser beam. Conversely, as confocal chromatic sensing is based on the optical design of the instrument which provides wavelengths having different focal planes, no need for such a calibration is needed. As such, at least some embodiments have an advantage over laser interferometry as the chromatic confocal sensor provides the absolute position and is also more robust to measuring tilted surfaces, which is beneficial for deflection measurements, for example, deflection of a cantilever and displacement of a surface thereof.

[0021] In accordance with the present disclosure, there is provided an apparatus comprising: an elastic element having a spring constant, and a confocal chromatic sensor configured to optically connect to a surface of the elastic element in order to measure the displacement of the surface caused by a force. Such a force may be gravity, electric force, magnetic force, pressure, friction, stiction, adhesion, vibration, drag, or a combination thereof, for example.

[0022] An “elastic element” in accordance with the present disclosure refers to an object or part thereof, that after application of a force, is arranged to return to the shape and / or position that said object had prior to the application of said force. An elastic element may be a helical coil, a leaf spring or a cantilever, for example. Elasticity is to be understood as a capability for an object or material to be able to resume its shape prior to application of a force. The elastic element may be defined at least in part by its spring constant. A “spring constant”, k, is a characteristic of an elastic element defining stiffness of said elastic element. In at least some embodiments, the spring constant of the elastic element is from 0.0001 to 1000 N / m, from 0.0054 N / m to 0.7 N / m, or from 0.01 to 1 N / m, newton per meter.

[0023] In at least some embodiments, the elastic element comprises at least one of: metal, plastic or ceramic. In at least some embodiments, the elastic element comprises a ceramic, for example glass, such as Borosilicate glass. In at least some embodiments, the elastic element comprises plastic, such as polylactic acid, PLA, nylon (a polyamide), acrylonitrile butadiene styrene, ABS or polycarbonate PC. In at least some embodiments,the elastic element comprises metal, such as at least one of: titanium, Ti, copper, Cu, or aluminium, Al. In at least some embodiments, the elastic element comprises titanium, Ti. In at least some embodiments, the elastic element comprises at least one of: titanium, copper, 4130 steel, 1080 spring steel, copper or glass.

[0024] The term “to optically connect” is to be understood such that the confocal chromatic sensor may operate such that at least part of the emitted photons of the confocal chromatic sensor are to be reflected back to said confocal chromatic sensor. In other words, a surface of an elastic element is configured to at least reflect at least part of the photons emitted thereto.

[0025] In at least some embodiments, at least part of the surface of the elastic element, via which confocal chromatic sensor is configured to optically connect, comprises a reflective surface. The reflectance of the reflective surface, may be for example, at least 10 % reflection of the received light, or at least 5% reflection of the received light. In at least some embodiments, reflective surface is smooth and / or reflective such that 40 % of the received light is reflected. In at least some embodiments, at least part of the surface via which the elastic element and confocal chromatic sensor are optically connected is polished so as to provide a reflective surface at least on a part of the surface of the elastic element.

[0026] Example of an apparatus 100 according to at least some embodiments is illustrated in FIG. 1A and FIG. IB. In FIG. 1A, an elastic element 110 having a spring constant k is illustrated. The elastic element 110 comprises a surface 110a to which the confocal chromatic sensor 120 is configured to optically connect. During operation, such as during a force measurement, the surface 110a of the elastic element may be displaced because of an applied force, as is illustrated in FIG. IB. The displacement Ax therefore describes the difference in position of the surface 110a at different stages (and / or time points), for example, between stages illustrated in FIG. 1A and FIG. IB. The displacement may be derived from wavelengths 121 having different focal planes, which are reflected from the surface 110a and received by the confocal chromatic sensor 120.

[0027] In at least some embodiments, the apparatus further comprises means for calculating the force applied to the elastic element, based on at least the spring constant and the measured displacement. In at least some embodiments, the apparatus comprises a computing device configured to calculate the force applied to the elastic element, based on at least the spring constant and the measured displacement.

[0028] An example of an apparatus 200 comprising an elastic element 210 having a spring constant k is illustrated in FIG. 2A and 2B. The elastic element 210 of FIG. 2A and 2B is a helical coil. The elastic element 210 comprises a surface 210a to which a confocal chromatic sensor 220 is configured to optically connect. As can be appreciated from the figures, when a force, such as a force inflicted by a mass 230 of FIG. 2B, is applied to the elastic element 210, the surface displaces a distance (i.e., a displacement Ax). As the surface displaces from the position of FIG. 2A to position of FIG. 2B, the displacement Ax may be obtained via the change in distance of the confocal chromatic sensor 220 and the surface 210a based on the focal planes of the employed wavelengths 221.

[0029] Using a measured displacement Ax and a spring constant k of the elastic element, a force F applied to the elastic element or part thereof may be calculated, for example using F= kAx. As such, the apparatus may be configured to measure a force applied to an object based on at least the spring constant of an elastic element and a measured displacement of the elastic element surface with respect to the confocal chromatic sensor.

[0030] An example of an elastic element is a cantilever. As used in the context of the present disclosure, the term “cantilever” is to be understood as a projecting structure that is supported (i.e., fixed) at one end and said projecting structure is un-supported (i.e., nonfixed) at the other end. In other words, a cantilever is an elongated structure extending from the fixed end to the non-fixed end. A cantilever may extend horizontally, for example. In accordance with the present disclosure there is provided an apparatus comprising: a cantilever having a spring constant; and a confocal chromatic sensor configured to optically connect to a surface of the cantilever in order to measure the displacement of the surface caused by a force.

[0031] In at least some embodiments, the cantilever has a rectangular or substantially rectangular cross-section perpendicular to the dimension to which said cantilever is elongated.

[0032] FIG. 3A and 3B illustrate an apparatus 300, wherein a cantilever 310 is the elastic element. Said cantilever 310 has a non-fixed end 311 and a fixed end 312. The cantilever 310 is attached to a mount 350 thereby fixing, or attaching, the fixed end 312. A confocal chromatic sensor 320 is configured to be optically connected to a surface 310a of the cantilever 310. The confocal chromatic sensor is configured to emit wavelengths 321 having different focal planes. An illustrative example of a graph 340a is also presented inFIG. 3 A, said graph 340a illustrating wavelengths 321 detected by the confocal chromatic sensor 320. Based on at least the reflected light, the position of the cantilever 310 surface 310a with respect to the confocal chromatic sensor 320 is calculated.

[0033] In FIG. 3B, an example displacement Ax is illustrated. Similarly to FIG. 3A, an illustrative example of a graph 340b is presented in FIG. 3B. Based on the wavelengths reflected by the surface of the cantilever and wavelengths detected by the confocal chromatic sensor 320, the position and / or distance of the cantilever 310 surface 310a with respect to the confocal chromatic sensor 320 may be calculated. Therefore, based on a force inflicted on the cantilever 310, a displacement Ax may be calculated based on the measured spectrum of wavelengths, such as the example illustrations of wavelength spectra in graphs 340a and 340b of FIG. 3 A and 3B, respectively.

[0034] In at least some embodiments, a force F applied to the elastic element, such as a cantilever, is calculated based at least on the displacement Ax, as measured using a confocal chromatic sensor, and the spring constant k of the elastic element, for example, using Hooke’s law and equation F=kAx.

[0035] At least some of the embodiments are suitable for measuring a force. Such embodiments may use a confocal chromatic displacement sensor for measuring cantilever deflection. The confocal chromatic sensor offers the best resolution for the deflection measurements and thus yields very good force resolution.

[0036] The confocal chromatic technology is based on dispersion of white light that causes different backscattering spectrum for different focal planes. The technology is utilized in the industry mainly for rapid and accurate product quality assessment on the production lines. This can be, for example, surface roughness or thickness measurements. In at least some embodiments, this technology is used to measure cantilever deflection with sub-micron accuracy in force sensing and mass measurement applications. The cantilever material and geometry can be tuned so that its spring constant matches the desired force resolution. In at least some embodiments, a material suitable for the force sensor cantilever comprises 0.05 mm thick titanium sheet, which should yield force resolution down to nanonewton level.

[0037] FIG. 4A and 4B illustrate schematic examples of the working principles of a force sensor 400a and a mass balance 400b setup, respectively.

[0038] In at least some embodiments, a force sensor is used for adhesion measurements with scanning droplet adhesion microscope, SDAM. At least such embodiments provide an advantage in that as the measured forces approach nano-newtons meaning that, for example, MEMS-based sensors start to struggle. SDAM is a technique for measuring a force, that comprises a force sensor having a liquid droplet probe and a multiaxis sample stage. The liquid droplet may comprise, for example, water. A sample is attached to the sample stage and brought into contact with the liquid droplet probe. The interaction between the sample and the probe is measured from which a force may be calculated.

[0039] FIG. 4A illustrates schematically parts of a scanning droplet adhesion microscope, SDAM, force sensor 400a. The output of the sensor 400a is the distance measurement that is given by a controller of the distance sensor, in other words, the confocal chromatic sensor 420. The chromatic confocal sensor 420 is connected to external hardware, such as a computing device, via an optical fibre 422. The lines 421 coming from the confocal probe 420 measuring head represent the dispersed light and the focal planes of different wavelengths.

[0040] In FIG. 4A a cantilever 410 is attached to a mount 450 said cantilever 410 thereby having a fixed-end 412 and a non-fixed end 411. A confocal chromatic sensor 420 is optically connected to the cantilever 410 via a surface 410a of the cantilever 410. The force sensor 400a according to FIG. 4A utilizes a SDAM probe head attached, or comprised in, the cantilever 410. In the SDAM probe head, a disk 416, such as a SU-8 disk, is attached to the cantilever 410.

[0041] In FIG. 4A, a sample 480 and a sample surface 480a thereof is also illustrated. The cantilever 410 has a disk, such as a SU-8 disk, attached thereto. Moreover, a droplet 418 of liquid is attached to said disk 416. The disk 416 and the droplet 418 form therefore a probe head for the apparatus 400a. As the apparatus 400a is suitable for SDAM measurements, surface properties, such as surface adhesion, may be deduced from the interaction between the droplet 418 and surface 480a of the sample 480 via a displacement of at least part of the cantilever and surface thereof. Thus, based on the deflection of the surface 410a of the cantilever 410, and measured wavelength distribution (i.e., a wavelength spectrum), a force caused by an interaction between the probe head and the sample 480 surface 480a may be calculated.

[0042] Measuring forces also allows for measuring weight, which means that a cantilever force sensor can be used for highly accurate mass measurements.

[0043] FIG. 4B illustrates an example of a mass balance setup 400b. In other words, an apparatus 400b suitable for measuring force caused by a mass 430 is illustrated. The confocal chromatic sensor 420 is configured to optically connect to a surface 410a of the cantilever 410. As with, FIG. 4A the cantilever 410 of FIG. 4B, has a fixed end 412 and a non-fixed end 411. Thus, based on the deflection of the cantilever 410, and measured wavelength distribution (i.e., a wavelength spectrum), the force inflicted by the mass 430 may be calculated.

[0044] There exist different cantilever-based force sensors and one typical example is the atomic force microscope, AFM. In at least some embodiments, the force sensor design differs from these (such as the AFM) in at least two ways: the force sensor uses a confocal chromatic sensor for distance measurements and the cantilever of such a force sensor is specially designed to render desired force resolution and is also easily tuneable for different applications.

[0045] The term “tuneable” is to be understood such that, based on at least the material of the elastic element and geometry of the elastic element, the elastic element may have a spring constant dependent on such geometric design and material decisions. In at least some embodiments, regarding a cantilever, such a “tuneable” property is at least to an extent dependent on dimensions of a hole (in other words, a “cut-out”) and the cantilever as well as material comprised in said cantilever. The proportion of hole dimensions to the cantilever dimensions may affect the spring constant, and therefore force resolution. In at least some embodiments, the hole is a rectangular hole or substantially rectangular hole

[0046] The confocal chromatic sensor has an advantage over laser interferometry in that the chromatic confocal sensor provides the absolute position and is also more robust to measuring tilted surfaces, which is important for deflection measurements.

[0047] FIG. 5 A and 5B illustrate an example of a force sensor cantilever 510 with a special geometry. It is noted that, a cantilever in accordance with the present disclosure may have a different geometry depending on the application and the embodiment.

[0048] In FIG. 5 A, a two-dimensional view of a cantilever 510 is illustrated while FIG. 5B provides a perspective view of said cantilever 510. The cantilever 510 is anelongated object. The cantilever 510 comprises a first end portion 511 and a second end portion 512, as well as a first strip 513 and a second strip 514. The first end portion 511, the second end 512, the first strip 513 and the second strip 514 define an elongated hole 515 elongated along the cantilever 510, said elongated hole being between the first end portion and the second end portion. A hole may also be known as a cut-out. The first end portion 511 comprises a surface 511a, to which a confocal chromatic sensor may be optically connectable.

[0049] In at least some embodiments, the outer dimensions of a cantilever are in the length direction (1) from 1 mm to 1000 mm, in the width direction (b) from 0.5 mm to 500 mm and in the thickness direction (t) from 0.01 mm to 50 mm. In at least some embodiments, wherein the cantilever comprises a hole, the hole has dimensions such that said hole is in length direction (lc) from 1 mm to 999 mm, and in the width (bc) direction from 0.3 mm to 499 mm.

[0050] In at least some embodiments, the outer dimensions of a cantilever are in the length direction (1) from 10 mm to 200 mm, in the width direction (b) from 1 mm to 10 mm and in the thickness direction (t) from 0.5 mm to 5 mm. In at least some embodiments, wherein the cantilever comprises a hole, the hole has dimensions such that said hole is in length direction (lc) from 5 mm to 80 mm, and in the width (bc) direction from 2 mm to 6 mm said hole dimensions selected such that the respective dimension of the hole is smaller than the corresponding outer dimension of the cantilever. In an embodiment, the width (b) is less than 75 % of the length (1), such as less than 50 % of the length (1). In an embodiment, the width (bc) is 25-95 % of the width (b). In a further embodiment, both the numerical values and the percentage values apply to the cantilever.

[0051] In at least some embodiments, the thickness (t) of the cantilever is from 0.1 to 0.5 mm, such as 0.2 mm, the length (1) of the cantilever is from 50 mm to 100 mm, such as 65 mm, and the width (b) of the cantilever is from 1 mm to 5 mm, such as 2 mm. In at least some embodiments, such a cantilever comprises a hole, said hole having dimensions from 25 mm to 75 mm in length (lc), such as 50 mm, and from 1.2 mm to 1.6 mm in width (bc), such as 1.3 mm, said hole dimensions selected such that the respective dimension of the hole is smaller than the corresponding outer dimension of the cantilever.

[0052] A “strip” is to be understood as a narrow band of material. In at least some embodiments, a strip, such as the first strip and / or the second strip, has a length from 1 mmto 999 mm, a thickness from 0.01 mm to 50 mm, and a width from 0.1 mm to 499 mm. In at least some embodiments, the width of a strip, such as a first strip and / or a second strip is from 0.1 mm to 50 mm, or from 0.5 mm to 25 mm. The strip dimensions provide the benefit in that, said dimensions at least to an extent affect the spring constant of the elastic element, and therefore, the measurable displacement.

[0053] A hole 515, and dimensions thereof, in the cantilever 510 may affect the spring constant k of the cantilever 510, and therefore sensing properties of an apparatus comprising such a cantilever 510. As such a cantilever may be “tuneable” to different force-sensitivities via geometry and construction that in turn, affect the spring constant k.

[0054] A cantilever comprising a hole, such as the cantilever illustrated in FIG. 5A and 5B, provides the advantage at least in that the cantilever structure may be constructed such that it has a pre-determined spring constant or a spring constant in a pre-determined range. In other words, the spring constant is affected by the cantilever geometry, such as the hole dimensions and width of the first strip 513 and second strip 514. Material of the cantilever also affects the spring constant value, or range of spring constant values.

[0055] In at least some embodiments, a force sensor setup is part of a scanning droplet adhesion microscopy, SDAM, device. The force sensor setup may be implemented onto a SDAM device. A force sensor cantilever geometry may be made using a laser cutter. These cantilevers may be made from 0.2 mm thick copper sheet metal and thus render a high spring constant compared to 0.05 mm titanium cantilevers. Still, preliminary tests with these cantilevers show good sensitivity results. A measurement, where a droplet is brought to contact with aluminium sample surface and then pulled off is shown in FIG. 7.

[0056] In FIG. 7, a measured force as a function of time is presented. Therein, an adhesion measurement with a 0.2 mm thick cantilever having a spring constant of 2.21 N / m is illustrated. Said cantilever comprises copper and has a cut-out geometry, i.e., said cantilever has an elongated hole. A droplet of liquid having a final volume of 5 microliters, is grown on SU-8 disk of the cantilever, result of which is seen, in FIG. 7, as a linear increase in force staying constant until the droplet snaps into the aluminium surface at approximately 80 seconds (“Snap-in”). Then, the sample stage is stopped, and pulling off the droplet is started (“Pull-off’). As the droplet detaches, at approximately 10 seconds, oscillations are observed. Thus, a cantilever design according to at least some embodiments of the presentdisclosure shows a promising force resolution because the mass (or weight) of a 5 -micro liter droplet is detectable.

[0057] In at least some embodiments, the SDAM force sensor is a droplet probe that comprises a cantilever with a SU-8 disk attached to said cantilever. The SU-8 disk may serve as a droplet holder. In other words, a droplet may be attached to said SU-8 disk, for example. Example components of a force sensor comprising an SU-8 disk is illustrated in FIG. 4A. The cantilever 410 is a main component of the sensor as its spring constant k and dynamic properties are important for the sensor quality. Dynamic properties include damping properties, for example. The chromatic confocal sensor (such as Micro-Epsilon confocal DT IFS2405-1 with 2451 controller) provides a plurality of wavelengths, and serves as a data output by receiving reflected wavelengths. In other words, the data obtained and output comprises plurality of wavelengths reflected from a surface of a cantilever. The distance sensor resolution combined with the cantilever properties defines the resolution of the force sensor.

[0058] Confocal displacement sensors may be used for contactless distance measurements in many applications. The confocal chromatic sensors have some advantages, such as safety and robustness against environment, compared to for example laser interferometry. The working principle of the sensor is based in part on dispersion of light and to confocal theory. The sensor may use an LED as a white light source. The white light is fed to the sensor head from the controller using an optical fibre. In the sensor head of the confocal chromatic sensor, a series of lenses focuses the beam to a small spot, for example, approximately 10 mm away from the sensor head of the confocal chromatic sensor. Due to dispersion of light, the different wavelengths have their focus point at different focal planes. When light scatters from the surface, the backscattered spectrum has an intensity distribution that is dependent on the wavelength focus points. This is the idea of the chromatic confocal theory. Analogy to confocal microscope may be made wherein the image is produced from objects that are on the focal plane (which usually has a small depth of field). For example, on the upper limit of the 1 mm measuring range, the backscattered spectrum is condensed to the long wavelength (red) spectrum. The spectrum may be analyzed in a controller of the confocal sensor. The signal may travel through an optical fibre from the confocal sensor to said controller. Initial testing has shown that the digital output reduces the noise notably compared to analog output paired with a 16-bit analog-to-digital converter. The Ethernet outputs data at a sample rate of 10 kHz, which can later be down-sampled in the controlsoftware. The fact that the confocal sensor uses dispersion allows it to reach a 28 nm resolution. This would not be possible with classical optics methods as there the wavelength of the white light (400-700 nm) would be the resolution limit. Also, the safety aspect of the confocal sensor is based on the fact that it uses white light and not a powerful laser.

[0059] In at least some embodiments, the resolution for the confocal displacement sensor is around ±0.1 pm, when measuring a distance to a static object and taking the standard deviation of the distance measurements. This means from Hooke’s law, P = k 8, where k is the cantilever spring constant, P is the force and 8 is the cantilever deflection, spring constant k of around 0.01 N / m is needed to reach a force resolution of 1 nN.

[0060] In at least some embodiments, the resolution for the confocal displacement sensor is ±1 nm, nanometers. Therefore, for a spring constant k of 0.01 N / m, a force resolution of 10 pN, piconewtons, may be obtained.

[0061] In at least some embodiments, the (force) resolution of the apparatus is less than 1 pN, micro-newton, or less than 1 nN, nano-newton. In at least some embodiments, such a force resolution is obtained with an elastic element having a spring constant from 0.0001 N / m to 1000 N / m, or from 0.005 N / m to 1 N / m.

[0062] As mentioned, the cantilever for a force sensor in accordance with at least some embodiments has a relatively low spring constant while still being able to tolerate noise from the environment (air flow and acoustic excitation) so that the noise level stays reasonable. The initial idea was to use a microscope glass slide, but inserting the material parameters of Borosilicate glass to analytical solution for k showed that rectangular cross-section glass slide could not easily reach the desired spring constant. This is why metallic cantilevers with cutouts were simulated.

[0063] After testing different cutout geometries, the rectangular cutout geometry, where a rectangular cantilever has an extruded rectangular cut in z-direction, was tested. At least some embodiments, wherein the elastic element is a cantilever, utilize a rectangular cutout. FIG. 5A and 5B visualize this geometry

[0064] Dynamic mode refers to a measurement mode wherein the displacement caused by the force is measured at at least two different time points. In at least some embodiments, the apparatus is configured to measure displacement in a dynamic mode. Moreover, the dynamic mode may comprise measuring oscillation of the elastic elementcaused by the force. The force may also be time-dependent, for example oscillate. Because oscillations of the elastic element caused by a force may continue, the elastic element, such as a cantilever, should have a suitable damping parameter.

[0065] When a structure having a low spring constant is used, minute or small forces may displace or deflect the structure. As such, although sensitive to small forces, the oscillations of the structure may hinder the force measurement, as the oscillations caused by a force continue for a prolonged time. Therefore, measures for damping the oscillations of the elastic element may be needed. In at least some embodiments, the damping may be reduced by applying means for reducing oscillations via a damping parameter from 0.01 1 / s to 10 000 1 / s, from 0.02 1 / s to 1 1 / s, or from 0.019 1 / s to 0.87 1 / s, one per second. In at least some embodiments wherein the elastic element is a cantilever, the damping may be obtained by having a cantilever comprising an off-set in the lengths of the first end portion (non-fixed end) and the second end portion (fixed end) of said cantilever. In other words, the length of the first end portion may be longer than the second end portion. In at least some embodiments, damping may be enhanced by a layered, or a “sandwich”, structure comprising a damping material, such as rubber. Examples of rubber include synthetic rubber. Synthetic rubbers include, for example, styrene-butadiene rubber, nitrile rubber and butyl rubber.

[0066] In at least some embodiments, the cutout of the cantilever is centered on y-axis and has a width of bcmm. The cutout length in x-direction is lc= (1 - 10) mm and has 2 mm offset from the fixed end of the cantilever. The reason for having unequal offset in at least some embodiments is that having more mass in the tip of the cantilever improves the damping. Also, in at least some embodiments, more material in the non-fixed end (i.e., first end portion) provides more options for attaching a probe head, such as an SU-8 disk at different locations and / or positions.

[0067] The spring constant in the cutout geometry of a cantilever is at least to an extent dependent on the dimensions of said cutout and cantilever. This means that the thickness t, length 1 and cutout dimensions bcand lcmay be important parameters as they influence the spring constant k. The tested thickness values were chosen according to commercially available sheet metal thicknesses and 60 mm was used as the starting point for the cantilever length 1. The cutout values were initially bc= 1.5 mm and lc= (1 - 10) mm and bcwas later optimized for fine-tuning the cantilever properties. It was chosen to keep the width b constantat 2 mm. The simulated cantilever materials were titanium, 6063 alloy, 4130 steel, 1080 steel and copper. For each material, the starting dimensions were (1 x b x t) = (60 mm x 2 mm x 0.1 mm) and (lcxbc) = (50 mm x 1,5 mm).

[0068] In addition to geometry optimization with parameters t, 1 and bc, the cantilever can also be tuned by adding a rubber layer that gives elastic damping and improves damping parameter A sandwich geometry with Ti-rubber-Ti layer structure is one option for this. FIG. 6A and FIG. 6B shows this sandwich structure. In at least some embodiments, a layered structure, such as a three-layered structure, for a cantilever comprises a metal-rubber-metal layer structure.

[0069] FIG. 6 A and FIG. 6B illustrate a cantilever 610 comprising a layered structure. Therein, a middle layer (a second layer) comprises a rubber material, whereas the “bottom layer” (first layer) and “top layer” (third layer) comprise metal. The first layer is on the second layer, and the second layer is on the third layer. FIG. 6B illustrates a close-up 690 of a region illustrated in FIG. 6A as a dashed region. The cantilever 610 comprises a cut-out 615 defined by a first end portion 611, second end portion 612, a first strip 613 and a second strip 614 of the cantilever 610. Regarding the first strip 613 and the second strip 614 shown in close-up 690 of FIG. 6B, the third layer 613c, 614c is on the second layer 613b, 614b, and the second layer 613b, 614b is on the first layer 613a, 614a. The first end portion 611 comprises a surface 611a to which a confocal chromatic sensor may be optically connectable.

[0070] To understand the properties of different cantilever materials and designs, the different options were simulated using COMSOL. The two types of solid mechanics simulations made were: Static simulations with a point load and time-dependent simulations with a ramp point load input. The static simulations were computationally lighter and thus they were used for optimizing cantilever dimensions. The time-dependent simulations, also known as dynamic mode simulations, provide information on the spring constant k and damping constant S, of the cantilever, which describe the resolution and the noise level of sensor.

[0071] For COMSOL simulations, the geometry was simplified from the model shown in FIG. 4A by modelling the droplet 418 and SU-8 disk 416 as a simple point load and considering that the clamped part (i.e., fixed-end) of the cantilever stays fixed. The point load assumption is well justified because the droplet 418 and the disk 416 have rotationalsymmetry around the z-axes and the load and cantilever width b are small, the bending in the y-direction may be negligible. The assumption of fixed clamped part (i.e., fixed to a mount) means that the cantilevers in simulations had fixed end at x = 0 and the cantilever length 1 was the length of the freely hanging part, also known as a non-fixed end. The point load location was assumed to be on the center line (y = 0) and 2 mm from the tip of the cantilever. The used materials from the COMSOL materials library were Ti Grade 1 [solid, annealed] for titanium, Aluminium 6063-T83 for aluminium, 4130 [solid, hardened and tempered] for 4130 steel, 1080 [solid, polished] for 1080 spring steel, copper [solid, polished] for copper and Borosilicate A for coverslip glass. Static simulations were performed by applying gravity and point load P and running the model. As these simulations were used to test and optimize multiple parameter combinations (1, t, bcand material), the workflow was automated using COMSOL LiveLink for MATLAB. This way the model geometry could be defined automatically and also the point load could be varied easily. The output was the deflection field z-component from the point load location w(l - 2) = 8. The point load P was varied for each set of parameters and a linear model was fitted to F(8) data to find the spring constant k.

[0072] For time-dependent simulations, the simulation duration was chosen to be 30 seconds with a time step of 0.01 seconds. The initial conditions for deflection field were set to zero, as the gravity component of the deflection was different for each cantilever. Therefore, the gravity was applied gradually. Otherwise, the simulation would not converge on the first time step due to gravity working as a step function-like load. Thus, the gravitational acceleration in the simulations was time-dependent as follows

[0073] The ramp input for the point load was chosen to be such that it goes from 0 pN to 1 pN in 3 seconds and then drops back to 0 pN for t < 0.2 mm cantilevers and for t > 0.2 mm levers the maximum was put to 10 pN. The ramp was chosen to start at t = 15 seconds as at that point agravity(t) has already reached steady value. For both time-dependent and static cases, the used mesh was COMSOL physics-controlled option with Extra fine element size option. This option had maximum element size of 2.1 mm, minimum size of 0.09 mm, maximum element growth rate 1.35, curvature factor 0.3 and resolution for narrow regions 0.85. For the final cantilever geometry, the mesh was manually refined to study the convergence.

[0074] FIG. 8A illustrates an example apparatus 800a at three different stages. The apparatus 800a comprises a cantilever 810 as the elastic element, said cantilever 810 comprising a probe head 818a. The confocal chromatic sensor 820 is optically connected to the cantilever 810 via confocal light 821 having a plurality of focal planes based on the wavelength. When a sample stage 880 is moved such that sample 881 is in contact with the probe head 818a, the surface properties of a sample 881 are measurable based on the displacement of the cantilever 810, said displacement being measurable with the confocal chromatic sensor 820. Surface properties of the sample 881 may be, for example, roughness of the surface of the sample 881, adhesion of the probe head 818a to the sample surface 881 and / or surface profile of the sample 881.

[0075] FIG. 8B illustrates an example apparatus 800b at three different stages. The apparatus 800b comprises a cantilever 810 as the elastic element, said cantilever 810 comprising a probe head 818b. Such a probe head 818b may comprise, tissues or cells, for example, thereby providing means for bio-adhesion measurements. The confocal chromatic sensor 820 is optically connected to the cantilever 810 via confocal light 821 having a plurality of focal planes based on the wavelength. When a sample stage 880 is arranged with respect to the cantilever such that sample 881 is in contact with the probe head 818b, the surface properties of a sample 881 are measurable based on the displacement of the surface of the cantilever 810, said displacement being measurable with the confocal chromatic sensor 820. Surface properties of the sample 881 may be, for example, roughness of the surface of the sample 881, adhesion of the probe head 818a to the sample 881 surface and / or surface profile of the sample 881.

[0076] FIG. 8C illustrates an example apparatus 800c comprising a cantilever 810 as the elastic element. As can be appreciated, the displacement of a surface of the cantilever, may be measured using a confocal chromatic sensor 820. Said displacement may be caused by a force, and in FIG. 8C said force is a gravitational force caused by a mass 830.

[0077] As can be appreciated, the elastic element design provides versatility in terms of measurement of force, such as mass measurement, or an adhesion (such as bio-adhesion) measurement. Depending on the embodiment, a different probe head, such as a probe head shown in FIG. 4A, 8A and 8B, may be utilized. Moreover, at least some embodiments may be utilized for lateral scanning of a surface of sample thereby providing information, forexample, at least one of: adhesion, stiffness, stiction, friction, or surface profile of the sample.

[0078] In accordance with the present disclosure, there is provided a method of manufacturing a cantilever, the method comprising: obtaining material, for example, in a form of a sheet; and forming, from the material, an elongated cantilever comprising a hole delimited by the first end, the second end, a first strip and a second strip. As such, a cantilever having a cut-out (i.e., a hole, such as an elongated hole) is provided. Such a cantilever has an advantage at least in that because the hole dimensions (i.e., cut-out dimensions) and cantilever outer dimensions may be chosen such that a suitable spring constant or ranges of spring constants is obtained for the cantilever.

[0079] In at least some embodiments, a cantilever in accordance with the present disclosure is manufactured using additive and / or subtractive manufacturing. Additive manufacturing, such as 3-D printing, may be used for manufacturing a cantilever, for example, using photopolymerization (e.g., UV resin manufacturing), or extrusion methods, such as fused deposition modelling, FDM, also known as fused filament fabrication, FFF.

[0080] In at least some embodiments, a cantilever is manufactured by laser cutting. A practical example of manufacture is as follows. A cantilever may be cut out of sheet metal using a laser cutter, such as a laser micro-machining system, LMS. LMS is a custom-made tool at Aalto Nanofab and allows cutting with a resolution of a few microns. The cantilever design may be given to LMS in .dxf format and in the LMS software the cutting is defined by hatching the cantilever outlines with 0.1 mm wide contour with spacing 0.02 mm. To reduce warping, the cut was performed stepwise so that the cutter made five repetition sets, after which the cut may be visually inspected and the need for extra repetitions was evaluated. The initial draft cantilevers were made from 0.2 mm thick copper sheet, which required four five-repetition sets (in total 20 repetitions) to cut through when using the full laser power (5 volts). The warping issue became even more pronounced for the titanium sheets with thicknesses of 0.05 mm and 0.127 mm, and the laser power was trimmed down to 10 % of the maximum (0.5 volts). This reduced warping, but the titanium sheets still twisted so much that the laser could no longer focus properly to cut. Thus, the copper levers were the only ones used for the experiments. The dimensions of those cantilevers are shown in Table 1. Reducing warping for the Ti sheets may be done, for example, using larger initialsheet size than the 50 x 50 mm sheets used here and using a cut-out aluminium block on top of the sheet as a weight and a cooling element.

[0081] Table 1 : The properties of the cantilevers that were used in the experiments. The "Cu rect" cantilever has no cutout so that it can be used to compare analytical, simulated and experimental spring constants. The length 1 here are actual ’free’ lengths measured after mounting.

[0082] In at least some embodiments, a cantilever may be fixed to a mount. FIG. 9A and FIG. 9B illustrate an example embodiment of a mount structures 950. The mount 950 has a designated slot 953 for the cantilever 910 and said mount 950 presses the cantilever 910 firmly between the top 952 and bottom 951 parts of the slot 953. Two 6 mm alignment pins 954a, 954b along with two M6 bolts make sure that the clamping force is uniform and that the twist of the mount may be prevented even though the cantilever 910 is only in a small part of the mount 950. FIG. 9B illustrates an example, wherein a cantilever 910 is attached to a mount 950 from the second end portion 912. The cantilever 910 is non-fixed from the first end portion 911. The cantilever 910 may be installed to the mount 950 by placing it on a 3D-printed holder 958a, 958b that aligns the cantilever 910 with a sample stage and then using the sample stage to position the cantilever 910 inside the mount and tightening the mount 950. This may ensure that the cantilever 910 is perpendicular to the mount 950 and optional rear-view camera (not shown) and optional parallel to the side-view camera (not shown).

[0083] In at least some embodiments, the mount comprises metal. In at least some embodiments, the bottom part 951 of a mount 950 comprises brass and the top part 952 comprises aluminium. The alignment pins 954a, 954b may comprise steel and may be fixed to the bottom 951 part with a H7 fit. The mount 950 may be designed to be mounted on a 25 mm aluminium profile using two bolts 955a, 955b and a notch 956 for alignment.

[0084] FIG. 10A, 10B and IOC illustrate at least some steps of a method for attaching a SU-8 disk 1016 to a cantilever 1010. In FIG. 10A, glue 1017 is dispensed from a dispenser 1018. In FIG. 10B, drop of UV-glue 1017, and an aligned SU-8 disk 1016 are shown. In FIG. 10C, the SU-8 disk 1016 is on the cantilever 1010 after placing said disk 1016 using a sample stage and curing the UV-glue with UV-light (a UV-light pen).

[0085] In at least some embodiments, a SU-8 disk may be attached to a cantilever as follows. The SU-8 disk is attached to the cantilever using UV glue, which ensures the joint’s flatness easier than double-sided tape. A small amount of glue is used in order to prevent said glue from propagating to the sides of the SU-8 disk. Otherwise, small amounts of the glue can dissolve to the droplet, which may contaminate the droplet.

[0086] The dispenser may be used to provide a small glue droplet to the desired location on the cantilever, example of which is illustrated in FIG. 10A. Therein a sideview of a cantilever 1010 and dispenser 1018 is illustrated. Since the UV glue has high viscosity, a large dispenser nozzle (such as BioFluidiX PipeJet 500-L) is used for dispensing the glue. After dispensing the glue (FIG. 10B), the SU-8 disk is brought to contact with the cantilever, example of which is illustrated in FIG. 10B and FIG. 10C. The UV glue is cured with a UV- light pen for approximately 2 minutes to establish a firm contact of the disk with the cantilever. FIG. 10C illustrates an established SU-8 disk 1016 on a cantilever 1010.

[0087] The static and dynamic COMSOL simulations may be used to find the optimal cantilever design in terms of geometry and material. Parameters, such as cantilever material, spring constants and damping parameters are presented in Table 2. From the table it may be observed that the static and dynamic simulations yield the same spring constant k except for the glass slide. From the spring constant results we see that with the same cut-out geometry, at least aluminium, titanium and copper seem to be the suitable candidates for reaching a 0.01 N / m spring constant. The last two titanium cantilevers in Table 2 have thickness that is easily available from standard laboratory equipment supplier and we see that actually the 0.05 mm thick Ti sheet provides even smaller spring constant than the desired spring constant.

[0088] In terms of the damping properties the 0.05 mm Ti cantilever is poor as thinner sheet thickness reduces the damping. Copper differs from the 0.1 mm thick sheets with k < 0.1 N / m by having the highest damping parameter S, of 0.22 1 / s. Though here it should be noted that the damping is mainly important in waiting the oscillation to settle. Suchoscillations may originate from dispensing the droplet and from pull-off events and here 10- 20 seconds is still acceptable time. Most of the COMSOL simulations had the step response oscillations damping out in that time. Furthermore, the simulations are made with empty SU- 8 disk, but when there is a droplet, it provides more mass to the cantilever and damps down the oscillations and changes the eigenfrequency of the system.

[0089] As the results in Table 2 suggested that 0.05 mm Ti sheet could provide low enough spring constant, it was used in geometry optimization. The varied parameter there was the cutout width bc. Running the static simulation with 76 different bcvalues ranging from 0.75 mm to 1.5 mm and varying the point load P allowed finding the spring constant as a function of bc. With 5 different values for P there were in total 380 simulations needed. The k(bc) results are shown in FIG. 11 and from there it may be observed that with cutout width bc= 1.3 mm the Ti 0.05 mm lever should achieve the desired spring constant. FIG. 11 illustrates a cut-out titanium cantilever spring constant with different cutout widths bc. As the results are simulated, there is numerical noise, but we can see that the general trend is that spring constant decreases as the cut-out width increases. This is logical as the cross- sectional area of the cut-out part, which is most of the cantilever length, gets smaller.

[0090] Table 2: Simulated spring constants k and damping parameters S, for different cantilevers from dynamic and static simulations. The static simulations had errors on the order 10-6 N / m or less for k. All cantilevers here have dimensions 1 = 60 mm, b = 2 mm, lc= 50 mm and bc= 1.5 mm. The thickness t is indicated in the cantilever type column.

[0091] One thing that the COMSOL simulations do not consider is the displacement limit Wmax between elastic and plastic deformation. This is not a problem if the cantilever displacement stays small, but it would be valuable information from the sensor properties perspective as the limit defines the force measuring range for the given cantilever. The limit Wmax can be experimentally tested with the SDAM setup as the sample stage can provide accurate displacement and cameras or the distance sensor can be used to observe the beginning of plastic deformation.

[0092] The force sensor noise and force resolution were tested with the evaporation experiment and the obtained force over time curve is shown in FIG. 12. In FIG. 12, a measured force Pm(t) and a calculated force Pc(t) from the evaporation experiment is illustrated. The image-analysis based calculation matches the measurement quite well, but a drift can be observed from the data. The inset in the figure shows the last 200 seconds of experiment and as can be observed, the calculated force is still over 0.3 pN, when the measured force can be negative due to noise. There the measured force is obtained with cantilever "Cu 0.2" and the calculated force is obtained with image analysis and volume computation. FIG. 12 shows that the measured force has quite much noise and a drift as the calculated force value is not in the center of the noise of the measured value throughout the whole experiment. The reason for this can be the drift of the distance sensor or difficulties in finding the correct baseline location in the volume calculation algorithm. Though, the fact that the difference is initially in positive and in the end negative suggests that the sensor drift is the most probable the cause. Thus, for very long scanning measurements, the force sensor should be recalibrated in between to remove the effect of the drift.

[0093] To determine the resolution of the force sensor with the cantilever "Cu 0.2" the absolute error between the calculated and measured force, |Pm_Pc|, was computed and it is shown in FIG. 13. In FIG. 13, absolute error between the measured and calculated force during the evaporation experiment is illustrated. The calculated value can be assumed to have notably smaller error than the measured one based on the accuracy of the calibration volume computation. The mean error is around 50 times larger than the error contribution from the distance sensor would suggest, which means that environment noises are significant.

[0094] From FIG. 13 we see that the average error is 0.2 pN, but there are also peaks nearly up to 2 pN. These peaks are likely due to environment noise as the evaporation experiment is fairly long (around 25 minutes) so there are for example people entering the lab and causing air-flows that can be seen in the sensor output. FIG. 13 also illustrates the sensor noise in the best case plotted with a dashed line. In this case the error would only come from the resolution of the distance sensor. This would correspond to resolution of 42 nN, but more sources of noise may be present. Thus, estimating from FIG. 13 suggests that the real resolution is around 0.5 pN as the force of interest has to be detectable from the noise.

[0095] On the other hand, one should note that these measurements were done without vibration isolation table and without having an enclosure for the setup. So the resolution of roughly 0.5 pN applies for the setup in the current state and will be significantly improved when the setup gets an enclosure and an active vibration isolation table. For further cantilever development such an approach may be needed as making a more sensitive cantilever makes sense, if the setup can be isolated so that the environment excitations are smaller than the distance sensor error.

[0096] As presented in at least some of the embodiments above, a spring constant may be obtained from, or approximated by, modelling the structure of the elastic element, such as a cantilever, using information on geometry and material. As such, the spring constant may be obtained by modelling the structure of the elastic element. Moreover, a spring constant for an elastic element, such as a cantilever, may also be obtained, for example, by applying a pre-determined force on the elastic element, measuring displacement of the surface of the elastic element, and calculating the spring constant of the elastic element based on the pre-determined force and the displacement of the surface, based on, for example, Hooke’s law.

[0097] An example of calibration and obtaining a spring constant for an elastic element is as follows. In order to obtain the spring constant, a known volume of liquid in the form of a droplet having a known density is applied on the elastic element in an apparatus, such as apparatus 100, 200, 300,400a, 400b, 800a, 800b or 800c, and the corresponding displacement of the surface of the elastic element is measured using confocal chromatic sensor. Then, based on the volume of the droplet and density of the liquid, a mass of the droplet, and thus, weight inflicted by the droplet, is calculated. Based on, for example,Hooke’s law, and equation k = F / Ax a spring constant k is obtained based on the displacement Ax of the surface of the elastic element and the force F applied to said elastic element.

[0098] FIG. 14A illustrates an example elastic element, said elastic element being a cantilever 1410a. The cantilever 1410a comprises a first end portion 1411 and a second end portion 1412 connected via a first strip 1413 and a second strip 1414, thereby defining an elongated hole 1415 between the first end portion 1413 and the second end portion 1414. A mesh structure may comprise at least one strand connecting the first strip and the second strip. As can be appreciated from FIG. 14A, a plurality of strands 1416a of a mesh structure 1416 connect the first strip 1413 and the second strip 1414 to one another. A mesh structure, may limit lateral motion of the cantilever, and thus provide rigidity to the structure. In at least some embodiments, the strand and / or the mesh comprises the same material as the cantilever.

[0099] In an embodiment, the cantilever is provided with sufficient lightness, elasticity and rigidity by means of a structure, wherein the cantilever comprises a first strip and a second strip such that the first strip and the second strip connect the first end portion and the second end portion. To provide rigidity, the cantilever further comprises at least one crossbar connecting the first strip to the second strip in an area between the first end portion and the second end portion. The number of crossbars may be for example one, two, three, four, five or more than five. In these embodiments, holes or openings are formed between the end portions and a crossbar. If the embodiment has at least two crossbars, at least one hole or opening is also formed between adjacent crossbars.

[0100] In an embodiment, the cantilever is provided with sufficient lightness, elasticity and rigidity by means of a structure, wherein the cantilever comprises at least two holes between the first end portion and the second end portion. In an embodiment, the cantilever has an elongated body connecting the first end portion and the second end portion and the holes area provided in the elongated body. The number of holes may be selected according to the desired properties of the cantilever. The number may be for example two, three, four, at least five or at least ten.

[0101] FIG. 14B illustrates an example elastic element, said elastic element being a cantilever 1410b. The cantilever 1410b comprises a first end portion 1411 and a second end portion 1412 connected via a first strip 1413 and a second strip 1414, thereby defining anelongated recess 1415b between the first end portion 1413 and the second end portion 1414. Such a recess 1415b, as shown in FIG. 14B as a region delimited by a dashed line, is therefore a cavity, or a depression in the cantilever 1410b. In other words, there is less material in the recess than in the surrounding cantilever structures. In at least some embodiments, the thickness (t) of the cantilever outside the recess is greater than the thickness in the recess (tr), that is, t > tr. The recess 1415b may provide rigidity in the lateral direction. In at least some embodiments, the recess 1415b comprises a mesh structure, for example similar to that presented in FIG. 14A.

[0102] In at least some embodiments, the environmental conditions, and / or medium in which the elastic element resides, may be for example, air and / or typical ambient conditions, such as standard temperature and pressure, STP. However, in at least some other embodiments, other medium may be used. For example, the medium may be liquid. In other words, at least part of the apparatus, for example the elastic element or part thereof, such as the probe head, may be immersed in liquid, for example underwater. In at least some embodiments, measurements may be made in microgravity, for example in space and / or in an artificial satellite.

[0103] It is to be understood that the embodiments of the invention disclosed are not limited to the particular structures, process steps, or materials disclosed herein, but are extended to equivalents thereof as would be recognized by those ordinarily skilled in the relevant arts. It should also be understood that terminology employed herein is used for the purpose of describing particular embodiments only and is not intended to be limiting.

[0104] Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment.

[0105] As used herein, a plurality of items, structural elements, compositional elements, and / or materials may be presented in a common list for convenience. However, these lists should be construed as though each member of the list is individually identified as a separate and unique member. Thus, no individual member of such list should be construed as a de facto equivalent of any other member of the same list solely based on theirpresentation in a common group without indications to the contrary. In addition, various embodiments and example of the present invention may be referred to herein along with alternatives for the various components thereof It is understood that such embodiments, examples, and alternatives are not to be construed as de facto equivalents of one another, but are to be considered as separate and autonomous representations of the present invention.

[0106] Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of lengths, widths, shapes, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.

[0107] While the forgoing examples are illustrative of the principles of the present invention in one or more particular applications, it will be apparent to those of ordinary skill in the art that numerous modifications in form, usage and details of implementation can be made without the exercise of inventive faculty, and without departing from the principles and concepts of the invention. Accordingly, it is not intended that the invention be limited, except as by the claims set forth below.

[0108] The verbs “to comprise” and “to include” are used in this document as open limitations that neither exclude nor require the existence of also un-recited features. The features recited in depending claims are mutually freely combinable unless otherwise explicitly stated. Furthermore, it is to be understood that the use of "a" or "an", i.e. a singular form, throughout this document does not exclude a plurality.INDUSTRIAL APPLICABILITY

[0109] At least some of the embodiments of the present disclosure find industrial applicability in the field of measuring and sensing of a force.ACRONYMS LISTAFM atomic force microscopyFFF fused filament fabricationFDM fused deposition modelling LED light emitting diodeLMS laser micro-machining systemMEMS micro-electromechanical systemPLA, polylactic acidABS acrylonitrile butadiene styrene PC polycarbonateSDAM scanning droplet adhesion microscopyREFERENCE SIGNS LIST

Claims

CLAIMS:

1. An apparatus for measuring a force comprising:- an elastic element having a spring constant; and- a confocal chromatic sensor configured to optically connect to a surface of the elastic element in order to measure the displacement of the surface caused by a force.

2. The apparatus according to claim 1, wherein the apparatus further comprises:- means for calculating the force applied to the elastic element, based on at least the spring constant and the measured displacement.

3. The apparatus according to claim 1 or claim 2, wherein the spring constant of the elastic element is from 0.0001 to 1000 N / m, or from 0.0054 to 0.7 N / m.

4. The apparatus according to any one of the preceding claims, wherein the elastic element has a damping parameter from 0.01 1 / s to 10000 1 / s, from 0.2 1 / s to 1 1 / s, or from 0.019 1 / s to 0.87 1 / s.

5. The apparatus according to any one of the preceding claims, wherein the apparatus is suitable for scanning droplet adhesion microscopy, SDAM, measurements.

6. The apparatus according to any one of the preceding claims, wherein the apparatus is configured to measure displacement in a dynamic mode wherein the displacement caused by the force is measured at at least two different time points.

7. The apparatus according to claim 6, wherein the dynamic mode comprises measuring oscillation caused by the force.

8. The apparatus according to any one of the preceding claims, wherein the elastic element comprises at least one of: titanium, copper, 4130 steel, 1080 spring steel, copper or glass.

9. The apparatus according to any one of the preceding claims, wherein the elastic element is a cantilever.

10. The apparatus according to claim 9, wherein the cantilever comprises a first end portion and a second end portion, wherein the first end portion is non-fixed, and a second end portion is fixed to a mount.

11. The apparatus according to claims 10, wherein the surface is at the first end portion of the cantilever.

12. The apparatus according to claim 10 or claim 11, wherein the cantilever comprises a first strip and a second strip connecting the first end portion and the second end portion such that the first strip and the second strip define an elongated hole in the cantilever between the first end portion and the second end portion.

13. The apparatus according to claim 10 or claim 11, wherein the cantilever comprises a first strip and a second strip connecting the first end portion and the second end portion such that the first strip and the second strip define an elongated recess in the cantilever between the first end portion and the second end portion.

14. The apparatus according to claim 12 or claim 13, wherein the elongated recess or the elongated hole comprises a mesh structure comprising at least one strand, said strand connecting the first strip and the second strip via the recess or the elongated hole.

15. The apparatus according to claim 10 or claim 11, wherein the cantilever comprises a first strip and a second strip, the first strip and the second strip connecting the first end portion and the second end portion, the cantilever comprising at least one crossbar connecting the first strip to the second strip in an area between the first end portion and the second end portion.

16. The apparatus according to claim 10 or claim 11, wherein the cantilever comprises at least two holes between the first end portion and the second end portion.

17. The apparatus according to any one of claims 9 to 14, wherein the cantilever comprises a layered structure, wherein the layered structure comprises a first layer, a second layer on the first layer and a third layer on the second layer.

18. The apparatus according claim 17, wherein the first layer comprises metal, the second layer comprises rubber and the third layer comprises metal.

19. The apparatus according to claim 17 or 18, wherein the first layer comprises titanium, the second layer comprises rubber and the third layer comprises titanium.

20. The apparatus according to any one of claims 9 to 19, wherein the outer dimensions of the cantilever are from 1 mm to 1000 mm in length, from 0.5 mm to 500 mm in width and from 0.01 mm to 50 mm in thickness, or from 50 mm to 100 mm in length, from 1 mm to 5 mm in width and from 0.1 to 0.5 mm in thickness.

21. The apparatus according to any one of the preceding claims, wherein the surface of the elastic element comprises a reflective surface, said reflective surface being smooth and / or reflective such that at least 10 % of the light is reflected.

22. A method comprising:- providing an elastic element having a spring constant;- directing a confocal chromatic beam of light on a surface of the elastic element; and- measuring, based on at least one wavelength of reflected light, displacement of the surface caused by a force.

23. The method according to claim 22, wherein the method further comprises:- calculating, based on the displacement and the spring constant, the value of the force causing said displacement.

24. The method according to claim 22 or claim 23, wherein said confocal chromatic beam of light comprises at least two different wavelengths having different focal planes.

25. The method according to any one of claims 22 to 24, wherein the measuring further comprises:- measuring displacement of the surface caused by the force at at least two time points; andcalculating, based on the displacement at the at least two different time points and the spring constant, the value of the force causing said displacement.

26. The method according to claim 25, wherein the measuring comprises measuring oscillation caused by the force27. The method according to any one of claims 22 to 26, wherein the elastic element is a cantilever comprising a first end portion, a second end portion, a first strip and a second strip, wherein the first end portion is non-fixed and the second end portion is fixed to a mount, and wherein the first strip and the second strip connect the first end portion and the second end portion such that the first strip and the second strip define an elongated hole in the cantilever between the first end portion and the second end portion.

28. The method according to any one of claims 22 to 27, wherein the method further comprises obtaining the spring constant of the elastic element by:- measuring, with the confocal chromatic sensor, a displacement of the surface of the elastic element caused by a pre-defined force; and- obtaining, based on the predefined force and the measured displacement, the spring constant of the elastic element.

29. The method according to claim 28, wherein the pre-defined force is obtained by:- applying a droplet of liquid having a known density and known volume at the elastic element, said droplet thereby causing a displacement of the surface of the elastic element; and- calculating, based on at least the volume of the droplet and density of the droplet, the pre-defined force.

30. A method for obtaining a spring constant, said method comprising- providing an elastic element;- applying a pre-defined force on the elastic element, thereby causing a displacement of a surface of the elastic element;- detecting, with a confocal chromatic sensor, the displacement of the surface of the elastic element; and- calculating, based on the pre-defined force and the displacement of the surface of the elastic element, the spring constant of the elastic element.

31. The method according to claim 30, wherein the pre-defined force is obtained by: - applying at least one droplet of liquid on the elastic element, said liquid having a known volume and known density; and- calculating, based on the known volume and known density, the pre-defined force.

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