When a diffuse surface or volume is illuminated by a laser beam, the coherent superposition of the scattered wavefronts results in a high-contrast, random intensity pattern known as laser speckle [1]. While a nuisance for many coherent optical techniques such as laser radar and holography, the unique characteristics of laser speckle have enabled many applications, including blood flow imaging [2,3], imaging through turbid media [4], the extraction of remote speech [5], and many others [6]. Here we report on a new materials characterization technique based on speckle imaging called photothermal speckle modulation (PSM). The approach involves measuring changes in the visible (532 nm) speckle pattern from a surface co-illuminated by a visible probe laser and an intensity-modulated long-wave infrared (LWIR) pump laser (7.5–8.7 μm). The absorption of the pump laser generates a time-varying thermoelastic surface motion [7], consequently leading to correlated fluctuations in the speckle pattern. Critically, inherent to PSM is the interferometric sensitivity on the intensity of each speckle lobe scattering diffusely from a surface and, therefore, this method is distinct from other pump-probe photothermal techniques [8–13] that primarily rely on measuring the deflection of a specular probe beam. Potential applications of PSM are broad and include remote chemical sensing of bulk, thin film, and powder materials, and noncontact characterization of surface and sub-surface thermal properties.

A schematic of the measurement scheme is illustrated in Fig. 1. A tunable (7.5–8.7 μm) pump quantum cascade laser (QCL) and a visible (532 nm), single frequency probe laser are projected onto a sample under interrogation so that their laser spots overlap. Diffusively scattered probe light from the sample generates a speckle pattern which is imaged onto a visible CMOS camera. The absorption of the pump photons by the sample results in surface heating and subsequent thermoelastic deformation of the surface, both out of plane and in plane, as depicted in Fig. 2. The pump laser power is intensity modulated (fully on to fully off), while the probe beam is on continuously. Photothermally induced surface deformations are excited at the frequency of the pump beam modulation, leading to speckle patterns that change in a periodic manner at the same frequency as the pump modulation. The pump modulation rate (typically 22 Hz or higher in our experiments) is selected to be faster than the timescale associated with natural speckle fluctuations due to vibrations or air currents, for example, thus allowing high-sensitivity lock-in detection at the modulation frequency. Moreover, in contrast to laser vibrometry techniques, which are only sensitive to out-of-plane surface motion, changes in the speckle pattern are affected by both the in-plane and out-of-plane surface deformations [6].

 

Fig. 1. PSM measurement scheme. (a) [Left] Tunable infrared laser (pump) and a 532 nm visible laser (probe) are projected onto the same location of a sample of interest such that their laser spots are coincident. A visible camera monitors changes in the visible laser speckle pattern as the sample’s surface is periodically heated and cooled by the modulated infrared laser. [Right] Illustration of the speckle pattern when the pump laser is on (green) and off (black). (b) Series of speckle images are captured by the visible camera. (c) FFT spectra of each pixel through the image stack are averaged together, exposing the PSM signal which exists at the infrared modulation frequency.

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Fig. 2. Photothermal surface deformation simulations using finite element analysis (Nastran) for a single cycle of a 1 mW average power (50% duty cycle, spot size $\mathrm{FWHM}=0.6\mathrm{mm}$), 20 Hz pump excitation beam incident onto a PMMA block. (a) Peak surface temperature response transient. (b) Normal-to-surface deformations of the surface at the start, middle, and end of a heating cycle. (c) In-plane, or radial deformations. Deformations are shown as a function of distance from the center of the heating spot.

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In a typical measurement, $\sim 1\mathrm{mW}$ average pump power is amplitude modulated with a 50% duty cycle and focused to a $\sim 0.6\mathrm{mm}$ (full width half-maximum, FWHM) spot on the surface of interest, while the $\sim 1\mathrm{mW}$ probe beam illuminates a $\sim 3\mathrm{mm}$ FWHM spot roughly concentric with the pump. In our experiments, the sample is positioned $\sim 1.8$ meters from the pump, probe, and CMOS camera. The focusing range, focal length, and F-stop of the camera’s lens are set to 1.5 m, 160 mm, and f/4, respectively. The lens is intentionally set to focus $\sim 0.3\mathrm{m}$ in front of the sample such that the average speckle lobe size is increased to approximately five pixels/speckle lobe. The CMOS camera records a stack of images which are processed to quantify the photothermal speckle modulation (PSM) signal. In a typical experiment, 20,000 images (frames) are collected at 500 frames per second, and each frame is 46 by 46 pixels [see Fig. 1(b) for an example of the speckle image stack]. The magnitude of the PSM signal is obtained from this image stack using the following algorithm: first, a fast Fourier transform (FFT) is applied to each pixel in the image stack individually. Second, the FFT spectrum for each pixel is averaged over all the pixels resulting in a PSM spectrum for that image stack, as shown in Fig. 1(c). As can be seen, the FFT spectrum contains a signal only at the pump modulation frequency (in this example, 22 Hz). By tuning the QCL’s wavelength over a molecular absorption feature, the amplitude spectrum of the speckle modulation is found to correlate to the IR absorption spectrum. In addition to absorption information, adjusting the rate of modulation of the pump beam and recording the associated modulation transfer to the probe beam, information about the thermal time constants of the surface can be discerned. This enables surface and even sub-surface materials discrimination based on differences in thermal conductivity.

We demonstrate the spectroscopic materials characterization capabilities of this technique on thin films of several polymers (PMMA, Teflon AF, and PDMS), each having distinct absorption features in a wavelength range that overlaps the wavelength tuning range of our QCL. Each polymer was dissolved in a solution and applied onto a potassium bromide (KBr) substrate using standard spin-coating techniques. The samples were dried on a hot plate at 100°C for five minutes to remove any residual solvent. The absorption spectrum for each sample was obtained on a Fourier transform infrared (FTIR) spectrometer (Bruker VERTEX 70 with a Seagull reflection accessory) by measuring both the transmission (T) and reflection (R) of the sample. Since KBr is transparent in the IR, the sample absorption (A) can be expressed as $\mathrm{A}=1-\mathrm{T}-\mathrm{R}$ (1). The surface roughness on the film resulting from the solvent drying step was sufficient to generate a speckle pattern; therefore, no further surface modifications or sample preparation steps were performed. Figure 3 shows the PSM magnitude spectrum for each material plotted versus pump wavelength, showing excellent agreement with the material’s absorption spectrum.

 

Fig. 3. PSM for spectroscopic materials analysis. PSM spectra of (top) a 2 μm Teflon AF film on a KBr substrate, (middle) a 10.4 μm PMMA film on a KBr substrate, and (bottom) a 4.4 μm PDMS film on a KBr substrate.

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A modification of this technique can be leveraged to distinguish between classes of materials based on their thermal conductivities. Instead of varying the pump laser wavelength, the frequency of the pump beam can be tuned, and the PSM signal can be analyzed as a function of pump modulation frequency. The photothermal response as a function of the pump excitation frequency can be understood by considering the step response of the material to an incident heat load over a small spot. Initially, the thermoelastic response rises nearly linearly with time before leveling off to a quasi-steady-state condition. This transient behavior is well described by Beck [14], and the apparent time constant can vary from a few milliseconds for materials with high conductivity to tens of milliseconds for materials for low conductivity. When the period of excitation is long, relative to the time constant, changes in the period (and frequency) of excitation produce very small changes in the peak thermoelastic response. In this region, the photothermal response versus frequency curve is relatively flat. When the period of excitation is small, relative to the time constant, the photothermal response becomes nearly proportional to the period (and inversely proportional to frequency). The transition frequency between these two regimes depends on the time constant, which is determined by the material’s conductivity, specific heat, and density. For higher conductivity materials, this transition occurs at higher frequencies. We demonstrate the ability to distinguish between bulk materials based on this rationale. Bars ($2\mathrm{mm}\times 6\mathrm{mm}\times 10\mathrm{cm}$) of PMMA, aluminum, and stainless steel were used as targets. The QCL wavelength and flux was fixed at 7.85 μm and $5\mathrm{W}/{\mathrm{cm}}^2$, respectively. The modulation frequency was tuned from 5–200 Hz, while the PSM signal was analyzed for several frequencies in this range. Figure 4(a) shows the results of this experiment compared with simulations performed for these materials and experimental conditions using finite element analysis (Nastran). As expected, aluminum (thermal conductivity of 200 W/mK) has a nearly flat response at low frequencies, while PMMA (thermal conductivity of 0.2 W/mK) shows a 1/frequency dependence starting around 10 Hz.

 

Fig. 4. Photothermal speckle modulation for thermal conductivity discrimination. Differences in PSM signal as a function of IR modulation frequency enables discriminating between (a) materials with different thermal conductivities and (b) different sub-surface materials with the same surface-coated material.

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An intriguing feature of this technique is the ability to distinguish between sub-surface properties of objects, for example, between different materials that have identical surface finishes. As a proof-of-principle demonstration, we applied a 4 μm layer of PMMA to two substrates that have different thermal conductivities: germanium (Ge) and KBr. Pump light from the QCL was incident onto each of the samples at the same fixed wavelength and average intensity (7.85 μm, $5\mathrm{W}/{\mathrm{cm}}^2$). The CMOS camera stored images at 500 frames per second with an exposure time of 0.19 milliseconds per frame. The pump light modulation frequency was tuned from 10–200 Hz, and the PSM signal was analyzed for each frequency. The results of this experiment are displayed in Fig. 4(b). For optically thin films, where the penetration depth of the pump beam is on the order of the film thickness, the photothermal surface response is still dominated by the thermal properties of the substrate, since it is the substrate which conducts most of the heat away from the surface film. Because the Ge substrate is a better thermal conductor than KBr, the PSM signal remains relatively flat to higher frequencies for Ge before it starts decreasing. In addition, since the coefficient of thermal expansion is larger for KBr than for Ge, the overall signal strength is higher for KBr compared to Ge. Thus, although the surface coating is the same, the difference between the functional forms of the PSM signal as a function of IR modulation frequency allows the two samples to be distinguished from each other.

Note that the PSM signal depends on a number of material properties, including thermal expansion coefficient, specific heat, density, and thermal conductivity. Because the thermal expansion coefficient affects only the scale of the response, the shape of the frequency response curves of Fig. 4 is primarily dependent on the specific heat, density, and thermal conductivity. These three properties are commonly combined into thermal diffusivity, which has dimensions of length squared divided by time. The thermal diffusivity is inversely proportional to the apparent thermal time constant, and (as explained above) the apparent time constant is responsible for the shape of the frequency response curve. This suggests that a quantitative method for measuring thermal diffusivity may be possible using this technique. Specifically, it is proposed that the transition between the flat and sloped portions of the curve occurs at a frequency that is proportional to the thermal diffusivity. The dimensions of diffusivity suggest that geometric factors such as the spot size, absorption depth, or thickness of the material may also influence the shape of the curve, perhaps requiring some calibration to obtain an absolute measure of diffusivity. Additional research is required to study both the limits and the efficacy of this approach.

In summary, we have developed a new noncontact, pump-probe materials characterization method based on visible-light speckle imaging. Using this technique, IR absorption spectra and thermoelastic time constants of materials can be evaluated by analyzing speckle-pattern modulations of the probe beam induced by surface absorption of an IR pump beam. The methods described here provide new opportunities for remote sensing and other materials characterization applications, including a range of non-destructive analyses, where material composition, subsurface features, and thermoelastic properties are of interest and can be obtained remotely and with high sensitivity using the PSM approach.