# Patent

## Title
Method and apparatus for infrared scattering scanning near-field optical microscopy

## Abstract

This invention involves measurement of optical properties of materials with sub-micron spatial resolution through infrared scattering scanning near field optical microscopy (s-SNOM). Specifically, the current invention provides substantial improvements over the prior art by achieving high signal to noise, high measurement speed and high accuracy of optical amplitude and phase. Additionally, it eliminates the need for an in situ reference to calculate wavelength dependent spectra of optical phase, or absorption spectra. These goals are achieved via improved asymmetric interferometry where the near field scattered light is interfered with a reference beam in an interferometer. The invention achieves dramatic improvements in background rejection by arranging a reference beam that is much more intense than the background scattered radiation. Combined with frequency selective demodulation techniques, the near-field scattered light can be efficiently and accurately discriminated from background scattered light. These goals are achieved via a range of improvements including a large dynamic range detector, careful control of relative beam intensities, and high bandwidth demodulation techniques.

## Background
BACKGROUND OF THE INVENTION
Scattering scanning near field optical microscopy (s-SNOM) operates by interacting a sharp probe tip of a probe microscope with a sample surface and collecting light scattered from the region of tip-sample interaction. Using this technique it is possible to measure the optical properties of samples with a spatial resolution far below the conventional diffraction limits. The resolution improvement comes from a local enhancement of the incident radiation field due to the sharp tip. The enhanced radiation field interacts with the sample and then scatters radiation into the far field. This near-field enhancement increases the amount of radiation scattered from the tip-sample region such that the scattered radiation can be more easily detected.
Referring to Inset A in FIG. 1, a probe 100 with a sharp tip 104 is interacted with a region of interest 106 of a sample 108. Light 110 with electric field intensity Ein is incident on the surface of a sample 108. The incident radiation field is enhanced in the region of the tip apex 104, leading to light scattered from the region of tip-sample interaction with electric field intensity Enf. It is the goal of a s-SNOM system to detect this scattered near field radiation Enf. Unfortunately, the incident radiation Ein also interacts with regions of the probe tip 102 that are away from the tip apex 104 and also with regions of the sample 108 that are away from the tip apex and even away from the region of interest 106. These unwanted interactions result in large background scattering Ebg. In practice, the background scattered field can be orders of magnitude larger than the tip apex scattered field Enf. For this reason it is highly desirable to have effective techniques to discriminate between light scattered from the tip apex region versus scattered from other sources.
Several techniques have been used to attempt to separate the near field light (scattered from the tip apex area) from background scattered light. A commonly used approach is to oscillate the tip, for example using the tip of an atomic force microscope and oscillating it at resonance, such as in tapping mode. Since the amount of near field light scattered from the sample depends strongly on the tip-sample distance, 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 an amplitude of tip-scattered light at the oscillation frequency or a higher harmonic of this oscillation frequency. Stephen Quake also demonstrated the technique of time gating collection of tip scattered photons from fluorescence to correspond with the times that the tip is closest to the sample as described in U.S. Pat. No. 6,953,927.
While each of these approaches has achieved experimental success, each has significant limitations. In the case of simple oscillation of the tip with lock-in detection, the amount of light scattered into the far field depends on both the real and imaginary coefficients of the sample index of refraction and on an unknown arbitrary phase, as well as an unknown and variable amount of background scattering.
Interferometric techniques have also been used to improve detection of tip scattered light. There have been two main approaches, so called “homodyne” approach as described by Taubner et al in Journal of Microscopy, Vol. 210, Pt 3 Jun. 2003, pp. 311-314 and a “pseudoheterodyne” approach as described by Ocelic, Hillenbrand and others, for example in U.S. Pat. No. 7,738,115.
These interferometric techniques are shown generically and schematically in FIG. 1. Light 122 from a light source 120 is directed through a beam splitter 124 to a sample 126 near the end 128 of probe 130. As indicated in prior description of Inset A, the light incident on the probe and sample, results in light 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 on a detector 140. The prior art has also employed well known interferometric techniques by directing a portion 134 of the incident beam at the beam splitter 124 to a reference mirror 136 and then interfering the reference beam with the sample scattered light at the detector 140. A modulator 138 may be used to periodically modulate the reference phase. This interferometric scheme is employed for three main purposes: (1) To provide wavelength sensitive measurements with broadband sources, as commonly performed with Fourier Transform Infrared (FTIR) spectroscopy; (2) to provide amplification for the weak tip-scattered field Enf, as will be explained below; (3) to provide separate measurements of the optical amplitude and phase.
We next consider the signal measured at the detector 140. The total electric field Etot at the detector is given by:

Etot=Enf+Ebg+Eref 

where each of these quantities are complex, to account for phase differences between the electric field components. Note that for simplicity, all collection efficiency factors and optical losses are being subsumed into the electric field strengths, i.e., 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, thus:

Id∝(Enf2+Ebg2+Eref2+2EnfEbg+2EnfEref+2EbgEref)

The interferometric scheme in FIG. 1 provides amplification of the near field scattered radiation through the crossterm ErefEnf. Unfortunately, in practice, there have been severe practical limits on amount of this amplification. Worse still, the background scattered light and reference beam light often have similar order of magnitude, and at best have a ratio of Eref:Ebg of  ̃3-10 (see for example U.S. Pat. No. 7,738,115, col. 2, lines 64ff). The fact that the reference intensity and background intensity are similar can lead to large errors in measurements of optical phase.
U.S. Pat. No. 7,738,115 describes method of overcoming these errors by separating near field and background fields using a “pseudoheterodyne” technique that uses sinusoidal oscillations of both the probe (130 in FIG. 1) and the reference mirror (138) to isolate the near field term Enf in frequency space. Using narrow band lock-in detection, this technique can obtain optical amplitude and phase measurements for the near field scattered radiation.
There are several disadvantages of the pseudoheterodyne approach, namely (1) loss in signal-to-noise; (2) loss in measurement speed; and (3) increased measurement complexity. The loss in signal-to-noise ratio comes from the fact that the pseudoheterodyne technique distributes the energy from the Enf signal across many frequency bands, specifically numerous sidebands around the cantilever oscillation frequency and its higher harmonics. (See for example FIG. 7 in U.S. Pat. No. 7,738,115 and the illustration in FIG. 3A). Thus demodulating at any single side band samples only a small portion of the original scattered energy. As a result the signal to noise ratio of the measurement is degraded—in the effort to reject background, much of the signal is discarded.
Additionally, the sidebands are very close to the original probe modulation frequency (and its harmonics). Specifically, the sidebands are separated from the cantilever 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 thus limited in practice to oscillations in the 100's of Hertz range. As such, it is necessary to demodulate the sidebands with a very narrow bandwidth lock-in amplifier, compared to the oscillation frequency of the probe which can be in the megahertz range. The narrow bandwidth required to demodulate the sideband thus slows down the measurement since it requires longer integration times and thus makes the entire measurement much slower.
The current invention overcomes these limitations by providing an optical arrangement that enables Eref>>Ebg. This allows direct demodulation of the scattered near field optical signal with high accuracy measurements of both optical amplitude and phase. Additionally, the technique of the current invention achieves much better signal-to-noise ratio as it can capture a much larger fraction of the signal in fewer and widely spaced frequency bands. This both substantially simplifies and speeds up the demodulation, thus supporting higher speed imaging and spectroscopy.
Another major limitation of prior art s-SNOM systems is the inability to easily calculate a spectrum that closely resembles a traditional infrared absorption spectrum without complicated post-processing involving an in situ reference. The pseudoheterodyne technique can output signals that are proportional to the amplitude and phase of the scattered light. Unfortunately, at each wavelength, the optical phase has an unknown and varying phase offset. Thus the phase versus wavelength (or wavenumber) plot does not closely resemble a conventional absorption spectrum. To convert the phase signal into something approaching an absorption spectrum, it has been necessary to use an in situ reference sample with well-known phase behavior over the wavelength range of interest. The in situ reference sample requirement has led to the need that samples be prepared with an additional known material directly adjacent to the sample of interest. In fact most if not all in situ reference measurements are performed such than a material of interest is sufficiently close to the in situ reference such that the material of interest and the reference material can be imaged in the same field of view of the same AFM image. The in situ reference sample also must have a flat or otherwise well-known phase behavior. This in situ reference requirement has dramatically limited the types of samples that can be successfully measured, as many if not most real world samples do not have a suitable reference material available. 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 an in situ reference sample adjacent to the material of interest.
Further, any errors in either the measured or assumed phase of the in situ reference sample lead directly to errors in the calculated spectrum of an unknown sample. In practice, absorption spectra calculated from prior art s-SNOM measurements have contained distortions in absorption band shapes, offsets in absorption peak positions, and errors in relative absorption peak heights. These errors lead to complications in the interpretation of s-SNOM spectra and discrepancies from the standard spectra known from materials databases.
DEFINITIONS
“Interacting 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 an area of the sample in proximity of the probe apex. The interaction can be contact mode, intermittent contact/tapping mode, non-contact mode, pulsed force mode, and/or any lateral modulation mode. The interaction can be constant or as in preferred embodiments, periodic. The periodic interaction may be sinusoidal or any arbitrary periodic waveform. Pulsed force modes and/or fast force curve techniques may also be used to periodically bring the probe to a desired level of interaction with a sample, followed by a hold period, and then a subsequent probe retraction.
“Illuminating” means to direct radiation at an object, for example a surface of a sample, the probe tip, and/or the region of probe-sample interaction. Illumination may preferably include radiation in the infrared wavelength range, but other wavelengths may also be used. Illumination may include any arbitrary configuration of radiation sources, reflecting elements, focusing elements and any other beam steering or conditioning elements. The source of infrared radiation may 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 cantilever probes or other microscopic heaters, and/or any other source that produces a beam of infrared radiation. The source emits infrared radiation in a preferred embodiment, but it can instead or also emit in other wavelength ranges, for example from ultraviolet to THz.
“Scattering” or “scattered” refers to radiation emitted from a region other than specular reflected light. Scattering can include a variety of mechanisms including elastic scattering, inelastic scattering, fluorescence, Raman scattering, and any other mechanism that involves radiation being emitted from a surface in response to incident radiation (other than simply reflected light).
“Collecting radiation” means to collect radiation at or with a suitable radiation detector, for example at a photodiode, photoconductor or similar detector that converts an radiation into a current, voltage, temperature or other signal that can be measured.
“Near-field selective amplification” refers to one or more techniques that are applied to selectively amplify and/or discriminate light that is scattered from the region of a sample in proximity to the probe apex, while diminishing the relative contribution from radiation scattered from other sources, for example scattered from regions of the sample away from the probe apex, and/or radiation scattered from the shank of the probe tip away from the tip apex and/or the cantilever body. “Near-field selective amplification” can include modulation of the probe-sample distance, time gating of collected radiation, asymmetric interferometric amplification, or frequency domain techniques that select 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, including but not limited to index of refraction, absorption coefficient, reflectivity, absorptivity, real and/or imaginary components of the index refraction, real and/or imaginary components of the sample dielectric function and/or any property that is mathematically derivable from one or more of these optical properties.
“In situ 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. The sample of interest is typically mounted directly on the in situ reference sample (for example a sample on a gold or silicon substrate) where some portion of the substrate is maintained bare (without a sample of interest covering it). Such samples can facilitate direct comparison between the phase of a known sample with a sample of interest. In situ reference samples are typically made by scratching away a portion of a sample of interest to reveal the underlying substrate or masking a region the substrate when the sample of interest is deposited.
“Background scattering” refers to radiation scattered from regions of the sample away from the probe apex, and/or radiation scattered from the shank of the probe tip away from the tip apex and/or the cantilever body.
“Interference,” “Interfering,” and “Interferometry” all refer to the coherent superposition of multiple electric field components from two or more sources at an optical detector. The intensity detected at the detector depends on the complex sum of the real and imaginary electric field components, or equivalently both the amplitude and optical phase of the electric field components. Interferometry is one of the techniques employed to obtain “Near-field selective amplification,” as described above.
“Reference beam” refers to an optical beam that takes an alternate optical path not including the sample and probe. The reference beam is typically interfered with the sample scattered beam at the detector.
“Signal indicative of” refers to a signal that is mathematically related to a property of interest. The signal may be an analog signal, a digital signal, and/or one or more numbers stored in a computer or other digital electronics.” The signal may be a voltage, a current, or any other signal that may be readily transduced and recorded. The signal may be mathematically identical to the property being measured, for example explicitly an absolute phase signal or an absorption coefficient. It may also be a signal that is mathematically related to one or more properties of interest, for example including linear or other scaling, offsets, inversion, or even complex mathematical manipulations.
A “transimpedance amplifier” refers to an electronic device that converts current to a voltage through active amplification. The most common transimpedance amplifier are circuits built with operational amplifiers and feedback resistors, but equivalent circuits can be built with discrete transistors. The transimpedance amplifiers can 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 biasing circuit provide bias to the photodetector.
SUMMARY OF THE INVENTION
Therefore, the object of the current invention is to overcome the limitations of the prior art in IR s-SNOM. Specifically, the current invention enables efficient, high sensitivity measurements of the amplitude and phase of the near field tip scattered light. It also enables high speed demodulation of the near field signal in support of high speed nanoscale spectroscopy and chemical imaging. The current invention also enables rapid and accurate calculations of near field phase while eliminating the need for an in situ reference sample.



BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be better understood by referring to the following figures.
FIG. 1 shows a simplified schematic diagram of scattering Scanning Near Field Microscopy (s-SNOM) under the prior art.
FIG. 2 shows a simplified schematic diagram of one embodiment of the current invention.
FIG. 3 shows an illustration comparing demodulation bandwidth requirements of the prior art pseudoheterodyne approach versus the current invention.
FIG. 4 shows an illustration of the improvement in amplitude and phase errors under the current invention.
FIG. 5 compares the linear range of infrared detectors used in the prior art versus one embodiment of the current invention.
FIG. 6 is a simplified schematic diagram showing filter positions in one embodiment of the current invention to achieve high levels of discrimination between near-field and background signals.
FIG. 7 shows an illustration of the ratio between reference intensity to background scattered light and amplitude/phase errors as a function of sample arm filter transmission ratio.
FIG. 8 shows a method under the current invention to obtain a wavelength dependent phase spectrum.
FIG. 9 shows an illustration of the method shown in FIG. 8.
FIG. 10 shows the difference between the near-field scattered radiation and the background scattered radiation as a function of tip-sample separation and frequency.
FIGS. 11A and 11B show a topography image and a near-field scattered radiation image of the same region of a sample.



DETAILED DESCRIPTION OF THE INVENTION
FIG. 2 shows a simplified schematic of an embodiment of the current invention. Infrared light 202 is emitted from source 200 towards a beam splitter 204. In FIG. 2, the light 202 is shown as diverging, but it may also be substantially collimated. Light 205 that passes through the beam splitter continues towards a focusing optic 206 that focuses the infrared light onto a sample 209 in the vicinity of the end 208 of a probe 210 of a probe microscope. (FIG. 2 shows a top view looking down on a sample and a cantilever probe—the probe tip and tip apex are not illustrated in this view.) Light scattered from the tip and sample is collected by collection optics. In the simplest implementation the collection optics are the same as focusing optics 206, but alternate and/or additional collection optics can be used instead. Light 207 collected from the collection optic is returned to the beam splitter 204 where it is focused via another focusing optic 212 onto the surface of an infrared detector 214.
A portion 216 of the incident light beam 202 is diverted at the beam splitter 204 towards a reference mirror 218. The light 217 reflected from reference mirror 218 is directed back through the beam splitter and along the same path as the tip/sample scattered beam, focused by focusing optic 212 onto the detector 214. The light in beam 217 is referred to as a “reference beam.” In this manner light from the reference arm is interfered with light scattered from the tip and sample. Actuator 220 is used to rapidly adjust the optical path length of the reference arm, thus adjusting optical phase of light reflected from the reference arm. In one embodiment, the actuator 220 is periodically moved λ/8, where λ is the center wavelength of the incident radiation. The actuator may be a piezoelectric device, a flexure-guided actuator, and/or an actuator employing electrostatic, magnetic, voice coil, electrostrictive or other actuation mechanisms. It may also be a precision linear motor or an intertial drive mechanism or any other mechanism that can move accurately on the scale of fractions of a wavelength. The λ/8 motion induces a total path length difference λ/4 (λ/8 both coming and going), resulting in a 90° optical phase shift. Measuring the detector signal at two phases 90° allows calculation of both the optical amplitude and the optical phase of the tip/sample scattered light. Specifically, if the detector signal is measured at two optical phases 90° apart, the amplitude A and phase φ can be calculated by:




  
    A
    =
    
      
        
          I
          0
          2
        
        +
        
          I
          90
          2
        
      
    
  
  ,
  
    φ
    =
    
      
        arc
        ⁢
        
          
        
        ⁢
        
          tan
          ⁡
          
            (
            
              
                I
                90
              
              
                I
                0
              
            
            )
          
        
      
      +
      
        φ
        0
      
    
  




where I0 and I90 are the detector intensities at a 90° phase shift and φ is an arbitrary constant (discussed later associated with FIGS. 8 & 9).

Referring back to Inset A in FIG. 1, the light scattered from the tip/sample contains two electric field terms. The field scattered from the tip apex 104 and a portion of region 106 of the sample interacting with the tip apex is indicated by Enf and this is the signal of interest. Background scattered radiation from other regions of the probe and sample is characterized by electric field strength Ebg. Note that these are both complex quantities and generally have an unknown phase offset. In general |Ebg|>>|Enf|. This is due to the fact that the illuminated area (i.e. the focused spot size) is many orders of magnitude larger than the tip apex. Thus the background scattered light often dwarfs the amount of light scattered from the tip apex region. (In some cases of extremely efficient tip-enhancement and/or very small background scattering, the near field signal Enf can be larger than the background.)
Referring back to FIG. 2, interference between the reference arm light 217 the tip/sample scattered light also provides amplified detection of the tip/sample scattered light. 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 that interferes with the scattered light at the detector. Thus:

Id∝(Enf2+Ebg2+Eref2+2EnfEbg+2EnfEref+2EbgEref)

The amplification of the tip/sample scattered light comes from the cross terms EnfEref and EnfEbg. In the prior art, there has been a competition between these two terms. The amplitude and phase of Ebg are generally unknown and can vary over a surface. As such, if not corrected, this cross term can cause significant errors in optical amplitude and phase measurements of the signal of interest Enf. The prior pseudoheterodyne techniques have attempted to separate out the background cross term from the reference cross term using sinusoidal modulation of the reference arm and then separating the Eref and Ebg cross terms in frequency space, as illustrated in FIG. 3. The current invention can avoid the need to modulate the reference arm phase by ensuring that Eref>>Ebg, such that the dominant interferometric amplification is performed via the Eref term. Separately, the current invention can employ the simpler frequency separation techniques of the prior art homodyne technique to discriminate between the EnfEref and EbgEref terms. This is achieved by taking advantage of the much steeper nonlinear dependence with tip-sample separation of the near field component versus the background component. FIG. 10 shows illustrations of the relative distance dependence of the background (A) and near field (B) components. The background signal varies slowly with tip-sample separation (the signal strength may actually increase or decrease based on the optical phase). The near field signal, on the other hand, increases very strongly at small tip-sample separations. When the tip is periodically interacted with the sample (e.g. oscillated in tapping mode), the resulting frequency dependent amplitudes are illustrated schematically in FIGS. 10C and 10D. The background signal Ebg (10C) has components primarily at the cantilever fundamental and the 1st harmonic, with negligible contributions at higher frequency. The near field component, Enf (10D), by comparison has a very large number of harmonic components due to the large non-linearity.
If the tip is oscillated at an angular frequency ω, the tip scattered light is proportional to:




  
    E
    nf
  
  ∝
  
    
      E
      0
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        ∞
      
      ⁢
      
        
          a
          n
        
        ⁢
        
          e
          
            i
            ⁢
            
              
            
            ⁢
            n
            ⁢
            
              
            
            ⁢
            ω
            ⁢
            
              
            
            ⁢
            t
          
        
      
    
  




The background scattered light is proportional to





  
    E
    bg
  
  ∝
  
    
      E
      0
    
    ⁢
    
      
        ∑
        
          n
          =
          0
        
        ∞
      
      ⁢
      
        
          b
          n
        
        ⁢
        
          e
          
            
              i
              ⁢
              
                
              
              ⁢
              n
              ⁢
              
                
              
              ⁢
              ω
              ⁢
              
                
              
              ⁢
              t
            
            +
            φ
          
        
      
    
  




b1, b2 are significant, but for n≧3, bn is negligible, as shown in FIG. 10C. The voltage at the detector is proportional to:

Id∝(Enf+Ebg+Eref)2 

Expanding the terms, we see the detector signal, including key cross-terms

Id∝(Enf2+Ebg2+Eref2+2EnfEbg+2EnfEref+2EbgEref)

Considering the scattered light, Enf, the component al is largest, but is hard to discriminate the near field scatter light Enf from background scattered light Ebg that also is modulated at ω. As such, demodulation at n≧3 is commonly used. It is also desirable to obtain amplitude and phase info separately. So in pseudoheterodyne the phase of Eref is modulated at another frequency such that the cross term is modulated at a different frequency. But this has a significant disadvantage as it spreads out energy from Enf to other sidebands, reducing the signal to noise ratio and increasing measurement time.
The current invention employs near-field selective amplification to discriminate the near field scattered radiation from background scattered radiation. The current invention avoids these problems with the pseudoheterodyne approach (U.S. Pat. No. 7,738,115) and also overcomes the large amplitude and phase error limitations of the earlier homodyne prior art described by Taubner (Journal of Microscopy, Vol. 210, Pt 3 Jun. 2003, pp. 311-314).
FIG. 3 demonstrates how the current invention employs a more robust approach than homodyne prior art to discriminate near field and background signals. FIGS. 3A and 3B show the amplitude error and phase error respectively for the homodyne prior art (solid lines) versus the current invention (dashed lines). The amplitude and phase errors for the homodyne approach were calculated using the equations in the background section of U.S. Pat. No. 7,738,115 when discussing the prior art homodyne approach.
To achieve these reductions in amplitude and phase error the current invention, in one embodiment, carefully arranges the relative field strengths such that Eref>>Ebg. In this case, it is possible to neglect the cross term EnfEbg since the EnfEref cross term is so much larger. FIG. 4C shows the dependence of the amplitude and phase errors on the ratio of Eref:Ebg. The prior art homodyne technique was limited to Eref:Ebg of 3-10, resulting in amplitude errors in excess of 40% and phase errors in excess of 25°. By contrast, the current invention achieves Eref:Ebg of >20, or preferably more than 50, and more than 150 in some embodiments. With an Eref:Ebg ratio of 150, the amplitude error is less than 1% (FIG. 4A) versus 28% under typical conditions as described in U.S. Pat. No. 7,738,115 (see Col 2, line 64-Col 3 line 4) Additionally, the phase error can be 0.5° or less (FIG. 3B) under the current invention, versus 19° described in the aforementioned patent. FIG. 4D tablulates the improvement in amplitude and phase error versus a homodyne prior art value of Eref:Ebg=5, described as typical in the '115 patent.
The relationship between amplitude and phase errors versus the Eref:Ebg ratio is illustrated in FIGS. 4C and 4D. The relationship is roughly an inverse law relationship, i.e., the amplitude and phase errors are roughly proportional to 1/(Eref:Ebg). The prior art has been restricted to Eref:Ebg, in the range of 3-10, contributing to amplitude errors of up to 47% and phase errors of up to 28°. Under the current invention, the inventors can achieve Eref:Ebg ratios of >20, or preferable more than 50, or even more preferably above 150. Even with a Eref:Ebg ratio of 20, the amplitude error can be  ̃7%, already 4× better than the typical prior art value. At Eref:Ebg=50, the amplitude error is 2.8%, 10× better than the prior art. And at Eref:Ebg=150, the amplitude error is 0.9%, roughly 30× better than the prior art. Similar improvements are seen in the phase error with roughly 4×, 10× and 30× reductions in the phase error with 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 the U.S. Pat. No. 7,738,115 patent as a motivation for their use of pseudoheterodyne techniques to attempt to overcome the problem. As mentioned previously and discussed elsewhere, the implementation of pseudoheterodyne leads to several performance limitations.
The current inventors have overcome the prior art limits on the Eref:Ebg ratio and thus eliminated the need to perform more complex pseudoheterodyne measurements. The inventors have overcome the prior art limits using three linked steps. First, the inventors have employed linear response mercury cadmium telluride detectors that can achieve a linear response regime at more than 30× higher intensity that detectors used in the prior art. Second, the inventors carefully adjust and/or attenuate the strength of the reference beam so that the intensity from the Eref2 term almost saturates the detector. Third, and somewhat counter intuitively, the inventors optionally attenuate the light in the sample arm to suppress the background scattered light, thus improving the Eref:Ebg ratio.
Returning to FIG. 2, the source of infrared radiation 200 may 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 cantilever probes or other microscopic heaters, and/or any other source that produces a beam of infrared radiation. Source 200 can alternately or additionally be a source of other wavelengths, for example from ultraviolet to terahertz radiation. Source 200 preferentially has high amplitude and phase stability to provide consistent amplification through the ErefEnf term. In some cases, it can be beneficial to take extra steps to stabilize the source energy, for example through dynamic adjustments of the laser cavity, limiting the bandwidth on the drive current, controlling the temperature of the source or other techniques that can maximize the stability of the Eref term.
Controller 236 can dynamically adjust the output power of radiation source 200 to maximize intensity at the detector 214 such that the intensity is near the limit of the linear range of the detector. Variable attenuator 228 can dynamically adjust the fraction of light that is incident on the sample and simultaneously attenuate the background scattered light Ebg. In one embodiment, variable attenuator 228 is a filter wheel with various neutral density filters 230 at a plurality of locations in the filter wheel. The neutral density filters can be made from metal meshes so that there is no wavelength dependent refraction from dispersive optical components with finite thickness. Neutral density filters may also be made from IR transparent materials, for example germanium, zinc selenide or other materials with suitable metal and/or dielectric coatings. Any other attenuating optical element may be used in place of or in addition to filters, including but not limited to iris diaphragms, polarizing optics or other attenuating devices. Additionally, one or more location 232 in the filter wheel may be empty to be used in the case of weak scattering from the sample or small background scatter that does 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 that is amplified by amplifier 234. Amplifier 234 may be a transimpedance amplifier that provides a large linear detection regime and maintains a small potential across the photodiode. (This is one approach to achieve a much larger linear range than a photoconductive detector thus enabling higher intensity reference beams and large Eref:Ebg ratios.) Alternative suitable detectors may be used for other wavelengths 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 cantilever probe. The current invention then also employs frequency space separation to achieve near-field selective amplification. The background signal Ebg generally only has significant AC components at the 1ω and 2ω frequencies, where ω is the frequency of interaction of the probe with the sample (e.g. an oscillation frequency). At n≧3, the near field signal dominates the background signal because the near field signal has a much higher nonlinearity (more significant increase at shorter tip-sample distances). At frequencies no) where n≧3, the near field signal dominates, i.e. Enf>>Ebg, as illustrated in FIG. 10C-D.
The controller 236 can include demodulation capabilities to extract the component of the signals from detector 214 and amplifier 234 at the oscillation frequencies and their harmonics. The controller may comprise multiple separate components, for example a piezo amplifier, a lock-in amplifier, data acquisition/control device, and a computer. Alternately, all controller functions may be contained within a single integrated device. Specifically, the demodulation capability can extract oscillatory components of the detector signal at n ωi, where n is an integer. The demodulator may be a conventional lock-in amplifier, or alternately a multifrequency lock-in 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 on digital electronics, for example using field programmable gate array (FPGA), digital signal processor (DSP) or similar technologies. The demodulation can also be performed rapidly on a personal computer by calculating discrete Fourier sums that correspond to a response at a desired frequency. The demodulator generally produces 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 may also be interacted with the sample with non-sinusoidal modulation and demodulation can use alternative basis functions, for example wavelets, Bessel function, or other functions selected 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 cantilever's fundamental oscillation frequency. For example a Fourier transform can be applied to extract any number of Fourier components at one or more frequencies corresponding to harmonics of the cantilever motion. Note also, it is not necessary to calculate an entire Fourier transform. It is possible to discretely calculate the response at any desired frequency with an appropriate Fourier sum, i.e. calculating the Fourier component at a specific desired frequency. Since the cantilever motion frequency is well known and determined in one embodiment by the SPM controller, the desired Fourier components can be calculated very quickly at well specified frequencies. It is also possible to sum the amplitudes at multiple Fourier components, for example at the 3rd-8th harmonics of the cantilever motion. One way to calculate the total intensity from a specified number of higher harmonics is to employ a circuit and/or a computation to determine total harmonic distortion (THD). Total harmonic distortion calculations or THD analyzers usually sum the harmonic component for some specified number of harmonics above the fundamental oscillation frequency. (In some cases it can be desirable to begin the THD sum starting at the third harmonic thus providing better rejection of the background scattered light that can have a component at the 2nd harmonic.)
In one embodiment, it is possible to perform demodulation at very high rates. For example it is possible to achieve high quality near field scattering images in <5 minutes, similar to conventional AFM imaging speed. It is also possible to achieve high quality near field scattering spectra in less than 1 minute. The reason is that it is possible to demodulate directly at a cantilever resonance or a higher harmonic of that resonance, rather than at a sideband as required for pseudoheterodyne techniques. FIG. 3 illustrates this issue. Under the pseudoheterodyne technique, the reference arm modulation introduces side bands 302 around the cantilever oscillation frequency 304 and its harmonics 306. To demodulate the amplitude of a sideband 302, it is necessary to employ a narrow bandwidth detection technique to avoid contamination from the often much larger signal at the adjacent harmonic frequency 306. An example bandwidth that would isolate a single sideband is shown schematically with dashed lines in FIG. 3A.
By contrast, the current invention need not apply sinusoidal modulation to the reference mirror and as such need not distribute energy to any sidebands. The demodulated peaks at the cantilever resonance (308) and higher harmonics (310) are much more widely separated, as indicated in FIG. 3B. Thus the current invention has one advantage in that it can apply wide bandwidth demodulation thus requiring very short integration times. In addition, with the larger values of Eref:Ebg it is possible to achieve much large asymmetric amplification of the near field scattered signal Enf. Thus the amplitudes of the demodulated response are much larger than the pseudoheterodyne approach, but also larger than the demodulated peak heights in conventional homodyne approaches. With higher signal to noise ratios versus the prior art homodyne approach (constrained by smaller Eref:Ebg) it is possible to take advantage of these increased bandwidths and short integration times. The shorter integration times dramatically increase measurement speed and improve the throughput of the instrument.
For example, if it is desired to demodulate at the 3rd harmonic of a fundamental cantilever resonance at 80 kHz, the separation between bands is 80 kHz. So when the signal to noise ratio permits, a demodulation bandwidth up to  ̃150 kHz can be used while avoiding contribution from other frequency bands. (The specific bandwidth and potential crosstalk from neighboring bands depends on demodulation factors like the properties of any window function used in the 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 one measurement point every 10 μsec. With sufficient signal to noise, a 200 point spectrum can be obtained in as little time as 2000 μsec. But even with a narrower bandwidth to provide more noise rejection, for example 2 kHz bandwidth can still achieve a 200 point spectrum in as little as 0.1 sec. To achieve these spectrum measurement times it is desirable to tune the IR source continuously, rather than in a step/settle/measure scheme. Even with step/settle/measure scheme it is possible to achieve a spectrum in less than a minute, for example with 200 points and 0.25 seconds of step/settle time. Similarly, a single wavelength scattering image with a pixel resolution of 200×200 points can achieved obtained in as little as 20 seconds with a 2 kHz demodulation bandwidth. FIG. 11 shows an example measurement of 200×200 points acquired with a bandwidth of 1.2 kHz and at a line rate of 0.2 seconds per line, corresponding to a bidirectional image time of 40 seconds. FIG. 11A shows a topographic image of an interface between gold and silicon. FIG. 11B shows an image indicative of near-field scattered radiation under the current invention of the same region. In addition to the bandwidth benefits, the direct demodulation at one or more major harmonic of the cantilever motion (not a side band) maintains much higher signal to noise, whereas pseudoheterodyne techniques move only a portion of the signal into sidebands, thus reducing signal to noise ratio.
As mentioned previously, the scattering and demodulation measurements are preferably performed at two position of the reference mirror 218 (FIG. 2), corresponding to two optical path lengths separated by 90° of optical phase. Measuring the demodulator outputs at two positions of the reference mirror with 90° of optical phase difference enables separate computation of the optical amplitude and optical phase of the scattered light. These measurements of optical amplitude and phase can be used to extract the optical properties of submicron regions of a sample surface. In particular, it is possible to calculate a near field absorption spectrum 238 from these measurements. The absorption spectrum primarily comes from the optical phase signal, a measure of dissipation, although it may be necessary to correct the measured optical phase due to wavelength dependent dispersive effects (i.e. changes in the real index of refraction).
The sample 209 and/or probe 210 may be translated relative to each other, for example with an XY scanner 211. This enables measurements of the spatial distribution of optical properties of the sample, with sub-micron spatial resolution. In one example, absorption spectra 238 or other optical properties can be mapped at a plurality of points 240 on a sample to create spatially resolved profiles of the optical properties of the sample. Alternately, the optical properties can be mapped at a plurality of regularly spaced XY points to create a chemical map 242 of the sample surface. In one embodiment, each pixel of the chemical map comprises measurements at a plurality of incident wavelengths. In other embodiments, the chemical map represents a scattering signal measured at a plurality of XY sample positions, but at a single wavelength.
Turning to FIG. 5, we discuss briefly 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 typically 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,” rather than a photoconductive MCT. As illustrated schematically in FIG. 5, the linear MCT photodiodes have a much larger dynamic range. While a photoconductive MCT may reach saturation around 10−3 W/cm2, the linear MCT photodiodes can provide a substantially linear response operate out to 0.1 to 1 W/cm2, depending on the transimpedance gain and bias conditions. This increase in dynamic range enables much more efficient asymmetric amplification of the near field signal. The reason is that the signal we are generally interested in results from the cross-term ErefEnf, i.e. the amplification of the near field signal by the reference arm field strength. The value of the Eref is limited in general by the dynamic range of the IR detector, specifically due to the Eref2 term. A low limit on the maximum detector intensity for photoconductive MCTs constrains the maximum value of Eref2 and hence the maximum amplification of the Enf term. By switching to a high D* linear MCT photodiode, Eref2 can be orders of magnitude larger, resulting in much higher Eref:Ebg ratios, enabling the improvement in amplitude and phase errors discussed above. One suitable linear MCT photodiode is for example model KLD-0-0.5-J1-3/11/DC from Kolmar. Other models can also be suitable depending on bandwidth requirements and focused spot size. Another alternative is thermoelectrically cooled MCT detectors which have saturation up to 1 W/cm2, up to 100× better than liquid nitrogen cooled. These detectors have much higher noise floors and may only be suitable with higher scattered intensities that are well above the detector noise floor. To achieve the highest Eref:Ebg ratios it is generally desirable to arrange the Eref term such that the total intensity at the detector (dominated by Eref2) is in the range 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 amplification is still greater than the decrease in sensitivity.
Turning to FIG. 6, we discuss next optimal attenuation of the interferometer beam components, including the counter-intuitive step of placing a filter in the sample arm. FIG. 6 shows a simplified version of the interferometric detection used in s-SNOM, except that a filter has been placed in each arm of the interferometer, e.g. 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 to beam splitter 624 where it is divided into two paths, on to reference mirror 636 and one towards probe tip 628 and sample 626. The light scattered from the tip apex region Enf and the background light scattered Ebg recombine with the reference arm light Eref at the detector 640. By tracing each of the beams through each filter and the beam splitter, we can determine the relative field strengths at the detector in the presence of the filters.
The strength of the electric field from the near field scattered light at the detector is given by:




  
    E
    nf
  
  =
  
    
      a
      nf
    
    ⁢
    
      E
      0
    
    ⁢
    
      
        
          F
          L
        
        ⁢
        
          F
          D
        
        ⁢
        
          F
          S
          2
        
        ⁢
        RT
      
    
  




where R and T are the reflection and transmission coefficients of beam splitter 624, □□□ is the near field scattering coefficient and E0 is the original electric field intensity from the source 620. Similarly, the background scattered light is given by:





  
    E
    bg
  
  =
  
    
      a
      bg
    
    ⁢
    
      E
      0
    
    ⁢
    
      
        
          F
          L
        
        ⁢
        
          F
          D
        
        ⁢
        
          F
          S
          2
        
        ⁢
        RT
      
    
  




where αbg is the background scattering coefficient.

The electric field from the reference arm is given by:




  
    E
    ref
  
  =
  
    
      E
      0
    
    ⁢
    
      
        
          F
          L
        
        ⁢
        
          F
          D
        
        ⁢
        
          F
          R
          2
        
        ⁢
        RT
      
    
  




The signal term that we are interested in is the cross term ErefEnf, whereas the unwanted background term is EbgEnf. Therefore, the signal to background ratio is given by:




  
    S
    B
  
  =
  
    
      
        
          E
          ref
        
        ⁢
        
          E
          nf
        
      
      
        
          E
          bg
        
        ⁢
        
          E
          nf
        
      
    
    =
    
      
        
          E
          ref
        
        
          E
          bg
        
      
      =
      
        
          
            
              E
              0
            
            ⁢
            
              
                
                  F
                  L
                
                ⁢
                
                  F
                  D
                
                ⁢
                
                  F
                  R
                  2
                
                ⁢
                RT
              
            
          
          
            
              a
              bg
            
            ⁢
            
              E
              0
            
            ⁢
            
              
                
                  F
                  L
                
                ⁢
                
                  F
                  D
                
                ⁢
                
                  F
                  R
                  2
                
                ⁢
                RT
              
            
          
        
        =
        
          
            F
            R
          
          
            
              a
              bg
            
            ⁢
            
              F
              S
            
          
        
      
    
  




Interestingly, this points out that the filter 606 in the detector arm and the filter in the source arm 602 have no impact on the signal to background ratio (as long as the detector operates in a linear regime). Instead to maximize the signal to background we wish to maximize the FR term and minimize the Fs term. The filter can have transmission coefficients between 0 and 1, so we may choose FR=1, its maximum value. Thus to increase the signal to background, we want to make Fs as small as practical. This seems counterintuitive, as a filter 608 in the sample arm also attenuates the signal of interest Enf. With the asymmetric interferometer, however, it is possible to substantially amplify the near field scattered light Enf through the cross term ErefEnf. In the prior art it had not been possible to make Eref very large due to limits on the linear response regime of the detectors used. But with the detectors used in the current invention, it is possible to use much higher values of Eref and hence smaller values of Enf to get the same overall signal intensity.
FIG. 7A shows an example relationship between the sample arm filter transmission coefficient and the ratio Eref:Ebg. The exact relationship will depend on a variety of experimental and sample parameters, but this figure shows the basic relationship. In this example, using parameters similar to those commonly used in s-SNOM, it is possible it is possible to achieve an Eref:Ebg value of 50× with a filter with a transmission of 10%. The corresponding amplitude and phase errors are shown in FIG. 7B. Again with a sample arm transmission coefficient of 10%, the amplitude error is less than 3% and the phase error is less than 2°. With currently available laser sources, especially when focused to a diffraction limited spot, it is possible to have sufficient excess radiation intensity to have a sample arm filter transmission of 10% or less. For example, in the current assignee's commercial nanolRTM AFM-based IR spectroscopy instrument, users often use 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 key benefits of the current invention is elimination of the need for an in situ reference in order to obtain wavelength dependent spectra. The challenge has been that as wavelength dependent measurements have been performed, there has been an arbitrary an unknown phase offset at each measurement wavelength. As mentioned previously, this has been addressed by creating a phase reference measurement on an in situ reference sample with either flat or known phase behavior. The current invention provides two alternatives to overcome the need for an in situ reference sample. Returning to FIG. 2, we point out some additional features. Repositionable mirror 222 can direct the incident beam in the sample arm 207 such that it is redirected to a sample arm reference mirror 224. Mirror 224 can optionally be positioned by actuator or translation stage 226. Mirror 224 is preferably placed at a distance along the optical path from beam splitter 204 that is the same as the optical path distance from the beam splitter 204 to the probe tip 208. Actuator/translator 226 can be used to adjust and optimize to match these distances. The distances should be equal to within the coherence length of the radiation source and better performance can be achieved with even better matching.
With mirror 222 positioned to direct the sample beam to 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 create a phase reference table that can be used to correct measurements when mirror 222 is removed, allowing light to be directed towards the sample 209 and probe tip 208. The correction process is shown in FIGS. 8-9 and described shortly. As an alternate 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 flat and/or known phase behavior and can be occasionally placed in the measurement system in place of a sample of interest. The ex situ sample is measured as one would measure a sample of interest. Analysis of the resulting phase measurements on the ex situ sample results in 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 FIGS. 8 and 9. Referring to FIG. 8, the first step 802 involves inserting an ex situ reference sample into the probe microscope or placing an additional reference mirror in the sample arm as described above. Next, step 804, the IR source is tuned to a desired wavelength and optical measurement is performed on light scattered from the ex situ reference sample or light reflected from the sample arm reference mirror. Specifically, a signal indicative of optical phase is measured (step 806). Tuning (804) and measuring optical phase (806) is repeated at all desired wavelengths, typically covering the tuning range of the IR source and with a spectral resolution corresponding to match that used for samples of interest. From the measurements of scattered/reflected radiation, the optical phase is extracted at each desired wavelength and a phase reference table is created (step 808). Next a sample of interest is inserted into the probe microscope (step 810) and the IR light is directed towards the sample of interest (away from the sample arm reference mirror, if used). The IR source is again tuned to a desired wavelength (step 812) and the amplitude and phase of the light scattered from the tip-sample area of the sample of interest is measured (step 814). An illustration of a raw phase spectrum obtained at this point is shown in FIG. 9A. Next the near field optical phase measurement is corrected, by subtracting off the correction values from the phase reference table (step 816), and as illustrated in FIG. 9B. The phase spectrum, even after correction by the phase table has a large number of discontinuities. This is due to the limited output range of inverse tangent functions that are used to calculate phase. These functions have a limited range, for example ±π/2 for a tan or ±π for a tan 2. When the measured phase crosses one of these range limits, a discontinuity is observed in the spectrum. These phase discontinuities can be eliminated, however, using a phase unwrapping process. For example the data can be scanned for discontinuities and an appropriate offset of is added or subtracted to points on one side of the discontinuity to eliminate the discontinuity. One suitable phase unwrapping scheme is described by National Instruments, describing 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 this point, for example in FIG. 9C. The unwrapped spectrum may still have benefit from further processing. In step 820 in FIG. 8, and FIG. 9D, the unwrapped phase can have baseline offset and baseline slope removed. A linear baseline slope can result from a slight 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 can result from a difference in the distance between the beam splitter (204 in FIG. 2) and the sample (209) versus 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. These optical path differences, however, create a constant propagation time error, resulting in a phase error that is linear with the optical frequency. Thus if the phase is plotted as a function of wavenumber, the phase error will result in a linear slope in the baseline. Thus it is possible to perform a linear fit to the baseline and subtract off this slope. An illustration of the baseline slope adjusted spectrum is shown in FIG. 9D.
An additional embodiment of the current invention includes the use of amplitude modulation. By modulating the amplitude of the reference arm it is possible to create a time/frequency dependence in the ErefEnf term. If the probe is being modulated at a frequency of ω0 and the reference arm is modulated at ωref, the ErefEnf will have components at nω0±ωref. Any demodulation technique that extracts one or more components at these frequencies can be used to create a measurement of optical properties of the sample. Amplitude modulation can have several advantages over phase modulation techniques of the prior art. First, phase modulation requires moving a large aperture mirror a reasonable fraction of a wavelength. In practice this requires large piezo 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 low kHz regime for large aperture, high performance mirrors. The limit on modulation frequency puts strict requirements on the bandwidth of any demodulation device. For example, if the reference mirror is modulated at 200 Hz, this modulation will create small side bands ±200 Hz from the cantilever oscillation frequency and its harmonics. To avoid contamination from the central band, it is necessary to use a narrow band filter and/or a narrow bandwidth demodulation system to isolate the sidebands. Such narrow band demodulation techniques take longer integration times to achieve such filtering. As a result, the measurement time performance of pseudoheterodyne mode (or any mode producing sidebands) depends inversely with demodulation bandwidth. A sideband 200 Hz 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 msec per measurement point. For this reason it is highly desirable to employ modulation technique that can be performed at high frequency, thus creating sidebands at much more widely spaced frequencies. Widely spaced sidebands allow high speed demodulation with short integration/filtering times. Under the current invention, amplitude modulation can create sidebands at 10-100× wider frequency separation. Amplitude modulation can be achieved using a variety of techniques. For example, traditional optical choppers can achieve amplitude modulation over 100 kHz. Scitek makes multi-slot choppers that can operate at rates up to at rates up to 120 kHz. Other devices such as photoelastic modulators, deformable micromirrors can also operate up to similar frequencies. Additionally devices such as voice coil fast steering mirrors, galvo mirrors and MEMS micromirrors can steer optical beams at rates from 500 Hz to 10 s of kHz. Such steering mirrors can achieve amplitude modulation by periodically steering the reference beam on and off the detector. Any of these amplitude modulation techniques can be employed to achieve sideband separation larger than conventional pseudoheterodyne techniques and thus achieve shorter spectral measurement times and image times.
The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims

## Claims

1. A method of obtaining an optical property of a sub micrometer region of a sample using a probe microscope comprising the steps of:
a. Interacting a probe of the probe microscope with a sample surface;
b. Illuminating the probe and sample surface with a source of radiation;
c. Collecting radiation scattered from the sample and probe;
d. Applying near-field selective amplification to discriminate scattered near-field radiation from radiation scattered from other sources;
e. Repeating steps a-d at a plurality of wavelengths;
f. Illuminating a reference sample with the radiation source, wherein the reference sample comprises at least one of an ex situ reference sample and a sample arm reference mirror;
g. Collecting radiation scattered and/or reflected from the reference sample to form a reference measurement;
h. Calculating a spectrum of an optical property of the sample as a function of wavelength, to correct at least a portion of the spectrum using the reference measurement.

2. A method of measuring an optical property of a sub micrometer region of a sample comprising the steps of:
a. Periodically interacting a probe tip of a probe microscope with a region of a surface of the sample at a frequency ω0;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of infrared radiation with a center wavelength λ, scattering light from the probe sample interaction region, characterized by a scattering field strength Enf, and the probe-sample region scattering occurs in the presence of background scattering characterized by a scattering field strength Ebg;
c. Interfering a reference beam with the probe-sample and background scattered light, wherein the reference beam has an adjustable phase and is characterized by an electric field strength Eref;
d. Arranging the strength of the reference beam such that Eref is at least 10 times larger than Ebg;
e. Collecting with an infrared detector at least a portion of the light resulting from interference between the scattered light and the reference beam.

3. The method of claim 2 further comprising the step of producing a signal indicative of the strength of the scattered field Enf.

4. The method of claim 2 wherein an interference cross-term Eref*Enf is at least 10 times larger than Ebg*Enf.

5. The method of claim 2 further comprising the step of arranging a filter or other attenuating optical element in a path between a beamsplitter and the sample, to maintain a total intensity at the infrared detector between 50-90% of a limit of a linear response regime of the infrared detector.

6. The method of claim 2 wherein the infrared detector has a substantially linear response up to an intensity of at least 0.1 W/cm2.

7. The method of claim 2 wherein the infrared detector is a mercury cadmium selenide photodiode connected to a transimpedence amplifier.

8. A method of measuring an optical property of a sub micrometer region of a sample comprising the steps of:
a. Oscillating a probe tip of a probe microscope at a frequency ω0 such that it interacts with a region of a surface of the sample;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λ;
c. Scattering light from the probe-sample interaction region;
d. Interfering a reference beam with the scattered light, wherein the reference beam has an adjustable phase and the reference beam has an electric field more than ten times larger than that from background scattered light;
e. Collecting at least a portion of the light resulting from interference between the scattered light and the reference beam at a detector;
f. Determining a signal indicative of a strength of the light collected at the detector;
g. Performing steps a-f at two phase values of the reference beam, wherein the two phase values are substantially λ/4 apart.

9. The method of claim 8 further comprising the step of extracting a signal indicative of modulation of the detector signal at a frequency nω0 where n is greater than or equal to two.

10. The method of claim 8 further comprising the step of calculating amplitude and phase of the scattered light.

11. The method of claim 8 further comprising the step of performing steps (a)-(f) at a plurality of wavelengths of the beam of radiation to determine a spectrum corresponding to a dependence of the scattered radiation on wavelength.

12. The method of claim 11 wherein the plurality of wavelengths covers a range of at least 1 μm.

13. The method of claim 12 wherein the spectrum is obtained in less than 1 minute.

14. The method of claim 8 further comprising the step of determining an absorption spectrum of the probe-sample interaction region.

15. The method of claim 8, further comprising the step of adjusting a strength of the reference beam Eref so as to amplify an interference cross-term Eref*Es.

16. The method of claim 15 wherein the reference beam strength Eref is adjusted such that the cross-term Eref*Es is substantially larger than competing cross-term Ebg*Es.

17. A method of measuring an optical property of a sub micrometer region of a sample comprising the steps of:
a. Periodically interacting a probe tip of a probe microscope with a region of a surface of a sample at a frequency ω0;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λ;
c. Scattering light from the probe-sample interaction region;
d. Interfering a reference beam with the scattered light, wherein the reference beam intensity is modulated at a frequency ω1;
e. Collecting the light resulting from interference between the scattered light and the reference beam at a detector.

18. The method of claim 17 further comprising the step of extracting a signal indicative of a modulation of the detector signal at a frequency mω1±nω0 where m and n are integers.

19. The method of claim 18 where n is greater than or equal to two.

20. The method of claim 17 wherein the optical phase of reference beam is periodically modulated by λ/4.

21. A method of measuring an optical property of a sub-micrometer region of a sample comprising the steps of:
a. Oscillating a probe tip of a probe microscope at a frequency ω0 such that it interacts with a region of a surface of the sample;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λ;
c. Scattering light from the probe-sample interaction region with a strength of Es;
d. Collecting at least a portion of the scattered light at a detector;
e. Producing a signal indicative of the light received by the detector
f. Determining from the detector signal a signal indicative of a strength of the scattered light Es using non-sinusoidal demodulation.

22. The method of claim 21 wherein the non-sinusoidal demodulation comprises using a time varying signal from the detector to calculate one or more coefficients of non-sinusoidal basis functions.

23. The method of claim 22 wherein the basis functions comprise at least one of wavelets and Bessel functions.

24. The method of claim 21 comprising the step of removing from the measured detector signal sinusoidal components at frequency ω0 and analyzing an amplitude of residual non-sinusoidal modulations repeating at frequency ω0.

25. A method of measuring an optical property of a sub micrometer region of a sample comprising the steps of:
a. Oscillating a probe tip of a probe microscope at a frequency ω0 such that it interacts with a region of a surface of the sample;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λ;
c. Scattering light from the probe-sample interaction region with a strength of Es;
d. Interfering a reference beam with the scattered light, wherein the reference beam has a strength of Eref;
e. Collecting at least a portion of the light resulting from interference between the scattered light and the reference beam at a detector;
f. Producing a signal indicative of the light received by the detector
g. Determining from the detector signal a signal indicative of a strength of an interference cross term Es*Eref using non-sinusoidal demodulation.

26. A method of obtaining an infrared spectrum of a sub-micron region of a sample with a probe microscope, the method comprising the steps of:
a. Interacting a probe of a probe microscope with the sub-micron region of the sample;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λi;
c. Scattering light from the probe-sample interaction;
d. Interfering a reference beam with the scattered light with an optical interferometer;
e. Collecting at a detector at least a portion of the light resulting from interference between the scattered light and the reference beam;
f. Producing a signal indicative of a relative optical phase of light collected by the detector;
g. Adjusting the optical phase signal by a reference phase collected on an ex situ reference sample for the center wavelength λi;
h. Repeating steps b-g at a plurality of wavelengths λl, to create a wavelength dependent infrared spectrum.

27. The method of claim 26 further comprising the steps of creating a table of reference phases for a plurality of center wavelengths.

28. The method of claim 27 wherein the reference phase table is created by measuring an optical phase of light scattered from an ex situ reference sample with a substantially known phase behavior over the range of the plurality of center wavelengths.

29. The method of claim 27 wherein the reference phase table is created by measuring an optical phase of light reflected from a reference mirror positioned in a sample arm of the interferometer.

30. The method of claim 29 wherein the reference mirror is positioned at an optical path distance from a beamsplitter in the interferometer that is substantially the same as an optical path distance between the beamsplitter and the sample surface.

31. A method of measuring an optical property of a sub micrometer region of a sample comprising the steps of:
a. Oscillating a probe tip of a probe microscope at a frequency ω0 such that it interacts with a region of a surface of the sample;
b. Illuminating a region of a sample comprising the region of probe-sample interaction with a beam of radiation with a center wavelength λ;
c. Scattering light from the probe-sample interaction region with a strength of Es;
d. Interfering a reference beam with the scattered light, wherein the reference beam has a strength of Eref;
e. Collecting at least a portion of the light resulting from interference between the scattered light and the reference beam at a detector;
f. Producing a signal indicative of the light received by the detector;
g. Determining from the detector signal a signal indicative of a total harmonic distortion of the detector signal calculated at frequency ω0.