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Reconfigurable Temperature Control at the Microscale by Light Shaping Chang Liu, Gilles Tessier, Sergio Iván Flores esparza, Marc Guillon, and Pascal Berto ACS Photonics, Just Accepted Manuscript • Publication Date (Web): 24 Jan 2019 Downloaded from http://pubs.acs.org on January 24, 2019
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Reconfigurable Temperature Control at the Microscale by Light Shaping Chang Liu1,2, Gilles Tessier1,2, Sergio Iván Flores Esparza2, Marc Guillon2, Pascal Berto1,2 1 Sorbonne Université, CNRS, INSERM, Institut de la Vision, 17 Rue Moreau, 75012 Paris, France. 2 Holographic Microscopy Group, Neurophotonics Laboratory, UMR 8250 CNRS, University Paris Descartes, 45 rue des Saints-Pères, 75006 Paris, France. Abstract From physics to biology, temperature is often a critical factor. Most existing techniques (e.g. ovens, incubators…) only provide global temperature control and incur strong inertia. Thermoplasmonic heating is drawing increasing interest by giving access to fast, local and contactless optical temperature control. However, tailoring temperature at the micro-scale is not straightforward since heat diffusion alters temperature patterns. In this article, we propose and demonstrate an accurate and reconfigurable microscale temperature shaping technique by precisely tailoring the illumination intensity that is sent on a homogeneous array of absorbing plasmonic nanoparticles. The method consists in (i) calculating a Heat Source Density (HSD) map which pre-compensates heat diffusion, and (ii) using a wavefront engineering technique to shape the illumination and reproduce this HSD in the nanoparticle plane. After heat diffusion, the tailored heat source distribution produces the desired microscale temperature pattern under a microscope. The method is validated using wavefront-sensing-based temperature imaging microscopy. Fast (sub-s), accurate, and reconfigurable temperature patterns are demonstrated over arbitrarily-shaped regions. In the context of cell biology, we finally propose a methodology combining fluorescence imaging with reconfigurable temperature shaping to thermally target a given population of cells or organelles of interest, opening new strategies to locally study their response to thermal activation. Keywords Wavefront engineering, Thermogenetic
Temperature
shaping,
Gold
nanoparticles,
Thermoplasmonic,
Introduction Heat is a diffusive phenomenon. In many respects, this makes it much harder to manipulate and shape than propagative phenomena. Most concepts and tools used to control waves like light or sound, e.g. spatial modulators or arrays of sources, are not available to shape thermal phenomena at small scales. Even the most basic functions, such as imposing a value in a chosen region of a plane, are easy to obtain with light (with e.g. a simple video projector) but much more difficult to achieve in practice with temperature. While optical cooling remains essentially out of reach, light can still be used to induce heating through absorption. The relation between absorbed light and temperature is not straightforward because of heat diffusion: uniform light absorption does not lead to uniform temperature distribution, an issue which has to be carefully addressed. With proper engineering, optical tools could therefore contribute to shaping temperature, which is essential in all fields of science, from physics to chemistry and biology. Here, we show that an optically absorbing but thermally insulating surface, a homogeneous array of plasmonic nanoparticles (NPs) on glass, can be used to obtain a chosen temperature pattern on a
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surface. An appropriate Heat Source Density (HSD) can be calculated in order to pre-compensate heat diffusion and create a temperature profile which optimally approaches desired values. This has been proposed and demonstrated experimentally by locally engineering the absorption of the substrate1. Assemblies of metal NPs were fabricated by e-beam lithography, with a local density of absorbers matching the desired HSD. A homogeneous illumination of these assemblies then yielded the desired temperature distribution. The average temperature could be changed easily by tuning the optical intensity, but the temperature distribution could not be modified after e-beam fabrication: the thermal pattern was fixed. Instead of shaping the substrate itself, we propose to use an absorbing layer that is homogeneous at the wavelength scale, and to pattern the illumination to produce the HSD, as illustrated in Fig. 1. Among the various available light-patterning techniques, we chose to use a phase Spatial Light Modulator (SLM) as it provides interesting speed and good powerefficiency. Using it to engineer the wavefront properly in the Fourier plane, we created chosen intensity patterns in the image plane. In the experiment, after calculating the HSD, the excitation wavefront is determined using the Gerchberg-Saxton algorithm2, displayed on the phase SLM, and projected in the sample plane to create the desired temperature map. This process can be carried out in real-time to reconfigure at will the temperature distribution spatially and temporally. In order to characterize the possibilities and limitations of the method, the resulting temperature maps are then deduced from heat-induced refractive index variations measured with a wavefront analyser. In addition to model shapes, we show, in the context of cell biology, that a simple fluorescence image can be used to determine targets, and heat chosen regions in a biological specimen. Since temperature is one of the main factors driving the kinetics of (bio)chemical processes, this localized thermal stimulation could become a powerful tool to selectively stimulate or alter the metabolism of chosen organelles and cells, and even to destroy them, in order to and understand their biological function. Moreover, microscale heating has the essential advantage of allowing fast (sub-s) temperature changes, while larger thermal chucks or incubators take minutes or hours to stabilize. This approach should open new possibilities for precise and reproducible local metabolism activation, stimulation, or hyperthermia of living cells.
Figure 1 Experimental setup. A layer of 28 nm diameter gold NPs distributed homogeneously on a glass coverslip is covered with glycerine and illuminated at =532 nm, near the NP resonance wavelength. The intensity distribution of the illumination is calculated and shaped using a Liquid Crystal SLM to obtain the desired temperature map. The temperature map is then deduced from the thermally-induced optical path difference (OPD) by illuminating the sample with a probe plane wave (=407 nm) and measuring wavefront changes.
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1. Determination of the heat source distribution and resulting temperature distribution. The complete workflow to generate a chosen temperature distribution is illustrated in Fig. 2. The procedure starts with a targeted temperature increase map ∆𝑇 = 𝑇 ― 𝑇0 (with 𝑇0 the ambient temperature), which can take any positive value: a homogeneous temperature in a square region as in Fig. 2, or a specific temperature gradient, or complex shapes obtained by sample imaging as shown in the final section using neuron images. Here, we aim at creating a 2D temperature pattern in a microscopic region of a macroscopic sample with thermal conductivity 𝜅. The whole sample typically has cm-range dimensions. It can therefore be assumed to remain at a constant bulk temperature 𝑇0, or can be actively stabilized at 𝑇0 if necessary. The 2D domain of interest (D), where ∆𝑇 is targeted, is meshed using 𝑁 identical square units, each with an area 𝑎2 and identical average absorption cross section 𝜎 since the substrate has a homogeneous absorption at the scale of 𝑎 (the number of absorbing nanoparticles within 𝑎2 is large enough to neglect variations). For each unit cell 𝑖, we note 𝑄𝑖 the dissipated heat source (in W) and ∆𝑇𝑖 the temperature rise. The ∆𝑇𝑖 distribution in the sample is actually the convolution of the 1
HSD with the thermal Green’s function 𝐺𝑇 = 4𝜋𝜅𝑟. To precisely control the temperature rise in a sample, the HSD must then be the deconvolution of the sought-for temperature pattern by 𝐺𝑇. This deconvolution can be computed numerically by a matrix inversion restricted to the domain D, as described by Baffou et al1. When applying a spatial HSD noted 𝐐 in vector form (𝐐 = (𝑄𝑖)𝑖 ∈ [1,𝑁]), where “𝑖” designates one of the 𝑁 location coordinates, the resulting temperature increase distribution ∆𝐓 (∆𝐓 = (∆𝑇𝑖)𝑖 ∈ [1,𝑁]) can be calculated using a simple matrix multiplication: ∆𝐓 = 𝔸𝐐, where 𝔸 is an 𝑁 × 𝑁 coupling matrix defined by: 𝔸𝑖𝑗 =
{
ln (1 + 2) 𝜋𝜅𝑎
, 𝑖=𝑗
1 , 𝑖 ≠𝑗 4𝜋𝜅𝑟𝑖𝑗
Each term 𝔸𝑖𝑗 corresponds to the contribution of the heat deposited in region 𝑗 to the temperature of region 𝑖, with 𝑟𝑖𝑗 the distance between these two different regions. Inverting this matrix therefore provides a way to calculate the HSD yielding the desired temperature map ∆𝐓 : 𝐐 = 𝔸 ―1∆𝐓. This HSD can be created by projecting onto the surface an optical intensity pattern 𝐈 = 𝐐/𝜎. While several techniques allow light patterning, parallel techniques based on SLMs have the advantage of offering much higher temporal resolution compared to scanning-based methods. Acting either on the phase or the intensity of the incident beam, SLMs provide in both cases an arbitrarily-defined intensity distribution of light in the focal plane of the objective. The main drawback of intensity modulators (such as Digital Mirror Device) is an extremely poor efficiency when creating sparse targets as most of the light is rejected out of the sample. Here, we modulate the phase using a Liquid Crystal SLM in order to preserve light power and efficiently generate heat sources. The appropriate phase pattern (see Fig. 2) is displayed on the SLM located in the Fourier plane of the microscope and illuminated by a plane wave. We use the iterative Gerchberg-Saxton algorithm2, which is one of the most common numerical techniques to calculate . As shown in Fig. 1, this pattern is projected by lens L1, which acts as a Fourier transformer, and imaged in an intermediate plane where a low-pass spatial filter mask cancels unwanted higher diffraction orders. After the lens L2 and the microscope objective, the desired intensity pattern 𝐈 is projected in the substrate plane and generates the temperature distribution ∆𝐓′. Within the chosen domain of interest D, this algorithm provides the targeted temperature map (∆𝐓′ = ∆𝐓). Clearly, since the temperature
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distribution is not constrained outside of D, temperature freely decays in 1/𝑟 due to thermal diffusion outside of D. However, as we only use heat sources (all values in the 𝐐 vector are strictly positive), some desired shapes with temperature gradients steeper than the 1/𝑟 decay imposed by diffusion are impossible to reproduce without resorting to patterned cooling in addition to heating. Temperature decay also appears along the vertical z direction away from the targeted plane, and depends on z and on the lateral size of the target1.
Figure 2 Reconfigurable temperature-shaping workflow (calculated images). 𝑻 is the desired temperature increase distribution; 𝑸 is the associated HSD distribution; 𝚽 is the corresponding phase distribution in the Fourier plane of the illumination pattern; 𝑰 is the light intensity distribution in the sample plane; ∆𝑻′is the resulting temperature increase distribution.
2. Experimental methods In order to efficiently convert optical intensity into heat, the substrate has to be covered with a homogeneous surface absorber, ideally with narrow-band absorption to allow transmission imaging at other wavelengths. We use a substrate consisting of an array of 28 nm diameter spherical gold NPs on a glass coverslip, with uniform quasi-hexagonal distribution, and 72 nm average interparticle distance. The sample was made by diblock copolymer micellar lithography, based on a protocol developed by J. Polleux3. Under illumination at NP resonance wavelength, near = 532 nm, the optical energy drives a resonant movement of the electronic cloud in the gold NP, the plasmon, which is converted into heat by Joule effect in the metal, an efficient process sometimes called thermoplasmonic conversion. This localized heat then diffuses into the surrounding medium, and the non-percolated gold nanoparticles are not expected to substantially change the lateral heat diffusivity of the glass substrate. The plasmonic resonance wavelength of the particles is well adapted to efficient absorption over a relatively narrow band near = 532 nm, and the biocompatibility of the system is excellent4. After photothermal stimulation of the substrate, the local temperature distribution is measured in order to verify the accuracy of the shaping. The refractive index of most materials being 𝑑𝑛
temperature-dependent (the linear approximation 𝛥𝑛 = 𝑑𝑇𝛥𝑇 is usually valid over limited temperature ranges), optical wavefront distortion occurs when crossing the heated sample. We use a shearing interferometry-based Phasics SID4 wavefront sensor5,6 in order to obtain this perturbation, from which the temperature map is deduced7.
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The sample is illuminated by a halogen lamp spectrally filtered around = 407nm (Δλ = 40nm). We use a Köhler illumination with closed aperture diaphragm to maximise the spatial coherence, and illuminate the sample with a plane wave. However, wavefront distortions in the setup need to be considered: a first reference phase image is acquired before any heating is applied, and the measured wavefront is subtracted from subsequent acquisitions in order to extract the thermallyinduced wavefront distortions. The measurements are performed in transmission: as the probe wave propagates through the sample, it accumulates thermo-optically-induced Optical Path Difference (OPD) in the glass 𝑑𝑛
𝑑𝑛
substrate8 (𝑑𝑇 = 3 .10-6 K-1), and a thin layer of glycerol9 (𝑑𝑇 = -2.3 .10-4 K-1). Considering the large difference between these thermo-optical coefficients (2 orders of magnitude), the wavefront distortion in glass is negligible, and only the glycerol layer is considered. The resulting OPD is therefore a result of heat diffusion in the system and the changes it induces in the probe wave. As 𝑑𝑛 ℎ shown in ref7, deconvolution by the Green’s function of OPD, 𝐺𝑂𝑃𝐷(𝜌) = 𝑑𝑇sinh ―1 ( 𝜌) (where 𝜌 is the radial coordinate and ℎ = 1 mm the thickness of the glycerol layer), associated to a Tikhonov regularization gives access to the temperature distribution. This wavefront analyser-based system can therefore give quick access (10 fps) to the temperature distribution of the sample, with a spatial resolution limited by both diffraction (/NA under spatially coherent illumination) and deconvolution inaccuracies. The phase resolution of the wavefront analyser for a single camera frame is 2 nm, which translates into a temperature measurement resolution of the order of 1K and can be improved at the expense of temporal resolution upon averaging. 3 Experimental validation In order to illustrate the possibilities of the method for shaping temperature, we start by imposing either a homogeneous HSD (Fig. 3.b) leading to a non-uniform temperature (fig. 3.e), or an engineered HSD (Fig. 3.f) leading to a uniform temperature (Fig. 3.a and i) over a square region of 40 µm × 40 µm. After calculating and displaying the appropriate phase pattern on the SLM, a uniform light intensity I = 8 µW.µm-2 is sent onto the sample in this square region (Fig. 3.c) and constitutes the HSD (note the speckling effect due to the coherent laser source). As shown in Fig. 3.b-e, a uniform illumination and HSD (Fig. 3.b-c) does not yield a uniform temperature distribution since collective effects induced by heat diffusion lead to higher temperatures at the centre than on the edges of the square (Fig. 3.e). The orange profile in Fig. 3.j clearly shows the bell-shaped thermal response of the system, with a temperature increase varying between 29.4 K and 36.3 K over the heated region. As discussed above, HSD engineering can compensate this effect. Fig. 3.f and g show the theoretical and experimental HSDs which yield a constant temperature rise ∆𝑇 over the square region when imposing I ≤ I0 at any position. As expected, the highest HSD is found near the edges, where lateral heat dissipation is strongest, and the resulting temperature distribution (Fig. 3.i-j) reaches the constant targeted value (∆𝑇 = 25 K) within the designated square region. In both cases (uniform HSD and uniform ∆𝑇), the absolute temperatures profiles are in good agreement with the expected values. The measured inhomogeneities (measured standard deviation: 1.3 K) therefore result from the measurement noise (1K), and possible variations in the local absorption or illumination. Since a coherent source is used to create HSDs, the intensity patterns in Fig. 3.c and g are clearly affected by speckle. Whether this speckle in turn induces inhomogeneity in the temperature distribution is an important question, driven in part by the size of the speckle grain, which varies as /NA, where NA is the numerical aperture used to project the pattern. Due to the limited spatial and thermal resolution of the wavefront analyser, this subtle effect is difficult to characterize
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experimentally. To predict these inhomogeneities, we use the fact that the Gerchberg-Saxton algorithm imposes the intensity (that of the target pattern), but leaves the phase (which is displayed on the SLM) as a free parameter, thus producing after Fourier transformation a speckle pattern representative of the experimental one for a given NA. Fig. 3.k shows temperature profiles obtained by convolving the Fourier transform of Gerchberg-Saxton solutions for various NA values with the thermal Green’s function7 𝐺𝑇, thus producing realistic, speckle-affected temperature profiles. For a low NA = 0.2, temperature variations are clearly visible, with a relative error
𝜎∆𝑇 ∆𝑇
= 2%. However, high-
spatial-frequency variations are smoothed out by heat diffusion, and the relative variations quickly fall below 1% as the speckle grain size decreases, becoming negligible in practice for NA > 0.5, as shown in Fig. 3.l. In our experiment, we used microscope objectives with NA = 0.85 (Olympus, UPlanSApo, 20x) or NA = 1.42 (Olympus, oil immersion Plan Apo N 60x) to minimize this effect. Several strategies can be proposed to reduce this speckle and improve temperature homogeneity in applications where NA is constrained to low values. Experimentally, speckle scrambling using e.g. a rotating diffuser is of course possible if time-resolution is not an issue. Alternatively, it is possible to improve the Gerchberg-Saxton algorithm by removing optical vortices responsible for intensity zeros. Such a control of both phase and intensity at the sample requires modulating both phase and amplitude in the Fourier plane which comes at the expense of critical optical power losses10 or by increasing complexity11. For low T values (in e.g. biological applications), measurements with a wavefront sensor limited to 1K resolution will become difficult. Nevertheless, the precision of the temperature shaping should remain satisfactory since it is driven only by laser noise (typ. 5%), local absorption variations (
