Atomic force microscope

Abstract

To provide an interferometer whose characteristics can be customized to suit a desired application of an atomic force microscope. An atomic force microscope ("AFM")-based interferometer uses a light source and a splitting optical interface that splits a light beam into a signal light beam and a reference light beam. Both the signal and reference light beams are focused near the AFM cantilever. A beam displacer introduces a lateral displacement between the signal and reference light beams, such that in at least one plane between the beam displacer and the focusing lens structure, the center of the signal light beam is separated from the center of the reference light beam by more than half the sum of their beam diameters in this plane. A detector operates to determine the difference in optical path length between the signal and reference light beams to determine information about cantilever movement.

Description

Background Art

[0001] An atomic force microscope (AFM) uses a microscope cantilever to convert the nanoscale force between a sharp tip on a cantilever and the sample being inspected into the measured displacement of the tip. There are numerous techniques for sensing the deflection of the cantilever, but most AFMs employ the technique of reflecting a focused light beam from the back of the cantilever because these techniques offer high sensitivity, low noise, and ease of use. These optical methods are broadly classified below into two categories: namely, interferometer detection methods and variants of the optical beam deflection (OBD) method.

[0002] Due to its design simplicity, high sensitivity, and good noise performance, most commercially available AFMs employ the OBD method. In this method, the reflected light beam is directed towards a split photodetector that enables the measurement of the angular deflection of the cantilever. The use of a quadrant photodetector enables the measurement of two-dimensional angular deflection called vertical and lateral deflection. Lateral deflection is particularly relevant to researchers studying tribology.

[0003] However, the angular deflection of the cantilever measured by the OBD method is an indirect measure of the tip displacement. As a result, numerous calibration methods have been devised to infer the tip displacement from the photodetector signal. Despite careful calibration of the measured cantilever angular deflection to the tip displacement, it can be difficult to reduce the calibration error to less than 10%. Since there is a lack of easily accessible standards for many cantilever measurement modes, the error is often not obvious to the user. In this case, large and systematic errors may be present in the signal, but the user may incorrectly believe that the OBD angular deflection signal represents the true cantilever tip displacement.

[0004] Another limitation of the OBD method is that the optimal signal-to-noise ratio (SNR) is achieved when the spot size matches the cantilever size. This makes it difficult to achieve the optimal SNR using one instrument on various cantilevers. For a given spot size, larger cantilevers will have higher noise. Additionally, some cantilevers have a triangular shape with a hollow base such that the light spot is size-limited and thus must provide a sub-optimal SNR.

[0005] On the other hand, interferometric spectroscopy is an alternative optical method that directly measures displacements directly related to the displacement of the tip at the end of the cantilever. This enables researchers to measure the relevant quantity, i.e., the tip displacement, without the need for additional calibration methodologies that can be time-consuming and highly inaccurate. Since the calibration is based on the wavelength of light, the calibration error can be reduced to less than a few percent. Additionally, interferometric spectroscopy can achieve better noise performance than the OBD method because it does not require matching the spot size to the size of the cantilever to optimize the SNR. In other words, displacements of cantilevers of various shapes and sizes can be measured with high SNR using a small focused light spot.

[0006] Although there is no shortage of academic papers on the design of interferometric AFM and their advantages, commercial AFM has not widely adopted such mainstream technologies due to their complexity. Fiber-based interferometers have also been widely adopted by academic researchers, but such interferometers lack the ease of use expected from commercial AFM due to the cumbersome positioning of the fiber near the cantilever and limited optical access.

[0007] Typical interferometers that enable high-quality optical access to the measurement target object and ease of use introduce the signal laser beam through the objective lens, while the reference light beam is reflected from a reference object such as a mirror at some distance from the target object. Typically, the reference light beam does not exit the optical system of the interferometer. Such interferometers can be used to measure the vibration of the target object, but the paths of the signal light beam and the reference light beam are very different and thus are subject to different thermal drifts and vibrations, resulting in very degraded stability at low frequencies. These artifacts are indistinguishable from the displacement of the target object. To mitigate this problem, all classes of differential interferometers have adopted a design principle in which both the signal light beam and the reference light beam traverse the objective lens. The signal light beam is focused on the target object, and the reference light beam is focused on a reference object close to the target object. The difference in the positions of the target object and the reference object becomes the measured interference signal. Maintaining the signal and reference light beams in close proximity to each other eliminates most of the unwanted drifts and vibrations of the instrument through common-mode rejection principles known to those skilled in the art. Such differential interferometer designs for AFM in the prior art rely on birefringent prisms positioned near the cantilever, so they greatly impede the optical quality of imaging through the objective lens, and as a result, they may be inferior in ease of use. Instead, other prior art designs place the birefringent prism at the back focal plane of the imaging lens, which also impedes high-quality optical access to the target object. Thus, there is a trade-off between high-performance differential interferometers in the context of AFM and ease of use and high-quality optical access to the cantilever.

[0008] A distinct difference between AFM based on the OBD method and the interferometer method lies in the requirements for the light source. The interferometer used in AFM utilizes a highly coherent laser light source such as a helium-neon (HeNe) laser or a laser diode as the light source, thereby ensuring a high-contrast interference signal. Also, the narrow spectral bandwidth of such a laser light source prevents any loss of signal contrast that may be caused by dispersion due to the optical glass used in the optical design. On the other hand, OBD AFM does not rely on the coherence of the light source, and they can use any highly coherent laser light source, or alternatively, they can use a low-coherence light source such as a superluminescent diode (SLD). The benefits of using a low-coherence light source include, for example, better long-term measurement stability and reduction of measurement artifacts caused by unwanted interference from back reflections. For these reasons, a superluminescent diode is preferred for certain experiments using OBD AFM where back reflection may cause artifacts, while it is known to those skilled in the art that a highly coherent laser is required for interferometer AFM.

[0009] On the other hand, SLDs may have higher noise compared to lasers, especially at high frequencies (US Patent 8370960B2). For this reason, some manufacturers of OBD AFM offer the option to choose from an SLD light source or a laser diode light source. Depending on the experiment in which OBD AFM is to be used, it may be more beneficial to utilize the lower noise of the laser diode or the reduction of back reflection artifacts of the SLD.

[0010] Unlike AFM based on the OBD method, interferometer AFM has been seen in various different implementations over the years. The simplest implementation of an interferometer is the Michelson interferometer, which was invented in the 1880s. It remains the basis behind much of today's interferometer technology.

[0011] Figure 1 depicts a simple design of a Michelson interferometer in the context of AFM. A laser 010 is coupled into a polarization-maintaining optical fiber 020 terminated with an optical fiber connector 030. The laser light diverges from the fiber end. The diverging light is collimated by a collimating lens 050 into a source light beam 040. The diameter 060 of the collimated source light beam 040 is determined by the divergence of the light beam exiting the optical fiber 030 and the focal length of the collimating lens. A polarizer 070 is used to ensure that the polarization is very linear and is differentially oriented at an angle optimal for maximizing the measurement sensitivity with respect to the optical system's residuals. Such a polarizer can be an absorptive film polarizer, a wire grid polarizer, a polarization cube beam splitter (the one shown in the drawing), or any such optical component having the function of transmitting or reflecting a single linear polarization state. Alternatively, the optical fiber can be eliminated and a collimated light beam directly emitted from a free-space laser source such as a helium-neon laser or a laser diode can be used instead of a fiber-coupled laser.

[0012] The collimated light beam is split into two light beams by a beam splitter 080 or any equivalent optical beam splitter. These two light beams are referred to herein as the signal light beam 090 and the reference light beam 100. Note that some people refer to the "signal" light beam as the "measurement" light beam.

[0013] The signal light beam 090 reflected from the semi-transmissive mirror 080 is focused onto the microscope cantilever 120 (target object) moored to the cantilever support clip 130 for handling purposes through the microscope objective lens 110. The diameter 062 of the signal light beam 090, which shrinks when the light reaches the cantilever, is shown. The cantilever support clip is a macroscopic object that AFM users generally touch with tweezers in order to introduce the cantilever into the AFM and fix it by pressing it with any clamping mechanism. The cantilever support clip generally has a length and width of about several millimeters and is usually thinner than 1 millimeter thick. The focused signal light beam 090 is reflected from the cantilever and returns through the objective system. The objective lens collimates the signal light beam 090, and then this beam returns to the semi-transmissive mirror 080.

[0014] The reference light beam 100 transmitted through the semi-transmissive mirror 080 reaches the reference mirror 140. The reference mirror 140 can be moved by a displacement mechanism 150, which can be either manual or somewhat automated. The reference light beam reflected from the reference mirror returns to the semi-transmissive mirror 080. The reference mirror 140 may require an inclination adjustment mechanism to ensure that the returning reference light beam 100 spatially overlaps the signal light beam 090 as described below.

[0015] Both return light beams are recombined by the beam splitter 080. A portion of each beam is recombined into the recombined light beam 200 and directed towards the photodetector 160. Since the law of conservation of energy requires that the total amount of light remains unchanged, the remainder of the return light beam returns towards the light source along the optical path of the source light beam 040. The amount of light reaching the photodetector 160 is a sine function of the difference between the optical path length that the signal light beam 090 travels and the optical path length that the reference light beam 100 travels, and the period of this sine function is λ / 2, which is determined by the wavelength λ of the laser light source. This period is shown in FIG. 1b. Note that the optical path length of the signal light beam 090 includes the sum of the path lengths along the incident portion before reflection from the cantilever added to the sum of the path lengths of the return portion (after reflection from the cantilever). Similarly, the optical path length of the reference light beam 100 is the sum of the incident optical path length and the return optical path length.

[0016] To optimize the sensitivity, the displacement mechanism 150 attached to the reference mirror 140 is adjusted so that half of the light returns to the light source and half reaches the photodetector 160. This condition, referred to herein as a centered interferometer, can be achieved by displacing the reference mirror 140 by up to λ / 4. This mechanism is necessary because the sensitivity becomes zero when all of the light reaches the photodetector 160 or when no light reaches it, and thus a signal cannot be detected thereafter. Similarly, the position of maximum sensitivity for this interferometer coincides with the maximum linear position where the sine wave response function is locally linear. That is, the signal response to changes in cantilever displacement is most linear when the interferometer is centered by proper positioning of the displacement mechanism 150.

[0017] More generally, the prior art teaches the advantage of having means for adjusting or modulating the phase difference between the signal light beam 090 and the reference light beam 100. The displacement mechanism 150 is one approach that brings about this adjustment or modulation, but in other cases, a liquid crystal device is used to adjust or modulate the phase difference between the two light beams. Note that in order to operate the interferometer under "centered interferometer" conditions, the means for adjusting the phase difference must be maintained in the correct state. When the adjustment means is an electrically actuated mechanism such as a piezoelectric element or a liquid crystal device, this mechanism must be continuously actuated or energized throughout the interferometric measurement. This can introduce noise and / or drift into the measured values.

[0018] When the wavelength of the laser light source is known, the sensitivity of the interferometer can be calibrated by translating the displacement mechanism 150 through approximately one wavelength cycle. At this point, any power change at the photodetector 160 can be calibrated to the exact displacement measurement of the cantilever in meters.

[0019] The simple Michelson interferometer shown in FIG. 1 has a significant drawback in that half of the light returns into the laser light source, which can cause instability in the laser oscillation. Such instability can cause refractive force changes that can lead to errors similar to the cantilever displacement measured by the photodetector 160. In this design, it is not possible to distinguish a change in power from a cantilever displacement. To reduce the instability of the laser oscillation, a Faraday isolator 170 can be installed along the optical fiber as shown in FIG. 2. Alternatively, in a free space laser, a free space isolator with similar advantages can be used.

[0020] This interferometer arrangement does not allow for an observation system with access to the cantilever. The alternative arrangement shown in Figure 3 uses a beam splitter 180 added between the purification polarizer 070 and the semi-transmissive mirror 080 of the design of Figure 2. This provides visual access for a camera system 190 that can be used to generate an image of the cantilever and the focused laser spot seen through the microscope objective system 110. Generally, the camera system 190 includes an image sensor, a lens for focusing collimated light onto the image sensor, a white light illumination system, and a beam splitter for introducing the illumination light. These elements can be arranged, modified, or eliminated in various ways depending on the characteristics of the microscope objective system 110 and the intended AFM application. While enabling access for the camera system 190, the semi-transmissive mirror 080 directs both the signal light beam 090 and the reference light beam 100 back towards the beam splitter 180, and then the beam splitter 180 reflects a portion of this light towards the photodetector 160. In this case, the recombined light beam 200 to be measured is sent back along the light source light beam 040 and then redirected to the photodetector 160. As in the case described above, the refractive force at the photodetector 160 is a measure of the cantilever displacement and varies sinusoidally with respect to the cantilever displacement. In different arrangements, the positions of the photodetector 160 and the camera system 190 can be exchanged using similar functions and performance.

[0021] This interferometer design has a dynamic range limited by the wavelength λ of the light. The maximum movement range of the cantilever displacement is λ / 4. At either end of this range, the sensitivity becomes zero, and thus the interferometer cannot measure the cantilever displacement at these positions. In practice, when particularly high accuracy and low noise are desired and non-linearity is to be avoided, the usable range of the interferometer is considerably smaller than λ / 4.

[0022] The limited dynamic range of the interferometer can be resolved by quadrature detection as used in Patent US6020963. Instead of monitoring the refractive force in the path of the recombined light beam 200 to measure the optical path difference between the paths of the signal light beam 090 and the reference light beam 100, the polarization state of the recombined light beam 200 is used. The step of measuring the polarization state is more complex than simply measuring the refractive force using a photodetector. This measurement method is used by the design of Figure 4.

[0023] Rather than splitting the source light beam 040 into two paths using the beam splitter 080, the signal light beam 090 and the reference light beam 100 are generated by splitting the source light beam 040 into two orthogonal polarization states using a polarization beam splitter 210 within a quadrature interferometer. When both the signal light beam 090 and the reference light beam 100 are recombined into the recombined light beam 200, the refractive force does not change as a function of the cantilever displacement so as to vary within the Michelson interferometer. Instead, the polarization state varies between a straight line, an ellipse, and a circle as a function of the cantilever displacement. The degree of ellipticity of the light beam polarization state (wherein the linearly polarized light and the circularly polarized light are extreme cases thereof) is directly related to the cantilever displacement. A part of the recombined light beam 200 reflected by the polarization beam splitter 210 can be analyzed, and the ellipticity of the polarization of this part can be determined by using the quadrature phase analyzer 220.

[0024] One possible configuration of the quadrature resolver is shown in FIG. 4b. This configuration includes the step of splitting the optical beam into two arms using a non-polarizing beam splitter 230. Along one arm, called the "in-phase" arm, two polarization states are mixed by rotating the extraordinary axis of its birefringence by 22.5° with respect to the polarization axis of the signal optical beam 090 or the polarization axis of the reference optical beam 100 using a half-wave plate 240. Next, using a polarization beam splitter 250, each half of the signal optical beam 090 and the reference optical beam 100 is directed towards two photodetectors 260 and 262 such as those in US6020963. Along the other arm, called the "orthogonal" arm, two polarization states are mixed by rotating the extraordinary axis of its birefringence by 45° with respect to the polarization axis of the signal optical beam 090 and the polarization axis of the reference optical beam 100 using a quarter-wave plate 270. Within this arm, using the same polarization beam splitter 280, each half of the signal optical beam 090 and the reference optical beam 100 is directed towards two photodetectors 264 and 266.

[0025] The difference in refractive power between photodetector 260 and photodetector 262 from the in-phase arm is divided by the sum of the refractive powers of both photodetectors, and this normalized difference becomes the in-phase signal I. Similarly, the quadrature signal Q is measured using both photodetectors 264 and 266 within the orthogonal arm. By plotting Q against I, the Lissajous plot shown in FIG. 4c is obtained. In an ideal interferometer, this response is the unit circle 284. In this case, any optical path configuration between the signal optical beam 090 and the reference optical beam 100 at any point in time results in a point called the phase state point 290 on the unit circle. A vector 286 can be defined between the origin of the Lissajous plot and the phase state point 290. The angle φ between this vector and the x-axis of the Lissajous plot can be calculated using the two-variable arctangent function as follows. TIFF0007692549000001.tif10150Here, TIFF0007692549000002.tif It is 13150, and both the integer m and the branch of the arctangent function are selected to give continuous results over an interval of width 2π, such as φ ∈ {−π, π}. This two-argument form of the arctangent function, atan2, is known to computer programmers and can be found in the FORTRAN language, the Perl language, and the standard math libraries for Java, C,.NET, and Python.

[0026] When the cantilever is displaced by λ / 2, the phase state point 290 measured by the quadrature phase resolver 220 makes a complete Lissajous figure. The angle φ is a directly measured value of the phase difference between the signal light beam and the reference light beam and can be used to infer the cantilever displacement d by the following equation. TIFF0007692549000003.tif17150 In the above equation, n is the refractive index of the medium surrounding the cantilever. In other words, the change in the optical path length of the signal arm caused by the displacement of the cantilever results in a phase difference between the signal light beam and the reference light beam that is measured as an angular change on the Lissajous plot. To avoid discontinuities in the displacement signal d, the output of the atan2 function must be unwrapped using methods known to those skilled in the art. This unwrapping is particularly important when the displacement signal will vary over a range greater than λ / 2.

[0027] Due to the imperfections of the optical components and the optical system assembly, the response to the cantilever displacement measured by the quadrature analyzer 220 is generally an ellipse 282 rather than the ideal unit circle 284 on the Lissajous plot. Simply assuming an ideal response will result in a periodic error in the reproduced displacement signal. To prevent the periodic error and ensure high-precision measurement of the cantilever displacement, the measured response on the ellipse 282 can be corrected by the following calibration procedure to infer the corresponding ideal unit circle 284 response of the system. The model used to correct the deviation from the ideal circle Lissajous is an elliptical Lissajous model as shown in Bellon et al., Opt. Commun. 207, 49-56 (2002). The step of measuring the five parameters that define the size, location, and angle of the ellipse includes the step of modulating the optical path difference between the signal arm and the reference arm (e.g., by intentionally displacing the cantilever) and the step of recording the Lissajous shape. Next, the elliptical function is fitted using the non-linear least squares method, and the most accurate parameters representing the Lissajous shape are determined. Thereafter, the photodetector response is interpreted as the accurate cantilever displacement using these five recorded parameters. Since the step of aligning the AFM may change one or more of these five parameters, it may be necessary to perform this calibration procedure before all experiments.

[0028] The step of generating this cantilever displacement signal from both the I signal and the Q signal requires non-linear calculations that can be performed using digital electronics such as a field programmable gate array (FPGA). This calculation must be performed at a much higher frequency than the cantilever displacement during measurement in order to reproduce the accurate cantilever displacement signal.

[0029] The main advantage of the quadrature resolver method is that in this case, the signal dynamic range can be made larger than λ / 4, and at the same time, low-noise performance can be maintained regardless of the cantilever displacement within certain limits set by the optical system. Furthermore, the linearity of this signal does not depend on the starting conditions of the interferometer and is not limited to displacement ≪ λ / 4. In other words, any starting point of the optical path difference between the path of the signal light beam 090 and the path of the reference light beam 100 is equal, enabling high linearity and low-noise measurements, so the interferometer does not need to be "centered" as described above.

[0030] Many configurations of the quadrature phase resolver 220 have been proposed. Some place a quarter-wave plate in front of the first beam splitter (TaeBong Eom et al., Meas. Sci. Technol. 12, 1734 (2001)). Some eliminate the half-wave phase retardation plate by mechanically rotating the quadrature phase resolver 220 by 45° around the optical axis of the light beam (Bellon et al., Opt. Commun. 207, 49 - 56 (2002)). Other proposals use a birefringent crystal instead of a polarization cube beam splitter (Paolino et al., Rev. Sci. Instrum. 84, 095001 (2013)). Other designs use only two photodetectors in total, one for each arm, to perform polarization measurements (Weber et al., Rev. Sci. Instrum. 90, 083503 (2019)). A more complex design (US2006 / 0087658A1) generates four phase shift signals (0°, 90°, 180°, 270°) that pass through polarizers before all reach their respective photodetectors, aiming to reduce the common mode error as compensation for the light lost by the polarizers. Each configuration has a certain compromise between performance and manufacturing simplicity.

[0031] One drawback of the design of FIG. 4 is that it is not differential. Thus, any mechanical movement, such as vibration or thermally induced drift, in either arm (signal light beam 090 or reference light beam 100) may be misperceived as a cantilever displacement. Further, the longer the path lengths of the signal light beam 090 and the reference light beam 100, the stronger the tendency for the system to be a source of these error sources.

[0032] In the prior art, some differential interferometer configurations have been proposed to reduce the optical path difference between the paths of both polarization states by using a birefringent material near the cantilever (Schonenberger et al., Rev. Sci. Instrum. 60, 3131 (1989)). This configuration is shown in FIG. 5, in which a calcite window 300 for splitting the source light beam 040 into two parallel beams having orthogonal polarization states is disposed near the cantilever. A drawback of this design is the presence of a fragile crystal that is easily damaged by liquid near the cantilever. Also, since information from light having different polarizations is offset differently in the camera, the camera views of the cantilever and the sample have double vision due to the birefringence of the calcite. Since the source light beam 040 is split into the signal light beam 090 and the reference light beam 100 near the cantilever, the polarizing beam splitter 210 used in the conventional implementation is replaced by a dichroic mirror 310 in this case. The advantage is that all the light arriving from the laser is reflected towards the cantilever within the incident path (before reflection from the cantilever), and further completely reflected on the return path (after reflection from the cantilever), while at the same time allowing some light of different wavelengths to reach the camera system 190 for observation. The diameter 064 of the reference light beam 100 converges in a manner similar to the diameter 062 of the signal light beam 090, because both of these light beams are focused through the same lens.

[0033] The signal light beam 090 travels towards the AFM cantilever, reflects from the cantilever, and then travels away along substantially the same signal light beam path from the cantilever. When it is necessary to distinguish between these beams, the signal light beam before reflection from the cantilever is called the "incident" signal light beam, and the beam after reflection from the cantilever is called the "return" light beam. These beams cannot be distinguished in the figure due to their spatial superposition, and both are labeled 090. Similarly, the reference light beam 100 is called "incident" before reflection from the cantilever and "return" after reflection.

[0034] Figure 6 shows a configuration (den Boef et al., Rev. Sci. Instrum. 62, 88 (1991)) in which an angular division birefringent prism 320 is used to split both polarization states into two beams that can be focused at two different locations on the cantilever. In this configuration, it is preferable to use a birefringent prism that generates two light beams having different angles, such as a Wollaston prism, a Rochon prism, or a Senarmont prism, as used in US5315373. For reasons explained below, in this design, the conventional microscope objective system 110 shown in the figures is replaced by an imaging lens 340. The geometry of the angular division birefringent prism 320 can be adjusted to generate the angular separation of both light beams that is specifically selected with respect to the imaging lens 340 to provide the desired separation of the light beams at the cantilever. To ensure that both beams have the same angle of incidence onto the cantilever, the angular division birefringent prism 320 must be positioned at the back focal plane 330 of the imaging lens 340.

[0035] Note that the back focal plane 330 of the microscope objective system 110 is physically located inside the microscope objective system 110, and it is considered impossible to place the birefringent prism 320 on the back focal plane 330. Therefore, in this arrangement, it is not possible to use the microscope objective system 110. Thus, the imaging lens 340 that must be used instead is a lower quality lens such as an achromatic doublet, a singlet lens, or other simple imaging lens. The imaging lens 340 not only provides a cantilever and a lower quality image around it, but the angular splitting birefringent prism 320 also generates two images in the camera system 190 because it splits the orthogonal polarized light into separate paths with different angles.

[0036] In this scenario, the signal light beam 090 and the reference light beam 100 follow very similar paths side by side with each other. The geometry and optical properties of the angular splitting birefringent prism 320 are optimized at the design stage to generate a defined separation distance between the signal light beam 090 and the reference light beam 100 with the cantilever. In this design, the ideal separation distance is slightly smaller than the length of the cantilever during measurement. The signal light beam 090 is at the cantilever end (target object), while the reference light beam 100 is at the cantilever base (reference object). This makes it possible to measure the displacement difference between these two locations that changes when the cantilever deflects under the force of the sample.

[0037] It is clear from FIG. 6 that this design cannot immediately accept cantilevers of various sizes. However, commercially available cantilevers with lengths ranging from about 10 μm to 500 μm and various shapes are available. One approach is to use a beam separation larger than the cantilever length such that one beam is focused on the cantilever and the other is focused on the cantilever support clip (Paolino et al., Rev. Sci. Instrum. 84, 095001 (2013)). In the case of a 500-μm-long cantilever, this separation is considered to imply a separation greater than 500 μm with the reference optical beam 100 focused on the cantilever support clip 130, which is the reference object in this context. However, the thickness of the cantilever support clip may be greater than the depth of focus of the laser focused through the imaging lens 340, leading to low contrast or even complete signal absence. Therefore, it is advantageous to introduce a difference in the on-axis focal positions of these two beams so that each beam can be focused on the surface on which they are reflected. As proposed by Cunningham et al. in 1994 (Cunningham et al., Meas. Sci. Technol. 5(11), 1350 (1994)), a defocusing glass window 350 is added to the signal optical beam as shown in FIG. 7 such that the signal optical beam 090 is focused on the cantilever 120 while simultaneously the reference optical beam 100 is focused on the cantilever support clip 130. In this arrangement, the deflections of both small and large cantilevers can be measured using the same optical system. Furthermore, the deflection of the cantilever 120 relative to the stationary cantilever support chip 130 is measured, and thus this measurement does not depend on the separation distance between the signal optical beam 090 and the reference optical beam 100.

[0038] Instead, Goto et al. used a birefringent defocusing lens to slightly defocus one of the polarizations in the source light beam 040 in order to change the relative focusing between the signal light beam 090 and the reference light beam 100 in the cantilever (Goto et al., Rev. Sci. Instrum. 66, 3182 (1995)). The birefringent lens is necessary because both the signal light beam 090 and the reference light beam 100 spatially substantially overlap, and thus the standard optical system cannot be used without affecting one of these light beams with respect to the other.

[0039] Note that the diameter 060 of the source light beam 040, in combination with the focal length of the microscope objective system 110 or the imaging lens 340, determines the divergence of the focused light beam at the cantilever, the spot diameter, and the depth of focus of the focused light beam. For a straight cantilever that does not remain or curve due to residual or thermally induced internal stress, it is considered that a source light beam 040 with a wide range of diameters results in a high-contrast signal. This is because these light beams will substantially overlap after reflection from the cantilever 120 and the chip 130 and recombination into the recombined light beam 200. Conversely, for a curved cantilever as shown in Fig. 7b, the reflected signal light beam 090 will return along a path slightly different from the path of the incident signal light beam 090. As a result, the signal light beam 090 and the reference light beam 100 will only partially overlap when recombined into the recombined light beam 200. This partial overlap results in a low interferometer contrast, a weak signal, and high measurement noise. However, by increasing the diameter of the source light beam 040, it leads to a strong signal, and as a result, it ensures a greater overlap between the reference light beam 100 and the signal light beam 090 in the recombined light beam 200, which results in low noise. In conclusion, by selecting a source light beam 040 with a large diameter, the system becomes more tolerant to unwanted cantilever curvature.

Summary of the Invention

Problems to be Solved by the Invention

[0040] Increasing the diameter of the light source light beam 040 on the other hand results in a small depth of focus, whereby the system becomes less tolerant to changes in the thickness of the cantilever support chip. The chip thickness error shown in FIG. 7b may be caused by differences in the substrate and microfabrication processes used to fabricate the cantilever. The result of the chip thickness error is that these light beams will be out of focus with respect to each other when the return signal light beam 090 and the return reference light beam 100 are recombined into the recombined light beam 200. This leads to low interferometer contrast, weak signals, and high measurement noise. However, a small beam diameter for a given error in the cantilever support chip thickness relative to the design thickness will result in a small contrast loss, strong signals, and low measurement noise. In conclusion, when selecting the diameter of the light source light beam 040, there is a trade-off in that a small diameter 060 of the light source light beam 040 provides higher tolerance to chip thickness errors but only lower tolerance to cantilever curvature, and vice versa. Similarly, a large beam diameter 060 of the light source light beam 040 results in low tolerance to chip tilt errors. The chip tilt error shown in FIG. 7b may be caused, for example, by machining tolerances of the chip holder. Any error in the chip tilt results in a relative defocus between these two light beams since the signal light beam 090 and the reference light beam 100 are separated by a certain distance. The relative defocus between these return light beams for any given amount of chip tilt error is greater for a large light beam diameter. In other words, a small beam diameter 060 of the light source light beam 040 provides high tolerance to chip tilt errors. To find a compromise between cantilever curvature and errors in chip thickness and chip tilt, an appropriate beam diameter 060 of the light source light beam 040 must be selected. In the prior art, the ability to make these design choices has been limited, and thus it has been difficult to customize the characteristics of the interferometer to suit the desired applications of the atomic force microscope.

Prior Art Documents

Patent Documents

[0041] [Patent Document 1] US8370960B2 [Patent Document 2] US6020963 [Patent Document 3] US2006 / 0087658A1 [Patent Document 4] US5315373 [Patent Document 5] Patent 13 / 999,614 [Patent Document 6] US10338096B2 [Non-Patent Document]

[0042] [Non-Patent Document 1] Bellon et al., Opt. Commun. 207, 49 - 56 (2002) [Non-Patent Document 2] TaeBong Eom et al., Meas. Sci. Technol. 12, 1734 (2001) [Non-Patent Document 3] Paolino et al., Rev. Sci. Instrum. 84, 095001 (2013) [Non-Patent Document 4] Weber et al., Rev. Sci. Instrum. 90, 083503 (2019) [Non-Patent Document 5] Schonenberger et al., Rev. Sci. Instrum. 60, 3131 (1989) [Non-Patent Document 6] den Boef et al., Rev. Sci. Instrum. 62, 88 (1991) [Non-Patent Document 7] Cunningham et al., Meas. Sci. Technol. 5(11), 1350 (1994) [Non-Patent Document 8] Goto et al., Rev. Sci. Instrum. 66, 3182 (1995) [Non-Patent Document 9] Labuda et al., Appl. Phys. Lett. 106, 253103 (2015) [Disclosure of the Invention] [Means for Solving the Problems]

[0043] The present invention relates to an atomic force microscope as defined by the claims. Embodiments of the invention use a differential interferometer for direct displacement measurement of the cantilever deflection caused by the force between the cantilever tip and the sample under inspection. Generally, a differential interferometer functions by splitting collimated light from a fiber-coupled light source into two arms having orthogonal polarization states using a lateral displacement beam splitter, with the signal arm light beam generally being focused onto the cantilever through an objective lens and the reference arm light beam generally being focused onto the cantilever support chip through the same objective lens. An advantageous feature is the complete spatial separation of these light beams before they are focused through the objective lens. This geometry allows for separate manipulation of these light beams using standard optical systems rather than birefringent optical systems. Preferably, an optical wedge is used to impart an angular deviation to the reference arm light beam so that the reference arm light beam impinges on the cantilever support chip rather than the cantilever. Preferably, the same wedge is appropriately positioned to ensure that the signal light beam and the reference light beam intersect at the back focal plane of the objective lens. An optical lens is generally used in the reference arm to defocus the focusing of this light beam relative to the signal arm so that the reference arm light beam is well focused on the cantilever support chip having a specified thickness and tilt angle. After reflection, both light beams are preferably collimated and recombined by the same optical system that sent them. Both the signal light beam and the reference light beam generally pass through a quarter-wave plate twice so that the path of the recombined light is changed by a lateral displacement beam splitter towards an orthogonal phase analyzer instead of back to the light source. Preferably, this orthogonal phase analyzer measures the optical path length difference between the reference light beam and the signal light beam using an orthogonal detection optical scheme that disperses the light onto four photodetectors using polarization optics. The interferometer can be calibrated by modulating a liquid crystal device and observing its response. Subsequently, digital electronics can reproduce the cantilever displacement signal from the four photodetector signals based on this calibration and the known wavelength of the light source.

[0044] The above-mentioned light source can be a laser or, preferably, a low-coherence light source such as a superluminescent diode. Due to the low coherence of such a light source, a compensation window is used to adapt the optical group path length between the signal light beam path and the reference light beam path. Further, before each experiment, the above-mentioned wedge can be mechanically actuated to very precisely change the optical group path length between both light beam paths so as to maximize the interferometer contrast. Further, a plurality of switchable lenses, each having a specific focal length, thickness, and material, make it possible to reconfigure both the focus of the reference arm and the optical group path length to accept different types of cantilevers having different thicknesses. Similarly, an additional optical system can be inserted into or removed from the optical system to compensate for changes in focus and optical group path length caused by the introduction of various fluids such as water around the cantilever.

[0045] Further, a beam splitter is used to sample a portion of the light beam returning from the cantilever and redirect this partial light beam towards a quadrant photodetector. This enables a two-dimensional measurement of the angular deflection of the cantilever using an optical beam deflection method also known as the optical lever method. This additional measurement is performed simultaneously with the interferometer displacement measurement obtained from the quadrature detection.

Brief Description of the Drawings

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DETAILED DESCRIPTION OF THE INVENTION

[0047] FIG. 8 shows a novel arrangement of a differential interferometer and is a first embodiment of the present invention. In this embodiment, the introduction of a birefringent lateral beam displacer 360 in combination with an angular division birefringent prism 320 enables the signal light beam 090 and the reference light beam 100 to intersect at points outside both prisms. Note that the light source light beam 040 refracts and divides at the birefringent interface 363 to generate the signal light beam 090 and the reference light beam 100. The birefringent lateral beam displacer 360 introduces a lateral displacement between the signal light beam 090 and the reference light beam 100, while the angular division birefringent prism 320 introduces a deflection angle of the reference light beam 100 with respect to the signal light beam 090.

[0048] The lateral displacement between two light beams is defined as a translation in a direction substantially perpendicular to any axis of the propagation axis of one light beam with respect to the propagation axis of the other light beam. This direction may be referred to as the transverse direction. Generally, the lateral displacement is introduced by refraction and / or reflection of one or both beams. As defined herein, the lateral displacement does not mean a change in distance caused simply by the non-parallelism of two non-parallel propagating light beams.

[0049] The embodiment of the present invention shown in FIG. 8 enables the intersection point 365 of the signal light beam 090 and the reference light beam 100 to be disposed outside both the birefringent lateral beam displacer 360 and the angularly splitting birefringent prism 320. Further, this intersection point 365 can be disposed inside the microscope objective system 110, for example, the microscope objective system 110 used in a previous arrangement. This arrangement is preferred because it is optimal for placing the intersection point 365 at the back focal plane 330 of the microscope objective system 110 to ensure that the light beam is perpendicular to both the cantilever and the chip upon reflection. Other embodiments are possible using different arrangements of the birefringent prism to achieve the same effect. For example, two angularly splitting birefringent prisms 320 or a specially designed single angularly splitting birefringent prism 320 can be used to generate the intersection point 365 at any location in space, for example, within the back focal plane 330 of the microscope objective system 110.

[0050] By moving the above prism pair outside the path between the microscope objective system 110 and the camera system 190, another embodiment of the present invention shown in FIG. 9 is provided. The light source light beam 040 is separated into a signal light beam 090 and a reference light beam 100 before reflection from the dichroic mirror 310. This enables high-quality imaging of the cantilever when captured by the camera system 190. Further, this optical access allows an additional optical beam positioning unit 370, as described in Patent 13 / 999,614 and Labuda et al., Appl. Phys. Lett. 106, 253103 (2015), to be introduced into the optical system using an auxiliary dichroic mirror 390. The auxiliary dichroic mirror 390 can be any type of beam splitting optical system, but preferably reflects the specific wavelength range in question while transmitting other wavelengths. This allows one or more auxiliary light beams 380 (only one is shown in FIG. 9), having functions such as photothermal excitation of the cantilever, local thermal probing, photoinduced excitation of the sample, vibrational spectroscopic excitation of the sample (required for local Raman infrared spectroscopy or Fourier transform infrared spectroscopy), photoelectron generation, or hole generation, to be introduced into the optical system. All of these examples can achieve advantages from these auxiliary light beams 380, which are focused on or near the cantilever and are controlled independently of the signal light beam 090 and the reference light beam 100.

[0051] It should be noted that the optical system depicted in FIG. 9 may have reflections from the dichroic mirror 310 that are oriented differently from actual implementation for illustrative reasons. This technique for assisting in drawing on a two-dimensional page is referred to as "folding of the optical system." Instead, in reality, the preferred embodiments can have reflections from the dichroic mirror 310 that direct the light beam at various angles so as to enter or exit the plane defined by the page. Similarly, due to the limitations of drawing, the other figures in this specification provide the light beam that can be directed to enter or exit the page in the plane of the page for embodiments of the present invention. Also, the figures in this specification may show elements of the apparatus as being in the plane of the page when in fact they are located in front of or behind the plane of the page.

[0052] If the signal light beam 090 and the reference light beam 100 are separated by a distance greater than the diameter 060 of these light beams from a predetermined distance from their intersection 365, then at this distance and beyond, the beams are considered to be spatially separated. The advantages of having the spatially separated signal light beam 090 and reference light beam 100 are that each beam can be independently shaped using a standard optical system and the optical path lengths of each arm can be independently adjusted. Since both polarization states are spatially separated, a birefringent lens as described in the prior art is not necessary. For example, FIG. 10 shows how the reference beam defocusing lens 400 can slightly defocus the focusing of the reference light beam 100 so that the reference light beam 100 is focused on the cantilever support chip instead of the cantilever, while the signal light beam 090 remains focused on the cantilever.

[0053] Previously, the diameter of the signal light beam 090 was selected by an optical design to reduce the overall error between the cantilever curvature, the chip thickness error, and the focus blur caused by the chip tilt error. The advantage of this embodiment is that both the diameter of the signal light beam 090 and the diameter of the reference light beam 100 can be adjusted independently. The diameter of the signal light beam 090 can be adjusted to accept the expected error of the cantilever curvature. On the other hand, the diameter of the reference light beam 100 can be adjusted to reduce the overall error between the cantilever curvature, the focus blur caused by the chip tilt error, and the focus blur caused by the chip thickness error. In other words, this additional degree of freedom makes it possible to design the optical system to be highly tolerant to errors from all three of these sources of origin.

[0054] Similarly, an off-axis lens 410 can be used to simultaneously provide two functions: blurring the light beam and giving it a desired deflection angle. This is shown in FIG. 11, where the off-axis lens 410 deflects the reference light beam 100 and blurs it at the same time. FIG. 11b shows how an off-axis lens can be manufactured from a standard lens by grinding away a certain portion of the standard lens to achieve this characteristic. Alternatively, a certain lens can be used off-axis without changing its geometry. However, in this special design, due to the proximity of the signal light beam 090 and the reference light beam 100, a grinding operation is required, and the design is such that only the reference light beam 100 passes through the off-axis lens 410. Other designs can use a single lens that is large enough to focus both the signal light beam 090 and the reference light beam 100, and simultaneously give a deflection angle to only one of the light beams or give a certain deflection angle to both light beams depending on the position of the lens axis relative to the axes of both light beams.

[0055] FIG. 12 shows an alternative embodiment of the present invention that achieves the same spatial separation optical beam geometry without using a birefringent crystal such as the birefringent lateral beam deflector 360. A lateral displacement beam splitter 420 separates the source optical beam 040 into a signal optical beam 090 and a reference optical beam 100. As shown in FIG. 12b, the lateral displacement beam splitter 420 is composed of a triangular prism 421 coupled to a parallelogram prism 422. Different from the lateral beam deflector that uses refraction to separate light, the lateral displacement beam splitter 420 divides the source optical beam 040 into a signal optical beam 090 and a reference optical beam 100 using a partially reflective optical interface 423, and then reflects the first-reflected beam using a total-reflective optical interface 424 parallel to the partially reflective optical interface 423. Due to this reflection, both the twice-reflected beam and the first-transmitted beam are emitted from the lateral displacement beam splitter as parallel beams separated by some distance in the transverse direction. In the embodiment illustrated by FIG. 12, a partially reflective optical interface 423 that polarizes the signal optical beam to have a polarization state substantially orthogonal to the polarization state of the reference optical beam is used. However, a non-polarizing lateral displacement beam splitter can be used at the expense of a lower SNR. In FIG. 12, the partially reflective optical interface 423 has a polarization-selective coating that reflects the signal optical beam 090 and transmits the reference optical beam 100. However, there is an equivalent optical arrangement where the signal optical beam 090 is transmitted and the reference optical beam 100 is reflected. On the other hand, the total-reflective optical interface 424 that redirects the signal optical beam 090 to be parallel to the reference optical beam 100 can utilize internal total reflection, a metal coating, or a dielectric coating.

[0056] After the signal light beam 090 and the reference light beam 100 are emitted from the lateral displacement beam splitter 420, a deflection angle is given to the reference light beam 100 using the optical path wedge 430. (Note that this wedge is called an "optical path wedge" because it will be used later to change the optical path length of the light beam). The wedge in this context is a prism or window designed such that both optical surfaces through which the light beam passes are intentionally not parallel to give a deflection angle to the light beam passing through it. The angle between the two optical surfaces is the wedge angle. The deflection angle Δθ of the transmitted light is determined by the wedge angle α and the refractive index n of the glass used to manufacture the wedge glass and is defined by the following equation. TIFF0007692549000004.tif13150 This equation is a good approximation for small angles α. The deflection angle can be designed to achieve the desired light beam separation between the signal light beam 090 and the reference light beam 100 with a cantilever. This separation is a function of the focal length of the microscope objective system 110 and the deflection angle between the reference light beam 100 and the signal light beam 090. This design is smaller than previous embodiments that rely on large birefringent optical systems. Also, the optical components in this embodiment can be manufactured at a lower cost and with higher optical quality than birefringent materials.

[0057] The embodiment illustrated in FIG. 12 generates two parallel beams using a lateral displacement beam splitter 420, one of which is later deflected using an optical path wedge 430. However, a single optical component can perform both functions. For example, an alternative beam splitter for the lateral displacement beam splitter 420 in which the parallelogram prism 422 is replaced by a trapezoidal prism can split the light source light beam 040 into a signal light beam and a reference light beam having an angle defined therebetween. The angle between both light beams emitted from such a beam splitter is a function of the angle between both reflecting surfaces of the trapezoidal prism and the refractive index of the trapezoidal prism material. Alternatively, a beam splitter having a geometry similar to the lateral displacement beam splitter 420 but manufactured from different glass types for the triangular prism 421 and the parallelogram prism 422 can deflect the transmitted light beam by an angle determined by the refractive indices of both glass types. These two proposed mechanisms are thought to provide the angular deviation between the signal beam and the reference beam without the need for a wedge prism.

[0058] Note that the lateral displacement beam splitter 420 can be replaced by two polarization cube beam splitters that either have a gap or are cemented together. Alternatively, a polarization cube beam splitter and a mirror can be used to provide the same function as the lateral displacement beam splitter 420. Since such prisms are readily available from most optical system manufacturers, these designs make it possible to reduce costs. Note that the function of the lateral displacement beam splitter 420 is to provide a lateral displacement between the first beam and the second beam, i.e., a displacement in a direction perpendicular to the axis of the first beam. Such a function can be introduced using many optical devices that use a combination of basic optical components. However, an arrangement in which both reflecting interfaces are part of a combined assembly of multiple optical elements is optimal because it reduces the possibility of drift and vibration between both reflecting interfaces that can introduce measurement errors in the cantilever displacement.

[0059] The optical path wedge 430 is attached to the actuator 440. The actuator 440 can translate the optical path wedge 430 in one direction, thereby changing the amount of glass through which the light beam passes without changing its deflection angle. The actuator can be, for example, a piezoelectric transducer, a stepper motor, an in-motor. The translation axis of the actuator can be in the same plane as any of these wedge optical surfaces or at any angle with respect to these optical surfaces. The displacement that brings about a change in the passing glass thickness of about the wavelength of light enables the change of the optical path difference between the path of the reference light beam 100 and the path of the signal light beam 090. This change enables the calibration of the interferometer by measuring the interferometer response function during the movement of the optical path wedge 430 and fitting the measured interferometer response function. Note that the optical path wedge 430 performs two functions: the deflection angle of the reference light beam 100 to achieve design spot separation with a cantilever, and the calibration of the interferometer by the operation of the optical path wedge 430 by the actuator 440.

[0060] Alternatively, the lateral displacement beam splitter 420 can be tilted to change the optical path difference between the path of the reference light beam 100 and the path of the signal light beam 090 by approximately one wavelength of light. This tilt can be achieved by operating a piezoelectric transducer to give the lateral displacement beam splitter 420 a deflection angle. The optical path wedge 430 requires translation to change the optical path length between the path of the signal light beam 090 and the path of the reference light beam 100, whereas the lateral displacement beam splitter 420 requires rotation to perform the same function. Other optical components can be operated to provide an optical path length difference between the path of the signal light beam 090 and the path of the reference light beam 100 for calibrating the interferometer. The optical path length difference required to properly calibrate the interferometer is ideally at least half the wavelength of light, but may be sufficient at a smaller ratio to provide an ellipse arc sufficient to fit the acquired data to an accurate interferometer model.

[0061] Piezoelectric actuators can move optical elements at high speed and with nanometer resolution. In the present invention, this movement is considered to enable the user to calibrate the reticle very quickly and with very high resolution. This calibration has advantages in some applications. However, in other applications, it may be advantageous to calibrate the reticle using a very stable method. Piezoelectric actuators are subject to creep due to time and temperature, and this creep may inappropriately change the optical path difference between the signal light beam 090 and the reference light beam 100 over time even after the actuation signal has been stopped. Such a change in the optical path difference may be mistaken for cantilever displacement.

[0062] FIG. 13 shows an embodiment of the present invention that provides a more stable technique for calibrating a resonator. Instead of actuating an optical path wedge 430 or other optical component to modulate the phase difference between a reference optical beam 100 and a signal optical beam 090, in this case a liquid crystal device 450 is used to provide a phase shift between the reference optical beam 100 and the signal optical beam 090. A liquid crystal device is a device that aligns the molecules of a special liquid between two transparent electrodes to change the birefringence properties of the liquid. The orientation of these molecules is induced by an electric field resulting from the applied voltage to the electrodes. The degree of phase shift generated by the liquid crystal device 450 depends on the intensity of the voltage applied to the liquid crystal device 450. The thickness of the liquid crystal material is selected to provide approximately one full turn around the resonator when fully actuated. Generally, liquid crystals have a non-linear relationship between the given difference and the applied voltage. The non-linearity of the liquid crystal response is advantageous because it prevents noise and drift from occurring when the liquid crystal device is stopped after calibration. When less than a predetermined voltage (generally around 1V), the liquid crystal stabilizes between both polarization states using a fixed and stable phase shift. When the liquid crystal device voltage is set near 0V, the noise on the voltage applied to the liquid crystal device has only an effect that can be ignored with respect to the measured cantilever displacement. Therefore, it is advantageous to electrically activate and use the liquid crystal device 450 to calibrate the interferometer response during the experimental setup. However, unlike the prior art, it is also advantageous to stop the liquid crystal device during measurement and maintain it in a non-operating state (near 0V). By electrically starting and stopping the liquid crystal device after resonator calibration, the liquid crystal device is prevented from increasing the noise of the cantilever displacement measurement. There may be cases where it is advantageous to temporarily stop the measurement, electrically activate the liquid crystal device 450 to recalibrate the interferometer response and the resonator shape, and then electrically start and stop the liquid crystal device to continue the measurement.

[0063] The liquid crystal device 450 can be disposed in the path of the signal light beam 090 or in the path of the reference light beam 100. Alternatively, the liquid crystal device 450 can be disposed in the path of the source light beam 040 or in the path of the recombination light beam 200 and oriented accordingly to impart a maximum phase shift to either the polarization axis of the signal light beam 090 or the polarization axis of the reference light beam 100. However, the liquid crystal device may result in both wavefront aberration that reduces the contrast of the interference signal and large back reflections. To reduce the effect of this non-ideal behavior, the liquid crystal device 450 can be disposed in the recombination light beam 200 as shown in FIG. 13. By orienting the polarization axis of the liquid crystal device 450 to match the polarization axis of either the signal light beam 090 or the reference light beam 100, the liquid crystal device 450 can differentially impart a phase shift to one polarization axis and substantially not affect the other. In this case, by modulating the liquid crystal device voltage, a phase shift is introduced that enables calibration of the Lissajous by simulating the effect of the cantilever displacement. Importantly, when the liquid crystal device 450 is disposed in the path of the recombination light beam 200 (not a separate path of the signal light beam 090 or the reference light beam 100), the slight distortion of the wavefront of the liquid crystal device 450 will not substantially degrade the contrast at the photodetectors 260, 262, 264, and 266. This is because such wavefront distortion will affect the signal light beam and the reference light beam equally. When the signal light beam interferes with the reference light beam within the quadrature phase analyzer 220, the phase of the signal light beam is subtracted from the phase of the reference light beam, and any phase shift from any slight wavefront distortion will also be subtracted.

[0064] For the same reason that the reference beam focus blur lens 400 was introduced in FIG. 10, the reference beam focus blur lens 400 can be used in combination with the lateral displacement beam splitter 420 and the liquid crystal device 450 for similar reasons and with similar advantages. This results in another embodiment of the present invention shown in FIG. 14.

[0065] The embodiment of the present invention shown in FIG. 15 reveals an optical system in which the reference light beam 100 passes through a beam expander composed of a positive lens 460 and a negative lens 470. Appropriate selection of these lenses and the distance between them will result in a desirable reduction of the beam diameter 064 of the reference light beam 100 with respect to the beam diameter 062 of the reference light beam 100. Reversing the order of the lenses will make it possible to expand the beam diameter 064 of the reference light beam 100. As discussed above, controlling this beam diameter enables optimization of the divergence and depth of focus of the reference light beam near the AFM cantilever. For optimizing the interferometer contrast for any given situation, different amounts of reduction or expansion of the beam diameter may be desirable depending on the situation. Similarly, these optical components can be arranged in the signal light beam 090 to adjust the divergence of the signal light beam 090 near the cantilever 120.

[0066] FIG. 15 also shows an operating mechanism, referred to herein as the beam expander actuator 480, which can be attached to one or both of the lenses (460 and 470) to change the distance between these lenses. The operating mechanism can be manual or computer-controlled. This allows for careful adjustment of the focus at the cantilever support chip while operating the instrument. This adjustment can be beneficial for increasing the contrast for various cantilever support chip thicknesses, especially when the depth of focus of the light beam is smaller than the change in the cantilever support chip thickness.

[0067] In the embodiments discussed so far, a Faraday isolator 170 was used to prevent light from returning to the light source and causing instability. This use was a result of the beam splitter 180 which reflects only a portion of the recombined light beam 200 towards the quadrature phase analyzer 220. The remainder of the light beam returned to the light source. FIG. 16 provides an embodiment of the present invention that uses a quarter-wave plate 490 to rotate the polarization state between the incident light and the return light by 90° for both the signal light beam 090 and the reference light beam 100. In FIG. 16, the polarization states of the incident light beam and the return light beam are labeled "S" and "P" according to the standard optical system nomenclature for a lateral displacement beam splitter 420. This 90° rotation can be implemented for both the signal light beam 090 and the reference light beam 100 using a single quarter-wave plate 490 through which both beams pass. Alternatively, a first quarter-wave plate can be placed in the signal light beam 090 and a second quarter-wave plate can be placed in the reference light beam 100. FIG. 16b shows the paths of the incident signal light beam 090 and the incident reference light beam 100. FIG. 16c shows the paths of the return signal light beam 090 and the return reference light beam 100 in which the quarter-wave plate 490 has interchanged the "S" polarization and the "P" polarization for both beams in this case. The result of this operation is that the recombined light beam 200 does not return along the path of the light source light beam 040. Instead, the polarization-selective coating within the lateral displacement beam splitter 420 redirects both the return reference light beam 100 and the return signal light beam 090 from the side facets of the lateral displacement beam splitter 420. This allows for the elimination of the beam splitter 180 used in conventional embodiments. Further, in this case, most of the light is directed towards the quadrature phase analyzer 220 and so little light returns to the light source that it can be ignored, allowing for the elimination of the Faraday isolator 170.

[0068] Particularly after removal of the Faraday isolator 170, it is desirable to reduce the amount of back reflection that can return into the laser 010. A typical cube beam splitter is designed to operate with a light beam perpendicular to its optical surface. Such a geometry results in back reflection where most of it can return into the laser 010, similar to the case of the polarization purifier 070 shown in FIG. 16. Since the beam splitting coating is designed to be suitable for an incident angle of 45°, rotating the cube beam splitter to prevent back reflection from returning to the laser may result in a degradation of the performance of the cube beam splitter. Also, the step of rotating the cube may cause drawbacks during assembly and manufacturing. The plate beam splitter is not a desirable option, as this beam splitter may be manufactured as a window where parallel interfaces can result in etalon fringes even when used at a large angle with respect to the optical beam axis. FIG. 17 provides a novel design of a polarization rhombic beam splitter 500 that avoids the incident light beam and the transmitted light beam perpendicular to the outer surface of the beam splitter. This ensures that any stray light reflected from the outer surface of the beam splitter is emitted from the optical system at a large angle rather than mostly returning to the laser 010. FIG. 17b shows a more detailed view of the polarization rhombic beam splitter and the geometry of the optical path. The polarization rhombic beam splitter is manufactured by joining two identical isosceles triangular prisms along the surface corresponding to the base of the triangle. The four surfaces corresponding to the sides other than the base of the triangle include the outer surface of the polarization rhombic beam splitter assembly. A polarization beam splitter coating is introduced onto at least one of the bonding target surfaces before bonding. Some or all of the outer surfaces can have an anti-reflection coating optimized for the light source wavelength and the incident angle to maximize the transmission of light passing through the polarization rhombic beam splitter. Further, some of the surfaces that are not used in the main intended function of the beam splitter can be ground to suppress specular reflection from these surfaces that may cause undesirable interference within the optical system.Furthermore, in order to further reduce these stray lights by absorption of any stray light that is considered to be reflected or scattered within the optical system, these ground surfaces can be painted black.

[0069] The outer surfaces of the polarizing rhomb beam splitter 500 are not perpendicular to each other, but the transmitted light beam is parallel to the incident light beam as in the case of a standard cube beam splitter. Also, when the polarizing rhomb beam splitter is oriented at an incident angle designed to match the polarizing rhomb beam splitter with respect to the incident light beam, the reflected beam is perpendicular to the incident light beam. θ inc A polarizing rhomb beam splitter designed to match an incident angle of θ = 5° has an apex angle ψ vertex manufactured from an isosceles triangular prism having = 80°. TIFF0007692549000005.tif10150

[0070] In this case, both prisms used to assemble this polarizing rhomb beam splitter are 50°-50°-80° triangular prisms. When operated at the designed incident angle, the light beam inside the polarizing rhomb beam splitter 500 is at some angle determined by the angle of the outer surface of the polarizing rhomb beam splitter 500 and the refractive index of the polarizing rhomb beam splitter 500. In this case, the incident angle onto the internal beam splitting interface can be calculated by the following formula. TIFF0007692549000006.tif23150In the above formula, n glass is the refractive index of the glass used to manufacture the prism. For optimum operation, the beam splitting coating is specially designed to match the operation at an incident angle of θ int For example, because the intended application is to ensure a highly linearly polarized light output, the coating used on the polarizing rhomb beam splitter 500 is designed to have a maximum polarization extinction ratio. As is apparent from FIG. 17b, the incident beam and the transmitted beam are not collinear, and therefore, the translation of the transmitted beam must be considered in the optomechanical design. FIG. 17b shows the incident angle θ intA polarization rhomb beam splitter 500 having θ = 5° is shown, but any angle that is sufficiently different from θ = 0° (corresponding to a cube beam splitter) may be beneficial in eliminating back reflections from the optical system. int Any angle that is sufficiently different from θ = 0° (corresponding to a cube beam splitter) may be beneficial in eliminating back reflections from the optical system.

[0071] A technique similar to that of the polarization rhomb beam splitter 500 can be applied to the lateral displacement beam splitter 420. The lateral displacement beam splitter 420 can be composed of prisms having angles between planes that are slightly different from 45°, 90°, and 135° in order to avoid the back reflection from returning to the laser 010.

[0072] In the embodiments of the present invention shown so far, a high coherence laser light source, that is, a light source having a long coherence length, is selected to ensure a high interference contrast due to the optical path length and the overall dispersion that both the signal light beam 090 and the reference light beam 100 encounter. As long as the coherence length is greater than the difference in optical path lengths (including errors due to the accumulation of tolerances in optical and mechanical designs), a high interference contrast can be observed. This is the case for a HeNe laser having a coherence length of about several tens of centimeters or more. Since an incompatibility between the optical path of the signal light beam 090 and the optical path of the reference light beam 100 is required to achieve a high contrast, the use of such a high coherence light source gives design freedom to the optical system. However, it is beneficial to match the optical path length of the reference arm and the optical path length of the signal arm. For example, an incompatibility in the optical path length between the signal light beam 090 and the reference light beam 100 may result in an undesirable drift or discontinuity in the interference signal. Any drift in the wavelength of the laser (e.g., due to temperature changes) results in a drift of the interference signal that varies in strength in proportion to the difference in the optical path lengths between the signal light beam 090 and the reference light beam 100. Similarly, mode hopping of the wavelength of the laser results in a discontinuity in the interference signal that is proportional to the optical path length difference. These problems are significantly reduced when the optical path length of the signal light beam 090 and the optical path length of the reference light beam 100 are matched, which is known to those skilled in the art as a desirable characteristic of an interferometer.

[0073] In a non - coherent light source such as a superluminescent diode (SLD) having a broad spectral bandwidth, any misalignment may not result in an interference signal, so the alignment requirements between both arms are very strict. The superluminescent diode has a coherence length of about 10 μm. This coherence length is smaller than the tolerances of most optical - mechanical components. For this reason, designers usually use an SLD for the optical beam deflection method in AFM, but the prior art teaches the use of a high - coherence laser source such as a HeNe laser or a laser diode as the basis for an interferometer in AFM. In other words, a skilled designer of the prior art selects a high - coherence laser for the interferometer despite the potential advantages of the SLD because the low coherence of the SLD is a significant problem.

[0074] Note that the alignment criteria between the signal light beam 090 and the reference light beam 100 to achieve interferometer contrast due to the dispersion and relatively broad spectral bandwidth of the SLD include the optical path length variable (discussed above) as well as the dispersion variable. The optical path length l of an optical component OPL is defined as the following formula. TIFF0007692549000007.tif10150In the above formula, x is the thickness of the optical component, and n O is the refractive index at the central wavelength λ of the low - coherence light source O . In contrast, the optical group path length includes the dispersion effect (first - order) and is defined as the following formula. TIFF0007692549000008.tif13150The ∂n / ∂λ term in the above formula represents the first - order dispersion of the glass. Similar to the case of the optical path length, the optical group path length of the signal light beam 090 is the sum of the incident part (before reflection from the cantilever) and the return part (after reflection from the cantilever), and the same is true for the optical group path length of the reference light beam 100.

[0075] In an interferometer design where the reference optical path and the signal optical path are not symmetric, simply matching the optical path lengths of both arms is not sufficient when using an SLD to achieve interferometer contrast. The criterion necessary to ensure high contrast is to match the total optical group path lengths between both arms taking into account the difference in dispersion between both arms involved in determining the conditions for optical contrast. In the following, the criterion for achieving contrast using an SLD is taken to mean not simply "matching of optical path lengths" in the absence of dispersion, but "matching of optical group path lengths" between the signal light beam 090 and the reference light beam 100.

[0076] For using the superluminescent diode 510 in the novel design shown in FIG. 18, the optical group path length of the reference arm has to be extended to achieve the interferometer contrast between the signal light beam 090 and the reference light beam 100. This extension can be achieved by deviating the light beam away from the optical axis using the wedge prism 515 as shown in FIG. 18. Next, the optical path wedge 430 can be used to deviate the light beam to a specified angle as required by the conventional design. The requirements regarding the angle of the optical path wedge 430 in this case are affected by the choice of the selected angle for the wedge prism 515. The distance between both wedges, as well as the selected wedge angles, can be adjusted to ensure that the reference light beam 100 has the same optical group path length as the signal light beam 090. By matching the optical group path lengths between both arms as required by the superluminescent diode 510, the advantages of such a low coherence light source, such as low background signal, periodic error, and artifacts, can be utilized in the context of this interferometer AFM. In other embodiments of the present invention, it should be noted that there may be cases where the optical group path length of the signal arm needs to be made longer than that of the reference arm, in which case a similar wedge is considered to be placed in the signal arm instead. Also, as mentioned above in the context of a free space laser light source, note that the use of a free space superluminescent diode in place of a fiber coupled superluminescent diode is optional.

[0077] The embodiment of the present invention shown in FIG. 19 proposes an alternative to the dual wedge design presented in FIG. 18. An optical group path matching window 520 is introduced into the reference optical beam 100 so that the optical group path lengths of both the reference optical beam 100 and the signal optical beam 090 are closely matched. This enables the matching of the optical group path lengths without the deviation of the optical beam using multiple wedges. The optical group path matching window 520 in this context is simply an optical window, and in this case, the type of glass is carefully selected with respect to its dispersion characteristics, and the thickness of the window is accurately adjusted to introduce an amount of optical group path length into the reference optical beam 100 that is sufficiently controlled so that the optical group path length of the reference optical beam 100 matches the optical group path length of the signal optical beam 090. Depending on the scenario, it may be necessary to introduce the optical group path matching window 520 into the signal optical beam 090, the reference optical beam 100, or both in order to achieve an ideal optical group path length match within the geometric optical constraints.

[0078] Due to the very short coherence length of the superluminescent diode 510, which is on the order of 10 μm, the matching of the optical group path lengths of both arms generally cannot be achieved in the manufacture and production of the instrument. For this reason, in order to precisely match both arms when the instrument is assembled and in an operating state, a device with an adjustable optical group path length must be introduced into the path of the signal light beam 090, the path of the reference light beam 100, or both paths. Preferably, the optical path wedge 430 can be moved in a direction perpendicular to the optical axis so as to change the amount of glass that the reference light beam 100 passes through, thereby changing the optical group path length of that arm. At typical wedge angles, this movement requires an actuator 440 that enables a movement of the optical path wedge 430 of about 1 mm to achieve a range sufficient to match both arms within optical tolerances and metal machining tolerances. Although separate wedges can be used for the matching of the optical group path lengths, it is preferred to also use the optical path wedge 430 previously used to change the angle of the reference light beam 100 in this situation. By using the optical path wedge 430 for both purposes, the number of optical components to be manufactured is reduced, and further, the number of back reflections and the complexity of the optical system are reduced. In this design, it should be noted that the optical path wedge 430 is used for three functions: giving a deflection angle to the reference light beam 100, calibrating the resurgence with a movement on the order of the wavelength of light, and matching the geometric path lengths between the reference light beam 100 and the signal light beam 090 with a large movement on the order of 1 mm.

[0079] Different cantilever types can have very different cantilever support chip thicknesses. For example, silicon chips are typically approximately 300 μm thick, while silicon nitride chips are typically approximately 500 μm thick. Switching between two such cantilevers requires two substantial changes to the optical design to achieve maximum contrast, namely changing the focal length of the reference beam defocusing lens 400 and adapting the optical group path length when a low coherence light source such as an SLD is used. The reference beam defocusing lens 400 can be changed to accept different cantilever thicknesses, but the change in the optical group path length may be greater than the range that can be compensated by the translation of the optical path wedge 430. For this reason, it may be preferable to switch between different types of optical group path adaptation windows 520 when switching between cantilever types. Each optical group path adaptation window 520 can be optimized for different cantilever support chip thicknesses. The fact that it may be necessary to replace two optical components after changing the cantilever type complicates the optical design of this instrument. Preferably, the embodiment of FIG. 20 combines the reference beam defocusing lens 400 and the optical group path adaptation window 520 into a single optical component called a solid beam defocuser 530. This optical component satisfies two functions: the change in focus and the change in optical group path length that occur when changing between cantilever types. This design combines both functions at the design level, thus making it possible to avoid adverse effects while the instrument is operating. Note that the solid beam defocuser 530 can be a simple single lens with a focal length and thickness adapted to a particular application, or any other type of optical lens. As shown in FIG. 20, the thickness of the solid beam defocuser 530 may need to be much greater than its diameter.

[0080] Furthermore, it is possible to combine the design of the solid beam focus blur device 530 with the third function of beam expansion or contraction described in the context of the embodiment of FIG. 14. In this case, using a thick meniscus lens as the solid beam expander 540 enables achieving all three functions that can be adjusted for any particular application and cantilever design. Note that the solid beam expander 540 and the solid beam focus blur device 530 can be manufactured from a single glass piece or, alternatively, from multiple glass pieces cemented together. Depending on the selection of the thickness and radius of curvature of any interface of the solid beam expander 540, the beam diameter 064 of the reference light beam 100 can be adjusted to be smaller or larger than the beam diameter 062 of the signal light beam 090.

[0081] Generally, the beam diameter 062 of the signal light beam 090 varies along the path of the signal light beam, and similarly the beam diameter 064 also varies along the path of the reference light beam 100. When comparing these diameters, it is advantageous to evaluate the diameter of each light beam at the back focal plane 330 of the microscope objective lens 110. When the diameter of the light beam measured at the back focal plane 330 is D BFP then the divergence of the same beam near the AFM cantilever is given by the following equation. TIFF0007692549000009.tif15150In the above equation, δ FFP is measured as the cone half-angle of the corresponding light beam near the cantilever, and f is the focal length of the objective lens 110. However, when determining whether the signal light beam 090 and the reference light beam 100 overlap, a plane substantially perpendicular to either the signal light beam or the reference light beam must be selected, and within this plane, the beam center and beam diameter must be evaluated by, for example, the first moment and the second moment as described in ISO11145:2018, according to methods known to those skilled in the art. For the purposes of the present invention, when the distance between the beam centers exceeds half the sum of their diameters, these beams are considered to be separated in a plane, i.e., they do not significantly overlap.

[0082] FIG. 20 shows a mechanical assembly 550 that enables switching between two or more solid beam expanders 540 or solid beam focus blurring devices 530, or any combination thereof. By enabling the user to manually switch between two or more modular solid beam expanders 540 or solid beam focus blurring devices 530, the optical system can be designed to accept several different cantilever types that can have different chip thicknesses, making it versatile in that regard.

[0083] To reduce the spectral bandwidth of the superluminescent diode 510, an optical bandpass filter 560 as shown in FIG. 21 can be used. By reducing the spectral bandwidth of the superluminescent diode 510, the coherence length increases at the expense of losing some refractive power. The coherence length l c is a function of the central wavelength λ0 of the light source and the spectral bandwidth λ BW as in the following equation. TIFF0007692549000010.tif20150 By reducing the spectral bandwidth, the range of available optical path differences between the path of the signal light beam 090 and the path of the reference light beam 100, which is determined by the coherence length, increases. Using a coherence length l c greater than the change in the thickness of the chip 130, the actuator 440 used to move the optical path wedge 430 to maximize the interferometer contrast can be eliminated from the design as shown in FIG. 21. This alternative embodiment simplifies manufacturing and usability.

[0084] During manufacturing, the optical bandpass filter 560 can be tilted to maximize the amount of transmitted light. This method enables adjustment of the effective central wavelength of the optical bandpass filter 560 to match the central wavelength of a specific superluminescent diode 510 of the instrument. This adjustment may be necessary since SLDs from a given model generally have a large manufacturing error in the central wavelength.

[0085] When introducing a fluid other than air, such as water or oil, around the cantilever, the optical group path lengths of both the reference light beam 100 and the signal light beam 090 are further affected. Another set of solid beam expanders 540 (or solid beam focus blurring devices 530) can be adapted to any combination of the cantilever type and the fluid surrounding it. To accommodate the four possible recombinations for two cantilever types and two fluids, it may be considered necessary to manufacture four solid beam expanders 540 as a possibility. Instead of this, the embodiment of FIG. 22 proposes the introduction into the system of additional optical elements that can accept the changes introduced by the introduction of the fluid around the cantilever. The reference light beam 100 requires blurring of the light beam using the fluid focus blurring lens 570, while any optical group path length difference between both arms is compensated by the introduction of the fluid compensation window 580 into the signal light beam 090. It should be noted that the fluid focus blurring lens 570 is simply any optical lens having a focal length, thickness, and material specially selected according to the application. Similarly, the fluid compensation window 580 is simply an optical window having a thickness and material selected to compensate the optical group path length as required by the optical design. To ensure that the optical group path length conforms closely enough as required by the optical system tolerances during manufacture, the thicknesses of both the fluid focus blurring lens 570 and the fluid compensation window 580 must be very carefully controlled. In this design, four recombinations can be accepted by combining the selection between two solid beam expanders 540 and the insertion or removal of both 570 and 580. The fluid compensation slider 590 of FIG. 22 is a mechanism that allows the user to slide both 570 and 580 together in and out of the optical system using a single actuation mechanism. The fluid compensation slider 590 can be actuated manually by the user or by an automatic mechanism that can be computer controlled.

[0086] Despite all the advantages of interferometry such as signal accuracy and low noise independent of the cantilever length, the deflection of the optical beam enables the measurement of the angular bending of the cantilever in two directions (vertical and horizontal) that interferometry cannot directly measure. For this reason, AFM users can achieve advantages by using OBD in combination with an interferometer that has been commercially available in recent years from Oxford Instruments. In this prior art instrument, two separate light sources and optical beam positioning units 370, as described in US10338096B2, are used simultaneously to provide the user with two independent measurement methods. In contrast, in the present invention shown in FIG. 23, the same light source is used for both the interferometer and the OBD system. There are obvious cost advantages and design simplicity in using a single light source to provide both functions. As shown in FIG. 23, an optical beam deflection beam splitter 600 is used in the path of the signal light beam 090 to reflect some of the light returning from the cantilever for use in the OBD optical path. This optical beam deflection beam splitter 600 can be any type of beam splitter, such as a cube beam splitter or a plate beam splitter, that divides the light beam into a transmitted light beam and a reflected light beam. Preferably, the optical beam deflection beam splitter 600 has the property of being polarized such that only a significant amount of light on the return signal light beam 090 is reflected, while only a minimal amount of light on the incident signal light beam 090 is lost by reflection. The reflected light beam is referred to as the optical beam deflection light beam 610. The optical beam deflection light beam 610 is then reflected from an optical beam mirror 620 that can be used to center the optical beam deflection light beam 610 relative to the optical beam photodetector 630 by using an optical beam gimbal 640 or other rotation mechanism. Another option not shown is to use a translation stage attached to the optical beam photodetector 630 to center the optical beam photodetector 630 relative to the optical beam deflection light beam 610 instead. By centering the optical beam deflection light beam 610 relative to the optical beam photodetector 630, maximum sensitivity is obtained, as is known to those skilled in the art of the OBD method.To measure the vertical and horizontal angular deflections of the cantilever, it is sufficient to reflect only a small component of the refractive power of the optical beam deflection optical beam 610 by the optical beam deflection beam splitter 600. These two measurements are independent of the interferometer displacement measurement that occurs simultaneously, even though all three of these measurements are made from a single optical beam that is focused on the cantilever.

[0087] In FIG. 23, the reflected light emitted from the optical beam deflection beam splitter 600 is shown to be in the same plane as the other optical beam reflected light within the optical system. However, in order to utilize the polarization optical beam deflection beam splitter 600 to avoid optical losses, it may be necessary for the beam splitter to reflect the light out of the same plane instead of within the same plane. This arrangement is not shown in FIG. 23 due to the constraints imposed by the two-dimensional drawing.

[0088] Another embodiment of the present invention is illustrated in FIG. 24 in which the functionality of the above-described optical beam deflection beam splitter 600 is integrated into the lateral displacement beam splitter 420 to form a single optical element coupling assembly, i.e., a lateral displacement beam splitter 635 with a sampler. The lateral displacement beam splitter 420 uses a fully reflective optical interface 424, whereas the lateral displacement beam splitter 635 with a sampler uses a partially reflective interface 636 shown in FIG. 24b to sample a portion of the light from the return signal light beam 090 for use in optical beam deflection measurements as shown in FIG. 24c. The partially reflective interface 636 replaces the functionality performed by the optical beam deflection beam splitter 600, i.e., the functionality of deflecting a portion of the return signal light beam 090 towards the optical beam photodetector 630. The reduction in the number of optical interfaces through which the signal light beam 090 used in the interferometric measurement passes improves the interferometer contrast. Note that the introduction of an additional triangular prism 637 (shown in FIG. 24b) into the lateral displacement beam splitter 635 with a sampler with respect to the lateral displacement beam splitter 420 is optional. The additional prism can be beneficial for redirecting the light towards the photodetector as shown in FIG. 24 and can further be beneficial for protecting the partially reflective interface 636. The partially reflective interface 636 can be a coating having no specific polarization properties. However, in a preferred embodiment, a polarization coating is used that reflects all of the light on the incident signal light beam 090 to avoid light loss and at the same time transmits a specified component of the light on the return signal light beam 090 as shown in FIG. 24c. The transmitted portion of the signal light beam 090, referred to as the optical beam deflection light beam 610, is redirected from the lateral displacement beam splitter 635 with a sampler by internal reflection and is reflected from the optical beam mirror 620 towards the optical beam photodetector 630 as in the case of the previous embodiment.

[0089] FIG. 25 shows an embodiment of the present invention where a cantilever is attached to a mechanical actuator 650, such as an assembly having a piezoelectric transducer. This embodiment enables the cantilever to be moved parallel to the optical axis of the microscope objective system 110 or at any angle with respect to the optical axis. Using this mechanical actuator 650, for example, the topography of a sample can be traced during AFM imaging. Due to the differential nature of the interferometer, the cantilever displacement signal continues to record the displacement difference between the cantilever and the cantilever support tip. Since this signal is proportional to the force acting on the cantilever tip, it is this signal for the AFM user. The usable range of motion for the mechanical actuator 650 is on the order of the depth of focus of the focused signal light beam 090 and the reference light beam 100. This depth of focus is sometimes referred to as the Rayleigh range of the focused light beam. If it is larger than this range of motion, a loss of interferometer contrast that results in higher noise is brought about. The depth of focus of the signal light beam 090 and the reference light beam 100 can be adjusted to match the required range of motion of the mechanical actuator 650 by the method of the present invention described above.

[0090] A mechanical actuator 650 that moves the cantilever along the optical axis near the focal plane of the microscope objective system 110 may introduce artifacts caused by crosstalk between this motion of the cantilever and any cantilever displacement with respect to the tip of the cantilever in the signal measured by the photodetector. To reduce this crosstalk, a back focal plane imaging lens 660 shown in FIG. 25 is introduced, and its focal length and location can be selected to project the back focal plane 330 of the microscope objective system 110 onto the optical beam photodetector 630. The back focal plane imaging lens 660 ensures that the photodetector measures substantially only the cantilever deflection signal while minimizing the effect of the motion of the mechanical actuator 650 on the measured signal. Further, the back focal plane imaging lens 660 can reduce the range required by the optical beam gimbal 640 to center the optical beam deflection light beam 610 with respect to the optical beam photodetector 630.

[0091] The use of superluminescent diodes with respect to lasers reduces the effect of stray reflections and maintains accurate measurement of cantilever displacement. Nevertheless, stray reflections can reduce accuracy and increase noise in some cases. For this reason, cementing optical components together can be optimal for reducing the number of air - glass interfaces that can cause back - reflection. The quadrature phase analyzer 220 shown in FIG. 25b is manufactured using optical components cemented together, namely, two polarizing beam splitters, a non - polarizing beam splitter, a half - wave plate, and a quarter - wave plate. The cement design prevents fine - tuning of the optical properties of the system by individually rotating and / or tilting the optical elements during assembly and testing of the AFM. For this reason, careful manufacture of the wave plates used in the quadrature phase analyzer 220 and strict specifications for phase shifts in coating are required to ensure the optical interferometer contrast. The advantages of assembling a cemented quadrature phase analyzer include not only the reduction of optical interfaces but also the robustness of the optical properties of the quadrature phase analyzer by making the optical system less susceptible to thermal drift, mechanical shock, or other forms of damage. Finally, the compactness of the cement design aids in the manufacturability of the instrument. This configuration of the quadrature phase analyzer 220 can be advantageously used in any of the arrangements of the present invention.

[0092] In one possible embodiment of the quadrature phase resolver 220, the quarter-wave plate 270 and the half-wave plate 240 are manufactured as true zero-order wave plates. A true zero-order wave plate is a wave plate that has a phase difference shorter than one wavelength between the ordinary ray and the extraordinary ray without using cancellation from a plurality of birefringent material pieces. To manufacture a true zero-order wave plate, it is necessary to grind and polish a birefringent material such as quartz to a thickness of several tens of micrometers with high precision. This additional cost of the manufacturing step is compensated for by the improvement in the performance of the quadrature phase resolver 220 and the low sensitivity of the performance of the quadrature phase resolver 220 to the angular error of the input light beam, as well as the low sensitivity to the difference between the design wavelength (of the wave plate) and the central wavelength of the light source. The reduction in sensitivity to the optical beam wavelength is particularly important in a low-coherence light source, which implies that a wide spectrum of the light source can only approximate the desired behavior of the wave plate. Since the true zero-order wave plate is not very wavelength-dependent, it has high-quality performance over the maximum spectral bandwidth of a low-coherence light source. For reasons of similar performance, it is preferable to make the quarter-wave plate 490 or other quarter-wave plates in the signal light beam and the reference light beam into true zero-order types.

[0093] In addition to this, there may be cases where the back reflection from the photodetector is large and it is difficult to reduce it using an antireflection coating. To avoid these back-reflected lights from entering the optical system, as shown in FIG. 25b, four quarter-wave plates 670 can be arranged between each of the polarization beam splitters 280 and 250 and the four photodetectors 260, 262, 264, and 266. The ordinary axis and the special axis of the quarter-wave plate must be rotated by 45° with respect to the beam splitter axis around the optical axis. In this arrangement, the light reflected from the photodetector will exit the unused facet of the quadrature phase resolver instead of interfering with the recombined light beam 200 in the quadrature phase resolver.

[0094] During the experiment, any drift between the optical path length of the reference light beam 100 and the optical path length of the signal light beam 090 may be misinterpreted as a cantilever displacement. This drift may be caused by the thermal dependence of the refractive index of the glass used in the optical system and the thermal expansion of the material holding the lenses relative to each other. A temperature control system can be used to stabilize the temperature of the metal platform connecting all the lenses, thereby keeping the optical system at a constant temperature even when the room temperature changes over time. Such a system can incorporate one or more temperature sensors, one or more elements capable of changing the temperature, such as a resistive heater or a Peltier thermoelectric cooler, an optional device for controlling the air flow, such as a blower, and a controller, such as a proportional-integral-derivative controller, capable of actuating the temperature-changing element in response to a signal from the temperature sensor. Such temperature control systems are known to those skilled in the art.

[0095] So far, the cantilever has been arranged perpendicular to the optical axis of the microscope objective system 110. This arrangement is a particular scenario that may not be optimal in certain situations. In a preferred embodiment, the light beam is incident off-center on the back focal plane 330, thereby focusing perpendicularly with a cantilever and a chip arranged at any non-vertical angle with respect to the optical axis of the microscope objective system 110 while the objective system emits at an angle with respect to its optical axis. Such an arrangement is described in detail in US8370960B2, where in this case, the AFM uses an angle of about 11°, and the light is incident off-axis on the objective system to accept this angle. All embodiments presented in this patent can be modified to achieve such a geometry. By satisfying the conditions necessary to accept an intentionally tilted cantilever, the conclusions drawn so far remain valid. For example, any tilt of the cantilever deviating from the designed angle of 0° defined in this embodiment can be considered to have a similar effect to any tilt deviation from the 11° cantilever defined in the embodiment optimized for 11°.

[0096] In summary, in the design of an atomic force microscope, it is desirable to achieve high accuracy, low noise, low drift, good optical access, and equally good position noise performance regardless of the user's choice of the type of AFM cantilever. For these and other reasons, the lens referred to herein as the "objective lens" advantageously constitutes an interferometer and is configured to focus the signal light beam and the reference light beam onto or near the AFM cantilever. The objective lens can be a microscope objective lens, a doublet lens, an imaging lens, or other types of lenses known to those skilled in the art. The typical width of an AFM cantilever is between 3 μm and 50 μm, and the width of the cantilever sets the maximum size of the signal light spot, and further the maximum size of the signal light spot sets the minimum divergence of the signal light beam in the space between the cantilever and the lens. Further, the typical length of an AFM cantilever is between 10 μm and 500 μm, and the diameter of the field of view of a typical microscope objective lens is less than 4 mm. These factors limit the maximum separation between the signal light beam and the reference light beam in the space between the AFM cantilever and the objective lens. These factors contemplate the overlap between the signal light beam and the reference light beam in the far field and make it difficult to independently manipulate these beams to achieve the design goals.

[0097] Embodiments of the present invention provide a differential interferometer suitable for use in an atomic force microscope in which a signal light beam 090 and a reference light beam 100 are focused near an AFM cantilever 120 using a lens 110 (the "objective lens") and the signal light beam and the reference light beam do not substantially overlap with respect to any portion of the optical space (the optical space referred to herein as the "infinity space") separated from the AFM cantilever 120 by the objective lens and are independently manipulated within the region of the infinity space. That is, in at least one plane within the region of the infinity space, the intersection of the axis of the signal light beam with this plane is separated by more than half the sum of the diameters of these beams from the intersection of the axis of the reference light beam with this plane. This differential interferometer is referred to as a separated-beam differential interferometer, and this basic innovative technique facilitates several refinements and improvements to be discussed below.

[0098] In a split-beam differential interferometer, the signal light beam 090 will generally be focused near the end of the AFM cantilever 120 or near the location on the cantilever where it interacts with the sample. The reference light beam 100 can be focused on the cantilever support tip 130 at the base of the cantilever 120 or on a reflective object rigidly attached to the cantilever support tip. The split-beam geometry provides design freedom for manipulating the lateral position, divergence, and axial position of the focus of the reference light spot without inserting undesirable optical elements between the objective lens 110 and the AFM cantilever 120.

[0099] In an atomic force microscope, it is advantageous to obtain a high-resolution, high-contrast optical image of the sample and the cantilever in order to select the region of interest to be explored using the AFM cantilever. In some applications, it is also advantageous to introduce additional separate optical paths (e.g., path 380 and optical beam positioning unit 370) for purposes such as illumination of the cantilever 120 with a laser for photothermal actuation of the bending of the cantilever, illumination of the sample to measure the photoelectrochemical response of the sample, and / or detection of light emitted from the sample. For this purpose, a combination with a microscope objective having a numerical aperture greater than 0.25, a combination with a microscope objective providing adjustable correction of spherical aberration, a combination with a microscope objective having semi-apochromatic correction or a better level of color correction, a combination of a microscope objective, a tube lens, and a camera system 190 that provides a resolution better than 2 μm in the sample plane, a combination of a microscope objective, a tube lens, and a camera system 190 that provides a modulation transfer function of 50% or better at 250 line pairs per millimeter in the sample plane, a combination of a microscope objective, a tube lens, and a camera system 190 having a resolution in the range of twice the diffraction limit with respect to the numerical aperture of the objective at the operating wavelength, it is advantageous to use a split-beam differential interference microscope in one or more of the above, with one or more optical paths providing a fixed or movable illumination spot for the cantilever and the sample, an optical path providing a movable time-modulated illumination spot configured for photothermal excitation of the cantilever, and one or more optical paths configured for detection of light from the sample or the cantilever.

[0100] In a differential interferometer, it is necessary to deviate the signal light beam 090 from the reference light beam 100 and then recombine these beams after reflection from the target object and the reference object. In many implementations of the present invention, it is advantageous to split and recombine these beams using a polarization-selective dielectric coating that is lower in cost, more readily available, easier to configure in design, and provides a large effective aperture and good transmitted wavefront specifications than the birefringent optical systems used in the prior art for splitting and recombining the signal and reference light beams. This use of the dielectric coating is only possible by the separation of the beams in the infinite space within the separated-beam differential interferometer.

[0101] One implementation of a split-beam differential interferometer using a polarization-selective dielectric coating incorporates a first cube beam splitter that divides a reference light beam from a signal light beam, and a second cube beam splitter that redirects the signal light beam so that it is substantially parallel to the reference light beam. Another implementation replaces the second cube beam splitter with a 45°-45°-90° prism arranged so that internal reflection redirects the signal light beam parallel to the reference light beam. Another implementation replaces the second cube beam splitter with a mirror or other reflective optical system to effect this path change. Another implementation combines the function of the first cube beam splitter and the second optical system into a monolithic composite prism referred to herein as a “lateral displacement beam splitter” 420, in which case a plurality of prism elements having appropriate coatings are joined together to form an assembly that divides the reference light beam from the signal light beam and guides these two beams substantially parallel to each other. For any of these implementations, as long as the other optical elements within the system are arranged so that the signal light beam and the reference light beam are properly focused on the target object and the reference object, respectively, one of ordinary skill in the optical design art can choose to divide the reference light beam from the signal light beam and then redirect the signal light beam, or alternatively can choose to divide the signal light beam from the reference light beam and then redirect the reference light beam. This separation of these beams in the novel split-beam differential interferometer improves the degree of freedom in selecting and arranging these components to achieve the design goals regarding the optical system.

[0102] A split-beam differential interferometer using a lateral displacement beam splitter 420 allows for yet another improvement to the design. First, it is desirable to transmit as much of the return signal light beam 090 and the return reference light beam 100 as possible to the photodetector. This provides the best noise performance of the photodetector and the best stability of the optical source. When the lateral displacement beam splitter or an equivalent optical arrangement discussed above is used in combination with a split-beam differential interferometer, substantially all of the return light can be transmitted to the photodetector by inserting one or more waveplates between the objective lens and the lateral displacement beam splitter. A single quarter-waveplate 490 with its special axis rotated by 45° can be arranged so that the signal light beam and the reference light beam pass through it. Alternatively, a first quarter-waveplate can be placed in the signal light beam and a second quarter-waveplate can be placed in the reference light beam. Other combinations of optical systems, such as dielectric coatings, can be used to produce an effect similar to that of the quarter-waveplate.

[0103] Another improvement is that the lateral displacement beam splitter can be operated to introduce a relative phase shift between the signal light beam and the reference light beam. This operation is desirable because it allows the user to calibrate the photodetector's response to the phase shift and produce a more accurate interpretation of the phase shift between the signal light beam and the reference light beam. This enables a more accurate measurement of the distance between the target object and the reference object.

[0104] In order to generate a desired transverse separation between the reference light beam and the signal light beam near the AFM cantilever, the optical system must be positioned to generate a corresponding angular difference between the reference light beam 100 and the signal light beam 090 in the infinite space. In the prior art, this angular difference is obtained using a birefringent optical system such as 320 to deviate these beams from each other. In an embodiment of the present invention, due to the separation between the signal light beam and the reference light beam in the separated beam differential interferometer, this angular difference can instead be generated by introducing an optical wedge prism 430 into the reference light beam rather than the signal light beam. By selecting the angle and refractive index of the optical wedge prism, the reference light beam can be deviated by a desired angle with respect to the signal light beam. Alternatively, the optical wedge prism can be introduced only into the signal light beam rather than the reference light beam, or wedges of different angles and / or refractive indices can be introduced into both the signal light beam and the reference light beam as long as the combined effect of these wedge elements generates a desired angular difference between the signal light beam and the reference light beam in the infinite space and correctly directs the reference light beam and the signal light beam to the reference object and the target object, respectively. For this purpose, the optical wedge prism is cheaper and more readily available than the birefringent optical system, and the advantages of using the optical wedge prism for this application can be realized for the first time by the separated beam in an embodiment of the present invention.

[0105] Using an optical wedge prism to generate a desirable angular difference within a split-beam differential interferometer provides an additional advantage to the present invention. For example, it may be desirable to configure the design such that the reference light beam and the signal light beam are substantially parallel near the cantilever, to maximize the focusing of the reflected light or to minimize misalignment caused by axial movement of the cantilever or the objective lens. To achieve a parallel beam near the cantilever, it is necessary to arrange the optical system such that the signal light beam and the reference light beam intersect within the back focal plane 330 of the objective lens 110. This intersection must be achieved while maintaining the declination reference discussed above. In a design using an optical wedge prism, this can be achieved by selecting the location of the wedge in combination with the magnitude of the lateral displacement between the signal light beam and the reference light beam. Alternatively, multiple optical wedge prisms, such as 515 and 430, can be arranged to provide the correct angular difference and intersection at the back focal plane.

[0106] According to embodiments of the present invention, yet another advantage is provided by using one or more optical wedge prisms within a split beam differential interferometer. Due to the splitting of these beams, the optical wedge prism can be present only within (or alternatively only within) the reference light beam. Such an optical wedge prism changes the optical group path length of only one of these beams and can be translated to do so without creating a substantial misalignment between the angles or locations of the beams. This translation generates an adjustable relative phase between the signal light beam and the reference light beam. This adjustment function is highly desirable. One application suitable for this adjustment function is to calibrate the photodetector response for a known phase difference between the signal light beam and the reference light beam. This enables a more accurate measurement of the height difference between the target object and the reference object. A second application is to adjust the initial value of the phase difference between the signal light beam and the reference light beam to any desired value. When the optical wedge prism has a small wedge angle, this adjustment can be made very precise, such as in the range of a small ratio of wavelengths, using conventional optomechanical components. The translation of the optical wedge prism can be achieved using an actuator 440, such as an electrically driven feed screw translation stage, a piezoelectric actuator, a combination of a feed screw stage and a piezoelectric actuator, or other translation means known to those skilled in the art.

[0107] In the present invention, the separation of the signal light beam from the reference light beam in a split-beam differential interferometer provides yet another advantage by enabling the introduction of optical lenses such as 400 or 460 and 470 into one or both of the beams. This allows for a desirable control of the properties of a portion of the light beam. For example, one configuration of a split-beam differential interferometer guides the signal light beam to the end of the AFM cantilever (target object) and the reference light beam to the cantilever support chip (reference object). To maintain the highest contrast, the axial position of the focus of the signal light beam must be on or near the surface of the target object, and the axial position of the focus of the reference light beam must be on or near the surface of the reference object. However, these surfaces are at different axial positions. The optical system must be configured to create this focus difference, and it is preferable to do so without introducing optical components between the objective lens and the cantilever. In a split-beam differential interferometer, this focus difference due to the beam separation can be achieved by introducing one or more lenses entirely into the infinite space within one or both of the signal light beam and the reference light beam. For example, a single lens or a compound lens having a net positive refractive power can be introduced into the reference light beam within the infinite space, and the focus of the reference light beam can be shifted axially towards the objective lens compared to the focus of the signal light beam. Alternatively, a similar effect can be achieved by introducing a lens having a net negative refractive power into the signal light beam within the infinite space. Alternatively, lenses can be introduced into both light beams as long as the combination of lenses produces the desired relative focus change (hereinafter "spot focus difference") between the signal light beam at the target object and the reference light beam at the reference object.

[0108] In an embodiment of the present invention, the lens can be used in a particular method that provides further advantages regarding the operation of a split-beam differential interferometer by introducing it independently into the signal light beam and the reference light beam. Desirable features for an AFM using such an interferometer are the ability to function with various different cantilever types (such as both silicon cantilevers and silicon nitride cantilevers), and the ability to image samples in various fluids (such as air, water, or oil). The various cantilever types have support chips with various thicknesses, and the support chips have various tolerance ranges with respect to the cantilever support chip thickness. The various fluids have various refractive index values, and the refractive index of the fluid affects the axial focal position of the signal light beam and the reference light beam near the AFM cantilever. These factors, in combination, mean that it is advantageous that the spot focal difference can be adjusted during operation. One way to achieve this adjustability is to introduce a combination of lenses (such as 530 and 540 etc. or 580 and 570) that can be adjusted to generate a variable spot focal difference into one or both of the light beams in the infinite space. Alternatively, one or more fixed lens assemblies, each of which produces a different effect on the spot focal difference, can be configured, and these fixed lens assemblies can be combined with one or more selection means such that the user can introduce one or more of the fixed lens assemblies into one or more of the beams in the infinite space. Preferably, the selection means is considered to allow the replacement of these assemblies so as to introduce each fixed lens assembly without the need for additional alignment by the user. By selecting one or more of these fixed lens assemblies for introduction into the signal light beam, the reference light beam, or both, the user can then select the desired spot focal difference that gives the best contrast for a particular combination of conditions, for example, optimized for a silicon cantilever in air on one day and optimized for a silicon nitride cantilever in water on another day.

[0109] In particular, in the case of an interchangeable fixed lens assembly, there will be a certain range of tolerances in the adaptation of the spot focus difference to the operating conditions. Therefore, in this case, it is possible to provide yet another advantage of controlling the depth of focus of the signal light beam, the reference light beam, or both of these beams near the AFM cantilever. This control is achieved by controlling the divergence of the signal light beam and the reference light beam near the AFM cantilever. This divergence can then be controlled by manipulating the diameter of the corresponding beam in the infinite space. Embodiments of the present invention provide the advantage of freely and independently manipulating these divergences by independently introducing lenses into one or both of the beams. This manipulation is adjusted so that the optical design of the variable combination of lenses or interchangeable fixed lens assemblies results in not only the desired positive or negative power but also the desired depth of focus for the corresponding light beam near the AFM cantilever, generating a beam diameter change as well. This can be done in combination with the variable spot focus difference design or the selectable spot focus difference design described above.

[0110] In contrast to conventional techniques, the inventor has found that operating an interferometer with a low-coherence light source, such as superluminescent diode 510, provides certain advantages. In the case of the invention considered herein, surfaces that are substantially farther from the AFM cantilever than the coherence length of the light source do not contribute to the interference signal. The use of a low-coherence light source suppresses periodic errors and artifacts that would otherwise be caused by partial reflections at other optical surfaces within the interferometer output. Herein, such periodic errors and artifacts are referred to as "three-wave mixing" regardless of the exact nature of the partial reflections that give rise to them. To operate the split-beam differential interferometer of the invention with a low-coherence light source, the optical group path length of the signal light beam and the optical group path length of the reference light beam need to be matched within a range that is substantially smaller than the coherence length of the light source, which is generally less than 20 μm for a superluminescent diode. The split-beam of the invention provides several advantages for achieving this match. One or more optical wedge prisms can be operated to match the optical group path lengths without causing misalignment of the light beam or its focus on the target and reference objects within one or both of the light beams. In the case of a small wedge angle, the optical group path length can be matched within a small fraction of the wavelength using a conventional optical positioner. Further, when there is a large mismatch between the optical group path lengths of the signal and reference light beams, a thick optical window 520 having a thickness and refractive index selected to approximately match the optical group path lengths between these beams can be fixed within one or the other beam. When selectable lens assemblies, such as 540 and 530, are introduced into one or both of the beams, these lens assemblies can be designed to incorporate a thick window having a thickness and refractive index selected to approximately match the optical group path lengths between these beams under all combinations of selectable lens assemblies by the user. In both of these cases, the match by the thick window must be close enough that the remaining optical group path length difference can be eliminated by adjustment of one or more optical wedge prisms.

[0111] In some embodiments of the present invention, it may be unduly burdensome to precisely match the optical group path length differences as described above. In such situations, it may be desirable to have a light source that has an intermediate coherence length that is short enough to partially suppress third-order mixing compared to a laser light source, but long enough to easily provide a sufficiently good match between the optical group path length of the signal light beam and the optical group path length of the reference light beam. Since a laser has an unduly long coherence length and a superluminescent diode has an unduly short coherence length, this light source may not be readily available. In this case, it is advantageous for a split-beam differential interferometer to be configured using a superluminescent diode light source 510, and then to insert a bandpass filter 560 between the light source and the optical system that splits the signal beam and the reference beam from each other. Preferably, this bandpass filter is selected to reduce the emission spectral width of the superluminescent diode light source, thereby increasing its coherence length to a desired intermediate value. It may be further desirable to provide a bandpass filter having an optomechanical mount that incorporates an adjustable tilt due to manufacturing variations in the center wavelength of the superluminescent diode and the center wavelength of the bandpass filter. Since the center wavelength of the bandpass filter depends on its tilt angle, this variable tilt can be adjusted to maximize the spectral overlap between the emission spectrum of the superluminescent diode and the transmission spectrum of the bandpass filter, thereby maximizing the optical throughput and the signal-to-noise ratio at the interferometer photodetector. Alternatively, other means such as combining a diode laser with an RF-modulated light source can be used to generate a beam having an intermediate coherence length.

[0112] According to an embodiment of the present invention, a separated-beam differential interferometer measures the displacement of an AFM cantilever regardless of the angle of the cantilever. In most applications, this measurement is sufficient, but in some applications, it is desirable or necessary to measure the vertical and horizontal angles of the cantilever. In a separated-beam differential interferometer, this angle measurement can be achieved by introducing an additional beam splitting element 600 into the signal light beam. This additional beam splitting element captures the light returning from the cantilever and redirects a portion of it (this portion is the "angle detection beam") to an angle light detector 630, such as a split photodiode, a quadrant photodiode, or a linear position sensitive detector, by a centering means (e.g., 640). The centering means can be a translation stage, a tilt stage-mounted mirror 640, or any other adjustable element that enables centering of the light on the angle light detector. When the lateral displacement beam splitter 420 described above is provided in the separated-beam differential interferometer, for example, the additional beam splitting element can be incorporated into the assembly of the lateral displacement beam splitter 635 with a sampler by replacing the surface that reflects the signal light beam parallel to the reference light beam with a partial reflection coating that separates the angle detection beam from the return signal light beam.

[0113] In addition, when one or more wave plates configured to transmit substantially all of the return light away from the light source are provided in the separated-beam differential interferometer, the additional beam splitting element can be designed to have a polarization selectivity coating so that substantially all of the return light reaches either the interferometer light detector or the angle light detector. By transmitting the light in this way, an unnecessary decrease in the signal-to-noise ratio on any of the interferometer light detectors 260, 262, 264, 266 or the angle light detector 630 is avoided.

[0114] In some applications of the atomic force microscope, it is advantageous to operate the AFM cantilever perpendicular to the sample as it traverses the sample surface during scanning. For example, the sample may be too large or heavy to be actuated quickly, and thus, by actuating the AFM cantilever, faster imaging of the sample can be achieved. In such cases, the split-beam interferometer of the present invention is advantageously combined with an AFM cantilever mounted on a mechanical actuator 650 that moves the cantilever support tip along an axis within 20° of the axis of the objective lens used to focus the signal and reference light beams.

[0115] In the split-beam differential interferometer according to an embodiment of the present invention, and in still other differential interferometers, it is desirable to calibrate the response of the photodetector as a function of the phase difference between the signal and reference light beams. It is advantageous to effect this calibration by introducing an electrically controlled birefringent liquid crystal device (LCD) 450 into the optical system. There are several LCD arrangements that can modulate the phase difference between the signal and reference light beams. The LCD 450 can be placed in the recombined light beam between the beam splitter optical system 420 and the quadrature phase analyzer 220 in a differentially oriented state to impart a substantial phase shift to only one of the signal and reference lights. Alternatively, the LCD can be placed between the light source and the beam splitter optical system in a differentially oriented state to impart a substantial phase shift to only one of the signal and reference lights. Alternatively, the LCD can be placed only within the signal light beam or only within the reference light beam within the space of the split-beam path, but only in the case of a split-beam differential interferometer. It may be further advantageous to electrically activate the LCD to calibrate the interferometer before measuring the cantilever, and then electrically turn the LCD on and off by setting the voltage of the LCD to be much lower than 1V during the measurement of the cantilever. This on-off operation reduces noise and drift in the measured values.

[0116] The present invention can incorporate a plurality of photodetectors (260, 262, 264, and 266) arranged in combination with an assembly incorporating one or more beam splitters and one or more waveplates (e.g., 230, 240, 250, 270, 280), and this optical element assembly is referred to herein as an "orthogonal phase resolver." Within a split-beam differential interferometer, the orthogonal phase resolver 220 causes the signal light beam and the reference light beam in at least two distinct optical paths, each having a substantially different additional phase shift between the signal light beam and the reference light beam, to interfere. It is advantageous to provide these optical elements as a monolithic optical assembly, where each optical element is coupled in direct optical contact with the adjacent optical element, and each element is coupled in the correct orientation and alignment. Such a monolithic assembly has only weak reflections compared to the reflections at the glass-air interfaces in prior art arrangements due to the refractive index matching at the coupling interfaces. The monolithic assembly thereby reduces unwanted signals and artifacts in the output of the interferometer. Further, the monolithic assembly has higher resistance than the prior art to mechanical drifts of the beam splitters and waveplates due to mechanical shocks and thermal induction, both of which introduce unwanted artifacts into the output of the interferometer. Implementing this monolithic assembly while maintaining desirable small component dimensions may require non-conventional optical component designs such as a square half-wave plate 240 with a special axis at an angle of 22.5° with respect to the edge and a square quarter-wave plate 270 with a special axis at an angle of 45° with respect to the edge. The configuration of the monolithic assembly may require tight specification tolerances and component alignment since alignment is not possible after bonding. However, when these tolerances are met, the completed monolithic assembly maintains stable alignment indefinitely and provides advantages for the operation of the interferometer. The novel use of the monolithic orthogonal phase resolver is not limited to split-beam differential interferometers suitable for use in atomic force microscopes.Instead, such a monolithic assembly can find use in other devices that interfere a signal light beam and a reference light beam in at least two distinct optical paths each having a substantially different additional phase shift between the signal light beam and the reference light beam, and incorporate a plurality of photodetectors. Such other uses can include split-beam differential interferometers for applications other than atomic force microscopy, orthogonal interferometers whether or not composed of differential schemes, and measurement of quantum states in quantum computing and quantum cryptography techniques.

[0117] More specifically, in some embodiments of the present invention, a particularly advantageous configuration of the monolithic quadrature phase analyzer includes a non-polarizing cube beam splitter 230 that receives a signal light beam and a reference light beam and splits both of them between two optical paths, an optional first waveplate 240 that generates a first additional phase shift (optionally zero) between these light beams, a first polarizing cube beam splitter 250 that interferes the light beams having the first additional phase shift and splits this light by polarization and directs each polarized light towards a photodetector, a second waveplate 270 that generates a second additional phase shift between these light beams, and a second polarizing cube beam splitter 280 that interferes the light beams having the second additional phase shift and splits this light by polarization and directs each polarized light towards a photodetector. In this arrangement, the first additional phase shift and the second additional phase shift must differ by only a value close to substantially 90°, close to 270°, or close to another odd multiple of 90°. There are many waveplate configurations that a person skilled in the art can select to complete this combination of additional phase shifts. For example, the first waveplate can be a half-wave plate with its special axis inclined at 22.5° with respect to the plane of the assembly, and the second waveplate can be a quarter-wave plate with its special axis inclined at 45° with respect to the plane of the assembly. Alternatively, the first waveplate can be eliminated, the second waveplate can be a quarter-wave plate with its special axis inclined at 45° with respect to the plane of the assembly, and the entire monolithic quadrature phase analyzer is arranged such that the plane of the assembly is at 45° with respect to the polarization of the signal light beam. Within this assembly, the components are monolithically coupled so as to suppress unwanted reflections, reduce drift, and improve the shock-resistant structure as described above. This particular embodiment of the monolithic quadrature phase analyzer can find applications in fields other than atomic force microscopes as detailed above.

[0118] Despite the advantages of the monolithic quadrature phase analyzer, this quadrature phase analyzer may still suffer from artifacts resulting from reflections from the surface of the photodetector. In embodiments of the present invention, there is yet another advantage of adding a waveplate 670 between each photodetector 260, 262, 264, 266 and the corresponding surface of the quadrature phase analyzer 220. This waveplate must be a quarter-wave plate with a special axis rotated 45° from the plane common to all beams in the quadrature phase analyzer. Such a waveplate changes the polarization of the back-reflected light from each photodetector, passes the reflected light to the unused surface of the quadrature phase analyzer, thereby reducing the artifacts that may be caused by the reflected light. These waveplates can be coupled to the above-described monolithic quadrature phase analyzer to further reduce the reflection effect and reduce the optical loss reaching the photodetector.

[0119] In the present invention, reflections from optical surfaces other than the target object and the reference object may cause undesirable signals and artifacts in the output of the interferometer, or may return light to the light source and cause instability in the light output. Dielectric polarization cube beam splitters, such as the purification polarizer 070, may be sources of reflection from their incident and exit surfaces. In a separated beam differential interferometer, it is advantageous to suppress these reflection effects by replacing the polarization cube beam splitter with a polarization rhombic beam splitter 500 (the "rhombic beam splitter") in the form of a rhombic prism. The polarization rhombic beam splitter can be assembled, for example, from two 50°-50°-80° triangular prisms, at least one of which has a suitable beam splitter coating on its wide face. Other angles can be selected as long as the polarization rhombic beam splitter deviates sufficiently from a cube in shape to project the reflected light outside the normal beam path of the optical system, thereby preventing artifact interferometer effects such as three-wave mixing and further reducing the amount of light returning to the light source. In the present invention described herein, the polarization rhombic beam splitter 500 replaces the purification polarizer 070, but an unpolarized rhombic beam splitter having a geometry similar to that of the polarization rhombic beam splitter 500 is considered advantageous for replacing an unpolarized cube beam splitter, such as the beam splitter 180, for example. More generally, a rhombic beam splitter having any type of optical coating on its internal interface can benefit from the rhombic geometry that reduces the effect of back reflection from its external interface. The optical coating on the internal interface can be polarized, unpolarized, dichroic (i.e., wavelength selective), or any combination thereof. Unlike a cube beam splitter, a rhombic beam splitter can use a simple optical mechanical mount with its base parallel to the optical axis, and even when mounted in such a way, the angle of incidence of the optical beam on the beam splitter coating can be maintained at its optimum value. Such a rhombic beam splitter may be advantageous for other optical systems that are adversely affected by reflections, such as an optical system for imaging a field of view (especially in a dark field configuration) or for detecting scattered light. Other embodiments of the present invention are described below. [Embodiment 1] An interferometer based on an atomic force microscope (“AFM”), a light source for emitting a light beam, a splitting optical interface arranged to split the light beam into a signal light beam and a reference light beam, an AFM cantilever, a focusing lens structure arranged to focus both the signal and reference light beams near the AFM cantilever, a beam displacer arranged to introduce a lateral displacement between the signal light beam and the reference light beam, the lateral displacement being such that the center of the signal light beam is separated from the center of the reference light beam by more than half of the sum of their beam diameters on the plane in at least one plane between the beam displacer and the focusing lens structure, the beam displacer, a detector operative to determine the difference in optical path length between the signal light beam and the reference light beam to determine information regarding movement of the cantilever, An interferometer characterized by comprising. [Embodiment 2] The interferometer according to Embodiment 1, wherein the signal light beam and the reference light beam are refracted differently at the splitting optical interface. [Embodiment 3] The interferometer according to Embodiment 2, wherein the splitting optical interface is an interface between two materials, at least one of which is birefringent. [Embodiment 4] The interferometer according to Embodiment 1, wherein one of the signal light beam and the reference light beam is reflected from the splitting optical interface and the other light beam passes through the splitting optical interface. [Embodiment 5] The interferometer according to Embodiment 4, wherein the splitting optical interface is a polarization selective dielectric coating. [Embodiment 6] The interferometer according to any one of Embodiments 1 to 5, wherein the focusing lens structure is a single lens. [Embodiment 7] The interferometer according to any one of Embodiments 1 to 6, wherein the focusing lens structure is a microscope objective lens. [Embodiment 8] The interferometer according to Embodiment 7, wherein the microscope objective lens has a numerical aperture greater than 0.25. [Embodiment 9] The interferometer according to any one of Embodiments 1 to 8, wherein the reference location is on the cantilever, and both the reference light beam and the signal light beam are focused on the cantilever. [Embodiment 10] The interferometer according to any one of Embodiments 1 to 9, wherein the signal light beam is focused at a location near the location on the AFM cantilever where the sample interacts with the sample, and the reference light beam is focused at another location that is one of the base of the cantilever, on the cantilever support chip, or on a reflective object rigidly connected to the cantilever support chip. [Embodiment 11] The interferometer according to any one of Embodiments 1 to 10, further comprising an additional optical system, an illumination optical system, and an image sensor that operate to provide an image of the sample near the AFM cantilever to the user. [Embodiment 12] The interferometer according to Embodiment 11, wherein the image of the sample has a resolution better than 2 μm measured in the sample plane. [Embodiment 13] The interferometer according to Embodiment 11 or 12, wherein the image of the sample has a modulation transfer function of 50% or higher at a spatial frequency of 250 line pairs per millimeter measured in the sample plane. [Embodiment 14] The interferometer according to any one of Embodiments 1 to 13, further comprising an additional optical system for introducing light from a second light source onto the sample near the AFM cantilever. [Embodiment 15] The interferometer according to any one of Embodiments 1 to 14, further comprising an additional optical system for detecting light emitted from the sample near the AFM cantilever and one or more photodetectors. [Embodiment 16] Further comprising an additional optical system for introducing light from a second light source such that the light from the second light source is focused on the AFM cantilever, wherein the light from the second light source causes movement of the cantilever, The interferometer according to any one of Embodiments 1 to 15, characterized by the above. [Embodiment 17] The beam displacer generates a lateral displacement between the signal light beam and the reference light beam in an infinite space separated from the AFM cantilever by the focusing lens structure, and the lateral displacement between the signal light beam and the reference light beam exceeds half the sum of the beam diameters of the signal light beam and the reference light beam. The interferometer according to any one of Embodiments 1 to 16, characterized in that [Embodiment 18] The interferometer according to Embodiment 17, characterized in that the split optical interface and the beam displacer are incorporated into an optical element coupling assembly. [Embodiment 19] The interferometer according to Embodiment 18, characterized in that the coupling assembly generates two substantially parallel light beams by reflecting at least one of the light beams twice or at least both of the light beams once. [Embodiment 20] The interferometer according to any one of Embodiments 1 to 19, further comprising one or more quarter-wave plates inserted into one or two or more of the signal light beam and the reference light beam, thereby redirecting the return light beam along a path different from that of the incident light beam after reflection near the cantilever. [Embodiment 21] The interferometer according to Embodiment 20, characterized in that a single quarter-wave plate is incorporated into both the signal light beam and the reference light beam. [Embodiment 22] The interferometer according to Embodiment 20, characterized in that a first quarter-wave plate is incorporated into the signal light beam and a second quarter-wave plate is incorporated into the reference light beam. [Embodiment 23] The interferometer according to Embodiment 21, characterized in that the quarter-wave plate is a true zero-order quarter-wave plate. [Embodiment 24] The interferometer according to Embodiment 22, characterized in that both quarter-wave plates are true zero-order quarter-wave plates. [Embodiment 25] The interferometer according to Embodiment 18, further comprising an actuator activated to move the coupling assembly so that the actuator changes the optical path length difference between the signal light beam and the reference light beam. [Embodiment 26] The interferometer according to Embodiment 18, characterized in that the coupling assembly incorporates at least one optical wedge prism. [Embodiment 27] The optical wedge prism has an angle and a wedge position for crossing the optical beams on the back focal plane of the focusing lens structure, and is the interferometer according to Embodiment 26. [Embodiment 28] The interferometer according to any one of Embodiments 1 to 17, further comprising at least one optical wedge prism disposed in at least one of the signal optical beam and the reference optical beam. [Embodiment 29] The interferometer according to Embodiment 28, further comprising an actuator that moves the optical wedge prism, thereby changing the optical path length difference between the signal optical beam and the reference optical beam. [Embodiment 30] The interferometer according to Embodiment 29, wherein the actuator is electrically actuated. [Embodiment 31] The interferometer according to Embodiment 29, wherein the actuator operates the wedge by a distance of about one millionth of a meter to calibrate the response of the detector to the optical path length difference between the signal and reference optical beams. [Embodiment 32] The interferometer according to any one of Embodiments 1 to 31, further comprising one or more optical lenses arranged such that for each lens, either the signal optical beam or the reference optical beam passes through the lens and the other optical beam does not pass through the lens. [Embodiment 33] The interferometer according to Embodiment 32, wherein the one or more optical lenses change any one of the divergence, diameter, and axial focal position of the signal optical beam, the reference optical beam, or both the signal and reference optical beams near the AFM cantilever. [Embodiment 34] The interferometer according to Embodiment 33, further comprising an actuator that moves at least one of the optical lenses, thereby changing any one of the divergence, diameter, and axial focal position of the signal optical beam, the reference optical beam, or both the signal and reference optical beams near the AFM cantilever. [Embodiment 35] The interferometer according to Embodiment 32, further comprising a mechanism for inserting and removing at least one of the one or more optical lenses into and from at least one of the signal optical beam and the reference optical beam. [Embodiment 36] The interferometer according to any one of Embodiments 1 to 35, wherein the light source is a low coherence light source. [Embodiment 37] The interferometer according to Embodiment 36, further comprising an additional adaptive optical element introduced into at least one of the signal light beam and the reference light beam such that the optical group path length of the signal light beam is equal to that of the reference light beam within 200 μm. [Embodiment 38] The interferometer according to Embodiment 37, wherein the adaptive optical element includes an optical window having a window thickness, refractive index, and dispersion such that the optical group path length of the signal light beam is substantially equal to that of the reference light beam. [Embodiment 39] The interferometer according to Embodiment 37 or Embodiment 38, wherein the low coherence light source is a superluminescent diode. [Embodiment 40] The additional adaptive optical element includes an optical wedge prism placed in either the signal light beam path or the reference light beam path, and an actuator that translates the optical wedge prism by a component of motion perpendicular to the axis of propagation of the light beam in which the optical wedge prism is placed, thereby adjusting the optical group path length difference between both light beam paths within the coherence length of the low coherence light source. The interferometer according to Embodiment 37, further comprising the actuator. [Embodiment 41] The interferometer according to Embodiment 40, wherein the optical wedge prism has an angle and a wedge position that cause the light beam to intersect at the back focal plane of the focusing lens structure. [Embodiment 42] The additional adaptive optical element includes a first optical wedge prism and a second optical wedge prism placed in either the signal light beam or the reference light beam, and one or more actuators that simultaneously move the wedges to reduce the translation of the light beam across the wedges. The interferometer according to Embodiment 37, further comprising the actuators. [Embodiment 43] The interferometer according to Embodiment 37, wherein the additional adaptive optical element includes a replaceable window for individually changing the optical group path length difference between the signal light beam and the reference light beam. [Embodiment 44] The interferometer according to Embodiment 37, wherein the additional adaptive optical element includes a replaceable lens having a specific thickness for changing the optical group path length and a specific refractive power and location for changing any one of the divergence, diameter, and axial focal position of the light beam near the AFM cantilever. [Embodiment 45] The additional adaptive optical element is an insertable and removable lens and an insertable and removable window for adjusting the optical group path length difference between the light beams and for adjusting any of the divergence, diameter, and axial focal position of the signal light beam, the reference light beam, or both light beams near the AFM cantilever. The interferometer according to Embodiment 37 is characterized by this. [Embodiment 46] Further comprising an exchange mechanism, Actuating the exchange mechanism changes the arrangement of the additional adaptive optical element in at least one of the signal light beam and the reference light beam, Actuating the exchange mechanism selects between two or more desirable combinations of the optical group path length and any of the divergence, diameter, and axial focal position of the light beam near the AFM cantilever, The interferometer according to Embodiment 45 is characterized by this. [Embodiment 47] The interferometer according to Embodiment 37 further comprises a band-pass filter that increases the coherence length of the light beam to a value that is short enough to partially suppress periodic errors and artifacts compared to the laser light source but long enough to exceed the difference between the optical group path length of the signal light beam and the optical group path length of the reference light beam. [Embodiment 48] The interferometer according to Embodiment 47 further comprises an actuator that rotates the band-pass filter to adapt the band-pass center wavelength to the light source center wavelength so as to maximize the light throughput. [Embodiment 49] Further comprising a second splitting optical interface and an optical beam photodetector, The second splitting optical interface separates a part of the light beam and guides it towards the optical beam photodetector, and the optical beam photodetector is operative to measure the angle of reflection of the signal light beam from the AFM cantilever. The interferometer according to Embodiment 1 is characterized by this. [Embodiment 50] The second splitting optical interface comprises a polarization-selective coating, The interferometer further comprises at least one quarter-wave plate, The quarter-wave plate and the polarization-selective coating are arranged such that the signal light beam before reflection from the AFM cantilever is not split by the second splitting interface, and the signal light beam after reflection from the AFM cantilever is split by the second splitting interface into two light beams, one of which is directed towards the optical beam photodetector. An interferometer according to embodiment 49, characterized in that. [Embodiment 51] The second splitting optical interface is incorporated into an optical element coupling assembly, and the optical element coupling assembly also incorporates the first splitting optical interface and the beam displacer. An interferometer according to embodiment 49, characterized in that. [Embodiment 52] An interferometer according to embodiment 1, further comprising an actuator for translating the cantilever support tip along an axis such that the angle between the axis and the axis of the focusing lens structure is less than 20°. [Embodiment 53] An interferometer based on an atomic force microscope, A light source for emitting a light beam, A splitting optical interface arranged to split the light beam into a signal light beam and a reference light beam, An AFM cantilever, An electrically controllable birefringent liquid crystal device that is electrically operable to modulate the optical path difference between the signal light beam and the reference light beam during calibration of the interferometer response, and is electrically activated and deactivated during measurement of the movement of the cantilever, An optical system for guiding the signal light beam and the reference light beam to be incident at two locations near the AFM cantilever, and for guiding the light reflected from the locations, A detector that receives the guided light reflected from the locations during use and operates to determine the difference in optical path length between the signal light beam and the reference light beam in order to determine information regarding the movement of the cantilever, An interferometer, characterized in that it comprises. [Embodiment 54] An interferometer according to embodiment 53, characterized in that the liquid crystal device is preferentially oriented to impart a phase shift to only one of the signal light beam and the reference light beam. [Embodiment 55] An interferometer according to embodiment 54, characterized in that the liquid crystal device is positioned between the light source and the splitting optical interface. [Embodiment 56] An interferometer according to embodiment 53, characterized in that the liquid crystal device imparts a phase shift to only the signal light beam. [Embodiment 57] The interferometer according to Embodiment 53, wherein the liquid crystal device imparts a phase shift only to the reference light beam. [Embodiment 58] Further comprising a beam displacer for introducing a lateral displacement between the signal light beam and the reference light beam, wherein the lateral displacement is greater than half the sum of the diameters of the signal light beam and the reference light beam so that the liquid crystal device can be positioned in the path of only one of the signal light beam and the reference light beam. The interferometer according to any one of Embodiments 53 to 57, characterized by the above. [Embodiment 59] The signal light beam and the reference light beam are combined into a recombined light beam after reflection from the AFM cantilever, wherein the liquid crystal device is positioned in the path of the recombined light beam and preferentially oriented to impart a phase shift to only one of the signal light beam and the reference light beam. The interferometer according to Embodiments 53 to 58, characterized by the above. [Embodiment 60] An interferometer, a light source for emitting a light beam, an optical splitter for splitting the light beam into a signal light beam and a reference light beam, an optical system for guiding the signal light beam and the reference light beam to be incident on a target object and a reference object, respectively, and guiding the light reflected from the target object and the reference object, a detector that operates to determine the optical path length difference between the signal light beam and the reference light beam in order to determine information regarding the movement of the target object relative to the reference object, comprising: The detector includes a monolithic quadrature phase analyzer and at least two photodetectors. The interferometer characterized by the above. [Embodiment 61] The monolithic quadrature phase analyzer includes a non-polarizing cube beam splitter, two polarizing cube beam splitters, and at least one wave plate oriented to shift the phase between the reference light beam and the signal light beam by 45°. The interferometer according to Embodiment 60, characterized by the above. [Embodiment 62] Further comprising a quarter-wave plate between the detector and the corresponding surface of the quadrature phase analyzer, wherein the quarter-wave plate has a special axis that is rotated 45° from a plane common to all the beams in the quadrature phase analyzer, thereby passing the reflected light through an unused surface of the quadrature phase analyzer. The interferometer according to Embodiment 60, characterized by the above. [Embodiment 63] The interferometer is an interferometer based on an atomic force microscope, and the target object is an AFM cantilever, and the interferometer according to any one of Embodiments 60 to 62 is characterized in that. [Embodiment 64] An interferometer, A light source for emitting a light beam, An optical splitter for splitting the light beam into a signal light beam and a reference light beam, An optical system for guiding the signal light beam and the reference light beam to be incident on a target object and a reference object respectively, and for guiding the light reflected from the target object and the reference object, A detector that operates to determine the difference in optical path length between the signal light beam and the reference light beam in order to determine information regarding the movement of the target object relative to the reference object, Comprising, At least one optical element in the interferometer is assembled from at least two glass isosceles triangular prisms each having an apex angle smaller than 89° or larger than 91°, An interferometer characterized by this. [Embodiment 65] The interferometer according to Embodiment 64, characterized in that at least one of the isosceles triangular prisms has a polarization selectivity coating on a surface corresponding to the base of the isosceles triangle. [Embodiment 66] The interferometer according to Embodiment 64, characterized in that at least one of the isosceles triangular prisms has a wavelength selectivity coating on a surface corresponding to the base of the isosceles triangle. [Embodiment 67] The interferometer according to Embodiment 64, characterized in that at least one of the isosceles triangular prisms has a non-polarizing beam splitter coating on a surface corresponding to the base of the isosceles triangle. [Embodiment 68] The interferometer according to Embodiment 65, characterized in that the optical element is assembled from two 50°-50°-80° triangular prisms at least one of which has a polarization selectivity coating on its widest surface. [Embodiment 69] The interferometer is an interferometer based on an atomic force microscope, and the target object is an AFM cantilever, and the interferometer according to any one of Embodiments 64 to 68 is characterized in that.

Explanation of Symbols

[0120] 070 Purification polarizer 090 Signal light beam 100 Reference light beam 120 Microscope cantilever 330 Inner focal plane

Claims

1. An interferometer based on an atomic force microscope ("AFM"), a light source (010) for emitting a light beam, a splitting optical interface (363, 423) arranged to split the light beam into a signal light beam (090) and a reference light beam (100), an AFM cantilever (120), a focusing lens structure (110) arranged to focus both the signal light beam and the reference light beam onto the AFM cantilever, a beam displacer arranged to introduce a lateral displacement between the signal light beam and the reference light beam, the lateral displacement being such that the center of the signal light beam is separated from the center of the reference light beam by more than half of the sum of their beam diameters on the plane in at least one plane between the beam displacer and the focusing lens structure, the beam displacer (360), a detector (190) operative to determine the difference in optical path length between the signal light beam and the reference light beam to determine information regarding the movement of the AFM cantilever, at least one optical wedge prism (430) arranged in at least one of the signal light beam and the reference light beam; An interferometer characterized by comprising the above.

2. The signal light beam is focused at a location on the AFM cantilever that is close to the location on the AFM cantilever that interacts with the sample, and the reference light beam is focused at another location that is one of on the base of the AFM cantilever, on the cantilever support chip (130), or on a reflective object rigidly connected to the cantilever support chip. The interferometer according to claim 1.

3. The beam displacer generates a lateral displacement between the signal light beam and the reference light beam in an infinite space separated from the AFM cantilever by the focusing lens structure, and the lateral displacement between the signal light beam and the reference light beam exceeds half of the sum of the beam diameters of the signal light beam and the reference light beam. The interferometer according to claim 1, characterized in that.

4. An interferometer based on an atomic force microscope ("AFM"), A light source (010) for emitting a light beam, A splitting optical interface (363, 423) arranged to split the light beam into a signal light beam (090) and a reference light beam (100), An AFM cantilever (120), A focusing lens structure (110) arranged to focus both the signal light beam and the reference light beam on the AFM cantilever, A beam displacer arranged to introduce a lateral displacement between the signal light beam and the reference light beam, wherein the lateral displacement is such that the center of the signal light beam is separated from the center of the reference light beam by more than half of the sum of their beam diameters on the plane in at least one plane between the beam displacer and the focusing lens structure. The beam displacer (360), A detector (190) operative to determine a difference in optical path length between the signal light beam and the reference light beam to determine information regarding movement of the AFM cantilever, Comprising, The beam displacer comprises a lateral displacement beam splitter (420) comprising a total reflection optical interface (424), The splitting optical interface comprises a partially reflecting optical interface (423) including a polarization selective coating of the lateral displacement beam splitter, The total reflection optical interface (424) is parallel to the partially reflecting optical interface (423), An interferometer further comprising one or more quarter-wave plates (490) inserted into one or two or more of the signal light beam and the reference light beam, thereby redirecting the return light beam (090) along a path different from that of the incident light beam (100) after reflection from the cantilever. **Claim 5** The interferometer according to claim 1, further comprising an actuator (440) for moving the optical wedge prism, thereby changing the optical path length difference between the signal light beam and the reference light beam. **Claim 6** An interferometer based on an atomic force microscope ("AFM"), a light source (010) for emitting a light beam, a splitting optical interface (363, 423) arranged to split the light beam into a signal light beam (090) and a reference light beam (100), an AFM cantilever (120), a focusing lens structure (110) arranged to focus both the signal light beam and the reference light beam onto the AFM cantilever, a beam displacer arranged to introduce a lateral displacement between the signal light beam and the reference light beam, the lateral displacement being such that the center of the signal light beam is separated from the center of the reference light beam by more than half the sum of their beam diameters in at least one plane between the beam displacer and the focusing lens structure, the beam displacer (360), a detector (190) operative to determine the difference in the optical path lengths between the signal light beam and the reference light beam in order to determine information regarding the movement of the AFM cantilever, one or more optical lenses arranged such that for each lens, either the signal light beam or the reference light beam passes through the lens and the other light beam does not pass through the lens, a mechanism (550) for inserting and removing at least one of the one or more optical lenses (530, 540) into at least one of the signal light beam or the reference light beam. An interferometer characterized by comprising

7. The interferometer according to claim 6, wherein the one or more optical lenses change any one of divergence, diameter, and axial focal position of the signal light beam, the reference light beam, or both the signal light beam and the reference light beam on the AFM cantilever.

8. Further comprising additional adaptive optical elements (520, 580) introduced such that the optical group path length of the signal light beam is equal within 200 μm to the optical group path length of the reference light beam in at least one of the signal light beam and the reference light beam, The interferometer according to claim 1, wherein the light source is a superluminescent diode (510).

9. The additional adaptive optical element comprises an optical wedge prism placed in either the signal light beam path or the reference light beam path, The interferometer according to claim 8, further comprising an actuator (440) that translates the optical wedge prism by a component of motion perpendicular to the axis of propagation of the light beam in which the optical wedge prism is placed, thereby adjusting the optical group path length difference between both light beam paths within the coherence length of a low coherence light source (510).

10. The interferometer according to claim 8, wherein the additional adaptive optical element comprises an exchangeable lens (570) having a specific thickness for changing the optical group path length and a specific refractive power and location for changing any one of divergence, diameter, and axial focal position of the light beam on the AFM cantilever.

11. The interferometer according to claim 8, further comprising a bandpass filter (560) that increases the coherence length of the light beam to a value that is short enough to partially suppress periodic errors and artifacts compared to a laser light source but long enough to exceed the difference between the optical group path length of the signal light beam and the optical group path length of the reference light beam. Interferometer based on an atomic force microscope ("AFM"), comprising: a light source (010) for emitting a light beam; a splitting optical interface (363, 423) arranged to split the light beam into a signal light beam (090) and a reference light beam (100); an AFM cantilever (120); a focusing lens structure (110) arranged to focus both the signal light beam and the reference light beam onto the AFM cantilever; a beam displacer arranged to introduce a lateral displacement between the signal light beam and the reference light beam, the lateral displacement being such that the center of the signal light beam is separated from the center of the reference light beam by more than half of the sum of their beam diameters in a plane between the beam displacer and the focusing lens structure, the beam displacer (360); a detector (190) operative to determine the difference in optical path length between the signal light beam and the reference light beam in order to determine information regarding the movement of the AFM cantilever; a second splitting optical interface (600, 636) and an optical beam photodetector (630); characterized in that the second splitting optical interface separates a part of the light beam and directs it towards the optical beam photodetector, and the optical beam photodetector is operative to measure the angle of reflection of the signal light beam from the AFM cantilever. Claim 13 The interferometer according to claim 1, further comprising an actuator (650) for translating the cantilever support tip along an axis such that the angle between the axis and the axis of the focusing lens structure is less than 20°.

Images