Atomic force microscope based interferometer

Abstract

An interferometer based on an atomic force microscope ("AFM") uses a light source and a beamsplitting optical interface to split a light beam into a signal beam and a reference beam. Both the signal beam and the reference beam are focused near an AFM cantilever. A beam displacer introduces a lateral displacement between the signal beam and the reference beam that causes the center of the signal beam to be separated from the center of the reference beam by more than half the sum of their beam diameters in at least one plane between the beam displacer and a focusing lens structure. A detector operates to determine a difference in the optical path length between the signal beam and the reference beam to determine information about movement of the cantilever.

Description

Background Technology

[0001] Atomic force microscopy (AFM) uses a microscopic cantilever to convert the nanoscale force between the sharp tip of the cantilever and the sample under study into a measured displacement of the tip. While many techniques exist for sensing cantilever deflection, most AFMs employ techniques that reflect the focused beam away from the back of the cantilever because these techniques offer high sensitivity, low noise, and ease of use. In this document, these optical methods will be broadly categorized into two classes: interferometric detection methods and variations of beam deflection (OBD) methods.

[0002] Due to its simple design, high sensitivity, and good noise performance, most commercial AFMs employ the OBD method. In this method, the reflected beam is guided towards a split photodetector that allows for the measurement of the angular deflection of the cantilever. Using a four-quadrant photodetector allows for the measurement of two-dimensional angular deflection, referred to as normal deflection and lateral deflection. Lateral deflection is of particular interest to researchers studying tribology.

[0003] However, the cantilever angle deflection measured by the OBD method is an indirect measurement of tip displacement. Therefore, many calibration methods have been devised to infer tip displacement from the photodetector signal. Even with careful calibration of the measured cantilever angle deflection to tip displacement, it can be difficult to reduce the calibration error to below 10%. Due to the lack of readily available standards for many cantilever measurement modes, the error is often imperceptible to the user. In such cases, large and systematic errors may exist in the signal, yet the user may mistakenly believe that the OBD angle 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 best SNR using a single instrument on a variety of cantilever arms. For a given spot size, a larger cantilever will have higher noise. Furthermore, some cantilever arms have a triangular shape with a hollow base, which necessitates a limitation on the spot size and thus provides a suboptimal SNR.

[0005] On the other hand, interferometry is an alternative optical method that directly measures the displacement of the cantilever's end, which is directly related to the displacement of its tip. This allows researchers to measure the quantity of interest—tip displacement—without requiring additional calibration methods, which are time-consuming and potentially highly inaccurate. Since calibration is based on the wavelength of light, calibration errors can be reduced to less than a few percent. Furthermore, interferometry can achieve better noise performance than OBD methods because the spot size does not need to be matched to the cantilever's size to optimize SNR. In other words, displacements of cantilevers of various shapes and sizes can be measured with high SNR using a small focused spot.

[0006] Although there is no shortage of academic papers on the design and advantages of interferometric AFMs, commercial AFMs have not yet been widely adopted in the mainstream due to their complexity. Fiber-optic interferometers have been widely used by academic researchers; however, these interferometers lack the ease of use expected of commercial AFMs due to the difficult positioning of the fiber near the cantilever and the limited optical path.

[0007] A typical interferometer (which enables high-quality optical access to the target object and is easy to use) introduces a signal laser beam through an objective lens; simultaneously, a reference beam is reflected away from a reference object (such as a mirror) at a distance from the target object. Typically, the reference beam does not leave the interferometer's optical system. Such interferometers can be used to measure vibrations of the target object, but suffer from very poor stability at low frequencies because the paths of the signal and reference beams are very different, and therefore subject to different thermal drifts and vibrations. These artifacts are indistinguishable from the displacement of the target object. To mitigate this problem, a whole class of differential interferometers employs a design principle in which both the signal and reference beams pass through an objective lens. The signal beam is focused onto the target object, and the reference beam is focused onto a reference object close to the target object. The difference between the positions of the target and reference objects becomes the interferometric measurement signal. Keeping the signal and reference beams close to each other suppresses most of the undesirable drift and vibration of the instrument through common-mode rejection principles known to those skilled in the art. Because this type of differential interferometer design in existing AFM relies on birefringent prisms located near the cantilever, they significantly impede the optical quality of imaging through the objective lens, and therefore can be quite unreliable. Alternatively, other prior art designs place the birefringent prism at the back focal plane of the imaging lens, which also prevents high-quality optical access to the target object. Therefore, there is a trade-off between high-performance differential interferometry in the context of AFM and ease of use versus high-quality optical access to the cantilever.

[0008] A key difference between OBD-based and interferometric AFM methods lies in the light source requirements. Interferometers used for AFM employ highly coherent laser sources, such as helium-neon (HeNe) lasers or laser diodes, to ensure high-contrast interferometric signals. Furthermore, the narrow spectral bandwidth of such laser sources prevents any loss of signal contrast that might be caused by dispersion from the optical glass used in the optical design. On the other hand, since OBD AFMs are not dependent on the coherence of the light source, they can also use highly coherent laser sources, or they can alternatively employ low-coherence sources, such as superluminescent diodes (SLDs). For example, the benefits of using a low-coherence source include better long-term stability of measurements and a reduction in measurement artifacts caused by unwanted interference from backreflections. For these reasons, it is well known to anyone skilled in the art that for certain experiments using OBD AFM where backreflections may cause artifacts, SLDs are preferred, while interferometric AFMs require highly coherent lasers.

[0009] On the other hand, SLDs can have higher noise levels compared to lasers, especially at high frequencies (US Patent 8370960B2). For this reason, some manufacturers of OBD AFMs offer options to choose between an SLD or laser diode light source. Depending on the experiments the OBD AFM will be used for, utilizing the lower noise of a laser diode or the reduction in back reflection artifacts of an SLD may be more advantageous.

[0010] Unlike OBD-based AFM, interferometric AFM has seen a wide variety of different implementations over the years. The simplest implementation of the interferometer is the Michelson interferometer, invented in the 1880s. It remains the foundation behind many of today's interferometric techniques.

[0011] Figure 1 A simplified design of a Michelson interferometer in the context of AFM is depicted. A laser 010 is coupled to a polarization-maintaining fiber 020 terminated by a fiber optic connector 030. The laser light diverges from the fiber end. A source beam 040 is collimated from the diverging light by a collimating lens 050. The diameter 060 of the collimated source beam 040 is determined by the focal length of the collimating lens along with the divergence of the beam exiting the fiber 030. A polarizer 070 is used to ensure that the polarization is highly linear and preferentially oriented at an optimal angle relative to the rest of the optical system to maximize measurement sensitivity. This polarizer can be an absorption film polarizer, a wire grating polarizer, a polarization cube beam splitter (as shown), or any such optical component capable of transmitting or reflecting a single linear polarization state. Alternatively, the fiber can be omitted, and a collimated beam emitted directly 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 beam is split into two beams by a semi-silvered mirror 080 or any equivalent optical beam splitter. These two beams will be referred to herein as the signal beam 090 and the reference beam 100. Note that some people refer to the “signal” beam as the “measurement” beam.

[0013] The signal beam 090, reflected off the semi-silvered mirror 080, is focused by the microscope objective 110 onto a microcantilever 120 (the target object), which is attached to a cantilever support chip 130 for processing purposes. The diameter 062 of the signal beam 090 is shown as decreasing as the light reaches the cantilever. The cantilever support chip is a macroscopic object that the AFM user contacts, typically equipped with tweezers to introduce the cantilever into the AFM and to hold the cantilever support chip downwards using clamping mechanisms. The cantilever support chip is typically on the order of a few millimeters in length and width and is usually less than one millimeter thick. The focused signal beam 090 is reflected off the cantilever and returns through the objective. The objective collimates the signal beam 090, and the beam then returns to the semi-silvered mirror 080.

[0014] The reference beam 100, transmitted through the semi-silvered mirror 080, reaches the reference mirror 140. The reference mirror 140 can be moved by a displacement mechanism 150, which may be manual or automatic to some extent. The reference beam reflected off the reference mirror returns to the semi-silvered mirror 080. The reference mirror 140 may require a tip and tilt adjustment mechanism to ensure that the returning reference beam 100 spatially overlaps with the signal beam 090, as described below.

[0015] The two returning beams are recombined at the semi-silvered mirror 080. A portion of each beam is recombined into a reconstituted beam 200 and directed toward the photodetector 160. The remainder of the returning beam returns to the source light source along the optical path of the source beam 040, as the law of conservation of energy requires the total amount of light to remain constant. The amount of light reaching the photodetector 160 is a sine function of the difference between the optical path length traversed by the signal beam 090 and the optical path length traversed by the reference beam 100, and the periodicity of this sine function is λ / 2, as determined by the wavelength λ of the laser source. This is in Figure 1 As shown in b. Note that the optical path length of signal beam 090 includes the sum of the path lengths along the incident portion (before reflection from the cantilever) plus the sum of the path lengths along the return portion (after reflection from the cantilever). Similarly, the optical path length of reference beam 100 is the sum of the incident optical path length and the return optical path length.

[0016] To optimize sensitivity, the displacement mechanism 150 attached to the reference mirror 140 is adjusted such that half the light returns to the light source and half reaches the light photodetector 160. This configuration (referred to herein as the "centered interferometer") can be achieved by displacing the reference mirror 140 by at most λ / 4. This mechanism is necessary because when all or no light reaches the light photodetector 160, the sensitivity becomes zero, making it impossible to detect any signal subsequently. Furthermore, the interferometer's maximum sensitivity position coincides with its maximum linearity position, where the sinusoidal response function is locally linear. That is, if the interferometer is centered by proper positioning of the displacement mechanism 150, the signal response to changes in cantilever displacement will be most linear.

[0017] More generally, the prior art teaches the advantages of having a device for tuning or modulating the phase difference between the signal beam 090 and the reference beam 100. While the displacement mechanism 150 is one way to achieve this, in other cases, liquid crystal devices are used to tune or modulate the phase difference between the two beams. Note that for the interferometer to operate under “centered interferometer” conditions, the device for tuning the phase difference must be kept in the correct state. If the tuning device is an electrically activated mechanism, such as a piezoelectric element or a liquid crystal device, it must remain continuously activated or energized throughout the interferometry. This may introduce noise and / or drift into the measurement.

[0018] By translating the displacement mechanism 150 through approximately one wavelength period, the sensitivity of the interferometer can be calibrated if the wavelength of the laser source is known. At this point, any change in power at the light photodetector 160 can be calibrated to a precise displacement measurement of the cantilever tip, in meters.

[0019] Figure 1 The simple Michelson interferometer design depicted has a major drawback: half the light returns to the laser source, which causes laser instability. This instability leads to fluctuations in optical power, which may erroneously resemble cantilever displacement as measured by the light photodetector 160. For cantilever displacement in this design, power variations are indistinguishable. To reduce laser instability, a Faraday isolator 170 can be mounted along the optical fiber, such as... Figure 2 As shown. Alternatively, for free-space lasers, free-space isolators can be used, offering similar advantages.

[0020] This interferometer arrangement does not allow the observation system to access the cantilever. Figure 3 The alternative arrangement shown uses a beam splitter 180, which is added to... Figure 2The design cleans the space between the polarizer 070 and the semi-silvered mirror 080. This creates visual access for the camera system 190, which can be used to create images of the cantilever and focused laser spot as seen through the microscope objective 110. The camera system 190 typically includes an image sensor, a lens that focuses parallel light onto the image sensor, a white light illumination system, and a beam splitter that introduces the illumination light. These components can be set, modified, or omitted in various ways, depending on the characteristics of the microscope objective 110 and the intended application of the AFM. While allowing access to the camera system 190, the semi-silvered mirror 080 also returns both the signal beam 090 and the reference beam 100 to the beam splitter 180, which then reflects a portion of the light to the light photodetector 160. Note that in this case, the reconstructed beam 200 to be measured returns along the source beam 040 before being redirected to the light photodetector 160. As previously stated, the optical power at the light 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 light photodetector 160 and the camera system 190 can be interchanged with similar functions and performance.

[0021] The interferometer is designed with a dynamic range limited by the wavelength λ of the light source. The entire range of motion for the cantilever displacement is λ / 4. At any extreme of this range, the sensitivity is zero, and therefore the interferometer cannot measure the cantilever displacement at these locations. In practice, the usable range of the interferometer is much smaller than λ / 4, especially when high accuracy and low noise are required, and nonlinearity must be avoided.

[0022] The limited dynamic range of an interferometer can be overcome by orthogonal detection, as used in patent US6020963. Instead of monitoring the optical power in the path of the reconstructed beam 200, the polarization state of the reconstructed beam 200 is used to measure the optical path difference between the path of the signal beam 090 and the path of the reference beam 100. Measuring the polarization state is more complex than simply measuring optical power using a photodetector. This measurement scheme is... Figure 4 The design adopted.

[0023] Instead of splitting the source beam 040 into two paths using a semi-silvered mirror 080, the signal beam 090 and reference beam 100 in the orthogonal interferometer are generated by splitting the source beam 040 into two orthogonal polarization states using a polarization beam splitter 210. When both the signal beam 090 and the reference beam 100 are recombined into the reconstituted beam 200, the optical power does not change as a function of cantilever displacement as in a Michelson interferometer. Instead, the polarization state varies between linear, elliptical, and circular polarization as a function of cantilever displacement. The ellipticity of the beam polarization state (with linear and circular polarization being the limiting cases) is directly related to the cantilever displacement. A portion of the reconstituted beam 200 reflected by the polarization beam splitter 210 can be analyzed using an orthogonal phase analyzer 220 to determine its polarization ellipticity.

[0024] One possible configuration of the quadrature phase analyzer is in Figure 4 As shown in b, it involves splitting the beam into two arms using a non-polarizing beam splitter 230. Along one arm (referred to as the "in-phase" arm), the two polarization states are mixed using a half-wave retarder 240, where their birefringence non-polarizing axis is rotated to 22.5° relative to the polarization axis of either the signal beam 090 or the reference beam 100. Next, a polarizing beam splitter 250 is used to direct half of each of the signal beam 090 and the reference beam 100 to two photodetectors 260 and 262, as in US6020963. Along the other arm (referred to as the "orthogonal" arm), the two polarization states are mixed using a quarter-wave retarder 270, where their birefringence non-polarizing axis is rotated to 45° relative to the polarization axes of both the signal beam 090 and the reference beam 100. In this arm, a polarizing beam splitter 280 is also used to direct half of each of the signal beam 090 and the reference beam 100 to two photodetectors 264 and 266.

[0025] The optical power difference between photodetectors 260 and 262 in the in-phase arm is calculated and divided by the sum of the optical powers of the two photodetectors; this normalized difference becomes the in-phase signal I. Similarly, the quadrature signal Q is measured using two photodetectors 264 and 266 in the quadrature arm. Plotting Q versus I yields a Lissajous diagram, as shown below. Figure 4 As shown in c. In an ideal interferometer, the response is the unit circle 284. In that case, any optical path configuration between the signal beam 090 and the reference beam 100 at any given time will result in a point on the unit circle, called the phase state point 290. Vector 286 can be defined between the origin of the Lissajous diagram and the phase state point 290. The angle between this vector and the x-axis of the Lissajous diagram... It can be calculated using the two-parameter arctangent function, i.e.

[0026]

[0027] in

[0028]

[0029] Furthermore, both the integer m and the branch of the arctangent function are chosen to give an interval of width 2π (such as...). The results are continuous on the arctangent function. This two-parameter form (atan2) of the arctangent function is known to computer programmers; it appears in the standard mathematical libraries of FORTRAN, Perl, Java, C, .NET, and Python.

[0030] When the cantilever is displaced by λ / 2, the phase state point 290, measured by the orthogonal phase analyzer 220, completes a full circle around Lissajous. (Angle) It is a direct measurement of the phase difference between the signal beam and the reference beam, and can be used to infer the cantilever displacement d using the following formula:

[0031]

[0032] Here, 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 beam and the reference beam, which is measured as a change in angle on the Lissajous diagram. To avoid discontinuities in the displacement signal d, the output of the function atan2 should be solved using methods known to those skilled in the art. This solution is particularly important if the displacement signal will vary over a range greater than λ / 2.

[0033] Due to imperfections in the optical components and optical system assemblies, the response to the cantilever displacement measured by the orthogonal phase analyzer 220 is typically an ellipse 282 on the Lissajous diagram, rather than an ideal unit circle 284. Simply assuming an ideal response leads to periodic errors in the reconstructed displacement signal. To prevent periodic errors and ensure high-precision measurement of the cantilever displacement, the measured response on ellipse 282 can be corrected to infer the corresponding ideal-unit-circle 284 response of the system using the following calibration procedure. The model used to correct the deviation from the ideal circular Lissajous is the elliptical Lissajous model, such as that proposed by Bellon et al., Opt. Commun. 207, 49-56 (2002). Measurements define five parameters—ellipse size, position, and angle—related to the optical path difference between the modulation signal arm and the reference arm (e.g., by deliberately moving the cantilever), and the Lissajous shape is recorded. The elliptic function is then fitted using a nonlinear least squares method to determine the most accurate parameters describing the Lissajous shape. These recorded five parameters are subsequently used to interpret the photodetector response as an accurate cantilever displacement. Since aligning the AFM can change one or more of these five parameters, the calibration procedure may need to be performed before each experiment.

[0034] Generating the cantilever displacement signal from both the I and Q signals requires nonlinear calculations, which are performed using digital electronic devices such as field-programmable gate arrays (FPGAs). The calculations must be performed at a frequency much higher than the measured cantilever displacement in order to reconstruct an accurate cantilever displacement signal.

[0035] The main advantage of the orthogonal analyzer scheme is that the signal dynamic range can now exceed λ / 4 while maintaining low noise performance, regardless of cantilever displacement—within certain limitations of the optical system setup. Furthermore, signal linearity is independent of the interferometer's startup conditions, and linearity is not limited to displacement << λ / 4. In other words, the interferometer does not need to be "centered" as previously stated, because any starting point in the optical path difference between the paths of the signal beam 090 and the reference beam 100 is equivalent, allowing for high linearity and low noise measurements.

[0036] Numerous configurations of the quadrature phase analyzer 220 have been proposed. Some place a quarter-wave plate before the first beam splitter (TaeBong Eom et al., Meas. Sci. Technol. 12, 1734 (2001)). Some omit the half-wave retarder plate by mechanically rotating the quadrature phase analyzer 220 45° about the optical axis of the beam (Bellon et al., Opt. Commun. 207, 49-56 (2002)). Others use a birefringent crystal instead of a polarization cube beam splitter (Paolino et al., Rev. Sci. Instrum. 84, 095001 (2013)). Still other designs use only two photodetectors in total (one in each arm) to perform polarization measurements (Weber et al., Rev. Sci. Instrum. 90, 083503 (2019)). The more detailed design (US 2006 / 0087658A1) generates four phase-shifted signals (0°, 90°, 180°, 270°), all of which pass through polarizers before reaching their respective photodetectors. This is intended to reduce common-mode error at the cost of light loss at the polarizers. Each configuration involves some trade-offs between performance and ease of manufacture.

[0037] Figure 4 One drawback of the design is that it is not differential. Therefore, any mechanical motion (such as vibration or thermally induced drift) in either arm (signal beam 090 or reference beam 100) can be incorrectly perceived as cantilever displacement. Furthermore, the longer the path lengths of the signal beam 090 and reference beam 100, the more susceptible the system is to these error sources.

[0038] In the prior art, several differential interferometer configurations have been proposed to reduce the optical path difference between the paths of two polarization states by using birefringent materials close to the cantilever (Schonenberger et al., Rev. Sci. Instrum. 60, 3131 (1989)). This is in Figure 5The image is shown in which a calcite window 300 is placed near the cantilever to split the source beam 040 into two parallel beams with orthogonal polarization states. A disadvantage of this design is the presence of fragile crystals near the cantilever, making them susceptible to damage from liquids. Furthermore, due to the birefringence of calcite, the camera view of the cantilever and the sample has a dual perspective, as information from light with different polarizations is offset differently at the camera. Because the source beam 040 is split into a signal beam 090 and a reference beam 100 near the cantilever, the polarizing beam splitter 210 used in the previous embodiment is replaced here by a dichroic mirror 310. The advantage is that all light from the laser is reflected towards the cantilever on the incident path (before reflection from the cantilever) and is also completely reflected on the return path (after reflection from the cantilever), while allowing some light of different wavelengths to reach the camera system 190 for observation. The diameter 064 of the reference beam 100 is converged in a manner similar to the diameter 062 of the signal beam 090, because both beams are focused through the same lens.

[0039] Signal beam 090 travels toward the AFM cantilever, is reflected from the cantilever, and then travels away from the cantilever along essentially the same signal beam path. Where differentiation is necessary, we refer to the signal beam before reflection from the cantilever as the "incident" signal beam, and the signal beam after reflection from the cantilever as the "return" beam. Due to their spatial overlap, they are indistinguishable in the diagram and are both designated as 090. Similarly, reference beam 100 is referred to as "incident" before its reflection and as "return" after its reflection from the cantilever.

[0040] Figure 6 A configuration is shown in which a birefringent prism 320 can be used to split two polarization states into two beams, which can be focused at two different locations on the cantilever (den Boef et al., Rev. Sci. Instrum. 62, 88 (1991)). In this configuration, a birefringent prism, such as that used in US5315373, is preferred, creating two beams with different angles, such as a Wollaston prism, a Rochon prism, or a Senarmont prism. For the reasons explained below, in this design, the microscope objective 110 shown in the previous figure is replaced by an imaging lens 340. The geometry of the birefringent prism 320 can be tuned to create angular separation of the two beams, and it is specifically chosen for the imaging lens 340 to achieve the desired beam separation at the cantilever. To ensure that the two beams have the same angle of incidence on the cantilever, the birefringent prism 320 must be located at the back focal plane 330 of the imaging lens 340.

[0041] Note that microscope objective 110 cannot be used in this arrangement because the back focal plane 330 of microscope objective 110 is physically located inside microscope objective 110, and it is impossible to place birefringent prism 320 at the back focal plane. Therefore, the imaging lens 340 that must be used is a lower-quality lens, such as an achromatic bilens, a single lens, or other simple imaging lens. Not only does the imaging lens 340 provide a lower-quality image of the cantilever and its surroundings, but the birefringent prism 320 also creates two images at camera system 190 because it splits orthogonal polarization into separate paths with different angles.

[0042] In this scenario, the signal beam 090 and the reference beam 100 run side-by-side, following very similar paths. The geometry and optical properties of the birefringent prism 320 were optimized during the design phase to create a prescribed separation distance between the signal beam 090 and the reference beam 100 at the cantilever. In this design, the ideal separation distance is slightly less than the length of the cantilever being measured. The signal beam 090 is located at the end of the cantilever (the target object), while the reference beam 100 is located at the base of the cantilever (the reference object). This allows for the measurement of the displacement difference between these two locations, which changes as the cantilever deflects under sample forces.

[0043] from Figure 6 It is clear that this design cannot easily accommodate cantilever of various sizes. However, commercially available cantilevers range in length from approximately 10 μm to 500 μm and come in various shapes. One solution is to employ beam splitting greater than the cantilever length, such that one beam is focused on the cantilever and the other on the cantilever support chip (Paolino et al., Rev. Sci. Instrum. 84, 095001 (2013)). In the case of a 500 μm long cantilever, this means a spacing greater than 500 μm, where reference beam 100 is focused on cantilever support chip 130, which is the reference object in this context. However, the thickness of the cantilever support chip can be greater than the depth of field of the laser focused by imaging lens 340, resulting in reduced contrast or even a complete lack of signal. Therefore, it is beneficial to introduce a difference in the axial focusing positions of the two beams, so that each beam can be focused on its surface from which it is reflected. For example, as proposed by Cunningham et al. in 1994 (Cunningham et al., Meas. Sci. Technol. 5(11), 1350(1994)), such as Figure 7As shown, a defocusing glass window 350 is added to the signal beam to focus the signal beam 090 onto the cantilever 120, while simultaneously focusing the reference beam 100 onto the cantilever support chip 130. In this arrangement, the deflection of both the small and large cantilever beams can be measured using the same optical system. Furthermore, the deflection of the cantilever 120 is measured relative to the fixed cantilever support chip 130, and therefore this measurement is independent of the separation distance between the signal beam 090 and the reference beam 100.

[0044] Alternatively, Goto et al. used a birefringent defocusing lens to slightly defocus one of the polarizations in the source beam 040 in order to change the relative focus of the signal beam 090 and the reference beam 100 at the cantilever (Goto et al., Rev. Sci. Instrum. 66, 3182 (1995)). The birefringent lens is necessary because both the signal beam 090 and the reference beam 100 are substantially overlapping in space, making it impossible to use standard optics on one of those beams without affecting the other.

[0045] Note that the combination of the diameter 060 of the source beam 040 and the focal length of the microscope objective 110 or imaging lens 340 determines the divergence of the focused beam, the spot diameter, and the depth of field of the focused beam at the cantilever. For a straight cantilever that does not bend due to residual or thermally induced internal stress, a wide range of diameters for the source beam 040 will result in a high-contrast signal. This is because the beams will substantially overlap after reflecting off the cantilever 120 and the chip 130 and recombining into the reconstituted beam 200. Conversely, for a straight cantilever that does not bend due to residual or thermally induced internal stress, a wide range of diameters for the source beam 040 will result in a high-contrast signal. Figure 7 As shown in Figure b, the curved cantilever causes the reflected signal beam 090 to return along a slightly different path than the incident signal beam 090. Therefore, the signal beam 090 and the reference beam 100 will only partially overlap when recombined into the reconstituted beam 200. This results in reduced interferometric contrast, lower signal strength, and higher measurement noise. However, increasing the diameter of the source beam 040 ensures greater overlap between the reference beam 100 and the signal beam 090 in the reconstituted beam 200, leading to higher signal strength and therefore lower noise. In summary, choosing a larger diameter source beam 040 makes the system more tolerant of undesirable cantilever curvature.

[0046] On the other hand, increasing the diameter of the source beam 040 reduces the depth of field, which decreases the system's tolerance to variations in the thickness of the cantilever support chip. Due to differences in the substrate and microfabrication process used to manufacture the cantilever, chip thickness errors (such as...) may occur. Figure 7(As shown in b). The chip thickness error results in the return signal beam 090 and the reference beam 100 being defocused relative to each other when they recombine into the recombined beam 200. This leads to reduced interferometric contrast, lower signal, and higher measurement noise. However, for a given error in the cantilever-supported chip thickness relative to the design thickness, a smaller beam diameter will result in less contrast loss, higher signal, and lower measurement noise. In summary, there is a trade-off in choosing the source beam 040 diameter: a smaller diameter 060 of the source beam 040 results in greater tolerance for chip thickness errors but less tolerance for cantilever curvature, and vice versa. Similarly, a larger beam diameter 060 of the source beam 040 results in less tolerance for chip tilt errors. For example, chip tilt errors (such as those caused by chip carrier machining tolerances) may occur. Figure 7 (as shown in b). Any error in chip tilt will cause relative defocusing between the signal beam 090 and the reference beam 100, because the two beams are spaced apart. For any given amount of chip tilt error, the relative defocusing between the return beams will be greater with larger beam diameters. In other words, a smaller beam diameter 060 of the source beam 040 results in greater tolerance for chip tilt errors, and vice versa. An appropriate beam diameter 060 of the source beam 040 must be chosen to compromise between cantilever curvature, chip thickness error, and chip tilt. In the prior art, the ability to make these design choices is limited, and therefore it is difficult to tailor the characteristics of the interferometer to the desired application of atomic force microscopy. Summary of the Invention

[0047] This invention relates to atomic force microscopy as claimed in claims. Embodiments of the invention employ differential interferometry to directly measure the displacement of the cantilever deflection caused by the force between the cantilever tip and the sample under study. Differential interferometers typically operate by splitting collimated light from an fiber-coupled source into two arms with orthogonal polarization states using a transverse displacement beam splitter; the signal arm beam is typically focused onto the cantilever through an objective lens, and the reference arm beam is typically focused onto the cantilever support chip through the same objective lens. An advantageous feature is the complete spatial separation of the signal and reference beams before they are focused through the objective lenses. This geometry allows for the individual manipulation of these beams using standard optics instead of birefringent optics. Preferably, an optical wedge is used to apply an angular deviation to the reference arm beam, causing it to target the cantilever support chip rather than the cantilever. The same wedge is preferably properly positioned to ensure that the signal and reference beams intersect at the back focal plane of the objective lens. Optical lenses are typically used in the reference arm to defocus the beam relative to the signal arm, ensuring it is well focused onto the cantilever support chip of a specific thickness and tilt angle. After reflection, the two beams are preferably collimated and recombined using the same optical system delivered to the beams. Both the signal beam and the reference beam typically pass through a quarter-wave plate twice, causing the recombined light to be redirected by a transverse displacement beam splitter to an orthogonal phase analyzer instead of returning to the source. This orthogonal phase analyzer preferably uses an orthogonal detection optics scheme to measure the optical path length difference between the reference and signal beams, which uses polarization optics to distribute the light onto four photodetectors. The interferometer can be calibrated by modulating a liquid crystal device and observing the response. Subsequently, digital electronics can reconstruct the cantilever displacement signal from the four photodetector signals based on the calibration and the known wavelength of the source.

[0048] The aforementioned 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 match the optical path length between the signal beam path and the reference beam path. Furthermore, the aforementioned wedge can be mechanically actuated to very precisely change the optical path length between the two beam paths to maximize interferometric contrast before each experiment. Additionally, each switchable lens with a specific focal length, thickness, and material allows for reconfiguration of both the focal point and optical path length of the reference arm to accommodate different types of cantilever with varying thicknesses. Furthermore, additional optics can be inserted or removed from the optical system to compensate for variations in the focal point and optical path length caused by the introduction of different fluids (such as water) around the cantilever.

[0049] Additionally, a beam splitter is used to pick up a portion of the beam returning from the cantilever and redirect that portion to a four-quadrant photodetector. This allows for the measurement of the cantilever's angular deflection in two dimensions using a beam deflection method (also known as the optical lever method). This additional measurement occurs simultaneously with the interferometric displacement measurement obtained from orthogonal detection. Attached Figure Description

[0050] Figure 1 A simple design of a Michelson interferometer in the context of AFM is depicted;

[0051] Figure 2 A Michelson interferometer is shown, with a Faraday isolator added;

[0052] Figure 3 A Michelson interferometer using a beam splitter is shown;

[0053] Figure 4 A Michelson interferometer for measuring polarization states is shown;

[0054] Figure 5 A differential interferometer configuration is shown to reduce the optical path difference between two polarization states by using a birefringent material close to the cantilever.

[0055] Figure 6 The configuration using a birefringent prism is shown;

[0056] Figure 7 The defocused glass window added to the signal beam is shown; Figure 7 B illustrates the error sources in the cantilever and the chip;

[0057] Figure 8 A novel arrangement of the differential interferometer is described;

[0058] Figure 9 This illustrates the path for moving the prism pair outside the space between the microscope objective and the camera system;

[0059] Figure 10 A defocusing lens for the reference beam is shown;

[0060] Figure 11 An off-axis lens is shown for defocusing a beam and applying a desired angular deviation;

[0061] Figure 11 b shows how to manufacture an off-axis lens from a standard lens by grinding away a portion of the standard lens;

[0062] Figure 12 This demonstrates the use of a lateral displacement beam splitter;

[0063] Figure 12 B shows a lateral displacement beam splitter using a triangular prism;

[0064] Figure 13 The calibration of Lissajous is shown;

[0065] Figure 14 A reference beam defocusing lens combined with a lateral displacement beam splitter and a liquid crystal device is shown.

[0066] Figure 15 An embodiment providing a reduced beam diameter is shown;

[0067] Figure 16 An example using a quarter-wave plate is shown;

[0068] Figure 16 b shows the paths of the incident signal beam and the incident reference beam;

[0069] Figure 16 c shows the paths for returning the signal beam and returning the reference beam;

[0070] Figure 17 An embodiment of a polarized rhomboid beam splitter 500 that avoids vertical incidence and transmission of beams is shown;

[0071] Figure 18 The use of wedge prism 515 to extend the optical path length of the reference arm is shown in order to enable interferometric measurement comparison between the signal beam and the reference beam;

[0072] Figure 19 It shows Figure 18 An alternative embodiment of the double-wedge design.

[0073] Figure 20 The reference beam defocusing lens and the optical path matching window are combined into a single solid beam defocuser.

[0074] Figure 21 An optical bandpass filter for reducing the spectral bandwidth of a superluminescent diode is shown.

[0075] Figure 22 The system shows additional optical elements that can accommodate variations introduced by fluid around the cantilever.

[0076] Figure 23 An embodiment is shown in which the same light source is used in both the interferometer and the beam deflection system;

[0077] Figure 24 An embodiment is shown in which the function of the beam splitter and the lateral displacement beam splitter are integrated into a single joining assembly; and

[0078] Figure 25 An embodiment in which the cantilever is attached to a mechanical actuator is shown. Detailed Implementation

[0079] Figure 8 A novel arrangement of a differential interferometer is depicted, representing a first embodiment of the invention. In this embodiment, the introduction of a birefringent lateral beam shifter 360 combined with a split-angle birefringent prism 320 allows the signal beam 090 and the reference beam 100 to intersect at a point outside the two prisms. Note that the source beam 040 is refracted and split at the birefringent interface 363, resulting in the signal beam 090 and the reference beam 100. The birefringent lateral beam shifter 360 introduces a lateral displacement between the signal beam 090 and the reference beam 100, while the split-angle birefringent prism 320 introduces an angular deviation relative to the signal beam 090 toward the reference beam 100.

[0080] The lateral displacement between two beams is defined as the translation of the propagation axis of one beam relative to the axis of the other beam in a direction substantially perpendicular to either axis. This direction may be referred to as the transverse direction. Typically, the lateral displacement is introduced via refraction and / or reflection of one or both beams. As defined herein, the lateral displacement is not generally considered to be the change in distance between two non-parallel propagating beams simply because they are non-parallel.

[0081] The present invention Figure 8 The illustrated embodiment allows the intersection 365 of the signal beam 090 and the reference beam 100 to be positioned outside both the birefringent lateral beam shifter 360 and the birefringent prism 320. This intersection 365 can then be positioned within a microscope objective 110, such as the one used in the previous arrangement. This is convenient because it is best to position the intersection 365 at the back focal plane 330 of the microscope objective 110 to ensure that the beam is orthogonal to both the cantilever and the chip upon reflection. Other embodiments using different arrangements of birefringent prisms can achieve the same effect. For example, two birefringent prisms 320 or a specially designed single birefringent reflection prism 320 can be used to produce the intersection 365 at any location in space, such as the back focal plane 330 of the microscope objective 110.

[0082] like Figure 9As shown, moving the prism pair outside the path between the microscope objective 110 and the camera system 190 creates another embodiment of the invention. The source beam 040 is split into a signal beam 090 and a reference beam 100 before being reflected from the dichroic mirror 310. This allows for higher quality imaging of the cantilever as seen in the camera system 190. Additionally, optical access allows for the introduction of an additional beam positioning unit 370, such as those described in patents 13 / 999,614 and Labuda et al., Appl. Phys. Lett. 106, 253103 (2015), into the optical system using an auxiliary dichroic mirror 390. The auxiliary dichroic mirror 390 can be any type of beam-splitting optics, but preferably reflects a specific wavelength range of interest while transmitting other wavelengths. This allows one or more auxiliary beams 380 ( Figure 9 (Only one is shown in the image) is introduced into an optical system with functions such as photothermal excitation of the cantilever, local thermal detection, photovoltaic excitation of the sample, vibrational spectral excitation of the sample (as required for local Raman or Fourier transform infrared spectroscopy), photo-electron or photo-hole generation, etc. These examples can all benefit from an auxiliary beam 380 focused on or near the cantilever and controlled independently of the signal beam 090 and the reference beam 100.

[0083] It is worth noting that, for illustrative reasons, Figure 9 The optical system depicted herein may have a dichroic mirror 310 with a different orientation than in the actual implementation. This technique is referred to as a “folded optical system” to aid in drawing on a two-dimensional page. In practice, the preferred embodiment may alternatively have the dichroic mirror 310 reflect light beams at various angles into or out of the plane defined by the page. Similarly, due to drawing limitations, other figures herein present light beams that may be guided into or out of the page in embodiments of the invention within the plane of the page. Furthermore, the figures herein may show elements of the apparatus as being in the plane of the page, when in reality they are positioned in front of or behind the plane of the page.

[0084] Beyond a certain distance of 365 degrees from their intersection point, the signal beam 090 and the reference beam 100 are spaced further than the distance of their diameter 060. At this distance and beyond, the beams are considered spatially separated. The advantage of spatially separating the signal beam 090 and the reference beam 100 is that each beam can be independently shaped using standard optics, and the optical path length of each arm can be independently tuned. As described in the prior art, a birefringent lens is not necessary because the two polarization states are spatially separated. For example, Figure 10 This illustrates how the reference beam defocusing lens 400 can slightly defocus the reference beam 100 so that it is focused on the cantilever support chip rather than on the cantilever, while the signal beam 090 remains focused on the cantilever.

[0085] Until now, the diameter of the source beam 040 has been selected through optical design to reduce the combined error between cantilever curvature and defocus caused by chip thickness and chip tilt errors. The advantage of the current embodiment is that the diameters of both the signal beam 090 and the reference beam 100 can be tuned independently. The diameter of the signal beam 090 can be tuned to accommodate the expected error of the cantilever curvature. Simultaneously, the diameter of the reference beam 100 can be tuned to reduce the combined error between cantilever curvature, defocus caused by chip tilt errors, and defocus caused by chip thickness errors. In other words, this additional degree of freedom allows for the design of an optical system that is more tolerant of errors from all three sources.

[0086] The off-axis lens 410 can also be used to achieve two functions simultaneously: to defocus the light beam and to apply a desired angular deviation. This is in Figure 11 As shown, the off-axis lens 410 deflects and defocuses the reference beam 100. Figure 11 b illustrates how to manufacture an off-axis lens from a standard lens by grinding away a portion of the standard lens to achieve this characteristic. Alternatively, the lens can be used off-axis without altering its geometry. However, due to the proximity between the signal beam 090 and the reference beam 100, the grinding operation is necessary in this particular design; only the reference beam 100 is designed to pass through the off-axis lens 410. Other designs can use a single lens large enough to focus both the signal beam 090 and the reference beam 100, while imposing an angular deviation on only one beam without the other, or imposing an angular deviation on both beams depending on the position of the lens axis relative to the axes of the two beams.

[0087] Figure 12 Alternative embodiments of the invention are shown, which also achieve spatially separated beam geometry without using birefringent crystals (such as birefringent lateral beam shifters 360). Lateral beam splitter 420 separates the source beam 040 into a signal beam 090 and a reference beam 100. Figure 12 As shown in Figure b, the lateral displacement beam splitter 420 consists of a triangular prism 421 incorporated into a parallelogram prism 422. Unlike lateral beam shifters that use refraction to separate light, the lateral displacement beam splitter 420 uses a partially reflective optical interface 423 to split the source beam 040 into a signal beam 090 and a reference beam 100; then, a total internal reflection optical interface 424 parallel to the partially reflective optical interface 423 is used to reflect the first reflected beam, such that both the double-reflected beam and the initial transmitted beam exit the lateral displacement beam splitter as parallel beams spaced a certain distance apart in the lateral direction. Figure 12In the described embodiment, a polarized partially reflective optical interface 423 is used, such that the signal beam has a polarization state substantially orthogonal to the polarization state of the reference beam. However, a non-polarized lateral displacement beamsplitter can also be used at the cost of a reduced signal-to-noise ratio. Figure 12 In this design, the partially reflective optical interface 423 has a polarization-selective coating that reflects the signal beam 090 and transmits the reference beam 100. However, there is an equivalent optical arrangement where the signal beam 090 is transmitted and the reference beam 100 is reflected. Meanwhile, the total internal reflection optical interface 424 that redirects the signal beam 090 to be parallel to the reference beam 100 can utilize total internal reflection, a metallic coating, or a dielectric coating.

[0088] After the signal beam 090 and reference beam 100 leave the lateral displacement beam splitter 420, an angular deviation is applied to the reference beam 100 using an optical path wedge 430. (Note that this wedge is called an "optical path wedge" because it will later be used to change the optical path length of the beam.) In this context, a wedge is a prism or window designed such that the two optical surfaces transmitting the beam are intentionally non-parallel in order to apply an angular deviation to the beam passing through it. The angle between the two optical surfaces is the wedge angle. The angular deviation Δθ of the transmitted light is determined by the glass n used to manufacture the wedge. glass The wedge angle α and the refractive index are defined by the following formula:

[0089] Δθ≈αn glass

[0090] This is a good approximation for a small angle α. This angular deviation can be designed to achieve desired beam separation between the signal beam 090 and the reference beam 100 at the cantilever. This separation is a function of the focal length of the microscope objective 110 and the angular deviation between the reference beam 100 and the signal beam 090. This design is more compact than previous embodiments that relied on large birefringent optics. Furthermore, the optical components in this embodiment can be manufactured in some respects at a lower cost and with higher optical quality than birefringent materials.

[0091] Figure 12The illustrated embodiment utilizes a lateral displacement beam splitter 420 to create two parallel beams, one of which is subsequently deflected using an optical wedge 430. However, a single optical component can perform both functions. For example, an alternative beam splitter to the lateral displacement beam splitter 420 (where the parallelogram prism 422 is replaced by a trapezoidal prism) can split the source beam 040 into a signal beam and a reference beam with a predetermined angle between them. The angle between the two beams emerging from such a beam splitter is a function of the angle between the two reflective surfaces of the trapezoidal prism and the refractive index of the trapezoidal prism's material. Alternatively, a beam splitter having a similar geometry to the lateral displacement beam splitter 420 but where the triangular prism 421 and the parallelogram prism 422 are made of different glass types can deflect the transmitted beam by an angle determined by the refractive indices of the two glass types. Both proposed mechanisms would result in an angular deviation between the signal beam and the reference beam without requiring a wedge prism.

[0092] Note that the lateral displacement beam splitter 420 can also be replaced by two polarization cube beam splitters with an air gap or bonded together. Alternatively, the same function as the lateral displacement beam splitter 420 can be achieved using polarization cube beam splitters and mirrors. These designs allow for cost reduction because such prisms are readily available from most optical manufacturers. It should be noted that the function of the lateral displacement beam splitter 420 is to apply a lateral displacement between the first beam and the second beam; that is, a displacement in a direction perpendicular to the axis of the first beam. Many optical arrangements can be used to introduce this function using a combination of basic optical components. However, an arrangement in which both reflective interfaces are part of a combined assembly of optical elements is optimal because it reduces the possibility of drift and vibration between the two reflective interfaces, which could introduce errors in the measurement of cantilever displacement.

[0093] An optical wedge 430 is attached to an actuator 440. The actuator 440 can translate the optical wedge 430 in one direction, changing the amount of glass the beam passes through without altering the beam's angular deviation. The actuator can be a piezoelectric transducer, a stepper motor, an inertial motor, to name a few. The actuator's translation axis can be in a plane with any of the wedge's optical surfaces, or at an angle relative to those surfaces. The displacement causing a change in the glass thickness on the order of the light wavelength allows for variation in the optical path difference between the paths of the reference beam 100 and the signal beam 090. This allows for the calibration of the Lissajous by measuring and fitting an interferometric response function measured during the movement of the optical wedge 430. Note that the optical wedge 430 performs two functions: angularly shifting the reference beam 100 to achieve designed spot separation at the cantilever, and calibrating the Lissajous by actuating the optical wedge 430 with the actuator 440.

[0094] Alternatively, the lateral displacement beam splitter 420 can be tilted to change the optical path difference between the paths of the reference beam 100 and the signal beam 090 by approximately one optical wavelength. This can be achieved by actuating the piezoelectric transducer to apply an angular deviation to the lateral displacement beam splitter 420. While the optical path wedge 430 requires translation to change the optical path length between the paths of the signal beam 090 and the reference beam 100, the lateral displacement beam splitter 420 requires rotation to perform the same function. Other optical components can also be actuated to apply an optical path length difference between the paths of the signal beam 090 and the reference beam 100 to calibrate the Lissajous. Ideally, the optical path length difference required for proper Lissajous calibration is at least half the optical wavelength, but a smaller fraction may be sufficient to provide a sufficient elliptical arc to fit an accurate Lissajous model to the acquired data.

[0095] Piezoelectric actuators can move optical elements at high speeds and nanometer resolution. In this invention, this will allow users to calibrate lissajous very quickly and with very high resolution. This is advantageous in some applications. However, in other applications, it may be advantageous to calibrate lissajous using a highly stable method. Piezoelectric actuators are susceptible to creep over time and temperature, and this creep can cause the optical path difference between the signal beam 090 and the reference beam 100 to change undesirably over time, even after the actuation signal has stopped. This change in optical path difference can be mistaken for cantilever displacement.

[0096] Figure 13An embodiment of the invention is illustrated, providing a more stable method for calibrating lissajous. Instead of actuating the optical wedge 430 or other optical components to modulate the phase difference between the reference beam 100 and the signal beam 090, a liquid crystal device 450 is used to apply a phase shift between the reference beam 100 and the signal beam 090. A liquid crystal device is a device that orients molecules of a special liquid between two transparent electrodes to alter the birefringence properties of the liquid. The orientation of the molecules is caused by an electric field originating from the applied voltage to the electrodes. The degree of phase shift produced by the liquid crystal device 450 depends on the magnitude of the voltage applied to the liquid crystal device 450. The thickness of the liquid crystal material is chosen to achieve approximately one circle around the lissajous when fully activated. Liquid crystals typically have a nonlinear relationship with the applied difference relative to the applied voltage. This nonlinearity in the liquid crystal response is advantageous because it prevents noise and drift when the liquid crystal device is turned off after calibration. Below a certain voltage (typically about 1V), the liquid crystal is stable, exhibiting a fixed and stable phase shift between the two polarization states. When the liquid crystal device voltage is set close to 0V, the noise applied to the voltage of the liquid crystal device has a negligible effect on the measured cantilever displacement. Therefore, unlike existing techniques, it is beneficial to electrically activate and use the liquid crystal device 450 during experimental setup to calibrate the interferometer response, but it is also beneficial to turn off the liquid crystal device and keep it in a deactivated state (close to 0V) during measurement. Electrically deactivating the liquid crystal device after Lissajous calibration prevents the liquid crystal device from adding noise to the cantilever displacement measurement. Sometimes, it is also beneficial to pause the measurement, electrically activate the liquid crystal device 450 to recalibrate the interferometer response and Lissajous shape, electrically deactivate the liquid crystal device, and continue the measurement.

[0097] The liquid crystal device 450 can be placed in the path of the signal beam 090 or the path of the reference beam 100. Alternatively, the liquid crystal device 450 can be placed in the path of the source beam 040 or the path of the reconstructed beam 200, and accordingly oriented to apply maximum phase shift to the polarization axis of the signal beam 090 or the polarization axis of the reference beam 100. However, the liquid crystal device can cause both wavefront aberration and large back reflection, which reduces the contrast of the interferometric measurement signal. To reduce the effects of this non-ideal behavior, such as... Figure 13As shown, the liquid crystal device 450 can be positioned within the reconstructed beam 200. By aligning the polarization axis of the liquid crystal device 450 with the polarization axis of the signal beam 090 or the reference beam 100, the liquid crystal device 450 can preferentially apply a phase shift to one polarization axis while substantially not affecting the other. In this case, modulating the liquid crystal device voltage introduces a phase shift, which allows for calibration of the Lissajous by simulating the effect of cantilever displacement. Importantly, if the liquid crystal device 450 is placed in the path of the reconstructed beam 200 (rather than in the separate paths of the signal beam 090 or the reference beam 100), the moderate wavefront distortion of the liquid crystal device 450 will not substantially reduce the contrast at photodetectors 260, 262, 264, and 266. This is because such wavefront distortion will affect both the signal beam and the reference beam equally. When the signal beam interferes with the reference beam within the quadrature phase analyzer 220, the phase of the signal beam is subtracted from the phase of the reference beam, and the phase shift from any moderate wavefront distortion will be subtracted.

[0098] Out of respect for Figure 10 For the same reason that the reference beam defocusing lens 400 is introduced, the reference beam defocusing 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 benefits. This results in another embodiment of the invention, such as... Figure 14 As shown.

[0099] Figure 15 The illustrated embodiment of the invention demonstrates an optical scheme in which a reference beam 100 passes through a beam expander consisting of a positive lens 460 and a negative lens 470. Appropriate selection of these lenses and the distance between them will result in a desired reduction in the beam diameter 064 of the reference beam 100 relative to the beam diameter 062 of the reference beam 100. Reversing the order of the lenses allows for an increase in the beam diameter 064 of the reference beam 100. As previously discussed, controlling this beam diameter allows for optimization of the divergence and depth of focus of the reference beam near the AFM cantilever. Depending on the circumstances, different amounts of reduction or increase in the beam diameter may be desired to optimize the interferometric measurement contrast in any given case. Similarly, these optical components can be positioned in the path of the signal beam 090 to tune the divergence of the signal beam 090 near the cantilever 120.

[0100] Figure 15 An actuation mechanism, referred to herein as beam expander actuator 480, is also shown, which can be attached to one or both lenses (460 and 470) to change the distance between them. The actuation mechanism can be manual or computer-controlled. This allows for careful tuning of the focus at the cantilever support chip while the instrument is running. This can be beneficial for increasing the contrast of various cantilever support chip thicknesses, especially if the depth of field of the beam is less than the variation in cantilever support chip thickness.

[0101] In the embodiments discussed so far, a Faraday isolator 170 is used to prevent light from returning to the source and causing instability. This is a result of the beam splitter 180 reflecting only a portion of the recombined beam 200 towards the quadrature phase analyzer 220. The remaining beam returns to the source. Figure 16 The diagram illustrates an embodiment of the invention in which a quarter-wave plate 490 is used such that the polarization state can be rotated by 90° between the incident and returned beams of both the signal beam 090 and the reference beam 100. According to the standard optical nomenclature of the lateral displacement beam splitter 420, the polarization states of the incident and returned beams are... Figure 16 The symbols are marked "S" and "P". A single quarter-wave plate 490 through which both beams pass can be used to perform this 90° rotation on both the signal beam 090 and the reference beam 100. Alternatively, a first quarter-wave plate can be placed in the signal beam 090 and a second quarter-wave plate can be placed in the reference beam 100. Figure 16 b shows the paths of the incident signal beam 090 and the incident reference beam 100. Figure 16 c illustrates the paths of the returning signal beam 090 and the returning reference beam 100, in which the quarter-wave plate 490 interchanges the “S” and “P” polarizations of the two beams. As a result of this operation, the reconstituted beam 200 does not return along the path of the source beam 040; instead, the polarization-selective coating in the lateral displacement beam splitter 420 redirects both the returning reference beam 100 and the returning signal beam 090 away from the side facets of the lateral displacement beam splitter 420. This allows for the elimination of the beam splitter 180 used in the previous embodiment. Furthermore, in this configuration, the Faraday isolator 170 can be omitted because almost all the light is now directed toward the quadrature phase analyzer 220, and a negligible amount of light returns to the source.

[0102] It is desirable to reduce the amount of back reflection that might return to laser 010, especially after removing Faraday isolator 170. Typical cube beam splitters are designed to operate using beams perpendicular to their optical planes. This geometry results in most of the back reflections that could return to laser 010, such as... Figure 16 The example shown is for cleaning polarizer 070. Rotating the cube beamsplitter to prevent back reflections back to the laser can lead to a degrade in cube beamsplitter performance because the beam-splitting coating is designed for a 45° incident angle. Furthermore, rotating the cube can introduce complexity during assembly and manufacturing. Plate beamsplitters are not the desired alternative; they are manufactured as windows with parallel interfaces, which can cause etalon fringes even when used at large angles relative to the beam axis. Figure 17The design of the polarization rhombic beam splitter 500 is presented, which avoids perpendicular incident and transmitted beams relative to the outer surface of the beam splitter. This ensures that any stray light reflected off the outer surface of the beam splitter leaves the optical system at a large angle, rather than mostly returning to the laser 010. Figure 17 b shows a more detailed view of the geometry and optical path of the polarizing rhombus beamsplitter. A polarizing rhombus beamsplitter is manufactured by gluing two identical isosceles triangular prisms together along their faces corresponding to a triangular base. The four faces corresponding to the triangular legs constitute the outer surfaces of the assembled polarizing rhombus beamsplitter. Prior to gluing, a polarizing beam-splitting coating is introduced on at least one of the gluing surfaces. Some or all of the outer surfaces may have an anti-reflective coating optimized for the light source wavelength and angle of incidence to maximize light transmission through the polarizing rhombus beamsplitter. Additionally, some faces not intended for the main function of the beamsplitter may be ground to suppress specular reflections from said faces, which could cause undesirable interference within the optical system. Furthermore, these grounded surfaces may be painted black to further reduce any stray light in the optical system by absorbing stray light that would otherwise be reflected or scattered within the optical system.

[0103] Although the outer surfaces of the polarizing rhombus beam splitter 500 are not orthogonal to each other, the transmitted beam is parallel to the incident beam, just like a standard cube beam splitter. Furthermore, if the polarizing rhombus beam splitter is oriented relative to the incident beam at the incident angle designed for it, the reflected beam is perpendicular to the incident beam. This is designed with an incident angle of θ. inc A 5° polarizing rhombus beam splitter is formed by the apex angle Ψ vertex A triangular prism with an angle of 80° is made, as calculated using the following formula:

[0104] Ψ vertex =90°-2θ inc

[0105] In this configuration, both prisms used to assemble the polarizing rhombus beam splitter are 50°–50°–80° triangular prisms. When operated at the designed incident angle, the beam inside the polarizing rhombus beam splitter 500 is positioned at angles defined by the angle of the outer surface of the polarizing rhombus beam splitter 500 and its refractive index. In this case, the incident angle at the inner beam splitting interface can be calculated using the following formula:

[0106]

[0107] Where, n glass It is the refractive index of the glass used to manufacture prisms. For optimal operation, the beam-splitting coating is specifically designed to be applied at θ. incOperation at the incident angle. For example, the coating used for the polarizing rhomboid beam splitter 500 is designed to have the maximum polarization extinction ratio because the intended application is to ensure high linearly polarized light output. (As from...) Figure 17 It is evident from b that the incident beam and the transmitted beam are not collinear; therefore, the translation of the transmitted beam must be taken into account in the optomechanical design. Figure 17 In b, the polarizing rhombic beam splitter 500 is shown as the incident angle θ. int =5°; however, with θ int =0° (equivalent to a cube beam splitter) Any angle that is sufficiently different may be beneficial in suppressing back reflections of the optical system.

[0108] A method similar to that of the rhomboid polarization 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 their faces that are slightly different from 45°, 90°, and 135° to avoid back reflections returning to the laser 010.

[0109] In the embodiments of the invention shown so far, a highly coherent laser source—i.e., a source with a long coherence length—is chosen to ensure high interferometric contrast due to the large difference in optical path length and total dispersion seen by both the signal beam 090 and the reference beam 100. High interferometric contrast can be observed as long as the coherence length is greater than the difference in optical path length (including errors due to the superposition of tolerances in optical and mechanical design). This is the case with HeNe lasers, which have coherence lengths on the order of tens of centimeters or more. Using such a highly coherent source allows for greater design freedom of the optical system, as matching between the optical paths of the signal beam 090 and the reference beam 100 is not necessary to achieve high contrast. However, matching the optical path lengths of the reference arm and the signal arm is beneficial. For example, a mismatch in the optical path lengths between the signal beam 090 and the reference beam 100 can lead to undesirable drift or discontinuities in the interferometric signal. Any drift in the laser wavelength (e.g., due to temperature variations) results in a drift in the interferometric signal that scales proportionally to the difference in optical path lengths between the signal beam 090 and the reference beam 100. Similarly, mode hopping in the laser wavelength causes discontinuities in the interferometric measurement signal, which are proportional to the difference in optical path length. These problems are greatly reduced if the optical path lengths of the signal beam 090 and the reference beam 100 are matched, which is a desirable characteristic of interferometers known to those skilled in the art.

[0110] For incoherent light sources with wide spectral bandwidths, such as superluminescent diodes (SLDs), the matching requirements between the two arms are extremely stringent, as even small mismatches can result in no interferometric measurement signal. SLDs have low coherence lengths on the order of 10 μm. This coherence length is less than the tolerance of most optomechanical components. For this reason, although designers routinely use SLDs in AFM for beam deflection methods, the prior art teaches the use of highly coherent laser sources, such as HeNe lasers or laser diodes, as the basis for interferometers in AFM. In other words, despite the potential benefits of SLDs, expert designers in the prior art choose highly coherent lasers for interferometers because the low coherence of SLDs is highly problematic.

[0111] Note that due to the dispersion and relatively wide spectral bandwidth of the SLD, the matching criteria used to achieve interferometric comparison between the signal beam 090 and the reference beam 100 include the optical path length parameter (discussed previously) and the dispersion parameter. The optical path length l of the optical component... QPL Defined as:

[0112] l OPL =xn O

[0113] Where x is the thickness of the optical component, and n O The center wavelength λ of a low-coherence light source O The refractive index at that point. Conversely, the path length of the optical system includes dispersion effects (up to the first order) and is defined as:

[0114]

[0115] in The term describes the first-order dispersion of the glass. Similar to the optical path length, the optical path length of the signal beam 090 is the sum of the optical path lengths of the incident portion (before reflection from the cantilever) and the returning portion (after reflection from the cantilever), and similarly for the optical path length of the reference beam 100.

[0116] For interferometer designs with asymmetrical reference and signal optical paths, the matching optical path lengths of the two arms are insufficient to achieve interferometric comparison with an SLD. A necessary criterion for ensuring high contrast is the total optical group path length between the matching arms, which takes into account the difference in dispersion between the two arms and plays a role in determining the conditions for optical contrast. Therefore, the criterion used to achieve comparison with an SLD will henceforth be referred to as the "matching optical group path length" between the signal beam 090 and the reference beam 100, rather than simply the "matching optical path length" (which is sufficient in the absence of dispersion).

[0117] In order to Figure 18The novel design shown uses a superluminescent diode 510, requiring a longer optical path length in the reference arm to enable interferometric comparison between the signal beam 090 and the reference beam 100. For example... Figure 18 As shown, this can be achieved by using a wedge prism 515 to deflect the beam off the optical axis. The optical path wedge 430 can then be used to deflect the beam to a specified angle as required by the previous design. In this case, the required angle of the optical path wedge 430 is influenced by the selection of the angle of the wedge prism 515. The distance between the two wedges and the selected wedge angle can be tuned to ensure that the reference beam 100 has the same optical path length as the signal beam 090. By matching the optical path length between the two arms required by the superluminescent diode 510, the advantages of this low-coherence light source, such as reduced background signal and periodic errors and artifacts, can be utilized in this context of interferometric AFM. Note that in other embodiments of the invention, the optical path length of the signal arm may need to be made longer than that of the reference arm; in this case, a similar wedge would be provided instead in the signal arm. Furthermore, note that using a free-space superluminescent diode instead of a fiber-coupled superluminescent diode, as previously mentioned in the context of a free-space laser source, is optional.

[0118] Figure 19 The embodiments of the present invention shown present... Figure 18 An alternative solution to the presented double-wedge design is to introduce an optical path matching window 520 into the reference beam 100, ensuring a close match of the optical path lengths of both the reference beam 100 and the signal beam 090. This allows for matching of optical path lengths without using multiple wedges to deflect the beam. In this context, the optical path matching window 520 is simply an optical window where the type of glass is carefully selected for its dispersive properties, and the window thickness is precisely tuned to introduce a well-controlled amount of optical path length into the reference beam 100, matching its optical path length with that of the signal beam 090. Depending on the scenario, it may be necessary to introduce the optical path matching window 520 into the signal beam 090, the reference beam 100, or both, to achieve ideal optical path length matching within geometrical optical constraints.

[0119] Because the coherence length of the superluminescent diode 510 is very short, on the order of 10 μm, it is generally impossible to match the optical path lengths of the two arms during instrument fabrication and production. For this reason, it is necessary to introduce devices with tunable optical path lengths in the signal beam 090 path, the reference beam 100 path, or both paths, so that the two arms can be matched with fine precision once the instrument is assembled and in operation. Conveniently, the optical path wedge 430 can be moved in a direction perpendicular to the optical axis to change the amount of glass through which the reference beam 100 passes, thereby changing the optical path length of that arm. For a typical wedge angle, this requires an actuator 440 that allows the optical path wedge 430 to move on the order of 1 mm to achieve a sufficient range to match the two arms within optical and metalworking tolerances. Although a separate wedge can be used for optical path length matching, the optical path wedge 430 previously used to change the angle of the reference beam 100 is also conveniently used in this context. Using the optical wedge 430 for these two purposes reduces the number of optical components that need to be manufactured, as well as the number of back reflections and the complexity of the optical system. Note that the optical wedge 430 is used for three functions in this instrument: applying an angular deviation to the reference beam 100, calibrating Lissajous with a small movement on the order of light wavelength, and matching the optical path length between the reference beam 100 and the signal beam 090 with a large movement on the order of 1 mm.

[0120] Different cantilever types can have very different cantilever support chip thicknesses. For example, silicon chips are typically about 300 μm thick, while silicon nitride chips are typically 500 μm thick. If a low-coherence light source (such as an SLD) is used, switching between two such cantilever types requires two substantial changes to the optical design to achieve maximum contrast: the focal length of the reference beam defocusing lens 400 must be changed, and the optical path length must be matched. While the reference beam defocusing lens 400 can be changed to accommodate different cantilever thicknesses, changes to the optical path length can exceed what the translation of the optical wedge 430 can compensate for. For this reason, when switching between cantilever types, it is convenient to switch between different versions of the optical path matching window 520. Each optical path matching window 520 can be optimized for different cantilever support chip thicknesses. The fact that two optical components may need to be replaced after changing the cantilever type complicates the optical design of the instrument. Conveniently, Figure 20The embodiment in the text combines the reference beam defocusing lens 400 and the optical path matching window 520 into a single optical component: a solid-state beam defocuser 530. This optical component performs two functions: focus variation and optical path length variation that occurs when changing between cantilever types. This design allows the two functions to be combined at the design level and thus avoids concurrent problems during instrument operation. Note that the solid-state beam defocuser 530 can be simply a single lens where the focal length and thickness are tuned for a specific application, or it can be any other type of optical lens. It may be necessary to make the thickness of the solid-state beam defocuser 530 significantly greater than its diameter, such as... Figure 20 What is depicted.

[0121] Furthermore, the third function can be combined with the design of the solid-beam defocuser 530: such as in Figure 14 The beam expansion or reduction described in the context of the embodiments. In this case, using a thick meniscus lens as the solid beam expander 540 allows all three functions to be tailored for any specific application and cantilever design. Note that the solid beam expander 540 and the solid beam defocuser 530 can be made from a single piece of glass, or alternatively from multiple pieces of glass bonded together. Depending on the selection of the thickness and radius of curvature of either interface of the solid beam expander 540, the beam diameter 064 of the reference beam 100 can be tuned to be smaller or larger than the beam diameter 062 of the signal beam 090.

[0122] Typically, the beam diameter 062 of the signal beam 090 changes along the path of the signal beam, and similarly, the beam diameter 064 changes along the path of the reference beam 100. When comparing diameters, it is useful to evaluate the diameter of each beam at the back focal plane 330 of the microscope objective 110. If the beam diameter measured at the back focal plane 330 is D... BFP Then the divergence of the same beam near the AFM cantilever is:

[0123]

[0124] Where δ FFP The measured value is the half-cone angle of the beam corresponding to the cantilever, and f is the focal length of objective lens 110. However, when determining whether the signal beam 090 and the reference beam 100 overlap, a plane substantially perpendicular to either the signal or reference beam should be chosen, and the beam center and beam diameter should be evaluated in this plane according to methods known to those skilled in the art (e.g., by the first and second moments as described in ISO 11145:2018). For the purposes of this invention, if the distance between the centers of the beams exceeds half the sum of their diameters, the beams are considered to be separated in the plane, i.e., they do not significantly overlap.

[0125] exist Figure 20The diagram illustrates a mechanical component 550 that allows switching between two or more solid beam expanders 540 or solid beam defocusers 530, or some combination thereof. Allowing the user to manually switch between two or more prefabricated solid beam expanders 540 or solid beam defocusers 530 makes the optical system versatile, as it can be designed to accommodate several different cantilever types that may have different chip thicknesses.

[0126] An optical bandpass filter 560 can be used to reduce the spectral bandwidth of a superluminescent diode 510, such as... Figure 21 As shown. The spectral bandwidth of the superluminescent diode 510 is reduced, at the cost of some optical power, to increase its coherence length. Coherence length l c The center wavelength λ0 and spectral bandwidth λ of the light source BW Functions, such as:

[0127]

[0128] Reducing the spectral bandwidth increases the range of available optical path difference between the paths of the signal beam 090 and the reference beam 100, as determined by the coherence length. This applies to coherence lengths greater than the thickness of the chip 130. c In this case, the actuator 440 used to move the optical path wedge 430 to maximize the contrast of the interferometric measurement can be omitted from the design, such as... Figure 21 As shown. This alternative embodiment simplifies manufacturing and is easy to use.

[0129] During manufacturing, the optical bandpass filter 560 can be tilted to maximize the amount of transmitted light. This method allows the effective center wavelength of the optical bandpass filter 560 to be tuned to the center wavelength of a specific superluminescent diode 510 in the instrument. This tuning may be necessary because SLDs from a given model typically have large manufacturer errors at the center wavelength.

[0130] When a fluid other than air (such as water or oil) is introduced around the cantilever, the path lengths of both the reference beam 100 and the signal beam 090 are further affected. Another set of solid beam expanders 540 (or solid beam defocusers 530) can be customized for any combination of cantilever type and surrounding fluid. To accommodate the two cantilever types and the four possible arrangements of the two fluids, four solid beam expanders 540 may need to be manufactured. Alternatively, Figure 22The embodiments described herein propose introducing additional optical elements into the system, which can accommodate variations introduced by fluid introduced around the cantilever. The reference beam 100 requires defocusing using a fluidic defocusing lens 570; simultaneously, any differences in the optical path length between the two arms are compensated by introducing a fluidic compensator window 580 into the signal beam 090. Note that the fluidic defocusing lens 570 is simply an optical lens with a focal length, thickness, and material, specifically chosen for the application. Furthermore, the fluidic compensator window 580 is simply an optical window whose thickness and material are chosen to compensate for the optical path length required by the optical design. During manufacturing, the thicknesses of both the fluidic defocusing lens 570 and the fluidic compensator window 580 must be carefully controlled to ensure a sufficiently tight match in the optical path lengths required by the optical system tolerances. In this design, four arrangements can be accommodated by selecting between two solid beam expanders 540 and by inserting or removing both 570 and 580 together. Figure 22 The fluid compensation slider 590 is a mechanism that allows the user to slide both 570 and 580 together into and out of the optical system using a single actuation mechanism. The fluid compensation slider 590 can be manually actuated by the user or by an automated mechanism that can be controlled by a computer.

[0131] Despite all the advantages of interferometry (such as signal accuracy and low noise independent of cantilever length), beam deflection provides a measure of cantilever angle bending in two directions (normal and transverse), which cannot be directly measured by interferometry. For this reason, AFM users may benefit from combining OBD with an interferometer, such as those commercially available in recent years via Oxford Instruments. In this prior art instrument, two separate light sources and beam positioning unit 370 are used simultaneously to provide the user with two independent measurement methods, as described in US10338096B2. On the other hand, in Figure 23 In this invention, the same light source is used for both the interferometer and the OBD system. Using a single light source to achieve both functions offers significant cost-effectiveness and design simplicity. Figure 23As shown, a beam deflector 600 is used in the path of the signal beam 090 to reflect some of the light returning from the cantilever for use in the OBD optical path. This beam deflector 600 can be any type of beam splitter that splits the beam into a transmitted beam and a reflected beam, such as a cube beam splitter or a plate beam splitter. Preferably, the beam deflector 600 can have polarization properties such that a large amount of light is reflected only on the returning signal beam 090, while a minimal amount of light is lost through reflection on the incident signal beam 090. The reflected beam is referred to as the beam deflection beam 610. The beam deflection beam 610 is then reflected by a beam mirror 620, which can be used to center the beam deflection beam 620 onto the beam photodetector 630 using a beam gimbal 640 or other rotating mechanism. Alternatively (not shown), a translation stage attached to the beam photodetector 630 can be used to center it onto the beam deflection beam 610. Centering the beam deflection method beam 610 on the beam photodetector 630 achieves the highest sensitivity known to anyone skilled in the art of OBD methods. A small fraction of the optical power of the beam deflection method beam 610 is sufficient to be reflected by the beam deflection beam splitter 600 to measure the normal and lateral angle deflections of the cantilever. These two measurements are independent of the simultaneously occurring interferometric displacement measurements, although all three measurements are performed from a single beam focused on the cantilever.

[0132] exist Figure 23 In the diagram, reflections from the beam deflector 600 are shown as in-plane reflections compared to other beams in the optical system. However, using the polarizing beam deflector 600 to avoid light loss may require the beam splitter to reflect light out of plane rather than in-plane. Due to the constraints imposed by the two-dimensional diagram, this arrangement... Figure 23 Not shown in the image.

[0133] Figure 24 Another embodiment of the invention is illustrated, wherein the functions of the previously described beam deflection beamsplitter 600 and the lateral displacement beamsplitter 420 are integrated into a single bonded assembly of optical elements: a lateral displacement beamsplitter with a pick-off 635. While the lateral displacement beamsplitter 420 uses a total internal reflection optical interface 424, the lateral displacement beamsplitter with the pick-off 635, in contrast, uses... Figure 24 The partially reflective interface 636 shown in b is used to reflect light from, for example... Figure 24Some light is picked up from the return signal beam 090 shown in Figure c for use in beam deflection measurements. The partially reflective interface 636 replaces the function performed by the beam deflection beam splitter 600; that is, it deflects some of the return signal beam 090 toward the beam photodetector 630. The reduced number of optical interfaces traversed by the signal beam 090 used for interferometry improves the interferometric contrast. Note that an additional triangular prism 637 is introduced in the lateral displacement beam splitter with pickup 635 relative to the lateral displacement beam splitter 420. Figure 24 (as shown in b) is optional. For example... Figure 24 As shown, the additional prism can be beneficial in redirecting light to the photodetector and can also be beneficial in protecting the partially reflective interface 636. The partially reflective interface 636 can be a coating without specific polarization characteristics. However, in a preferred embodiment, a polarizing coating is used that reflects all light on the incident signal beam 090 to avoid light loss, while transmitting a predetermined portion of the light returning to the signal beam 090, such as... Figure 24 As shown in c. A portion of the transmitted signal beam 090, referred to as beam deflection beam 610, is redirected by internal reflection from the lateral displacement beam splitter with pickup 635, and reflected from beam mirror 620 toward beam photodetector 630, as in the previous embodiment.

[0134] Figure 25 An embodiment of the invention is illustrated, in which a cantilever is attached to a mechanical actuator 650, such as an assembly with a piezoelectric transducer. This allows the cantilever to move parallel to the optical axis of the microscope objective 110 or at an angle relative to the optical axis. For example, the mechanical actuator 650 can be used to track the topography of a sample during AFM imaging. Due to the differential nature of the interferometer, the cantilever displacement signal continues to report the displacement difference between the cantilever tip and the cantilever support chip. This is a signal of interest to the AFM user because it is proportional to the force applied to the cantilever tip. The usable range of motion of the mechanical actuator 650 is approximately the depth of field of the focused signal beam 090 and the reference beam 100. The depth of field is sometimes referred to as the Rayleigh range of the focused beam. Exceeding this range of motion results in a loss of interferometric contrast, which leads to higher noise. The depth of field of the signal beam 090 and the reference beam 100 can be tuned in the manner described above in this invention to match the desired range of motion of the mechanical actuator 650.

[0135] A mechanical actuator 650 that moves a cantilever along the optical axis near the focal plane of microscope objective 110 can introduce artifacts into the signal measured by a photodetector, caused by crosstalk between the cantilever's movement and any cantilever displacement relative to its chip. For example... Figure 25As shown, a back focal plane imaging lens 660 can be introduced, and its focal length and position selected, to project the back focal plane 330 of the microscope objective 110 onto the beam photodetector 630 to reduce crosstalk. The back focal plane imaging lens 660 ensures that the photodetector measures essentially only the cantilever deflection signal, while minimizing the influence of the mechanical actuator 650's movement on the measurement signal. Furthermore, the back focal plane imaging lens 660 can reduce the range required by the beam gimbal 640 to center the beam deflection beam 610 onto the beam photodetector 630.

[0136] While using superluminescent diodes (SLEDs) reduces stray reflections compared to lasers and maintains accurate measurement of cantilever displacement, stray reflections can degrade accuracy and increase noise. For this reason, gluing the optical components together may be optimal for reducing the number of air-glass interfaces that could cause back reflections. Figure 25 The orthogonal phase analyzer 220 depicted in section b is manufactured from cemented optical components: two polarizing beamsplitters, an unpolarizing beamsplitter, a half-wave plate, and a quarter-wave plate. The cemented design prevents fine-tuning of the system's optical properties by independently rotating and / or tilting the optical elements during assembly and testing of the AFM. For this reason, ensuring optical interferometric contrast requires careful fabrication of the waveplates and strict specification of the phase shift in the coatings used in the orthogonal phase analyzer 220. The benefits of assembling a cemented orthogonal phase analyzer include not only reduced optical interfaces but also robustness of the orthogonal phase analyzer's optical properties by making the optical system less susceptible to thermal drift, mechanical shock, or other forms of damage. Finally, the compactness of the cemented design contributes to the instrument's manufacturability. This configuration of the orthogonal phase analyzer 220 can be advantageously used in any arrangement of the invention.

[0137] In one possible embodiment of the quadrature phase analyzer 220, the quarter-wave plate 270 and the half-wave plate 240 are fabricated as true zero-order waveplates. A true zero-order waveplate is a waveplate that has a phase difference of less than one wavelength between ordinary and extraordinary rays without using cancellation from multiple birefringent materials. Fabricating true zero-order waveplates requires grinding and polishing birefringent materials, such as quartz, to a thickness as low as tens of micrometers with high precision. The increased cost of this fabrication step is compensated by improvements in the performance of the quadrature phase analyzer 220 and its sensitivity to reductions in angular errors in the input beam and to reductions in sensitivity to the difference between the design wavelength (of the waveplate) and the center wavelength of the light source. The reduced sensitivity to beam wavelength is particularly important for low-coherence light sources, where the broad spectrum of the light source means that a single-wavelength waveplate can only approximate the desired behavior of the waveplate. Because true zero-order waveplates are less dependent on wavelength, they exhibit high quality performance across the full spectral bandwidth of low-coherence light sources. For similar performance reasons, the quarter-wave plate 490 or other quarter-wave plates in the signal beam and reference beam are preferably of the true zero-order type.

[0138] Furthermore, back reflections from the photodetectors can be significant and difficult to reduce using anti-reflective coatings. To prevent these back reflections from entering the optical system, four quarter-wave plates 670 can be placed between polarization beamsplitters 280 and 250 and each of the four photodetectors 260, 262, 264, and 266, as follows: Figure 25 As shown in b, the normal and abnormal axes of the quarter-wave plate should be rotated 45° about the optical axis relative to the beam splitter axis. In this arrangement, the light reflected from the photodetector will leave the unused small plane of the quadrature phase analyzer, rather than the reconstructed beam 200 in the interferometric quadrature phase analyzer.

[0139] During the experiment, any drift between the optical path lengths of the reference beam 100 and the signal beam 090 could be misinterpreted as cantilever displacement. This drift could be caused by the thermal dependence of the refractive index of the glass used in the optical system and the thermal expansion of the materials holding the lenses relative to each other. A temperature control system can be used to stabilize the temperature of the metal stage connecting all the lenses, thereby maintaining the optical system at a constant temperature even as room temperature fluctuates over time. Such a system may include one or more temperature sensors; one or more elements capable of changing the temperature, such as resistance heaters or Peltier thermoelectric coolers; optional devices for controlling airflow, such as fans; and controllers that can actuate the temperature-changing elements in response to signals from the temperature sensors, such as proportional-integral-derivative controllers. Such temperature control systems are well known to those skilled in the art.

[0140] Up to this point, the cantilever has been positioned perpendicular to the optical axis of the microscope objective 110. This is a specific scenario and may not be optimal for some situations. In a preferred embodiment, the light beam enters the rear focal plane 330 off-center, such that it exits the microscope objective 110 at an angle relative to its optical axis, while being focused perpendicular to the cantilever and the chip, which are positioned at a non-perpendicular angle relative to the optical axis of the objective. This arrangement is described in detail in US8370960B2, where the AFM uses an angle of approximately 11°, and the light enters the objective off-axis to accommodate this angle. All embodiments presented in this patent can be modified to achieve this geometry. All conclusions reached to date remain valid by satisfying the conditions required to accommodate a deliberately tilted cantilever. For example, any tilt of the cantilever deviating from the prescribed 0° design angle in the current embodiment can be considered to have a similar effect to any tilt of the cantilever deviating from the prescribed 11° angle in an embodiment optimized for 11°.

[0141] In summary, it is desirable to achieve high precision, low noise, low drift, good optical access, and equally good positional noise performance in the design of atomic force microscopes (AFMs) independent of the user's choice of AFM cantilever type. For these and other reasons, it is advantageous to construct a differential interferometer and configure it such that the lens (referred to herein as the "objective") focuses the signal beam and reference beam onto or near the AFM cantilever. The objective can be a microscope objective, a bilens, an imaging lens, or other types of lenses known to those skilled in the art. Typical widths of AFM cantilevers are between 3 μm and 50 μm; the width of the cantilever sets the maximum size of the signal spot, which in turn sets the minimum divergence of the signal beam in the space between the cantilever and the lens. Furthermore, typical lengths of AFM cantilevers are between 10 μm and 500 μm, and the field-of-view diameter of typical microscope objectives is less than 4 mm. These factors limit the maximum separation of the signal beam and reference beam in the space between the AFM cantilever and the objective. These factors collectively lead to overlap between the signal beam and the reference beam in the far field, making it difficult to independently manipulate those beams to achieve the design objectives.

[0142] Embodiments of the present invention provide a differential interferometer for atomic force microscopy, wherein a signal beam 090 and a reference beam 100 are focused near an AFM cantilever 120 by a lens 110 (“objective”); and, for certain portions of the optical space separated from the AFM cantilever 120 by the objective (referred to herein as “infinite space”), the signal beam and the reference beam substantially do not overlap, allowing independent manipulation of the beams within this region of infinite space. That is, in at least one plane within this region of infinite space, the intersection of the axis of the signal beam with that plane and the intersection of the axis of the reference beam with that plane are separated by more than half the sum of their beam diameters. This will be referred to as a split-beam differential interferometer, and several improvements and refinements, which will be discussed below, are derived from this fundamental innovation.

[0143] In a split-beam differential interferometer, the signal beam 090 is typically focused at or near the end of the AFM cantilever 120, close to the location on the cantilever that interacts with the sample. The reference beam 100 can be focused at the base of the cantilever 120, on the cantilever support chip 130, or on a reflective object rigidly attached to the cantilever support chip. The geometry of the split beam provides design freedom to manipulate the lateral position, divergence, and axial position of the focal point of the reference beam without inserting undesirable optics between the objective lens 110 and the AFM cantilever 120.

[0144] In atomic force microscopy (AFM), obtaining high-resolution, high-contrast optical images of the sample and cantilever is advantageous, allowing for the selection of regions of interest for probing using the AFM cantilever. For certain applications, it is also advantageous to introduce additional, separate optical paths (e.g., path 380 and beam positioning unit 370) for purposes such as illuminating cantilever 120 with a laser to photothermally actuate its bending; illuminating a sample to measure its photovoltaic response; and / or detecting light emitted from the sample. Therefore, it is advantageous to use a split-beam differential interferometer in one or more of the following combinations: a microscope objective with a numerical aperture greater than 0.25; a microscope objective with adjustable correction for spherical aberration; a microscope objective with a semi-apochromatic correction level or higher; a microscope objective, tube lens, and camera system 190 providing a resolution better than 2 μm at the sample plane; a microscope objective, tube lens, and camera system 190 providing a modulation transfer function of 50% or better at 250 line pairs per millimeter at the sample plane; a microscope objective, tube lens, and camera system 190 with a resolution within twice the diffraction limit of the numerical aperture of the objective at the operating wavelength; coupled to one or more optical paths providing an illumination point that is fixed or movable relative to the cantilever and sample; coupled to an optical path providing a movable, time-modulated illumination point configured for photothermal excitation of the cantilever; coupled to one or more optical paths configured for detecting light from the sample or cantilever.

[0145] In a differential interferometer, it is necessary to deflect the signal beam 090 away from the reference beam 100 and then recombine them after reflection from the target and reference objects. In many embodiments of the invention, it is advantageous to use a polarization-selective dielectric coating that is less costly, more readily available, easier to configure in the design, and provides a larger, clearer aperture and better transmission wavefront specifications than birefringent optics used in the prior art for splitting and recombining these beams. This use of the dielectric coating is merely possible due to the separation of the beams in infinite space in a split-beam differential interferometer.

[0146] One embodiment of a split-beam differential interferometer with a polarization-selective dielectric coating includes a first cubic beam splitter that separates a reference beam from a signal beam and a second cubic beam splitter that redirects the signal beam to be substantially parallel to the reference beam. Another embodiment replaces the second cubic beam splitter with a 45°–45°–90° prism arranged such that its internal reflection redirects the signal beam to be parallel to the reference beam. Another embodiment replaces the second cubic beam splitter with a mirror or other reflective optics to achieve this redirection. Yet another embodiment combines the functions of the first cubic beam splitter and the second optics into a monolithic composite prism (here referred to as a “lateral displacement beam splitter” 420), wherein multiple prism elements with suitable coatings are bonded together to form an assembly that splits the reference beam from the signal beam and guides the two beams substantially parallel to each other. In any of these implementations, those skilled in the art of optical design may choose to split the reference beam from the signal beam and then redirect the signal beam, or they may choose to split the signal beam from the reference beam and then redirect the reference beam, provided that other optical elements in the system are arranged such that the signal beam and the reference beam are correctly focused onto the target object and the reference object, respectively. By splitting the beam in a novel split-beam differential interferometer, the freedom to select and arrange these components to achieve optical system design goals is increased.

[0147] A split-beam differential interferometer with a lateral displacement beamsplitter 420 allows for further design refinement. First, it is desirable to route as many of the returning signal beams 090 and reference beams 100 as possible to the photodetector. This provides optimal noise performance for the photodetector, as well as optimal stability of the light source. When the lateral displacement beamsplitter, or equivalent optical arrangements as discussed above, are used with the split-beam differential interferometer, virtually all the returning light can be routed to the photodetector by inserting one or more waveplates between the objective and the lateral displacement beamsplitter. A single quarter-wave plate 490 with a non-circular axis rotated at 45° can be positioned such that both the signal beam and the reference beam pass through it. Alternatively, a first quarter-wave plate can be placed in the signal beam, and a second quarter-wave plate can be placed in the reference beam. Other combinations of optics, such as dielectric coatings, can be used to produce a similar effect to the quarter-wave plate.

[0148] Another improvement is the ability to actuate a lateral displacement beam splitter to introduce a relative phase shift between the signal and reference beams. This is desirable because it allows users to calibrate the photodetector's response to the phase shift, resulting in a more accurate interpretation of the phase shift between the signal and reference beams. This allows for more precise measurements of the distance between the target and reference objects.

[0149] To generate the desired lateral separation between the reference beam and the signal beam near the AFM cantilever, the optical system must be arranged to produce a corresponding angular difference between the reference beam 100 and the signal beam 090 in infinite space. In the prior art, this is achieved using birefringent optics (such as 320) to deflect the beams relative to each other. In embodiments of the present invention, due to the separation between the signal beam and the reference beam in the split-beam differential interferometer, the angular difference can instead be generated by introducing an optical wedge prism 430 into the reference beam instead of the signal beam. By selecting the angle and refractive index of the optical wedge prism, the reference beam can be deflected relative to the signal beam by a desired angle. Alternatively, the optical wedge prism can be introduced only into the signal beam and not into the reference beam, or wedges of different angles and / or refractive indices can be introduced into both the signal and reference beams, provided that the combined effect of these elements is to generate the desired angular difference between the signal beam and the reference beam in infinite space and to correctly guide the reference beam and the signal beam to the reference object and the target object, respectively. For this purpose, optical wedge prisms are cheaper and more readily available than birefringent optics, and in embodiments of the invention, the advantage of using optical wedge prisms for this application is realized solely because of the separated beams.

[0150] The use of optical wedge prisms to generate the desired angular difference in a split-beam differential interferometer provides additional advantages in this invention. It may be desirable to configure the design such that the reference beam and the signal beam are substantially parallel near the cantilever; for example, to maximize the collection of reflected light or minimize misalignment caused by axial movement of the cantilever or objective. Achieving parallel beams near the cantilever requires the optical system to be arranged such that the signal beam and the reference beam intersect in the back focal plane 330 of objective 110. This intersection must be achieved while maintaining the angular deviation criteria discussed above. In a design employing optical wedge prisms, this can be achieved by selecting the wedge position by incorporating the magnitude of the lateral displacement between the signal beam and the reference beam. Alternatively, multiple optical wedge prisms, such as 515 and 430, can be arranged in such a way that they both produce the correct angular difference and the intersection in the back focal plane.

[0151] Further advantages are achieved by using one or more optical wedge prisms in a split-beam differential interferometer according to an embodiment of the invention. Due to the separation of the beams, the optical wedge prism can exist only in the reference beam (or, alternatively, only in the signal beam). This optical wedge prism can be translated in such a way that it changes the path length of the optical group only in one of the beams, and does so without causing substantial misalignment of the beam angle or position. This translation produces an adjustable relative phase shift between the signal beam and the reference beam. This adjustability is highly desirable. One application of this is calibrating the response of a photodetector to a known phase difference between the signal beam and the reference beam. This allows for more accurate measurement of the height difference between the target object and the reference object. A second application is adjusting the initial value of the phase difference between the signal beam and the reference beam to any desired value. If the optical wedge prism has a small wedge angle, this adjustment can be performed very precisely using common optical-mechanical components, such as within a small fraction of the wavelength. Translation of the optical wedge prism can be achieved by actuator 440, such as an electric lead screw translation stage, a piezoelectric actuator, a combination of a lead screw stage and a piezoelectric actuator, or other translation devices known to those skilled in the art.

[0152] In this invention, further advantages are provided by enabling the introduction of optical lenses (such as 400, 460, and 470) into one or both beams to separate the reference beam from the signal beam in a split-beam differential interferometer. This allows for desired control over several characteristics of the beams. For example, one configuration of a split-beam differential interferometer directs the signal beam to the end of the AFM cantilever (target object) and the reference beam to the cantilever support chip (reference object). To maintain maximum contrast, the axial position of the focal point of the signal beam must be on or near the surface of the target object, and the axial position of the focal point of the reference beam must be on or near the surface of the reference object. However, these surfaces are in different axial positions. The optical system must be configured to produce this focal difference, and it is advantageous to do so without introducing optical components between the objective lens and the cantilever. In a split-beam differential interferometer, due to the separation of the beams, this focal difference can be achieved by introducing one or more lenses into one or both of the signal and reference beams, all within infinite space. For example, a simple or compound lens with net positive optical power can be introduced into the reference beam in infinite space, shifting the focus of the reference beam axially toward the objective lens compared to the focus of the signal beam. Alternatively, a similar effect can be achieved by introducing a lens with net negative optical power into the signal beam in infinite space. Alternatively, the lens can be introduced into both beams as long as the combination of lenses produces the desired relative change in focus (hereinafter referred to as "spot focus difference") between the signal beam at the target object and the reference beam at the reference object.

[0153] In embodiments of the invention, the ability to independently introduce lenses into the signal beam and reference beam can be employed in a specific manner to generate even more advantages for the operation of a split-beam differential interferometer. A desirable feature of an AFM using such an interferometer is its ability to work with a variety of different cantilever types (such as both silicon and silicon nitride cantilever) and to image samples in a variety of fluids (such as air, water, or oil). Different cantilever types have support chips of varying thicknesses, and support chips with different tolerance ranges for cantilever support chip thickness. Different fluids have different refractive index values, and the refractive index of the fluid affects the axial focal position of the signal beam and reference beam near the AFM cantilever. Combined, these factors mean that it is advantageous to be able to adjust the spot focus difference during operation. One way to achieve this adjustability is to introduce combinations of lenses (such as 530 and 540, or 580 and 570) into one or both beams in an infinite space, the combinations of lenses being actuated to produce a variable spot focus difference. Alternatively, one can construct one or more fixed lens assemblies, each producing a different effect on spot focus aberration, and combine these fixed lens assemblies with one or more selection devices, allowing the user to introduce one or more fixed lens assemblies into one or more beams in infinite space. Preferably, the selection devices will allow these components to be interchanged in such a way that introducing each fixed lens assembly does not require additional alignment by the user. By selecting one or more of these fixed lens assemblies for introduction into a signal beam, a reference beam, or both, the user can then select the desired spot focus aberration to provide optimal contrast for a specific combination of conditions; for example, optimizing for a silicon cantilever in air one day and for a silicon nitride cantilever in water another day.

[0154] Especially with interchangeable fixed lens assemblies, there will be a certain range of tolerances in matching the spot focus difference with the operating conditions. Therefore, controlling the focus depth of the signal beam, reference beam, or both beams near the AFM cantilever can provide further advantages. This is achieved by controlling the divergence of the signal beam and reference beam near the AFM cantilever. In turn, this divergence can be controlled by manipulating the diameter of the corresponding beam in infinite space. Embodiments of the invention provide the advantage of freely and independently manipulating these divergences by introducing lenses independently in one or two beams. This can be accomplished in conjunction with the aforementioned variable spot focus difference or selective spot focus difference design—by adjusting the optical design of the variable lens combination or interchangeable fixed lens assembly so that they not only produce the desired positive or negative power but also produce a change in beam diameter—this change is selected to produce the desired focus depth of the corresponding beam near the AFM cantilever.

[0155] Compared to existing methods, we have found that operating the interferometer using a low-coherence light source (such as a superluminescent diode 510) offers 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 source contribute no further to the interference signal. Therefore, the use of a low-coherence light source suppresses periodic errors and artifacts in the interferometer output that would otherwise be caused by partial reflections at other optical surfaces. These periodic errors and artifacts will be referred to herein as “three-wave mixing,” regardless of the precise nature of the partial reflections that cause them. To operate the split-beam differential interferometer of this application using a low-coherence light source, it is necessary to match the optical path lengths of the signal beam and the reference beam within a range much smaller than the coherence length of the light source, typically less than 20 μm for a superluminescent diode. The split-beam design of the present invention offers several advantages for achieving this matching. One or more optical wedge prisms can be actuated in one or both beams in such a way that the optical path lengths are matched without causing misalignment of the beams or their focal points on the target and reference objects. By using a small wedge angle, a common optomechanical positioner can be used to match the optical path length within a small fraction of the wavelength. Alternatively, if there is a significant mismatch between the optical path lengths of the signal beam and the reference beam, a thick optical window 520 can be fixed in one or the other beam, where the thickness and refractive index of the window are selected to approximately match the optical path length of the beam. In the presence of optional lens assemblies (such as 540 and 530) introduced into one or both beams, these lens assemblies can be designed to include thick windows, where the thickness and refractive index are selected such that they almost perfectly match the optical path length of the beam in all combinations of user-selectable lens assemblies. In both cases, the match from the thick window should be close enough that the remaining optical path length difference can be eliminated by adjusting the optical wedge prism or multiple prisms.

[0156] In some embodiments of the invention, precisely matching the optical path length difference as described above may be too cumbersome. In such cases, a light source with an intermediate coherence length may be desirable: short enough to partially suppress three-wave mixing compared to a laser source, but long enough to easily achieve a sufficiently good match between the optical path lengths of the signal beam and the reference beam. Such a light source may not be readily available because the coherence length of a laser is too long, and the coherence length of a superluminescent diode is too short. In this case, it is advantageous to configure a beam splitter differential interferometer with a superluminescent diode light source 510, and then insert a bandpass filter 560 between the light source and the optics that separate the signal beam and the reference beam from each other. Preferably, this bandpass filter is selected to reduce the spectral width of the emission from the superluminescent diode light source, thereby increasing its coherence length to a desired intermediate value. Due to the manufacturing variability of the center wavelength of the superluminescent diode and the center wavelength of the bandpass filter, it may be further desirable to provide the bandpass filter with an optomechanical mount that includes adjustable tilt. Because 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 signal-to-noise ratio at the interferometer photodetector. Alternatively, other devices can be used to generate a beam with an intermediate coherence length, such as combining a diode laser with an RF modulation source.

[0157] According to embodiments of the invention, a split-beam differential interferometer measures the displacement of an AFM cantilever regardless of its angle. This is sufficient for most applications, but for some applications, it is desirable or necessary to measure the angle of the cantilever in the normal or lateral direction. In a split-beam differential interferometer, this can be achieved by introducing an additional beam-splitting element 600 into the signal beam. This additional beam-splitting element intercepts the light returning from the cantilever and redirects a portion of it (this portion being the “angle detection beam”) to a split photodiode, quadrant photodiode, or linear position-sensitive detector (“angle photodetector”, 630) via a centering device (e.g., 640). The centering device can be a translation stage, a tilting stage 640 with a mirror mounted, or some other adjustable element that allows the light to be centered on the angle photodetector. If the split-beam differential interferometer is equipped with the lateral displacement beam splitter 420 as described above, the additional beam splitting element can be incorporated into the assembly of the lateral displacement beam splitter having pickup 635, for example, by replacing the surface that reflects the signal beam parallel to the reference beam with a partially reflective coating that separates the angle detection beam from the returning signal beam.

[0158] Additionally, if the split-beam differential interferometer is equipped with one or more waveplates configured to route substantially all of the returning light away from the light source, the additional beam-splitting elements can be designed with a polarization-selective coating, ensuring that substantially all of the returning light reaches the interferometer photodetector or angle photodetector. This routing of light avoids an unnecessary reduction in the signal-to-noise ratio on the interferometer photodetectors 260, 262, 264, 266, or the angle photodetector 630.

[0159] For some applications of atomic force microscopy (AFM), it is advantageous to actuate an AFM cantilever perpendicular to the sample during scanning to track the sample surface. For example, the sample may be too large or heavy to actuate quickly, and therefore actuating the AFM cantilever can provide faster imaging of the sample. In such cases, it is advantageous to combine the split-beam interferometer of the present invention with the AFM cantilever mounted on a mechanical actuator 650 that moves the cantilever-supporting chip along an axis within 20° of the axis of the objective lens used to focus the signal and reference beams.

[0160] In a split-beam differential interferometer according to an embodiment of the invention, and further in other differential interferometers, it is desirable to calibrate the response of a photodetector based on the phase difference between the signal beam and the reference beam. It is advantageous to achieve this by incorporating an electrically controlled birefringent liquid crystal device (LCD) 450 into the optical system. Several arrangements of the LCD exist that can modulate the phase difference between the signal beam and the reference beam. The LCD 450 can be placed in the reconstituted beam between the beam splitter optics 420 and the orthogonal phase analyzer 220, wherein the LCD is preferentially oriented such that it applies a substantial phase shift to only one of the signal beam and the reference beam. Alternatively, the LCD can be placed between the light source and the beam splitter optics, wherein the LCD is preferentially oriented such that it applies a substantial phase shift to only one of the signal beam and the reference beam. Alternatively, only in the case of a split-beam differential interferometer, the LCD can be placed in either the signal beam only or the reference beam only within the space of the split beam path. It may be further advantageous to electrically activate the LCD to calibrate the Lissajous before measuring the cantilever, and then electrically deactivate the LCD by setting its voltage to a voltage much less than 1V during the cantilever measurement. This deactivation reduces noise and drift in measurements.

[0161] The present invention may comprise multiple photodetectors (260, 262, 264, and 266) arranged in combination with an assembly comprising one or more beam splitters and one or more waveplates (e.g., 230, 240, 250, 270, 280); such an assembly of optical elements is referred herein to as an "orthogonal phase analyzer". Within a split-beam differential interferometer, the orthogonal phase analyzer 220 interferes the signal beam with a reference beam in at least two distinct optical paths, each path having a substantially different increase in phase shift between the signal beam and the reference beam. Advantageously, these optical elements are fabricated as a monolithic optical assembly, wherein each optical element is joined in direct optical contact with its adjacent optical elements, each element being joined with correct orientation and alignment. Compared to reflections at the glass-air interface in prior art arrangements, this monolithic assembly exhibits lower reflections due to refractive index matching at the joint interface. The monolithic assembly thus reduces unwanted signals and artifacts in the interferometer output. Furthermore, the monolithic assembly is more resistant to mechanical shock and thermally induced mechanical drift in the beam splitter and waveplate positions than existing technologies, both of which introduce unwanted artifacts into the interferometer output. Implementing such a monolithic assembly while maintaining a desired small component size may require unconventional optical component designs, such as a square half-wave plate 240 with its non-axis at a 22.5° angle to its edge, and a square quarter-wave plate 270 with its non-axis at a 45° angle to its edge. The construction of the monolithic assembly may require strict tolerances in component specifications and alignment, as misalignment may occur after assembly. However, once these tolerances are met, the completed monolithic assembly maintains stable alignment indefinitely, thus providing an advantage for interferometer operation. The application of the novel monolithic orthogonal phase analyzer is not limited to split-beam differential interferometers used in atomic force microscopy. Instead, such a monolithic assembly can be found in other devices that interfere a signal beam with a reference beam in at least two different optical paths, each path having a substantially different increase in phase shift between the signal and reference beams, and these devices also include multiple photodetectors. Such other applications can include split-beam differential interferometers for applications other than atomic force microscopy; orthogonal interferometers, whether or not they are configured differentially; and quantum state measurements in quantum computing and quantum cryptography.

[0162] More specifically, in some embodiments of the invention, a particularly useful configuration of a monolithic orthogonal phase analyzer combines: a non-polarized cube beam splitter 230 that receives the signal beam and the reference beam and separates them between the two optical paths; an optional first waveplate 240 that produces a first incremental phase shift (optionally zero) between the beams; a first polarized cube beam splitter 250 that interferes with the beams with the first incremental phase shift, passes the polarization-separated beam, and directs each polarization to a photodetector; a second waveplate 270 that produces a second incremental phase shift between the beams; and a second polarized cube beam splitter 280 that interferes with the beams with the second incremental phase shift, passes the polarization-separated beam, and directs each polarization to a photodetector. In this arrangement, the first and second incremental phase shifts should differ by a value substantially close to 90°, close to 270°, or another odd multiple of 90°. Many configurations of waveplates are available that can be selected by those skilled in the art to accomplish this combination of incremental phase shifts. For example, the first waveplate may be a half-wave plate whose non-axis is tilted at 22.5° with respect to the component plane, and the second waveplate may be a quarter-wave plate whose non-axis is tilted at 45° with respect to the component plane. Alternatively, the first waveplate may be omitted, the second waveplate may be a quarter-wave plate whose non-axis is tilted at 45° with respect to the component plane, and the entire monolithic quadrature phase analyzer is arranged such that the plane of the component is polarized at 45° with respect to the signal beam. In this component, the parts are integrally combined to suppress unwanted reflections, reduce drift, and improve shock resistance, as described above. This particular embodiment of the monolithic quadrature phase analyzer can also be found in fields beyond atomic force microscopy, as described above.

[0163] While monolithic quadrature phase analyzers offer advantages, they can still be susceptible to artifacts due to reflections from the photodetector surfaces. In embodiments of the invention, adding a waveplate 670 between the corresponding surfaces of each photodetector 260, 262, 264, 266 and the quadrature phase analyzer 220 provides further advantages. This waveplate should be a quarter-waveplate, with its non-circular axis rotated 45° from the plane shared by all beams in the quadrature phase analyzer. This waveplate alters the polarization of backreflections from each photodetector, causing reflected light to propagate to unused surfaces of the quadrature phase analyzer, thereby mitigating artifacts caused by these reflections. These waveplates can be coupled to the aforementioned monolithic quadrature phase analyzer to further mitigate the effects of reflections and reduce light loss reaching the photodetectors.

[0164] In this invention, reflections from optical surfaces other than the target and reference objects can cause unwanted signals and artifacts in the interferometer output, or may cause light to return to the source and lead to instabilities in the light output. Dielectric polarization cube beamsplitters (such as clean polarizer 070) can be sources of reflection from their incident and exit surfaces. In split-beam differential interferometers, it is advantageous to suppress these effects of reflections by replacing the polarization cube beamsplitters with polarization rhombic beamsplitters 500 (“rhombic beamsplitters”) in the form of rhombic prisms. The polarization rhombic beamsplitter can be assembled, for example, from two 50°–50°–80° triangular prisms, wherein at least one prism has a suitable beamsplitter coating on its wide face. Other angles can be chosen as long as the polarization rhombic beamsplitter is deviated from the cube in shape sufficiently to project reflections outside the normal beam path of the optical system, thereby preventing pseudo-interference effects such as three-wave mixing, and thus also reducing the amount of light returning to the source. Although a polarized rhombic beamsplitter 500 replaces the clean polarizer 070 in the invention described herein, a non-polarized rhombic beamsplitter, for example, having a similar geometry to the polarized rhombic beamsplitter 500, would be advantageous in replacing a non-polarized cubic beamsplitter (such as beamsplitter 180). More generally, rhombic beamsplitters with any type of optical coating on their internal interfaces can benefit from the rhombic geometry to reduce the effects of backreflections from their external interfaces. The optical coating on the internal interface can be polarized, non-polarized, dichroic (i.e., wavelength-selective), or some combination thereof. Unlike cubic beamsplitters, rhombic beamsplitters can be mounted with a simple optomechanical arrangement, where their substrate is parallel to the optical axis, and in such a mounting, the angle of incidence of the beam on the beamsplitter coating can be maintained at its optimal value. Such rhombic beamsplitters may be advantageous in other optical systems adversely affected by reflections, such as those used for field imaging (especially in dark-field configurations) or for detecting scattered light.

Claims

1. An interferometer based on atomic force microscopy ("AFM"), comprising: Light source (010), used to emit a beam of light; The beam splitting optical interface (363, 423) is arranged to split the beam into a signal beam (090) and a reference beam (100). AFM cantilever (120); A focusing lens structure (110) is arranged to focus both the signal beam and the reference beam near the AFM cantilever; A beam shifter (360) is arranged to introduce a lateral displacement between a signal beam and a reference beam, the lateral displacement such that in at least one plane between the beam shifter and the focusing lens structure, the center of the signal beam is separated from the center of the reference beam by more than half the sum of their beam diameters in that plane. as well as The detector (190) operates to determine the difference in optical path length between the signal beam and the reference beam in order to determine information about the movement of the cantilever.

2. The interferometer according to claim 1, wherein, The signal beam and the reference beam are refracted differently at the beam splitting optical interface.

3. The interferometer according to claim 2, wherein, The spectral interface is an interface between two materials, at least one of which is birefringent.

4. The interferometer according to claim 1, wherein, The focusing lens structure is a single lens.

5. The interferometer according to claim 1, wherein, The focusing lens structure (110) is a microscope objective.

6. The interferometer according to claim 5, wherein, The microscope objective has a numerical aperture greater than 0.

25.

7. The interferometer according to claim 1, wherein, The reference position is on the cantilever, and both the reference beam and the signal beam are focused on the cantilever.

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

9. The interferometer of claim 1 further includes additional optics, illumination optics, and an image sensor, which operate to provide a user with an image of the sample near the AFM cantilever.

10. The interferometer according to claim 9, wherein, The image of the sample has a resolution better than 2 μm when measured at the sample plane.

11. The interferometer according to claim 9 or 10, 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 at the plane of the sample.

12. The interferometer according to claim 1, further comprising: Light from a second light source is introduced into additional optics on the sample near the AFM cantilever.

13. The interferometer according to claim 1, further comprising: Additional optics and one or more photodetectors are provided, the photodetectors detecting light emitted from a sample near the AFM cantilever.

14. The interferometer according to claim 1, further comprising: Additional optical components are used to introduce light from a second light source, such that the light from the second light source is focused onto the AFM cantilever. The light from the second light source causes the cantilever to move.

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

16. The interferometer according to claim 15, wherein, The beam splitting optical interface and the beam shifter are integrated into the bonding assembly (420, 635) of the optical element.

17. The interferometer according to claim 16, wherein, The joining components (420, 635) generate two substantially parallel beams by reflecting at least one beam twice or at least two beams once.

18. The interferometer according to claim 1, wherein, The beam shifter includes a lateral shift beam splitter (420) comprising a total internal reflection optical interface (424), wherein the beam splitter comprises a partial internal reflection optical interface (423) comprising a polarization-selective coating of the lateral shift beam splitter, wherein the total internal reflection optical interface (424) is parallel to the partial internal reflection optical interface (423), and the interferometer further includes one or more quarter-wave plates (490) interposed in one or more of the signal beam and the reference beam, thereby redirecting the return beam (090) along a different path from the incident beam (100) after reflection from near the cantilever.

19. The interferometer according to claim 18, wherein, A single quarter-wave plate (490) is incorporated into both the signal beam and the reference beam.

20. The interferometer according to claim 18, wherein, A first quarter-wave plate is incorporated into the signal beam, and a second quarter-wave plate is incorporated into the reference beam.

21. The interferometer according to claim 19, wherein, A quarter-wave plate is a true zero-order quarter-wave plate.

22. The interferometer according to claim 20, wherein, Both quarter-wave plates are true zero-order quarter-wave plates.

23. The interferometer of claim 16 further includes an actuator (440) energized to move the engagement assembly such that the actuator alters the optical path length difference between the signal beam and the reference beam.

24. The interferometer according to claim 16, wherein, The bonding assembly includes at least one optical wedge prism (430).

25. The interferometer according to claim 24, wherein, The optical wedge prism has an angle and a wedge position that cause the light beams to intersect at the back focal plane of the focusing lens structure.

26. The interferometer according to claim 1, further comprising at least one optical wedge prism (430) disposed in at least one of the signal beam and the reference beam.

27. The interferometer according to claim 26, further comprising an actuator (440) that moves the optical wedge prism to change the optical path length difference between the signal beam and the reference beam.

28. The interferometer according to claim 27, wherein, The actuator is electrically operated.

29. The interferometer according to claim 27, wherein, The actuator actuates the wedge at a distance on the order of one millionth of a meter to calibrate the detector's response to the optical path length difference between the signal beam and the reference beam.

30. The interferometer of claim 1 further comprises one or more optical lenses arranged such that, for each lens, either the signal beam or the reference beam passes through the lens, while the other beam does not pass through the lens.

31. The interferometer according to claim 30, wherein, The one or more optical lenses alter any one of the divergence, diameter, and axial focusing position of the signal beam, the reference beam, or both the signal beam and the reference beam near the AFM cantilever.

32. The interferometer of claim 31 further includes an actuator (480) that moves at least one of the optical lenses (460, 470) and thereby changes any one of the divergence, diameter, and axial focusing position of the signal beam, the reference beam, or both the signal reference and the reference beam near the AFM cantilever.

33. The interferometer according to claim 30, further comprising: A mechanism (550) for inserting and removing at least one of the one or more optical lenses (530, 540) from at least one of the signal beam or the reference beam.

34. The interferometer according to claim 1, wherein the light source is a low-coherence light source (510), and the interferometer further comprises: Additional matching optics (520, 580) are introduced into at least one of the signal beam and the reference beam such that the optical path length of the signal beam is equal to the optical path length of the reference beam within 200 μm.

35. The interferometer according to claim 34, wherein, The matching optical element includes an optical window, wherein the thickness, refractive index, and dispersion of the window are such that the optical path length of the signal beam is substantially equal to the optical path length of the reference beam.

36. The interferometer according to claim 34, wherein, The additional matching optical element includes an optical wedge prism placed in either the signal beam path or the reference beam path, and also includes an actuator (440) that translates the optical wedge prism in a direction perpendicular to the propagation axis of the beam path in which the optical wedge prism is disposed, thereby tuning the optical path length difference between the two beam paths to within the coherence length of the low coherence light source (510).

37. The interferometer according to claim 36, wherein, The optical wedge prism has an angle and a wedge position that cause the light beam to intersect at the back focal plane (330) of the focusing lens structure.

38. The interferometer according to claim 34, wherein, The additional matching optical elements include a first optical wedge prism (430) and a second optical wedge prism (515) placed in the signal beam or the reference beam, and also include one or more actuators that simultaneously move the first optical wedge prism and the second optical wedge prism to reduce the lateral deviation of the beam relative to the optical axis as the beam passes through the first optical wedge prism and the second optical wedge prism.

39. The interferometer according to claim 34, wherein, The additional matching optics include interchangeable windows (580) to discretely change the optical path length difference between the signal beam and the reference beam.

40. The interferometer according to claim 34, wherein, The additional matching optical elements include interchangeable lenses (570) having a specific thickness to change the optical path length and specific optical power and position to change any one of the beam divergence, diameter and axial focusing position near the AFM cantilever.

41. The interferometer according to claim 34, wherein, The additional matching optics include insertable and removable lenses and insertable and removable windows to tune the optical path length difference between the beams and to tune the divergence, diameter, and axial focusing position of the signal beam, reference beam, or both beams near the AFM cantilever.

42. The interferometer according to claim 41, further comprising a switching mechanism (550), wherein, The switching mechanism is operated to change the arrangement of additional matching optical elements in at least one of the signal beam and the reference beam, and wherein the switching mechanism is operated to select between two or more desired combinations of the optical group path length and any one of the beam divergence, diameter and axial focusing position near the AFM cantilever.

43. The interferometer of claim 34 further includes a bandpass filter (560) to increase the coherence length of the beam to a value that is short enough to partially suppress periodic errors and artifacts compared to the laser source, but long enough to exceed the difference between the optical path length of the signal beam and the optical path length of the reference beam.

44. The interferometer of claim 43 further includes an actuator that rotates the bandpass filter to match the center wavelength of the bandpass with the center wavelength of the light source to maximize optical throughput.

45. The interferometer of claim 1 further comprises a second beam-splitting optical interface (600, 636) and a beam photodetector (630), wherein the second beam-splitting optical interface separates a portion of the beam and directs it toward the beam photodetector, and the beam photodetector operates to measure the reflection angle of the signal beam from the AFM cantilever.

46. ​​The interferometer according to claim 45, wherein, The second beam-splitting optical interface includes a polarization-selective coating and at least one quarter-wave plate, wherein the quarter-wave plate and polarization-selective coating are configured such that the signal beam before reflection from the AFM cantilever is not split by the second beam-splitting optical interface, and that the signal beam after reflection from the AFM cantilever is split into two beams by the second beam-splitting optical interface, one of which points toward the beam photodetector.

47. The interferometer according to claim 45, wherein, The second beam-splitting optical interface is incorporated into the bonding assembly of the optical element, wherein the bonding assembly of the optical element further includes the first beam-splitting optical interface and a beam shifter.

48. The interferometer according to claim 1 further includes an actuator (650) that translates the cantilever support chip along an axis such that the angle between the axis and the axis of the focusing lens structure is less than 20°.

Images