Methods for optical infrared scattering scanning near-field microscopy with high-speed point spectroscopy

Abstract

A method for measuring an optical property of a submicrometer region of a sample, comprising the following steps: a. Interacting a probe tip of a probe microscope with a region of the sample; b. Illuminating the sample with a light beam from at least one tunable source with a medium wavelength < λg such that light is scattered from the probe-sample interaction region, the scattered light comprising near-field light scattered from the probe tip and background scatter; c. Interfering a reference beam with the scattered light, the reference beam having an adjustable relative phase; d. Collecting at least some of the light resulting from the interference between the scattered light and the reference beam with a detector; e. Swiping across the relative phase to produce an interferogram; f.Comparing a property of the interferogram measured in the area of ​​the sample with a property of a reference interferogram to obtain a relative measurement of the scattered light; g. Repeating steps af at several medium wavelengths; and wherein an electric field strength of the reference beam is more than 20 times an electric field strength of the background scattered light.

Description

Near-field optical scattering microscopy (s-SNOM) works by the interaction of a probe microscope's sharp probe tip with a sample surface and the collection of light scattered from the tip-sample interaction area. Using this technique, it is possible to measure the optical properties of samples with a spatial resolution far below the conventional diffraction limits. The improved resolution results from a local amplification of the incident radiation field due to the sharp tip. The amplified radiation field interacts with the sample and then scatters radiation into the far field. This near-field amplification increases the amount of radiation scattered from the tip-sample area to such an extent that the scattered radiation can be more easily detected. Referring to Fig. 1B, a probe 100 with a sharp tip 104 interacts with a region of interest 106 of a sample 108. Light 110 with an electric field strength E1 is incident on the surface of a sample 108. The incident radiation field is amplified in the region of the tip 104, causing light from the tip-sample interaction area with electric field strength Ef to be scattered. The aim of an s-SNOM system is to detect this scattered near-field radiation Ef. Unfortunately, the incident radiation Ef also interacts with regions of the probe tip 102 that are away from the tip 104, and also with regions of the sample 108 that are away from the tip and even away from the region of interest 106. These unwanted interactions lead to a large background scattering Ebg. In practice, the scattered background field can be orders of magnitude larger than the scattered field at the tip of the head.For this reason, it is highly desirable to have effective methods to distinguish between light scattered from the tip of the head region and light scattered from other sources. Several methods have been used to separate the near-field light (scattered from the tip region) from the scattered background light. One commonly used approach is to oscillate the tip, for example, using the tip of an atomic force microscope, and to oscillate it at resonance, as in tapping mode. Since the amount of near-field light scattered by the sample depends strongly on the distance between the tip and the sample, oscillating the tip in and out of contact with the surface modulates the light scattered into the far field. Several approaches have been used to demodulate the tip-scattered light from an oscillating AFM tip. The simplest approach is to use a lock-in amplifier to measure the amplitude of the tip-scattered light at the oscillation frequency or at a higher harmonic of that oscillation frequency.Stephen Quake also demonstrated the method of fade-out time collection of tip-scattered photons from fluorescence to match the times when the tip is closest to the sample, as described in US patent US 6 953 927 B2. Although each of these approaches has achieved experimental success, each has considerable limitations. In the case of simple tip oscillations with lock-in detection, the amount of light scattered into the far field depends on both the real and imaginary coefficients of the sample's refractive index, an unknown arbitrary phase, and an unknown and variable amount of background scattering. Interferometric methods have also been used to improve the detection of point-scattered light. There have been two main approaches so far: the so-called "homodyne" approach, as described by Taubner et al. in the Journal of Microscopy, Vol. 210, Pt 3 June 2003, pp. 311-314, and a "pseudoheterodyne" approach, as described by Ocelic, Hillenbrand and others, for example in US patent US 7,738,115 B2. These interferometric methods are shown generally and schematically in Fig. 1A. Light 122 from a light source 120 is directed by a beam splitter 124 onto a sample 126 near the end 128 of the probe 130. As indicated in the previous description of Fig. 1B, the light incident on the probe and sample results in light that is scattered both from the region of interest (Enf) and from background sources (Ebg). This scattered light can be directed back to the beam splitter 124 and then focused onto a detector 140. Prior art has also employed known interferometric methods in which a portion 134 of the incident beam is directed at the beam splitter 124 onto a reference mirror 136, and then the reference beam interferes with the sample-scattered light at the detector 140. A Modulator 138 can be used to periodically modulate the reference phase.This interferometric setup is used for three main purposes: (1) to provide wavelength-sensitive measurements with broadband sources, as are commonly performed in Fourier Transform Infrared (FTIR) spectroscopy; (2) to provide amplification for the weak peak-scattered field Enf, as explained below; (3) to provide separate measurements of optical amplitude and phase. Next, we consider the signal measured at detector 140. The total electric field Etotam detector is given by: where each of these quantities is complex to detect phase differences between the electric field components. Note that for simplicity, all collection efficiency factors and optical losses are subsumed into the electric field strengths; that is, these are the electric field strengths at the detector surface, not at the sources. The light intensity at the detector is proportional to |Etot|², so: The interferometric scheme in Fig. 1A provides the gain of the near-field scattered radiation through the cross term ErerEnf. In practice, there have unfortunately been several practical limitations on the magnitude of this gain. Even worse, the background-scattered light and the light of the reference beam are often of a similar order of magnitude and, at best, have an Eref:Ebg ratio of -3 to -10 (see, for example, US Patent US 7,738,115 B2, column 2, lines 64ff.). The fact that the reference intensity and the background intensity are similar can lead to large errors in optical phase measurements. US patent US 7,738,115 B2 describes a method to overcome these errors by separating the near field and background fields using a "pseudoheterodyne" technique that employs sinusoidal oscillations of both the probe (130 in Fig. 1) and the reference mirror (138) to isolate the near-field term Enfim from the frequency domain. Using narrowband lock-in detection, this method allows optical amplitude and phase measurements of the near-field scattered radiation to be obtained. There are several disadvantages to the pseudoheterodyne approach, namely (1) a loss in the signal-to-noise ratio; (2) a loss in measurement speed; and (3) increased measurement complexity. The loss in signal-to-noise ratio stems from the fact that the pseudoheterodyne method spreads the energy from the Enf signal across many frequency bands, specifically numerous sidebands around the boom oscillation frequency and its higher harmonics. (See, for example, Fig. 7 in US Patent US 7,738,115 B2 and the illustration in Fig. 3A.) Demodulating at a single sideband thus samples only a small portion of the original scattered energy. As a result, the signal-to-noise ratio of the measurement is degraded—in an effort to filter out the background, a large portion of the signal is discarded. Furthermore, the sidebands are very close to the original probe modulation frequency (and its harmonics). Specifically, the sidebands are separated from the boom oscillation frequencies by fref, the modulation frequency of the reference arm mirror. The reference arm mirror and associated actuators are relatively large mechanical devices and are therefore, in practice, limited to oscillations in the 100 Hz range. As such, it is necessary to demodulate the sidebands with a very narrowband lock-in amplifier compared to the probe's oscillation frequency, which can be in the megahertz range. The narrow bandwidth required to demodulate the sideband thus slows down the measurement, as it necessitates longer integration times, thereby significantly slowing down the overall measurement. The current invention overcomes these limitations by providing an optical arrangement that enables Eref>>Ebger. This allows for the direct demodulation of the scattered near-field optical signal with highly accurate measurements of both the optical amplitude and phase. Furthermore, the method of the present invention achieves a much better signal-to-noise ratio because it can capture a much larger portion of the signal in fewer and more clearly separated frequency bands. This significantly simplifies and accelerates demodulation, thereby supporting higher-speed imaging and spectroscopy. Another major limitation of the state of the art for s-SNOM systems is the inability to easily compute a spectrum closely resembling a conventional infrared absorption spectrum without complex post-processing or the involvement of a local reference. The pseudoheterodyne method can output signals proportional to the amplitude and phase of the scattered light. Unfortunately, at each wavelength, the optical phase has an unknown and varying phase shift. Therefore, plotting the phase as a function of wavelength (or wavenumber) does not closely resemble a conventional absorption spectrum. To transform the phase signal into something approximating an absorption spectrum, it has been necessary to use a local reference sample with a known phase response as a function of the wavelength range of interest.The requirement for a local reference sample has led to the necessity of preparing samples with an additional known material directly adjacent to the sample of interest. In fact, most, if not all, local reference measurements are performed in such a way that the material of interest is sufficiently close to the local reference that the material of interest and the reference material can be viewed in the same field of view of the same AFM image. The local reference sample must also have a flat or otherwise known phase profile. This requirement for a local reference has dramatically limited the types of samples that can be successfully measured, as a suitable reference material is not available for many, if not most, real-world samples.Therefore, special sample preparation steps are required to prepare a sample with material of interest on a substrate that can serve as a reference material, or to prepare the material of interest with a local reference sample next to the material of interest. Furthermore, any errors in the measured or assumed phase of the local reference sample directly lead to errors in the calculated spectrum of an unknown sample. In practice, absorption spectra calculated from prior art s-SNOM measurements have exhibited distortions in the shapes of the absorption bands, misalignment of absorption peak positions, and errors in the relative absorption peak heights. These errors lead to complications in the interpretation of s-SNOM spectra and to discrepancies with standard spectra known from material databases. Additional errors may be present in systems such as Fig. 1, or in other systems with similar arrangements. The scattered light from the tip-sample area 110 interferes with light in the reference arm 134, which may be completely separate from the sample arm of the interferometer 122.This interferometer design amplifies the weak, point-scattered light and also allows measurements of the optical phase of the scattered light. The disadvantage of interferometric detection is that it is extremely sensitive to differential changes in the optical path length between the sample arm and the reference arm, for example, due to temperature or airflow fluctuations. Next, we turn to problems of state-of-the-art spectroscopic measurements using s-SNOM techniques. For many years, s-SNOM was primarily an imaging technique, but in recent years it has become possible to collect optical spectra from submicrometer ranges in a sample. There have been two basic approaches. In one approach, a broadband laser is used to illuminate the sample simultaneously with light of several wavelengths. In this case, interferometric Fourier transform techniques are used to unfold the wavelength-dependent scattering to obtain near-field spectra. This method is outlined, for example, in publications from Hillenbrand research, such as Amenabar et al. Nat Commun 4 (2013). This method requires sophisticated femtosecond lasers, which can be expensive, complex, have limited power, and restricted spectral coverage. Alternatively, a method sometimes called "spatial spectral imaging" is used. In this case, a narrowband tunable source, for example, a quantum cascade laser, is used to acquire a series of s-SNOM images at different wavelengths. However, acquiring spectra using this method is usually extremely laborious. For example, each s-SNOM image at each medium wavelength can require 5–20 minutes of acquisition time. Acquiring just a minimal spectrum at 10 different wavelengths would, for example, require 50–200 minutes just to obtain the images. For a more meaningful spectrum, acquiring, for example, 400 cm⁻¹ with 4 cm⁻¹ spectral resolution, 10¹ points would be required, which would therefore take 505–2020 minutes, or 8–33 hours. As such, it has been impractical to use the spatial spectral method for fast point spectroscopy, i.e., measuring the absorption spectrum of a single point.The AFM-IR method described in US patent US 8001830B2 does not require a local reference for comparison, and point spectra can be obtained in approximately one minute. However, some samples are not suitable for measurement with AFM-IR, and it is desirable to have a method for obtaining point spectra using the s-SNOM method on similar timescales. Furthermore, the following is disclosed in the prior art: XG Xu, L. Gilburd, and GO. Walker: “Phase stabilized homodyne of infrared scattering type scanning near-field optical microscopy”, Appl. Phys. Lett. 105, 263104 (2014) discloses a phase stabilization mechanism for homodyne, infrared s-SNOM in which an additional He-Ne reference interferometer shares the nearly identical beam path with the IR interferometer and stabilizes the reference phase via PID control (π / 2 or in-phase condition), which significantly reduces phase noise and drift. An effective phase stability of -0.05 rad in the mid-IR is achieved, thus improving image quality and vibration-sensitive spectra; this is demonstrated, among other things, on boron nitride nanotubes (BNNTs) with clearer near-field images, a robust phase angle map, and the detection of local defects. Methodologically, a tunable QCL-IR laser, AFM-Tapping operation with demodulation (e.g. 3.Harmonic and homodyne phase switching (in-phase / π / 2) is used for the separate amplification of the real and imaginary signal components, respectively. S. Mastel et al.: “Nanoscale-resolved chemical identification of thin organic films using infrared near-field spectroscopy and standard Fourier transform infrared references”, Appl. Phys. Lett. 106, 023113 (Jan. 2015) reveals how thin organic films can be chemically identified on a nanoscale using s-SNOM / nano-FTIR and provides clear comparison rules to standard FTIR: The near-field phase (q) exhibits absorption-like peaks, is almost thickness-independent in its peak position, and is blue-shifted by a few cm⁻¹ compared to GI-FTIR, making it suitable for approximate assignment even with unknown sample thickness.In contrast, the near-field absorption a = s·sin(q) agrees well with GI-FTIR for ultrathin films (d << tip radius) and with transmission-FTIR for thick films; at medium thicknesses, the peak shifts continuously, which should be quantified by modeling (e.g., finite dipole model). S. Amarie, T. Ganz, and F. Keilmann: “Mid-infrared near-field spectroscopy”, Opt. Express 17, pp. 21794-21801 (2009) reveals broadband mid-IR near-field spectroscopy by combining dispersive FTIR with s-SNOM in a Michelson configuration, allowing simultaneous acquisition of amplitude and phase of local spectra from -20 nm sample areas (spectral resolution ∼6 cm⁻¹, DFG source in GaSe). The SiC phonon resonance serves as a touchstone for background-free measurement: The near-field influence dominates from demodulation order n ≥ 2, while n = 1 often contains background.By analyzing temporal interferograms (pulse / “ringing” signatures), the near-field component can be temporally separated from the background even at n = 1, which speeds up the setup. EC Kinzel et al.: “Phase resolved near-field mode imaging for the design of frequency-selective surfaces”, Opt. Express 20, pp. 11986-11993 (2012) reveals how phase-resolved s-SNOM near-field imaging improves the design of frequency-selective surfaces (FSS) by capturing both the amplitude and phase of the local modes with high resolution in crossed dipole metasurfaces in the IR and comparing them with HFSS simulations and far-field measurements. Furthermore, it is revealed that near-field phase information is indispensable for the targeted design of FSS (e.g., reflective phase plates, controllable reflectors, highly absorbing metasurfaces), especially in semi-periodic / finite layouts, which would be difficult to interpret unambiguously using far-field-based methods. Definitions“Interaction of a probe with a sample” refers to bringing the probe tip close enough to the surface of a sample such that one or more near-field interactions occur, for example, the attractive and / or repulsive tip-sample forces, and / or the generation and / or amplification of radiation scattered from a region of the sample near the probe tip. The interaction can be a contact mode, intermittent contact / tapping mode, non-contact mode, pulse force mode, and / or any lateral modulation mode. The interaction can be constant or, as in preferred embodiments, periodic. The periodic interaction can be sinusoidal or of any periodic waveform.Impulse force modes and / or fast force curve methods can also be used to periodically bring the probe into a desired degree of interaction with a sample, followed by a holding period and then a subsequent withdrawal of the probe. "Illumination" means direct radiation onto an object, for example, the surface of a sample, the sample tip, and / or the probe-sample interaction area. Illumination preferably includes radiation in the infrared wavelength range, but other wavelengths can also be used. Illumination can include any configuration of radiation sources, reflecting elements, focusing elements, and other beam control or conditioning elements.The source of infrared radiation can be one of a large number of sources, including thermal or globar sources, supercontinuum laser sources, optical parametric oscillators (OPOs), optical parametric generators (OPGs), quantum cascade lasers (QCLs), nanosecond, picosecond, and femtosecond laser systems, CO2 lasers, heated boom probes, or other microscopic heating devices, and / or any other source that generates a beam of infrared radiation. In a preferred embodiment, the source emits infrared radiation, but it can also emit in other wavelength ranges, for example, from ultraviolet to THz. "Scattering" or "scattered" refers to radiation emitted from a region by a mechanism other than mirrored reflected light. Scattering can encompass a variety of mechanisms, including elastic scattering, inelastic scattering, fluorescence, Raman scattering, and any other mechanism involving radiation emitted from a surface in response to incident radiation (that is not simply reflected light). “Collection of radiation” means the collection of radiation at or near a suitable radiation detector, for example a photodiode, photoconductor or similar detector that converts radiation into a current, voltage, temperature or other signal that can be measured. Near-field selective amplification refers to one or more techniques used to selectively amplify and / or discriminate light scattered from the area of ​​a sample near the probe tip, while reducing the relative contribution of radiation scattered from other sources, such as areas of the sample away from the probe tip and / or radiation scattered from the probe tip leg away from the probe tip and / or the boom body. Near-field selective amplification may include modulation of the probe-sample distance, temporal silencing of the collected radiation, asymmetric interferometric amplification, or frequency banding that selects frequency components at frequencies corresponding to higher harmonics of the probe motion. “Spectrum” refers to a measurement of one or more properties of a sample as a function of wavelength or equivalently (and more commonly) as a function of wavenumber. “Optical property” refers to an optical property of a sample, which may include the refractive index, absorption coefficient, reflectivity, absorptivity, real and / or imaginary components of the refractive index, real and / or imaginary components of the sample dielectric function and / or any property that can be mathematically derived from one or more of these optical properties, without being limited thereto. A "local reference" is a material and / or sample in close proximity to a sample of interest with a flat and / or known phase dependence over a wavelength range of interest. Typically, the sample of interest is mounted directly onto the local reference (for example, a sample on a gold or silicon substrate), leaving a portion of the substrate exposed (without the sample of interest covering it). Such references facilitate direct comparison between the phase of a known sample and that of a sample of interest. Local references are typically prepared by scraping away a portion of the sample of interest to expose the underlying substrate or to mask a region of the substrate when the sample of interest is deposited. “Background scatter” refers to scattering that is scattered from areas of the sample away from the head tip, and / or scattering that is scattered from the limb of the sample tip away from the head sample and / or the boom body. “Interference,” “interfering,” and “interferometry” all refer to the coherent superposition of multiple electric field components from two or more sources. In interference, beams reach a detector intensity, measured at the detector, which depends on the complex sum of the real and imaginary electric field components, or equivalently, on both the amplitude and the optical phase of the electric field components. Interferometry is one of the techniques used to obtain “near-field selective gain,” as described above. "Reference beam" refers to an optical auxiliary beam that interferes with the sample-scattered beam at the detector. "Signal indicating" refers to a signal that is mathematically related to a property of interest. The signal can be an analog signal, a digital signal, and / or one or more numbers stored in a computer or other digital electronics. The signal can be a voltage, a current, or any other signal that can be readily transmitted and recorded. The signal can be mathematically identical to the measured property, for example, explicitly an absolute phase signal or an absorption coefficient. It can also be a signal that is mathematically related to one or more properties of interest, for example, involving linear or other scaling, offset, inversion, or even complex mathematical manipulations. A "transimpedance amplifier" refers to an electronic device that converts current into a voltage through active amplification. The most common transimpedance amplifiers are circuits built with operational amplifiers and feedback resistors; however, equivalent circuits can be built using discrete transistors. Transimpedance amplifiers have fixed gain, a limited set of fixed gain values, and / or variable gain. Similarly, the bandwidth can be fixed or adjustable. The transimpedance amplifier may include a bias circuit that provides a bias voltage for the photodetector. "Tunable narrowband radiation source" refers to a source of radiation that emits radiation with an adjustable medium wavelength, but with a half-maximum bandwidth at full width of less than 8 cm⁻¹ or preferably less than 1 cm⁻¹. An example of a tunable narrowband source is a quantum cascade laser (QCL) and / or an array of quantum cascade lasers. Other tunable narrowband radiation sources may include optical parametric oscillators and other laser technologies, provided they exhibit the medium-wavelength stability and narrowband emission described above. Brief description of the invention Therefore, the objective of the present invention is to overcome the limitations of the prior art in IR-s-SNOM. The solution according to the invention is defined in claims 1, 20, 21, and 28. More specifically, the present invention enables efficient, highly sensitive measurements of the amplitude and phase of the light scattered from the near-field tip. It also enables high-speed demodulation of the near-field signal to support high-speed spectroscopy at the nanoscale and chemical imaging. The present invention also allows for fast and accurate calculations of the near-field phase while simultaneously eliminating the need for a local reference sample. In some embodiments, errors due to the interferometer path length and physical separation are reduced.In other embodiments, suitable samples of interest are mounted on or in close proximity to a reference region with constant or known properties over the wavelength range of interest, while still enabling a fast and efficient method for generating reflection / absorption spectra over a range of wavelengths. In some embodiments, the spectra can include IR absorption spectra, allowing for chemical analysis and identification. Brief description of the drawings The invention will be better understood by reference to the following figures. Figures 1A and 1B show a simplified schematic diagram of prior art scattering scanning near-field microscopy (s-SNOM). Figure 2 shows a simplified schematic diagram of an embodiment of the present invention. Figures 3A and 3B illustrate the demodulation bandwidth requirements of the pseudoheterodyne approach according to the prior art and the present invention. Figures 4A and 4B illustrate the improvement in amplitude and phase errors according to the present invention. Figure 5 compares the linear range of infrared detectors used according to the prior art with that of an embodiment of the present invention.Figure 6 is a simplified schematic diagram showing filter positions in one embodiment of the present invention to achieve high degrees of discrimination between near-field and background signals. Figures 7A and 7B illustrate the relationship between reference intensity and scattered background light, and the amplitude / phase error as a function of a sample arm-filter transfer ratio. Figure 8 shows a method according to the present invention for obtaining a wavelength-dependent phase spectrum. Figures 9A, 9B, 9C, and 9D illustrate the results of the steps of the method shown in Figure 8. Figures 10A, 10B, 10C, and 10D illustrate the difference between the scattered near-field radiation and the scattered background radiation as a function of the tip-sample distance and frequency. Figures 11A and 11D illustrate the difference between the scattered near-field radiation and the scattered background radiation as a function of the tip-sample distance and frequency.Figure 11B shows a topographic image and a near-field scattered radiation image of the same area of ​​a sample. Figure 12 shows a simplified schematic diagram of an embodiment of an s-SNOM with improved measurement stability. Figure 13 shows an alternative embodiment compared to the embodiment of Figure 12. Figures 14A and 14B show two examples of data generated by an s-SNOM of the embodiment of Figure 13. Figures 15A and 15B illustrate two interferograms, one obtained from a reference area of ​​a sample with known properties and one obtained from an area to be analyzed. Figure 16 is a flowchart of an illustrative embodiment. Figures 17A, 17B, 17C, 17D, and 17E illustrate a series of interferograms from a reference area and unknown areas of a sample, obtained at different illumination wavelengths. Fig.Figure 18 illustrates the derivation of an absorption spectrum from the interferograms of Figures 17A-17E by plotting the phase and amplitude differences of the reference region and of unknown region interferograms as a function of the illumination wavelength. Figure 19 illustrates the power variation of a quantum cascade laser (QCL) as an illumination source as a function of wavelength. Detailed description of the invention Fig. 2 shows a simplified schematic representation of an embodiment of the present invention. Infrared light 202 is emitted from the source 200 to a beam splitter 204. In Fig. 2, the light 202 is shown as diverging, but it can also be substantially collimated. Light 205 passing through the beam splitter continues to a focusing optic 206, which focuses the infrared light onto a sample 209 near the end 208 of a probe 210 of a probe microscope. (Fig. 2 shows a top view of a sample and a boom probe—the probe tip and head tip are not shown in this view.) Light scattered from the tip and the sample is collected by a collecting optic. In the simplest implementation, the collecting optic is the same as the focusing optic 206, but alternative and / or additional collecting optics can be used instead.Light 207, collected by the collecting optics, is returned to the beam splitter 204, where it is focused via a further focusing optics 212 onto the surface of an infrared detector 214. A portion 216 of the incident light beam 202 is deflected by the beam splitter 204 to a reference mirror 218. The light 217 reflected from the reference mirror 218 is directed back through the beam splitter and focused along the same path as the tip / sample-scattered beam by focusing optics 212 onto the detector 214. The light in beam 217 is referred to as the "reference beam." In this way, light from the reference arm interferes with light scattered from the tip and the sample. The actuator 220 is used to rapidly adjust the optical path length of the reference arm, thereby adjusting the optical phase of light reflected from the reference arm. In one embodiment, the actuator 220 is moved periodically by λ / 8, where λ is the mean wavelength of the incident radiation.The actuator can be a piezoelectric device, a bending-guided actuator, and / or an actuator using electrostatic, magnetic, voice coil, electrostrictive, or other actuation mechanisms. It can also be a precision linear motor, an inertial drive mechanism, or any other mechanism capable of moving with precision on the scale of fractions of a wavelength. The λ / 8 movement involves a total path length difference of λ / 4 (where λ / 8 occurs both on the approach and the departure), resulting in an optical 90° phase shift. Measuring the detector signal at two 90° phase shifts allows for the calculation of both the optical amplitude and the optical phase of the peak / sample scattered light.If specifically the detector signal is measured at two phases separated by 90°, the amplitude A and the phase Τ can be calculated as follows: where I0 and I90 are the detector intensities at a 90° phase shift and Τ is an arbitrary constant (discussed later in connection with Fig. 8 and Fig. 9). Referring back to Fig. 1b, the light scattered from the tip / sample contains two electric field terms. The field scattered from the tip 104 and part of the sample region 106 interacting with the tip is denoted by Enf, and this is the signal of interest. Background scattered radiation from other regions of the probe and sample is characterized by the electric field strength Ebg. Note that these are both complex quantities and generally have an unknown phase shift. In general, |Ebg| >> |Enf|. This is due to the fact that the illuminated region (i.e., the focused spot size) is many orders of magnitude larger than the tip. The background scattered light often overshadows the amount of light scattered from the tip region.(In some cases of extremely efficient peak gain and / or very small background dispersion, the near-field signal may be larger than the background.)

[0033] Referring back to Fig. 2, the interference between the light 217 of the reference arm and the light scattered by the tip / sample ensures enhanced detection of the light scattered by the tip / sample. The light intensity at the detector Id is proportional to |Etot|2, where Etot is the complex sum of the light from the near-field scattering, Enf, the background-scattered light Ebg, and the reference arm light Eref, which interferes with the scattered light at the detector. Therefore: The amplification of the light scattered from the tip / sample originates from the cross terms EnfErefund EnfEbg. In the prior art, there has also been competition between these two terms. The amplitude and phase of Ebg are generally unknown and can vary over an area. If this cross term is not corrected, it can, as such, cause considerable errors in optical amplitude and phase measurements of the signal of interest, Enf. Prior art pseudoheterodyne methods have attempted to separate the background cross term from the reference cross term using sinusoidal modulation of the reference arm and then to separate the cross terms Erefund Ebg in the frequency domain, as illustrated in Fig. 3. The present invention can avoid the need to modulate the reference arm phase by ensuring that Eref >> Ebg, so that the dominant interferometric amplification is performed via the Eref term.In particular, the present invention can employ the simpler frequency separation methods of the prior art homodyne method to discriminate between the EntEref and EbgEref terms. This is achieved by taking advantage of the much steeper nonlinear dependence of the near-field component compared to the background component during tip / sample separation. Figures 10A, 10B, 10C, and 10D illustrate the relative distance dependence of the background (10A) and near-field (10B) components. The background signal varies slowly with the tip-sample distance (the signal strength can actually increase or decrease based on the optical phase). On the other hand, the near-field signal increases very sharply at small tip-sample distances. If the tip interacts periodically with the sample (for example, oscillates in tapping mode), the resulting frequency-dependent amplitudes are schematically shown in the figures.Figures 10C and 10D illustrate this. The background signal Ebg(10C) has components primarily at the fundamental frequency of the boom and the first harmonic, with negligible contributions at higher frequencies. In comparison, the near-field component, Enf(10D), has a very large number of harmonic components due to its high nonlinearity. If the tip oscillates with an angular frequency ω, the tip-scattered light is proportional to: The background scattered light is proportional to b1; b2 is significant, but for n ≥ 3, bn is negligible, as shown in Fig. 10C. The voltage at the detector is proportional to: Expanding the terms, we see the detector signal, including important cross terms. Considering the scattered light, Enf, the component a1 is the largest; however, it is difficult to distinguish the near-field scattered light Enf from the background scattered light Ebg, which is also modulated at ω. Demodulation as such is frequently used for n ≥ 3. It is also desirable to obtain amplitude and phase information separately. Thus, in pseudoheterodyne, the phase of Eref is modulated at a different frequency such that the cross term is modulated at a different frequency. However, this has a considerable disadvantage, as energy from Enf is spread to other sidebands, thereby reducing the signal-to-noise ratio and increasing the measurement time. The present invention employs near-field selective amplification to distinguish near-field scattered radiation from background scattered radiation. The present invention avoids these problems with the pseudoheterodyne approach (US Patent US 7,738,115 B2) and also overcomes the large amplitude and phase error limitations of the earlier homodyne according to the prior art, as described by Taubner (Journal of Microscopy, Vol. 210, Pt 3 June 2003, pp. 311-314). Figures 3A and 3B demonstrate how the present invention employs a more robust approach than prior art homodyne to distinguish near-field and background signals. Figures 3A and 3B show the amplitude and phase errors for prior art homodyne (solid lines) versus the present invention (dashed lines). The amplitude and phase errors for the homodyne approach were calculated using the equations in the background section of US Patent US 7,738,115 B2, which discusses the prior art homodyne approach. To achieve these reductions in amplitude and phase errors, the present invention, in one embodiment, carefully arranges the relative field strengths such that Ere >> Ebg. In this case, it is possible to neglect the cross term EnfEbgzu, since the cross term EnfErefso is much larger. Fig. 4C shows the dependence of the amplitude and phase errors on the ratio Eref:Ebg. The prior art homodyne method was limited to Eref:Ebg ratios of 3–10, which resulted in amplitude errors of more than 40% and phase errors of more than 25°. In contrast, the present invention achieves Eref:Ebg ratios of >20 or preferably more than 50 and in some embodiments more than 150. At an Eref:Ebg ratio of 150, the amplitude error is less than 1% (Fig. 4A) compared to 28% under typical conditions described in US Patent US 7,738,115 B2 (see column 2, line 64 to column 3, line 4).Furthermore, the phase error can be 0.5° or less (Fig. 3B) according to the present invention, compared to 19° specified in the aforementioned patent. Fig. 4D tabulates the improvement in amplitude and phase error compared to a prior art homodyne value of Eref:Ebg=5, as described as typical in the 115 patent. The relationship between amplitude and phase errors compared to the Eref:Ebg ratio is illustrated in Fig. 4C and Fig. 4D. Roughly speaking, the relationship is inverse, meaning that the amplitude and phase errors are roughly proportional to 1 / (Eref:Ebg). Prior art has been limited to Eref:Ebg ratios in the range of 3-10, resulting in amplitude errors of up to 47% and phase errors of up to 28°. According to the present invention, the inventors achieve Eref:Ebg ratios of >20, or preferably more than 50, or even preferably more than 150. Even at an Eref:Ebg ratio of 20, the amplitude error can be -7%, which is already 4 times better than the typical prior art value. At Eref:Ebg = 50, the amplitude error is 2.8%, 10 times better than the prior art. And at Eref:Ebg= 150, the amplitude error is 0.9%, roughly 30x better than the state of the art.Similar improvements are seen in the phase error, with reductions of approximately 4x, 10x, and 30x at Eref:Ebg = 20, 50, and 150, respectively. This relationship between amplitude / phase errors and the Eref:Ebg ratio was understood by Ocelic and Hillenbrand and discussed in patent 7,738,115 as the motivation for their use of pseudoheterodyne methods to attempt to overcome the problem. As previously mentioned and discussed elsewhere, the implementation of pseudoheterodynes leads to several limitations in performance. The current inventors have overcome the limitations of the prior art for the Eref:Ebg ratio, thereby eliminating the need to perform more complex pseudoheterodyne measurements. They achieved this through three interconnected steps. First, they employed linear-response mercury-cadmium telluride detectors capable of achieving a linear response regime at more than 30 times the intensity of prior art detectors. Second, they carefully adjusted and / or attenuated the reference beam intensity so that the intensity from the Eref2 term nearly saturated the detector. Third, and somewhat counterintuitively, they optionally attenuated the sample arm light to suppress background scattered light, thereby improving the Eref:Ebg ratio. Returning to Fig. 2, the source of infrared radiation can be one of a large number of sources, including thermal or globar sources, supercontinuum laser sources, optical parametric oscillators (OPOs), optical parametric generators (OPGs), quantum cascade lasers (QCLs), nanosecond, picosecond, and femtosecond laser systems, CO2 lasers, heated boom probes, or other microscopic heating devices, and / or any other source that generates a beam of infrared radiation. Source 200 can alternatively or additionally be a source of other wavelengths, for example, ultraviolet to terahertz radiation. Source 200 preferably has high amplitude and phase stability to ensure consistent amplification by the term ErefEnf.In some cases, it may be advantageous to take additional steps to stabilize the source energy, for example by dynamically adjusting the laser resonator, limiting the bandwidth for the driving current, controlling the temperature of the source, or other methods that can maximize the stability of the term. The controller 236 can dynamically adjust the output power of the radiation source 200 to maximize the intensity at the detector 214 such that the intensity approaches the limit of the detector's linear range. The variable attenuator 228 can dynamically adjust the fraction of light incident on the sample while simultaneously attenuating the background scattered light Ebg. In one embodiment, the variable attenuator 228 is a filter wheel with various neutral density filters 230 at multiple locations within the filter wheel. The neutral density filters can be made of metal gratings, thus eliminating wavelength-dependent refraction from dispersive optical components of limited thickness. Neutral density filters can also be made of IR-transparent materials, such as germanium, zinc selenide, or other materials with suitable metal and / or dielectric coatings.Any other attenuating optical element can be used instead of or in addition to filters, including, but not limited to, iris diaphragms, polarizing optics, or other attenuating devices. Furthermore, one or more locations 232 in the filter wheel can be left empty for use in cases of weak scattering from the sample or low background scattering that do not require attenuation. Additional filter wheels can be placed in the reference arm and / or the source arm and / or detector arm (not shown). The infrared detector 214 generates a photocurrent which is amplified by amplifier 234. Amplifier 234 can be a transimpedance amplifier, which provides a large linear detection regime and maintains a small potential across the photodiode. (This is an approach to achieve a much larger linear range than a photoconductive detector, thus enabling higher intensity reference beams and large Eef:Eb ratios.) Alternative suitable detectors can be used for wavelengths other than infrared. The probe end 208 is oscillated or otherwise modulated at one or more frequencies ωi, for example by exciting one or more mechanical resonances of a boom probe. The present invention also utilizes frequency-space separation to achieve near-field selective amplification. The background signal Ebg generally has significant AC components only at frequencies 1ω and 2ω, where ω is the frequency of the probe's interaction with the sample (e.g., an oscillation frequency). For n ≥ 3, the near-field signal dominates the background signal because the near-field signal exhibits much stronger nonlinearity (a more pronounced rise at shorter tip-sample distances). At frequencies nω, where n ≥ 3, the near-field signal, i.e., Enf >> Ebg, dominates, as illustrated in Fig. 10C-D. The controller 236 can include demodulation capabilities to extract the oscillation frequency and harmonic components of the signals from detector 214 and amplifier 234. The controller can comprise several separate components, such as a piezo amplifier, a lock-in amplifier, a data acquisition / control device, and a computer. Alternatively, all controller functions can be integrated into a single device. Specifically, the demodulation capability can extract oscillatory components of the detector signal at nωi, where n is an integer. The demodulator can be a conventional lock-in amplifier or, alternatively, a multi-frequency lock-in amplifier from Zurich Instruments.In a preferred embodiment, the lock-in is a digital lock-in amplifier that acquires analog measurements from the detector / amplifier and then performs discrete digital calculations to determine the oscillatory components at one or more integer multiples of an oscillation frequency. The demodulator can be implemented in digital electronics, for example, using a field-programmable gate array (FPGA), digital signal processor (DSP), or similar technologies. Demodulation can also be performed rapidly on a personal computer by calculating discrete Fourier sums corresponding to a response at a desired frequency. The demodulator generally generates two or more terms for each demodulation frequency, for example, magnitude and phase, or in-phase (X) and quadrature (Y).Note that the probe end can also be brought into interaction with the sample with non-sinusoidal modulation, and the demodulation can use alternative fundamental functions, for example wavelets, Bessel function or other functions chosen to model the nonlinear tip-sample-distance dependence of the near-field scattered radiation. The demodulator can also analyze any number of higher harmonic amplitudes, excluding components at the fundamental oscillation frequency of the boom. For example, a Fourier transform can be applied to extract a number of Fourier components at one or more frequencies corresponding to the harmonics of the boom motion. It is also worth noting that it is not necessary to compute an entire Fourier transform. It is possible to discretely calculate the response at a desired frequency using a suitable Fourier sum, i.e., to compute the Fourier component at a specific desired frequency. Since the frequency of the boom motion is known and, in one embodiment, determined by the SPM controller, the desired Fourier components can be calculated very quickly at specified frequencies.It is also possible to sum the amplitudes at several Fourier components, for example, at the 3rd to 8th harmonics of the boom movement. One way to calculate the total intensity from a specified number of higher harmonics is to use a circuit and / or calculation to determine the total harmonic distortion (THD). Total harmonic distortion calculations, or THD analyzers, sum the harmonic component for a specified number of harmonics above the fundamental oscillation frequency. (In some cases, it may be desirable to start the THD sum at the third harmonic to better reject background scattered light, which may have a component at the second harmonic.) In one embodiment, it is possible to perform demodulation at very high rates. For example, it is possible to obtain high-quality near-field scattering images in <5 minutes, similar to the conventional AFM imaging rate. It is also possible to obtain high-quality near-field scattering spectra in less than 1 minute. The reason is that it is possible to demodulate directly at a boom resonance or a higher harmonic of this resonance, instead of in a sideband, as is required for pseudoheterodyne methods. Fig. 3 illustrates this problem. In the pseudoheterodyne method, the modulation of the reference arm introduces sidebands 302 around the boom oscillation frequency 304 and its harmonics 306. To demodulate the amplitude of a sideband 302, it is necessary to use a narrowband detection method to avoid contamination from the often much larger signal at the adjacent harmonic frequency 306.An exemplary bandwidth that would isolate a single sideband is shown with dashed lines in Fig. 3A. In contrast, the present invention does not require sinusoidal modulation for the reference mirror and, as such, does not need to distribute energy across sidebands. The demodulated peaks at the boom resonance (308) and higher harmonics (310) are much more widely separated, as shown in Fig. 3B. The present invention thus has the advantage of being able to employ broadband demodulation, which requires very short integration times. Furthermore, at the larger values ​​of Eref:Ebg, it is possible to achieve a much greater asymmetric gain of the near-field scattered signal Enfzu. Therefore, the amplitudes of the demodulated response are much larger than in the pseudoheterodyne approach, and also larger than the demodulated peak heights in conventional homodyne approaches.At higher signal-to-noise ratios compared to the state-of-the-art homodyne approach (inhibited by a smaller Eef:Eb ratio), it is possible to benefit from these increased bandwidths and short integration times. The shorter integration times dramatically increase the measurement speed and improve the instrument's throughput. For example, if it is desired to demodulate at the 3rd harmonic of a fundamental boom resonance at 80 kHz, the spacing between bands is 80 kHz. Therefore, if the signal-to-noise ratio allows, a demodulation bandwidth of up to -150 kHz can be used while avoiding contributions from other frequency bands. (The specific bandwidth and potential crosstalk from adjacent bands depend on demodulation factors, such as the properties of a window function used in demodulation.) Because the demodulation bandwidth can be very fast, the scattered radiation can be measured very quickly. For example, a bandwidth of 100 kHz allows a measurement point every 10 μs. With a sufficient signal-to-noise ratio, a 200-point spectrum can be obtained in as little as 2000 μs.Even with a smaller bandwidth to achieve stronger noise reduction, for example, a 2 kHz bandwidth, a 200-point spectrum can still be obtained in just 0.1 seconds. To achieve these spectrum measurement times, it is desirable to be able to continuously tune the IR source rather than using a step / set / measurement scheme. Even with the step / set / measurement scheme, it is possible to obtain a spectrum in less than 1 minute, for example, with 200 points and a step / set time of 0.25 seconds. Similarly, a scatter image at a single wavelength with a pixel resolution of 200 × 200 points can be obtained in just 20 seconds with a demodulation bandwidth of 2 kHz. Figures 11A and B show an exemplary measurement of 200 × 200 points, acquired at a bandwidth of 1.2 kHz and a line rate of 0.2 seconds per line, which corresponds to a bidirectional image time of 40 seconds.Fig. 11A shows a topographic image of a cross-sectional area between gold and silicon. Fig. 11B shows an image indicative of the near-field scattered radiation of the same area according to the present invention. In addition to the bandwidth advantages, direct demodulation at one or more principal harmonics of the cantilever motion (no sideband) preserves a much higher signal-to-noise ratio, whereas pseudoheterodyne methods only shift a portion of the signal into the sidebands, thereby reducing the signal-to-noise ratio. As previously mentioned, the scattering and demodulation measurements are preferably performed at two positions of the reference mirror 218 (Fig. 2), corresponding to two optical path lengths separated by 90° optical phase. Measuring the demodulator outputs at two positions of the reference mirror with a 90° optical phase difference allows the separate calculation of the optical amplitude and optical phase of the scattered light. Measurements of the optical amplitude and phase can be used to extract the optical properties of submicrometer regions of a sample surface. In particular, it is possible to calculate a near-field absorption spectrum 238 from these measurements. The absorption spectrum is derived primarily from the optical phase signal, a measure of dissipation, although it may be necessary to correct the measured optical phase due to wavelength-dependent dispersion effects (i.e., changes in the real refractive index). The sample 209 and / or probe 210 can be moved relative to each other, for example, using an XY scanner 211. This enables measurements of the spatial distribution of the sample's optical properties with submicrometer spatial resolution. In one example, absorption spectra 238 or other optical properties can be mapped at a multitude of points 240 on a sample to generate spatially resolved profiles of the sample's optical properties. Alternatively, the optical properties can be recorded at several regularly spaced XY points to generate a chemical map 242 of the sample surface. In one embodiment, each pixel of the chemical map comprises measurements at a multitude of incident wavelengths. In other embodiments, the chemical map can represent a scattering signal measured at multiple XY sample positions but at a single wavelength. Turning to Fig. 5, we briefly discuss the selection of an infrared detector. Most, if not all, prior art measurements in IR-s-SNOM have been performed with photoconductive mercury-cadmium telluride (MCT) detectors. For example, Hillenbrand's group apparently normally uses a Judson Teledyne J15D12-M204-S050U photoconductive MCT detector (see Nature Materials, Vol. 10, May 2011, p. 352, DOI: 10.1038 / NMAT3006). The current inventors have built their s-SNOM with a high-D linear MCT photodiode instead of a photoconductive MCT. As schematically illustrated in Fig. 5, the linear MCT photodiodes have a much larger dynamic range. Although a photoconductive MCT can reach saturation at about 10-3W / cm2, linear MCT photodiodes can provide an essentially linear response, operating up to 0.1 to 1 W / cm2, depending on transimpedance gain and bias conditions.This increase in the dynamic range allows for much more efficient asymmetric amplification of the near-field signal. The reason for this is that the signal we are generally interested in results from the cross term ErefEnfer, i.e., the amplification of the near-field signal by the field strength of the reference arm. The value of Eref is generally limited by the dynamic range of the IR detector, specifically due to the Eref2 term. A low limit at maximum detector intensity for photoconductive MCTs limits the maximum value of Eref2 and thus the maximum amplification of the Enf term. By switching to a linear MCT photodiode with a high D*, Eref2 can be orders of magnitude larger, leading to much larger Eref:Ebg ratios and enabling the improvement in amplitude and phase errors discussed above. A suitable linear MCT photodiode is, for example, the Kolmar model KLD-0-0.5-J1-3 / 11 / DC.Other models may also be suitable, depending on the bandwidth requirements and the focusing spot size. Another alternative is thermoelectrically cooled MCT detectors, which have a saturation of up to 1 W / cm², up to 100 times better than liquid nitrogen-cooled detectors. These detectors have much higher noise floors and may only be suitable at higher scattered intensities, well above the detector's noise floor. To achieve the highest Eref:Ebg ratios, it is generally desirable to design the Eref term such that the total intensity at the detector (dominated by Eref²) lies between 10% and 90% of the detector's linear range. It is also possible to work with intensities slightly above the linear range limit, where the increase in gain is still greater than the decrease in sensitivity. Turning to Fig. 6, we next discuss the optimal attenuation of the components of the interferometer beam, including the counterintuitive step of placing a filter in the sample arm. Fig. 6 shows a simplified version of the interferometric detection used at s-SNOM, except that a filter has been placed in each arm of the interferometer, for example, a filter 602 in the laser source arm, a filter 604 in the reference arm, a filter 606 in the detector arm, and a filter 608 in the sample arm. The transmission coefficients of each of these filters are given by FL, FR, FD, and FS, respectively. As before, light from source 620 is directed onto the beam splitter 624, where it is split into two paths: one to the reference mirror 636 and one to the probe tip 628 and sample 626. The light scattered by the tip region Enf and the scattered background light Ebg recombine with the light from the reference arm detector 640.By tracing each beam through each filter and the beam splitter, we can determine the relative field strengths at the detector when the filters are present. The strength of the electric field from the near-field scattered light at the detector is given by: where R and T are the reflection and transmission coefficients of the beam splitter 624, αnf is the near-field scattering coefficient, and E0 is the original electric field strength from the source 620. Similarly, the background scattered light is given by: where αbg is the background scattering coefficient. The electric field from the reference arm is given by: The signal term we are interested in is the cross term ErefEnf, while the unwanted background term is EbgEnfist. Therefore, the signal-to-background ratio is given by: Interestingly, this indicates that the filter 606 in the detector arm and the filter 602 in the source arm have no effect on the signal-to-background ratio (as long as the detector operates in a linear region). Instead of maximizing the signal-to-background ratio, we want to maximize the FR term and minimize the FS term. The filter can have transmission coefficients between 0 and 1, so we can choose FR = 1, its maximum value. Thus, to increase the signal-to-background ratio, we want to make FS as small as practically possible. This seems counterintuitive, since a filter 608 in the sample arm also attenuates the signal of interest, Enf. However, in asymmetric interferometry, it is possible to essentially enhance the near-field scattered light, Enf, through the cross term ErefEnf. In the prior art, it has not been possible to make Eref very large due to the limitations on the linear response of the detector used.However, with the detectors used in the present invention, it is possible to use much higher values ​​of Erefzu and therefore smaller values ​​of Enf to obtain the same overall signal intensity. Fig. 7A shows an exemplary relationship between the transmission coefficient of the sample arm filter and the Eref:Ebg ratio. The exact relationship depends on a variety of experimental and sample parameters, but this figure illustrates the basic relationship. In this example, using parameters similar to those commonly used in s-SNOM, it is possible to achieve an Eref:Ebg value of 50x with a filter having a transmission of 10%. The corresponding amplitude and phase errors are shown in Fig. 7B. Again with a transmission coefficient of 10% for the sample arm, the amplitude error is less than 3% and the phase error is less than 2°. With currently available laser sources, especially when focused on a diffraction-limited spot, it is possible to have sufficient excess radiation intensity to utilize a sample arm filter transmission of 10% or less.For example, users of the current Commissioner's commercial nanoIR™ AFM-based IR spectroscopy instrument often employ filter transmission coefficients of 10% or even 1% and still achieve sufficient sensitivity. In fact, at higher intensities, it is possible to melt or burn samples at wavelengths with high absorption and / or high source intensity. One of the main advantages of the present invention is the elimination of the need for a local reference to obtain wavelength-dependent spectra. The challenge has been that, since wavelength-dependent measurements were performed, there is an arbitrary unknown phase shift at each measurement wavelength. As mentioned previously, this has been addressed by generating a phase reference measurement on a local reference sample with either constant or known phase behavior. The present invention provides two alternatives to overcome the need for a local reference sample. Turning to Fig. 2, we will point out some additional features. The movable mirror 222 can direct the incident beam into the sample arm 207 such that it is deflected onto a reference mirror 224 of the sample arm. The mirror 224 can optionally be positioned by an actuator or the displacement stage 226.The mirror 224 is preferably positioned at a distance along the optical path from the beam splitter 204 that is the same as the optical path distance from the beam splitter 204 to the probe tip 208. The actuator / converter 226 can be used to adjust and optimize these distances. The distances should be equal within the coherence length of the radiation source, and improved performance can be achieved with further fine-tuning. When mirror 222 is positioned to direct the sample beam onto mirror 224, it is possible to perform a reference measurement of the phase of the light in the sample arm relative to the reference arm. These measurements can be used to generate a phase reference table, which can be used to correct measurements when mirror 222 is removed, allowing the light to be directed to sample 209 and probe tip 208. The correction process is shown and briefly described in Figures 8-9. As an alternative to an additional reference mirror, it is possible, and in some cases preferable, to use an ex-situ reference sample. The ex-situ reference sample is a sample that has a flat and / or known phase response and can occasionally be introduced into the measurement system in place of a sample of interest. The ex-situ sample is measured as if it were a sample of interest.The analysis of the resulting phase measurements on the ex-situ sample leads to a phase correction table that can be applied to samples of interest. A detailed procedure for eliminating the need for an in-situ reference sample is shown in Figures 8 and 9. Referring to Figure 8, the first step, 802, involves introducing an ex-situ reference sample into the probe microscope or placing an additional reference mirror in the sample arm, as described above. Next, in step 804, the IR source is tuned to a desired wavelength, and an optical measurement is performed on the light scattered by the ex-situ reference sample or on light reflected by the reference mirror of the sample arm. Specifically, a signal indicating the optical phase is measured (step 806). The tuning (804) and measurement of the optical phase (806) are repeated at all desired wavelengths, typically covering the tuning range of the IR source and using a spectral line resolution corresponding to the sample of interest.From the measurements of the scattered / reflected radiation, the optical phase at each desired wavelength is extracted, and a phase reference table is generated (step 808). Next, a sample of interest is inserted into the probe microscope (step 810), and the IR light is directed toward the sample of interest (away from the sample arm's reference mirror, if one is used). The IR source is again tuned to a desired wavelength (step 812), and the amplitude and phase of the light scattered by the tip-sample area of ​​the sample of interest are measured (step 814). An illustration of a crude phase spectrum obtained at this point is shown in Fig. 9A. Next, the near-field optical phase measurement is corrected by subtracting the correction value from the phase reference table (step 816), as illustrated in Fig. 9B.The phase spectrum, even after correction using the phase table, exhibits a large number of discontinuities. This is due to the limited output range of inverse tangent functions used to calculate the phase. These functions have a limited range, for example, ±π / 2 for atan or ±π for atan². If the measured phase exceeds one of these range limits, a discontinuity is observed in the spectrum. However, these phase discontinuities can be eliminated using a phase unwrap process. For example, the data can be scanned for discontinuities, and a suitable offset is added to or subtracted from points on one side of the discontinuity to eliminate the discontinuity. A suitable phase unwrap scheme is described by National Instruments; they describe their “Unwrap Phase VI”, for example at http: / / zone.ni.com / reference / en-XX / help / 371361J-01 / Ivanls / unwrap_phase / .Once the phase is unwrapped, a signal resembling a traditional absorption spectrum may be visible at that point, for example, in Fig. 9C. The unwrapped spectrum may benefit from further processing. In step 820 in Fig. 8 and Fig. 9D, the unwrapped phase may have a baseline offset, and the baseline slope may be eliminated. A linear baseline slope may result from a small optical path difference between the phase reference measurement and a measurement on a sample of interest. In the case of using a sample arm reference mirror (224 in Fig. 2), this optical path difference may result from a difference in the distance between the beam splitter (204 in Fig. 2) and the sample (209) as a function of the distance between the beam splitter and the sample arm reference mirror.In the case of an ex-situ reference sample, the optical path difference can result from the thickness difference between the reference sample and a sample of interest. However, these optical path differences introduce a constant propagation time error, which leads to a phase error that is linear with respect to the optical frequency. Therefore, if the phase is plotted as a function of the wavenumber, the phase error results in a linear slope in the baseline. It is thus possible to perform a linear fit to the baseline and subtract this slope. An illustration of the spectrum fitted to the baseline slope is shown in Fig. 9D. An additional embodiment of the present invention involves the use of amplitude modulation. By modulating the amplitude of the reference arm, it is possible to generate a time / frequency dependence in the term ErefEnf. If the probe is modulated at a frequency of ω0 and the reference arm is modulated at ωref, ErefEnf has components at nω0±ωref. Any demodulation method that extracts one or more components at these frequencies can be used to generate a measurement of the optical properties of the sample. Amplitude modulation can have several advantages over prior art phase modulation methods. First, phase modulation requires moving a mirror with a large aperture by a considerable fraction of a wavelength. In practice, this requires large piezoelectric actuators with significant current and bandwidth requirements.In practice, the maximum oscillation frequency is generally in the range of a few hundred Hz to perhaps a few kilohertz for large-aperture, high-power mirrors. The limiting modulation frequency places strict demands on the bandwidth of any modulation device. For example, if the reference mirror is modulated at 200 Hz, this modulation generates small sidebands ±200 Hz from the boom oscillation frequency and its harmonics. To avoid contamination from the midband, it is necessary to use a narrowband filter and / or a narrowband demodulation system to isolate the sidebands. Such narrowband demodulation methods require longer integration times to achieve this filtering. As a result, the measurement time performance of the pseudoheterodyne mode (or any mode that generates sidebands) depends inversely on the demodulation bandwidth.A 200 Hz sideband from a central Fourier peak might require a bandwidth of 50 Hz to achieve good isolation from the central peak, resulting in a measurement time of at least 20 ms per measurement point. Therefore, it is highly desirable to employ a modulation technique that can be performed at high frequencies, thereby generating sidebands at much more widely separated frequencies. Widely separated sidebands enable high-speed demodulation with short integration / filter times. According to the present invention, amplitude modulation can generate sidebands with 10-100 times greater frequency separation. Amplitude modulation can be achieved using a number of techniques. For example, conventional optical choppers can achieve amplitude modulation exceeding 100 kHz. Scitek manufactures multi-slot choppers capable of operating at rates up to 120 kHz.Other devices, such as photoelastic modulators and deformable micromirrors, can also operate at similar frequencies. Furthermore, devices such as voice coil fast-control mirrors, galvo mirrors, and MEMS micromirrors can control optical beams at rates from 500 Hz up to several tens of kHz. Such control mirrors can achieve amplitude modulation by periodically switching the reference beam on and off at the detector. Each of these amplitude modulation techniques can be used to achieve sideband separation greater than that of conventional pseudoheterodyne methods, thus enabling shorter spectral acquisition and imaging times. s-SNOM interference measurements are critically dependent on the optical phase between the tip-scattered light and that of the reference beam. It would be advantageous to obtain measurements of the optical phase variation across a sample or as a function of wavelength. Unfortunately, these measurements are easily affected by slight path length shifts between the reference and sample arms. These path lengths are sensitive to path temperature and atmospheric variations between the reference and sample arms of the interferometer. Consider, for example, a sample or reference arm with an arm length of -100 cm. (This refers to the distance from the diagonal beam splitter to the tip or reference mirror and back.) A difference of 1 K in path temperature for a reference arm length of 100 cm and a coefficient of thermal expansion of approximately 10⁻⁵ / K would result in a path length difference of 10 μm.For a path length of 6 μm, this path length error would represent an optical phase shift of 600°. This phase error is orders of magnitude larger than the likely near-field phase measurements of most samples. Additional errors can be introduced due to air currents or temperature-dependent changes in the refractive index. Exemplary measurements of the phase instability problem according to the prior art are shown in Fig. 14A. These interferograms measure the intensity of the light detected at the infrared detector as a function of a reference partial reflector position, with the reference reflector effectively moved sequentially through periods of constructive and destructive interference. These measurements were performed using a conventional Michelson interferometer in a typical laboratory setting, with the s-SNOM interferometer open to the laboratory air, i.e., without an enclosure. A series of interferograms was measured over a period of 5 minutes, resulting in observed phase shifts of nearly 90°, for example, a phase drift rate of ∼15–20° / min. The improved results (Fig. 14B) are discussed below. An alternative s-SNOM embodiment that can reduce these effects is shown schematically in Figures 12 and 13. In Figure 12, the source 1200 illuminates a probe 1230, sample 1226 interaction area 1228 with radiation 1220 through a beam splitter 1224, which, for illustrative embodiments, may be mounted diagonally to the radiation beam. A partial reflector 1236, which can be actuated, is arranged between the beam splitter 1224 and the tip sample area 1228, possibly by means of optional control optics 1225. The partial reflector 1236 may, in some embodiments, be arranged substantially perpendicular to the illumination beam 1220, and in some embodiments, it may be located in close proximity to the tip sample area.Part of the illumination 1210 can be directed by the partial reflector 1236 onto the tip sample area 1228, which forms the sample arm of the interferometer, and part 1234 can be reflected by the partial reflector 1236, which forms the reference arm of the interferometer. The partial reflector can be actuated to the same extent and by similar mechanisms as previously described in this application with respect to the reference mirror in the embodiments of Figs. 1, 2, and 6. The radiation from both the sample and reference arms is directed by the beam splitter 1224 onto the detector 1240, where the interference product of the light scattered by the tip sample area and the reference beam is collected and measured. Unlike the standard s-SNOM interferometer according to the prior art, the sample and reference paths of the s-SNOM of Fig. 12 essentially overlap in this embodiment. Because the optical paths are essentially the same, any variations in temperature or airflow affect both the sample arm and the reference arm essentially identically. As a result, undesirable phase shifts caused by variations in temperature and airflow can be largely reduced. More precisely, the reference and sample paths can be completely overlapped up to the point of the last focusing element. This embodiment can be particularly advantageous for s-SNOM pseudoheterodyne phase measurements, where phase stability from a few degrees to several tens of minutes can be achieved. The s-SNOM embodiment of Fig. 12 can be combined with the other embodiments of this application or can be used in other s-SNOM systems. Therefore, this embodiment can also include the ability to move the probe to a series of points on the sample surface to create a map of the collected light. The light source can be a variable-wavelength source, the wavelength of which can be varied over a range of wavelengths during collection to generate a spectrum. The variable-wavelength source can vary over a range of the infrared spectrum, and the spectrum can be indicative of the IR absorption, which in turn is indicative of the chemical composition.The imaging and spectral collection can be combined to create a spectral map of the surface, which can be a map of the chemical composition. An alternative and more detailed arrangement of the embodiments of Fig. 12 is shown in Fig. 13. The source 1200 is positioned off-axis and is deflected by the optional mirror 123 to the diagonal beam splitter 1224, which splits the incident beam into two paths, a reflected and a transmitted one. One of these two beams is then directed to the partially reflective reference reflector 1234. In some illustrative embodiments, the partially reflective reference reflector can be positioned substantially perpendicular to the incident beam of the radiation such that it reflects a portion of the incident radiation substantially back along the incident path. This reflected beam acts as a reference beam that interferes with the tip-sample scattered radiation to enable amplification and / or phase-sensitive measurements of the tip-scattered radiation.Figure 13 shows a configuration where the beam transmitted through the diagonal beam splitter is directed onto the reference reflector 1234. This embodiment can operate equivalently to a configuration where the beam reflected through the diagonal beam splitter 1224 is directed onto the reference reflector 1234. In either case, the beam transmitted through the reference reflector 1234 is directed onto the parabolic reflector 1242 towards the tip 1230, allowing the tip sample area to be illuminated by a focused beam of light. Light scattered from the tip sample area is collected by the parabolic reflector 1242 and directed back through the partial reflector 1234 and back to the diagonal beam splitter 1224. At this point, two beams are spatially overlapped: the tip-scattered radiation and the reference radiation reflected by the partial reflector 1234.These two beams are then reflected or transferred through the diagonal beam splitter (depending on the configuration), and the light is then directed to the detector 1240. A focusing optic 1243 (for example, a parabolic mirror or a lens) is optionally used to focus the light onto the surface of the detector 1240. The focusing optic 1243 focuses the beams from both the peak-scattered radiation and the reference radiation reflected by the partial reflector 1234 such that the two beams interfere at the detector 1240. The reference reflector can be mounted on a displacement stage, for example, a piezoelectric actuator. The actuator is configured to move the reference reflector essentially in the direction of the incident beam in order to adjust the relative phase between the peak-scattered light (Enf) and the reference beam (Eref) reflected by the reference reflector.By adjusting this phase, it is possible to perform interferometric experiments as previously described in this application and as are known in other methods in the field. For example, it is possible to move the reference reflector between two different phases to obtain two phase homodyne measurements. It is also possible to move the reference reflector back and forth to perform phase modulation / pseudoheterodyne measurements. Furthermore, in one embodiment, the reference reflector is mounted on a tip-tilt stage to allow alignment and adjustment of the reference reflector to achieve optimal interference at the detector. The tip-tilt stage can be controlled manually or electronically, for example, using an actuated mirror assembly or a fast-actuating mirror.In one embodiment, the reference reflector can be actuated by a voice coil-operated, fast-acting mirror, which can provide both alignment and modulation functions. For example, the voice coil-operated, fast-acting mirror can be used to modulate the amplitude of the reference beam in order to perform amplitude modulation experiments. The embodiments shown in Figures 12-13 arrange the reference arm and the tip sample arms of the interferometer such that they are essentially spatially overlapped. This contrasts with the Michelson interferometer conventionally used for s-SNOM experiments, where phase modulation is performed in a separate reference arm that does not include the sample arm. The spatially overlapped sample and reference arms ensure that any temperature or airflow disturbance affects these interferometer arms equally, dramatically improving the measurement stability of the system. Fig. 14B shows a series of interferograms measured over a period of a few minutes using an s-SNOM with the embodiments of Figs. 12 and 13. Fig. 14A shows measurements of successive interferograms taken with the interferometer similar to that of Fig. 1. As mentioned previously, the interferograms of Fig. 14A are not repeatable in an unshielded laboratory environment due to temperature fluctuations and air currents. Fig. 14B shows the improved performance when using the s-SNOM of Figs. 12 and 13. In one embodiment, the final focusing element is an off-axis parabolic mirror with an effective focal length of 2.5 cm. Therefore, it is possible to reduce the differential path to just twice this length, for example, 6 cm. This arrangement achieves an approximately 17x improvement over the example above. Using the interferometric setup of Fig.12-13 an interferometric stability of -1-2° / min was achieved in a normal laboratory environment without a temperature-stabilizing enclosure. It is also possible to enclose all or part of the interferometer to protect it from air currents. Active temperature control can also be used to achieve very high temperature stability, for example, better than 0.1 °C or preferably better than 0.01 °C. It is also possible to use materials with a low coefficient of thermal expansion, such as Invar or Super-Invar, Zerodur, or other similar materials, to construct thermally very stable interferometers. When using materials with low thermal expansion and a temperature-stabilized enclosure, it is possible to achieve phase stability better than 0.04°. For example, with a differential path length of 0.06 m and a coefficient of expansion of 10⁻⁶ / K, the differential path would change by 0.06 μm / K. With a path length of 6 μm, this would represent a phase shift of 3.6° / K.Using a temperature-stabilized system and a temperature stability of 0.01 K / min, the change in differential path would be 0.6 nm. At a wavelength of 6 μm, this corresponds to a phase shift of 0.036° / min, which is stable enough to detect even very small optical phase shifts of tip-sample scattered light. Fast point spectroscopy with a reference sample We now turn to another embodiment of the present invention. This embodiment can acquire near-field spectra from submicrometer regions of a sample at very high velocities using a tunable narrowband source. This approach overcomes many limitations of prior art s-SNOM, including problems with phase instability, long acquisition times, and the need for expensive and complex laser sources. The approach of this embodiment can be applied to a variety of SNOM arrays, including those shown in Figures 1A and B, 2, 12, and 13. For the novel spectral analysis method, the source for SNOM is a tunable source capable of generating radiation over a range of selectable mid-wavelengths. One such source is a quantum cascade laser (QCL), as described above. Quantum cascade lasers are available that are both narrowband and broadly tunable. For example, QCLs from Daylight Solutions are available that have a linewidth of less than 100 MHz full width at half maximum, which corresponds to a linewidth of ~0.003 cm⁻¹ when measured in wavenumbers. This contrasts with broadband sources, such as picosecond and femtosecond sources, which intentionally have large linewidths to cover several spectroscopic wavelengths simultaneously. In comparison, QCLs have linewidths that are generally much narrower than a single mid-infrared absorption peak for solids.Currently available QCL chips also have a tuning range of up to 120 cm⁻¹ per chip, and this range is increasing as the technology matures. Multiple QCL chips can be combined to cover most of the mid-infrared wavelength range. QCLs are also being extended into the terahertz range. When using a tunable narrowband light source, as described above, an illumination mid-wavelength is selected, and the probe is placed on a "reference region" on the sample. Ideally, a reference region should have flat, or at least known, optical properties over the wavelength range of interest. For example, in the case of a constant absorption coefficient over a wavelength range of interest, the light scattered by that wavelength range has a constant optical phase. Therefore, the phase measurement at the reference region can serve as a constant baseline to act as a reference for measurements in regions of interest on the sample. (Note that, unfortunately, the word "reference" is used in the s-SNOM literature for two unrelated purposes. In one instance, it is used to describe the light from the moving mirror arm of the interferometer.)Therefore, "reference phase" refers to the optical phase of the light in this arm. The word reference is also used to describe a sample or region of a sample that has flat or otherwise known optical properties, as described above. To avoid confusion, we explicitly state whether we are referring to the reference arm of the interferometer or to a reference region of the sample. The relative phase of the reference arm is traversed while measuring a signal indicative of the light collected by the detector. The phase sweep can be linear, sinusoidal, or performed at a series of discrete phase points at arbitrary intervals. At most of the relative phase points, the detector signal can be analyzed to measure the amplitude at the boom oscillation frequency, or at a harmonic of the boom oscillation frequency and / or one or more sidebands generated by multiple modulations of the boom and the reference amplitude or phase. Measuring any of these signals as a function of the relative phase of the reference arm produces an interferogram. For example, an interferogram of the interaction between the reference and the third harmonic of the tip-scattered light is shown in Fig. 15A.The probe is then moved to the area of ​​interest, and the other interferogram shown in Fig. 15A is generated. Note that there is both an amplitude and a phase shift between the two interferograms. Both shifts are due to the relative optical properties of the two areas. The relative phase can be set in many ways. One approach is to shift the reference mirror linearly, for example, by applying a ramp, triangular, or sawtooth drive signal to the reference mirror, typically a fraction of the center wavelength up to several wavelengths. For IR radiation, the displacement would be on the order of a few micrometers to a few tens of micrometers, although shorter or longer displacements can be used. The interferograms in Fig. 15A were acquired with a ramp signal applied to the reference mirror actuator, resulting in a total mirror displacement of ~12.5 micrometers in a fraction of a second to a few seconds. (Note that the relative optical path difference is twice the movement of the reference mirror.)It is only necessary to shift the reference by a distance sufficient to obtain a good mathematical fit to the interferogram. This may require only a fraction of a wavelength to just a few wavelengths, so suitable interferograms can be acquired very quickly. Another way to allow the phase to sweep would be to introduce objects into the reference beam that effectively change the reference path, such as a wheel with a variety of transmission elements of different lengths that are rotated through the reference arm, or an electrically active element whose refractive index or length can be changed in a controllable manner. To perform this relative measurement, interferograms are collected alternately between one or more regions of interest on a sample and one or more reference regions. An illustrative sample setup is shown in Fig. 15B. For this example, a sample region to be analyzed can be a material placed on or adjacent to a reference region with constant or at least known optical properties. For example, ideally, a reference region should have a constant or known absorption coefficient over a wavelength range of interest, such that the light scattered by this region has a constant optical phase.Provided that the two regions of the sample can be accessed sequentially by the probe of the probe microscope, for example, within the scan range or the probe displacement range, a novel approach that generates a spectrum very quickly can be employed. In the case shown in Fig. 15B, a material is placed on a gold or silicon substrate such that the material and exposed parts of the substrate lie within the scan range of the microscope, in this case within a 50 µm spacing. Such a substrate has no resonant response in IR wavelengths; it is essentially reflective and therefore provides a suitable reference region for an IR absorption analysis of a sample that nevertheless exhibits a resonant response to IR radiation. Other suitable reference surfaces could be used, provided their resonant behavior in the wavelength range of interest is known. An exemplary measurement flow for an embodiment of the present invention is shown in Fig. 16. First, the tunable source is tuned to a desired medium wavelength (1601). Next, the AFM tip is moved to an area of ​​interest on the sample (step 1603), for example, an area where a spectroscopic measurement is desired. Next, in step 1605, an interferogram is measured in the area of ​​interest by sweeping through the relative reference phase. The phase is normally traversed by at least 180°, for example, an optical path difference of at least half the wavelength, but shorter and longer phase sweeps can be used, depending on the requirements for the spectrum signal-to-noise ratio and the instrument sensitivity. After acquiring an interferogram in the area of ​​interest, the process is repeated in a reference area of ​​the sample.To repeat the process, the AFM tip is moved to a reference region of the sample (1607), and the relative reference phase of the interferometer is traversed again (step 1609) to generate a reference interferogram, i.e., an interferogram in a reference region of the sample. Next, the interferograms are analyzed to extract one or more properties of the interferograms (step 1611), such as the amplitude and / or phase of the interferograms. These properties can be obtained by curve-fitting techniques, for example, by fitting sine waves to the interferograms. It is also possible to use any number of other techniques, including fast Fourier transforms, the Goertzel algorithm, digital lock-in amplifiers, or similar methods that can be used to analyze a sinusoidal signal to extract amplitude and / or phase information.Note that in general the wavelength for a narrowband light source is known, so this can be an input to adjust the interferogram to ensure faster convergence and / or to limit the frequency range to be analyzed. Next (step 1613), the properties of the interferograms between the area of ​​interest and the reference area of ​​the sample are compared to generate a relative measurement of the light scattered by the area of ​​interest. This comparison / relative measurement can, for example, provide the difference or ratio between the measurements in the area of ​​interest compared to the reference area. In the case where the extracted property is the scattered amplitude, the amplitude of the light scattered by an area of ​​interest can be divided by the amount of light scattered by a reference area of ​​the sample to obtain a ratiometric measurement of the relative amount of light scattered by the area of ​​interest.If the scattering properties of the reference region are known, the ratio of the scattered amplitude can, in principle, be used to perform absolute measurements of the scattering properties of the unknown region of interest. Furthermore, a similar relative measurement of the phase of the scattered light can be performed by subtracting the phase of the reference interferogram from the phase of the interferogram in the region of interest. From this comparison, it is possible to extract the optical phase shift resulting from the interaction of the incident light with the region of interest in the sample under the AFM tip. For certain materials, this phase shift can be indicative of the absorption coefficient of the region of interest in the sample.More accurate measurements of the absorption coefficient can also be obtained by using the amplitude and phase of the scattered light and converting them into real and imaginary amplitudes of the scattered light. The sample's absorption coefficient is more directly related to the imaginary amplitude of the scattered light. More complex comparison / normalization systems can also be employed, including those that correct for non-zero or non-planar baselines, and algorithms that perform filtering / smoothing and noise reduction on measurements from the region of interest and / or reference regions. After comparing the properties of the interferograms of the reference and area of ​​interest, steps 1601-1613 are repeated at several medium wavelengths until all desired wavelengths have been measured (decision point 1615). By plotting the relative amplitude, phase, or other relative property as a function of the medium wavelength (or equivalently frequency, wavenumber, etc.), a point spectrum of the submicrometer range of the sample is generated (step 1617). Figures 17A-17E show a series of interferograms over reference and regions of interest, recorded at many medium wavelengths of the illumination source. (Each interferogram is identified by the wavenumber (cm⁻¹) at which it was measured. 'Wavenumber' is a representation of the frequency of the illumination light, inversely proportional to the wavelength, and is commonly used in chemical spectroscopy. The term 'many medium wavelengths' refers equivalently to multiple medium wavelengths.) Note that the interferograms in Figures 17A-17E are essentially sinusoidal waveforms. In the case of using a narrowband source according to the current embodiment, the interferogram is the result of constructive / destructive interference of the scattered light essentially at a single wavelength, yielding a single sine wave.Therefore, the amplitude and phase shift can be easily identified and varied in each interferogram in Figs. 17A-E. The relative phase and amplitude for each wavelength / wavenumber can be analyzed by curve fitting or other methods previously described. Fig. 18 shows near-field spectra of a submicrometer region of interest from a sample, calculated by plotting the relative phase and amplitude derived from interferograms such as those in Figs. 17A-E, using the measurement and analysis steps of Fig. 16. These graphs show relative amplitude and relative phase as a function of the illumination center wavelength for two experiments (two successive passes over a range of center wavelengths).The s-SNOM literature has shown that in some cases the relative signal is representative of an absorption spectrum, while the amplitude signal exhibits dispersive behavior. The maximum in the phase spectra corresponds at least approximately to the absorption peaks measured by conventional IR spectroscopy; therefore, the positions of the phase maxima can be used to identify the material being analyzed. These point spectra can be generated extremely quickly compared to the state of the art. The reference mirror can be swung to obtain an interferogram within a fraction of a second. Consider a scenario, for example, where each of the following steps takes 1 second: (1) setting the medium wavelength; (2) moving the tip into the region of interest; (3) capturing the interferogram in the region of interest; (4) moving the tip to the reference region; (5) acquiring the reference interferogram. In this case, the relative optical amplitude or phase for each medium wavelength can be acquired in 5 seconds. Generating a spectrum with 101 points (say, over 400 cm⁻¹ with 4 cm⁻¹ spectral resolution) would require only 505 seconds, about 8.4 minutes, which is significantly faster than state-of-the-art spatial spectral imaging.In practice, however, it is possible to significantly increase the speed of many of these steps. For example, it is possible to switch between regions of interest and reference regions of the sample within a few milliseconds using a well-designed scanner, especially when employing fast scan AFM technologies. The same applies to tuning the mid-wavelengths on tunable lasers, particularly for closely spaced wavelengths, as is the case with adjacent wavelengths in an optical spectrum. The most time-consuming step can be the time required to acquire the interferogram, since signal levels may be low and slower propagation times can help ensure longer signal integration.In the case where one second is still allocated to each interferogram, but the movement and tuning times are negligible, the time for each spectral point is 2 seconds, and the total time for a spectrum of 101 points is 202 seconds, or 3.4 minutes. It is also possible to perform a continuous scan of the tunable source such that there are no stepping or setting times. (In this case, the sweep rate of the tunable source is set to a speed such that the changes in wavenumbers are smaller than the desired spectral resolution during the time required for the interferogram.) It is also highly desirable in this case for the interferometer arms to have very carefully matched optical path lengths so that the small path length shifts do not cause phase shifts.In the case of a high signal-to-noise ratio, for example with materials that are strong scatterers of light, it may be possible to measure an interferogram of sufficient quality in just a few milliseconds. For example, with a sample that is a strong scatterer, and using a tunable laser and SPM scanner, both optimized for fast scan and / or step and set times, it is possible to achieve each of these steps in < 10 ms: (1) tune wavelength; (2) move tip to the area of ​​interest; (3) acquire interferogram at the area of ​​interest; (4) move to the reference area; (5) acquire reference interferogram. In this case, a measurement at each medium wavelength can be acquired in 50 ms. Thus, a spectrum over 400 cm⁻¹ with 101 points can be obtained in just 5050 ms, or -5 seconds. These times of 10 ms / step can be achieved with careful design of subcomponents.Piezoelectric scanning elements are available, for example from Piezomechanics, offering ranges in the 10–30 micrometer range with resonant frequencies of a few tens of kilohertz. These actuators can be sufficiently damped to achieve settling times in the range of <10 ms or even <1 ms. Carefully designed tunable IR sources can also be traversed and / or balanced in <10 ms / medium wavelength. Tuning such a source is usually accomplished by shifting or rotating a nonlinear optical crystal or a diffraction grating. These objects can have a very low mass, such that the high-speed shift / rotation stages can be used for tuning. For example, inventors built a tunable IR laser using a Dover MMG-50 linear motor stage that could traverse the entire tuning range from 2.5 to 3.5 micrometers in 80 ms.For angle tuning, for example, Newport manufactures rotation stages with accelerations of up to 60,000° / s² and maximum speeds of 1000° / s. Such a stage can rotate 1° (acceleration and deceleration) in ~8 ms. As mentioned in Section

[63] and related sections, it is possible to demodulate the third harmonic of the s-SNOM-scattered light with a bandwidth of 100 kHz, which allows a measurement point every 10 μs, or a 200-point interferogram can be obtained in just 2000 μs. But even with a smaller bandwidth to provide stronger noise suppression, for example a 2 kHz bandwidth, a 200-point spectrum can still be obtained in just 0.1 seconds.Therefore, when using the methods described in this section and also in the approach in paragraph

[63] and the associated discussion, it is easily possible to achieve acquisition times for point spectra of less than 10 minutes, less than 5 minutes per spectrum, and even less than 1 minute per spectrum using the approach of the present invention. These times are in dramatic contrast to the 8-33 hours required according to the prior art to obtain spectra using the prior art s-SNOM spatial spectral imaging method. This approach benefits from illumination with a narrow bandwidth around any mid-frequency, less than 8 cm⁻¹ or preferably less than 1 cm⁻¹, because it does not require a long-running interferometer to achieve high spectral resolution. With a broadband source, for example a femtosecond laser, it is necessary to use a long-running interferometer to develop the broadband response. The approach of the present invention can also support fast arrays of point spectra at any set of locations. For example, it is possible to acquire an AFM image and then program a set of locations to be measured for point spectra. These locations can be any selected location of interest in a rectangular grid or in a linear arrangement, for example, across an interface between two materials. Regardless of the array of points, each measurement can be referenced to a measurement that is automatically performed at a reference location or locations. The reference location is typically programmed into the system by a laser, for example, using an AFM image to determine a location of a material with substantially constant or otherwise known optical properties across the medium wavelength of interest.The reference interferogram can be measured, if desired, before and / or after each measurement of a sample area of ​​interest. It is also possible to measure the reference interferograms at a lower frequency, say every 2nd, 5th, or 10th measurement point. The frequency of the reference measurement is determined by the thermal stability of the interferometric measurement system. It is desirable to acquire a reference interferogram frequently enough so that the phase drift between reference measurements is less than the desired noise level. Note that in the flowchart in Fig. 16, steps are shown in a specific order for convenience. However, this order need not be followed. For example, it is possible to move the probe tip to a desired location and then tune the center wavelength or its inverse.Some steps, such as adjusting the medium wavelength and moving to a new location, can be performed in parallel. The interferograms can be generated first at the area of ​​interest or at the reference area. However, a key element of this embodiment is that one or more areas of interest are identified by the user, and point spectra from these areas can be automatically acquired without further user intervention. This means that the software automatically runs through a pattern of interferogram collection in areas of interest and a reference area across many medium wavelengths. It is not necessary for the user to manually change the wavelength or manually acquire the interferograms. From Figures 17A-17E, it can be observed that the reference interferogram varies in amplitude with the medium wavelength. For a purely reflective surface, such as gold, this should not be the case. The reason for this is that, as shown in Figure 18, the power output of a QCL varies with the medium wavelength. Accordingly, it is desirable to acquire the reference interferograms at each medium wavelength. Alternatively, it is possible to simply measure the power spectrum from the tunable light source and use this to normalize the amplitude response. In this case, it is only necessary to measure the reference interferogram frequently enough to compensate for drift in phase, i.e., the relative path difference between the sample arm and the reference arm. If the instrument is designed to be extremely thermally stable, i.e.,For materials with a low coefficient of thermal expansion and / or in a temperature-controlled enclosure, it may be necessary to measure the reference interferogram less frequently, for example, once every 10 medium wavelengths or once per spectrum. Note that one way to minimize the frequency at which the reference interferograms need to be measured is to match the path length extremely precisely for both the sample and reference arms of the interferometer. This is not usually necessary for narrowband tunable sources, such as QCL sources. A QCL laser with a linewidth of <1 cm⁻¹ can have a coherence length of more than 1 m. Thus, it is possible to acquire interferograms with sample and reference arms of very different lengths because the beams from the two interferometer arms are still coherent.However, although it is possible to obtain interferograms, it may not be possible to obtain good spectra. This is because if the sample arm and the reference arm have different lengths, the length difference leads to a wavelength-dependent phase shift, and this phase shift changes as a function of temperature. For example, with a path length mismatch of 5 mm and a coefficient of thermal expansion of 10⁻⁵ / °C, this would result in a path length change of 50 nm / °C, leading to a phase shift at a wavelength of 2.5 µm of 360° × (50 nm / 2500 nm) = 7.2° / °C. Since the phase spectra of some materials, especially polymers and biological materials, can have small peak amplitudes on the scale of a few degrees, it is desirable to perform phase measurements with greater precision.This path length offset, if constant over longer periods, would result in a non-zero phase baseline, which could be subtracted using a static reference phase spectrum acquired on a reference material. However, in practice, if the interferometer arms experience different temperatures during a measurement, the differential thermal expansion can lead to drifts in the relative phase over time, which can undermine the phase spectral measurements. That is, the phase on the reference material would not be sufficiently stable to act as a stable baseline against which the measurement of the region of interest is referenced.As such, it is desirable that (1) the reference and sample interferometer arms are as short as possible; (2) the temperature of the two interferometer arms is as closely matched as possible; and (3) the length of the two interferometer arms is as closely matched to each other as possible. Under these conditions (and if the power spectrum of the source is known and stable), it may be possible to measure reference interferograms less frequently. Accordingly, one embodiment of the present invention comprises an adjustment in the reference arm such that the lengths of the reference and sample arms can be very closely matched to each other, preferably to less than 1 mm, such that temperature fluctuations cause a differential path length change of less than 10 nm / °C.With a path length match of less than 1 mm and a coefficient of thermal expansion of 10⁻⁵ / °C, this would result in a path length change of 10⁻⁵ mm = 10 nm, leading to a phase shift of 1.44° / °C. Materials with low thermal expansion of ∼10⁻⁶ / °C or active temperature stabilization can reduce this phase shift by another order of magnitude. It is also possible, through careful tuning, to match the two interferometer arms to better than 0.1 mm or better. This tuning can be performed with extreme precision using a broadband source, for example, an inexpensive thermal "globar" source. In the case of a broadband source, there is a peak in the interferogram around 0 optical path length difference, where all wavelengths are in phase. Adjusting the interferometer to center the reference mirror on the interferogram peak of the thermal source ensures minimal phase drift for tunable sources.Alternatively, this point can be empirically determined for a tunable narrowband source by observing and minimizing the phase drift through successful measurements of interferograms on the same material. That is, the position of the reference mirror is slowly adjusted while the phase drift between successive interferograms is measured. The optimal setting is found at the point where the phase drift is at its minimum. Careful matching of the interferometer arm lengths provides a further advantage, which is of particular importance for tunable light sources. Tunable light sources often use a mechanical element to select the emission wavelength, for example, a displacement or rotation stage to shift or rotate a nonlinear crystal or diffraction grating. Changing from one center wavelength to another involves a displacement / rotation step followed by a stabilization period, during which the emission wavelength may change slightly. The changes in wavelength are generally small and may not be significant compared to the desired spectral line resolution. However, even small changes in wavelength can lead to large phase shifts if the interferometer path lengths are not precisely matched.For example, imagine a QCL source tuned to 1500 cm⁻¹, and that during stabilization the output drifts by 1 cm⁻¹, i.e., from a wavelength of 6667 nm to 6671 nm. This is smaller than most absorption linewidths for solids, so this wavelength instability, in itself, is not excessively detrimental. However, with an interferometer path misalignment of even 1 mm, this wavelength stabilization period would lead to a phase error of 36° (the difference in phase between the two wavelengths over 1 mm). This phase error is unacceptably large. For interferometrics with only small path misalignments, it would be necessary to wait for complete wavelength stabilization, which impacts the measurement time for acquiring near-field point spectra.However, if the interferometer arms are aligned in path length to 0.1 mm or better, the phase drift caused by this wavelength stabilization problem can be minimized. Of course, the required path length alignment accuracy depends on the wavelength drift of the source, and larger path length errors can be accommodated with sources exhibiting smaller wavelength drift. The use of such terms and expressions is not intended to exclude equivalents of the features (or parts thereof) shown and described; however, it is acknowledged that various modifications are possible within the scope of the claims. It is therefore understood that those skilled in the art may refer to modifications and variations of the concepts disclosed herein, although the present invention has been specifically disclosed by means of the preferred embodiments and optional features, and such modifications and variations are considered to be within the scope of the invention.

Claims

A method for measuring an optical property of a submicrometer region of a sample, comprising the following steps: a. Interacting a probe tip of a probe microscope with a region of the sample; b. Illuminating the sample with a light beam from at least one tunable source having a medium wavelength λ such that light is scattered from the probe-sample interaction region, the scattered light comprising near-field light scattered from the probe tip and background scatter; c. Interfering a reference beam with the scattered light, the reference beam having an adjustable relative phase; d. Collecting at least some of the light resulting from the interference between the scattered light and the reference beam with a detector; e. Swiping across the relative phase to produce an interferogram; f.Comparing a property of the interferogram measured in the area of ​​the sample with a property of a reference interferogram to obtain a relative measurement of the scattered light; g. Repeating steps af at several medium wavelengths; and wherein an electric field strength of the reference beam is more than 20 times an electric field strength of the background scattered light. Method according to claim 1, wherein the tunable source is a tunable infrared source. Method according to claim 2, wherein the tunable source is a quantum cascade laser (QCL). Method according to claim 2, wherein the tunable source has a half-maximum bandwidth with full width around the medium wavelength of less than 8 cm-1. Method according to claim 2, wherein the tunable source has a half-maximum bandwidth with full width around the medium wavelength of less than 1 cm-1. Method according to any one of claims 1 to 5, wherein the compared property is at least one of a relative phase or amplitude between the two interferograms. The method of claim 6, further comprising the step of recording at least one of these properties as a function of the medium wavelength or wavenumber of the tunable source, resulting in a near-field spectrum in the submicrometer range. Method according to any one of claims 1 to 7, wherein the spectrum is measured over a medium wave number range encompassing at least 100 cm-1. Method according to any one of claims 1 to 8, wherein the reference area of ​​the sample comprises an area of ​​the sample within a scan area of ​​the probe microscope which has a substantially flat optical response over the multiple medium wavelengths. Method according to any one of claims 1 to 9, wherein the reference beam, the illumination and the collection arms are of an interferometer. Method according to claim 10, wherein the reference arm and the collection arm either have the same length or overlap. The method of claim 10 or 11, further comprising the step of adjusting the relative optical path length of the arms of the interferometer such that the reference and collection arms of the interferometer have the same length within 1 millimeter. Method according to one of claims 10 to 12, further comprising the step of adjusting the relative optical path length of the arms of the interferometer such that the reference and collecting arms of the interferometer substantially minimize the phase drift when measuring the relative phase of the scattered light. Method according to any one of claims 1 to 13, wherein the sweeping of the phase is achieved by at least one element of the following: tilting a reference beam mirror or inserting a variable index of a refractive element into the reference beam. Method according to claim 14, wherein the relative measurement at the multiple wavelengths is used to generate a near-field spectrum for the sub-micrometer range. Method according to claim 15, wherein the near-field spectrum comprises measurements at at least 10 different medium wavelengths. Method according to claim 15, wherein the near-field spectrum comprises measurements at at least 100 different medium wavelengths. Method according to claim 16, wherein the near-field spectrum is acquired in less than 10 minutes. Method according to claim 16, wherein the near-field spectrum is acquired in less than 5 minutes. A method for measuring an optical property of a submicrometer region of a sample, comprising the following steps: a. Interacting a probe tip of a probe microscope with a region of the sample; b. Illuminating the sample with a light beam from a quantum cascade laser (QCL) with selectable mid-wavelengths λ such that light is scattered from the probe-sample interaction region, the scattered light comprising near-field light scattered from the probe tip and background scatter; c. Interfering a reference beam with the scattered light, the reference beam having an adjustable relative phase; d. Collecting at least some of the light resulting from the interference between the scattered light and the reference beam with a detector; e. Swiping across the relative phase to generate an interferogram; f.Placing the probe tip on a reference region and sweeping over the relative phase to generate a reference interferogram; g. Comparing at least one element of a phase and amplitude of the interferogram measured in the sample region with at least one element of a phase and amplitude of the reference interferogram; h. Repeating steps a, b, c, d, e, g and optionally f at several medium wavelengths; i. Recording at least one of the compared phase or amplitude as a function of the medium wavelength to generate a curve indicative of the IR absorption spectrum of the sample region; and wherein an electric field strength of the reference beam is more than 20 times an electric field strength of the background scattered light. A method for measuring an optical property of a submicrometer region of a sample, comprising the following steps: a. Interacting a probe tip of a probe microscope with a region of interest in the sample; b. Illuminating the sample with a light beam from at least one tunable source with a medium wavelength λ such that light is scattered from the probe-sample interaction region, the scattered light comprising near-field light scattered from the probe tip and background scatter; c. Interfering a reference beam with the scattered light, the reference beam having an adjustable relative phase; d. Collecting at least a portion of the light resulting from the interference between the scattered light and the reference beam with a detector; e. Swiping across the relative phase between the reference beam phase and the scattered light to generate an interferogram; f.Repeating steps ae on a reference region of the sample to generate a reference interferogram; g. Comparing a property of the interferogram measured in the region of interest of the sample with a property of a reference interferogram to obtain a relative measurement of the scattered light; h. Repeating steps ag at several medium wavelengths; i. Using the relative measurement at the several wavelengths to generate a spectrum for the submicrometer range of the sample; and wherein an electric field strength of the reference beam is more than 20 times an electric field strength of the background scattered light. Method according to claim 21, wherein the probe tip is automatically moved between the area of ​​interest and the reference area to collect interferograms at each of the several medium wavelengths. Method according to claim 21 or 22, wherein each interferogram is measured in less than five seconds at each medium wavelength. Method according to one of claims 21 to 23, wherein the near-field spectrum comprises measurements at at least 10 different medium wavelengths. Method according to one of claims 21 to 24, wherein the acquisition of the near field spectrum is completed in less than 10 minutes. Method according to one of claims 21 to 24, wherein the acquisition of the near field spectrum is completed in less than 5 minutes. Method according to any one of claims 21 to 26, wherein the near-field spectrum has a spectral resolution of 4 cm-1 or better. A method for measuring an optical property of a submicrometer region of a sample, comprising the following steps: a. Interacting a probe tip of a probe microscope with a region of the sample; b. Illuminating the sample with a light beam from a tunable, narrowband radiation source with selectable center wavelengths λ such that light is scattered from the probe-sample interaction region, the scattered light comprising near-field light scattered from the probe tip and background scatter; c. Collecting the light scattered from the submicrometer region; d. Measuring a property of the light scattered from the submicrometer region; e. Repeating steps a) at least 10 center wavelengths to generate a point spectrum of the submicrometer region; f.Completing the point spectrum in less than 10 minutes; and where the electric field strength of the reference beam is more than 20 times the electric field strength of the background scattered light. Method according to claim 28, wherein the tunable narrowband radiation source is a quantum cascade laser. Method according to claim 28 or 29, wherein the measurement step comprises a measurement of interferograms on a sample area of ​​interest and a reference area. Method according to one of claims 28 to 30, wherein the measured property comprises at least one of the relative amplitude and phase of the scattered light. Method according to any one of claims 28 to 31, wherein the tunable source has a half-maximum bandwidth with full width around the medium wavelength of less than 1 cm-1. Method according to any one of claims 28 to 32, wherein the point spectrum comprises a recording of at least one of a relative amplitude and a relative phase of the scattered light as a function of the mean wavelength or the wavenumber of the tunable source. Method according to any one of claims 28 to 33, wherein the spectrum is measured over a medium wave number range encompassing at least 100 cm-1. Method according to claims 1 to 34, wherein the electric field strength of the reference beam is more than 50 times the electric field strength of the background scattered light.

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