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The direct observation of nanoscale objects is a challenging task for optical microscopy because the scattering from an individual nanoparticle is typically weak at optical wavelengths. Electron microscopy therefore remains one of the gold standard visualization methods for nanoparticles, despite its high cost, limited throughput and restricted field-of-view. Here, we describe a high-throughput, on-chip detection scheme that uses biocompatible wetting films to self-assemble aspheric liquid nanolenses around individual nanoparticles to enhance the contrast between the scattered and background light. We model the effect of the nanolens as a spatial phase mask centred on the particle and show that the holographic diffraction pattern of this effective phase mask allows detection of sub-100 nm particles across a large field-of-view of >20 mm2. As a proof-of-concept demonstration, we report on-chip detection of individual polystyrene nanoparticles, adenoviruses and influenza A (H1N1) viral particles.
Nanoscale objects are difficult to visualize directly using optical techniques because of their small size compared to the optical wavelength, resulting in a weak scattering signal from individual nanoparticles. To mitigate this challenge, various techniques1–20 have been used for imaging sub-100 nm particles and viruses, including near-field optical microscopy1–4, super-resolution microscopy5–8,19,20, atomic force microscopy9,10, electron microscopy11–14 and other recently developed imaging techniques15–18. While generally providing excellent resolution, all of these existing approaches for imaging individual nanoparticles are relatively bulky and low throughput, with a limited imaging field-of-view (FOV), typically less than 0.2 mm2 without mechanical scanning. These limitations pose challenges for the detection and enumeration of sparse nanoscale objects, such as viral particles at low concentrations. This can be particularly critical in early-stage disease diagnosis in point-of-care settings or resource-limited environments, which ideally demand field-portable, cost-effective and wide-field imaging and detection modalities.
Here, we introduce a compact, cost-effective and high-throughput optical microscopy technique that can detect individual sub-100 nm particles and moderately sized viruses across an ultralarge FOV of, for example, 20.5 mm2 (Fig. 1a). Unlike some of the alternative techniques listed above, our technique does not circumvent the optical diffraction limit to boost spatial resolution and therefore cannot serve as a replacement for an ultrahigh-resolution microscopy modality, but instead it dramatically improves the signal-to-noise ratio (SNR) and contrast to enable detection of single nanoparticles over a very large FOV. At the heart of our approach lie two complementary techniques: (i) self-assembled liquid nanolenses and (ii) lensfree computational microscopy on a chip21–27. Note here that the term ‘lensfree’ refers to the lack of an ‘imaging’ lens or its equivalent between the sample and the sensor planes; that is, these self-assembled liquid nanolenses or the microlenses installed on each pixel of an optoelectronic sensor array are not considered as ‘imaging’ lenses. Using a sample preparation technique that only involves portable equipment and non-toxic chemicals, liquid nanolenses are assembled around each nanoparticle seated on a hydrophilic surface (Fig. 1b,c). These liquid lenses are composed of a biocompatible buffer that is stable for more than an hour at room temperature without significant evaporative loss. This buffer helps to prevent nanoparticle aggregation while also acting as a spatial phase mask that relatively enhances the lensfree diffraction signature of the embedded nanoparticle/nanolens assembly, as explained by our fluid and optical models of the system. Liquid film coatings with different compositions and sample preparation methods have been previously used in conjunction with optical microscopy; however, these earlier methods used thick (for example, ~1 μm) and continuous films rather than isolated nanolenses self-assembled around individual particles, as a result of which they could not detect single nanoparticles smaller than ~0.5–1 μm in width or diameter21,28.
One of the most appropriate optical techniques to image such nanoscale objects is holography, because it converts the phase information into intensity oscillations through a heterodyne detection gain. We therefore used partially coherent lensfree digital in-line holography21–27,29–35 to sample the interference between the unscattered background light and the far-field diffraction patterns of individual nanolens/nanoparticle complexes using an optoelectronic sensor array (Fig. 1a). Because this platform operates under unit magnification without the use of any imaging lenses, its object FOV is equal to the active area of the sensor array, easily reaching, for example, 20–30 mm2 using the state-of-the-art complementary metal oxide semiconductor (CMOS) imaging chips that are now commonplace in modern cellphones26,27, or 10–20 cm2 with charge-coupled device (CCD) imaging chips (see, for example, Supplementary Figs S1,S2). The native resolution of these optoelectronic chips and the SNR of holographically reconstructed images can be further improved by pixel super-resolution techniques19,20,36–38. Here, we implement pixel super-resolution by source shifting23,24,26, as illustrated in Fig. 1a. This technique captures several lensfree diffraction holograms from the same nano-particle, where the partially coherent light source is shifted in small increments, on the order of, for example, 0.1 mm. A single pixel super-resolved holographic image is then synthesized from these sub-pixel shifted holograms, and is finally reconstructed to yield phase and amplitude images of the individual nanoparticles together with their surrounding self-assembled liquid lenses.
These self-assembled nanolenses are generated using a sample preparation procedure that is described in Fig. 1c. In our experiments, we worked with concentrated nanoparticle solutions (polystyrene beads, Corpuscular), as well as cultured influenza A (H1N1) viral particles and adenoviruses, diluted in 0.1 M Tris-HCl with 10% polyethylene glycol (PEG) 600 buffer (Sigma Aldrich). We then prepared a hydrophilic substrate by plasma-treating a glass coverslip using a portable and lightweight plasma generator for ~5 min, which is a critical step in enabling self-assembled liquid nanolens formation.
Immediately after plasma treatment, a 5–10 μl droplet of the dilute nanobead/virus suspension was transferred to the centre of the hydrophilic glass substrate (Fig. 1c,i). The sample was held flat for 3 min to allow for partial sedimentation of the nanoparticles, and then tilted with a slope of 3–5° so that gravity slowly drove the droplet towards the edge of the substrate with an average speed of less than 1 mm s−1 (Fig. 1c,ii). A sparse monolayer of nanoobjects with surrounding liquid lenses remained in the wake of the droplet (Fig. 1c,iii). Once the droplet reached the edge of the substrate, the excess fluid was removed by tilting the sample at an angle of 15–20° (Fig. 1c,iv). Following this last step, the nanoparticle/virus sample was then flipped through 180° and placed onto a CMOS sensor array for lensfree holographic image acquisition (Fig. 1a and c,v). At this point, the remaining fluid volume in each nanolens was so small that its three-dimensional geometry was mainly determined by surface tension, making the effect of gravity negligible. In other words, this final 180° rotation step does not affect the nanolens geometry. This entire sample preparation process takes less than 10 min and is performed without the use of a cleanroom.
After sample preparation, lensfree holographic image acquisition was performed using either only the green pixels of a 16 megapixel colour (RGB) CMOS chip or a large-area monochrome CCD chip (Supplementary Figs S1,S2). The sample was illuminated with a quasi-monochromatic fibre-coupled light source located at Z1 = 8–12 cm above the sensor array, as shown in Fig. 1a. For further miniaturization and field portability, the light source can also be a single light-emitting diode (LED) or an array of LEDs, enabling a compact microscopy architecture as demonstrated in our earlier work22,23,26. Because of the small object-to-sensor distance, as shown in Fig. 1a (Z2 ≈ 300 μm), the spatial coherence, temporal coherence and illumination alignment requirements for our microscopy setup are all relaxed, significantly reducing the speckle and multiple reflection noise artefacts over the entire active area of the CMOS array. On the other hand, because of unit magnification and the finite CMOS pixel size (1.12 μm), individual lensfree holograms are undersampled, partially limiting the achievable spatial resolution and SNR. To mitigate this limitation, we implemented a pixel super-resolution technique, which digitally merges multiple holographic images that are shifted with respect to one another by sub-pixel pitch distances into a single high-resolution image23,24. Discrete source shifts of ~0.1 mm translate to sub-micrometre hologram shifts at the detector plane due to the large Z1 to Z2 ratio of >200. These pixel super-resolved high-resolution holograms were then used to digitally reconstruct the complex object field at the sample plane using iterative phase retrieval techniques to eliminate twin image noise and obtain higher SNR microscopic images of the sample23,24 (see Supplementary Methods). As shown in Figs 2 and and33 and Supplementary Fig. S1, this reconstruction process is robust even at distant regions on the sensor array.
The effect of the number of holographic frames used for pixel super-resolution on the contrast and SNR of our nanoparticle images is characterized in the lower set of panels in Fig. 3. In these experiments, various lensfree holographic images of 95 nm beads were reconstructed from pixel super-resolved images synthesized using, for example, 1, 4, 8, 16, 36 and 64 sub-pixel shifted holographic frames, respectively. Reconstruction of a single lensfree frame did not provide any satisfactory result for detection of these 95 nm particles, whereas increasing the number of holographic frames used in our pixel super-resolution algorithm significantly enhanced the contrast and the SNR of individual nanoparticles (Fig. 3). Similar results were also obtained for 198 nm beads (Supplementary Fig. S7).
The combination of self-assembled liquid nanolenses and holographic computational on-chip microscopy enables the detection of individual sub-100 nm particles (Figs 2–4) that are not visible with holographic imaging techniques alone, and have extremely low contrast even under conventional oil-immersion objective lenses (for example, with a numerical aperture (NA) of 1.25). As an example, we demonstrate in Fig. 4 that without the nanolenses, neither 198-nm- nor 95-nm-diameter polystyrene beads provide a signal above the background noise level in our lensfree holographic microscopy setup. However, with the formation of the above discussed nanolenses, these nanoparticles become clearly visible in both phase and amplitude reconstructions, as illustrated in Fig. 4 (Supplementary Figs S1–S8). Both with and without the liquid lenses, the presence of the nanoparticles on the substrate is confirmed in these experiments using oil-immersion bright-field microscopy, although the contrast and SNR of these images are rather low despite the use of a high-power objective lens (×100, NA = 1.25; Fig. 4). On the other hand, using lensfree on-chip microscopy, the contrast of the same nanoparticles is significantly improved (Fig. 4) after the formation of the nanolenses, which act as spatial phase masks enhancing the diffraction holograms of individual nanoparticles.
This contrast enhancement observed in our experiments is also supported by our fluid and optical system models. To shed more light on our observations, we begin by modelling the shape of the nanolens meniscus around each nanoparticle using the Young–Laplace equation39–41:
where Δp is the over-pressure within the meniscus, ρ is the fluid density, g is the gravitational acceleration constant, h is the height of the meniscus, γ is the surface tension and 1/R1 and 1/R2 are the curvatures of the meniscus along its two principal directions. The Young–Laplace equation holds in general at length scales greater than a few tens of nanometres; below this scale, additional forces such as dispersion, van der Waals, steric or electrostatic forces must also be taken into account41,42.
We can non-dimensionalize equation (1) by the characteristic pressure , which presents the capillary length scale :
For water, c ≈ 2 mm, while for aqueous PEG solutions such as ours the surface tension can be a factor of two smaller over a wide range of concentrations with similar density, making the capillary length shorter but still of roughly millimetre length43. The overpressure in the film, Δp, is coupled to the volume of the fluid surrounding the nanoparticle, and is determined by the formation process of the liquid nanolenses. As the fluid slowly drains due to the <5° tilt applied during sample preparation, the sparse nanoparticles pin the receding contact line until the surface tension of the fluid in contact with a nanoparticle can no longer support the hydrostatic pressure of the deformed contact line, at which point the fluidic bridge between the nanoparticle and the bulk receding contact line ruptures44–46. The maximum extent of the contact line deformation before rupture is on the order of the nanoparticle size47. Therefore the overpressure in the film immediately before and after rupture is on the order of ρgRp, which makes of order Rp/c ≈ 1 × 10−4. Note also that the gravitational term h/c is of the same order. However, the curvature terms are of order c/Rp ≈ 1 × 104. From this scaling analysis, we find that we are in the low Bond number limit where only the curvature terms are significant40. It is important to note that this approximation, Δp ≈ 0, neglects the rapid rupture process, where the fluid bridge pinches off and additional overpressure may be introduced. However, quantifying this effect requires numerical fluid dynamic simulations47,48 that are beyond the scope of this manuscript. More importantly, with the Δp ≈ 0 approximation, we find good agreement with our nanoparticle detection experiments.
where r = r(z) is the radial coordinate of the meniscus at an elevation z above the substrate, and primes indicate derivatives with respect to z. The general solution to this nonlinear second-order ordinary differential equation can be written as a hyperbolic cosine:
We refer to this last equation as the ‘nanolens equation’, which is used to determine the three-dimensional geometry of the self-assembled liquid lens around each nanoparticle. In this equation, a and b are constants that are determined by the contact angle at the particle (θp), the contact angle at the substrate (θs), as well as the particle radius Rp:
where z0 is the elevation of the meniscus–particle contact line and β(z0) is defined as
The elevation z0 of the contact line can be determined by numerically solving the following transcendental equation derived from the intersection between the spherical particle surface and the meniscus shape, resulting in
The particle diameter Rp linearly scales with both the height and lateral extent of the meniscus, but does not affect its shape or aspect ratio. Although both θs and θp influence all aspects of the meniscus shape, θs most significantly affects the radial extent of the meniscus, while θp moderately affects its thickness.
Some representative solutions of nanolens equation (4) for different contact angles are shown in Fig. 1b,i–iii. The measured contact angle of a ~1-mm-radius droplet on a plasma-treated glass coverslip is θs = 10°, and the measured contact angle on a polystyrene surface is θp = 50°. We use these macroscopic contact angles as nominal values for the microscopic system in Fig. 1b,i as we cannot directly measure the contact angles at our size scale. Small variations in contact angles can affect the aspect ratio of the meniscus, as illustrated in Fig. 1b,ii and iii, but do not alter its general shape. The scanning electron microscopy (SEM) image shown in Fig. 1b,iv is typical of the nanolens after it has been desiccated by the vacuum required in SEM sample preparation. Although the original shape of the liquid film has not been preserved because of the vacuum, it is clear that the liquid residue from the film only extends a distance on the order of the particle diameter, in good agreement with our model predictions (for example, see the curve in Fig. 1b,iv).
To evaluate the optical effects of each nanolens on the recorded lensfree holograms of the nanoparticles, we use two numerical models: (i) a finite-difference time-domain (FDTD) simulation followed by Rayleigh–Sommerfeld wave propagation and (ii) a thin-lens model followed by Rayleigh–Sommerfeld wave propagation. In the FDTD model (Fig. 1b) we simulate the particle (np = 1.61)49, the nanolens (nf = 1.35)50 and the substrate (ns = 1.52) within a simulation volume of 20 × 20 × 5 μm3, calculating the amplitude and phase of the transmitted optical field 3 μm beyond the glass–air interface; that is, no evanescent waves are considered as our detection occurs beyond the near-field. These results are then substituted at the centre of a larger (100 × 100 μm2) homogeneous field (that is, uniform plane wave) that is numerically propagated a distance of 297 μm (Z2 − 3 μm), resulting in a simulated lensfree diffraction hologram. In the thin lens model, however, we ignore three-dimensional scattering and represent the particle and its surrounding nanolens as a single two-dimensional phase-only object whose phase delay as a function of the radial coordinate is the free-space wavenumber k0 times the line integral of the optical path length in z through the entire depth of the materials at that coordinate (Supplementary Fig. S9). For both of these optical models, the nanolens equation (4), described above, is used to estimate the three-dimensional geometry of the liquid lens that forms around each nanoparticle.
To provide a fair comparison to our experimental results, we downsample the numerically generated lensfree holograms to a super-resolved effective pixel size (that is, 0.28 μm), then add randomly generated Gaussian noise to each hologram and quantize the pixel values to 10-bit levels. In Fig. 5, these numerically generated noisy holograms are used to attempt to reconstruct 95 nm particles with and without nanolenses. For both the FDTD and thin-lens models, the nanolenses significantly improve the image contrast such that the nanoparticle can be clearly distinguished from the background noise in both the amplitude and phase reconstructions. Without the liquid nanolens, however, the same numerical models reveal that the signature of the 95 nm particle is effectively lost within the background noise (Fig. 5), also agreeing with our experimental observations in Fig. 4. A more detailed comparison between the experimental and theoretical nanolens phase functions is illustrated in Supplementary Fig. S10, which provides an independent verification of the nanolens shape predicted by our theoretical analysis. Furthermore, a numerical study of the effects of the nanolens film properties (such as refractive index, extinction coefficient, substrate contact angle) is also presented in Supplementary Fig. S11, shedding more light on the detection limits of our approach.
Finally, using the same lensfree platform we demonstrated computational on-chip detection of single H1N1 virus particles and sub-100 nm adenoviruses (Fig. 6). Different super-resolved holographic regions of interest were digitally cropped from a much larger FOV (20.5 mm2) for these virus samples, and were then digitally reconstructed to yield both lensfree amplitude and phase images of the viral particles. For comparison, ×100 oil-immersion objective (NA = 1.25) and SEM images of the same samples are also shown, which match our reconstructed images very well. For the particularly small adenoviruses, we find phase reconstructions perform better than amplitude images, as they exhibit greater SNR and contrast.
In conclusion, we have introduced a compact, cost-effective and high-throughput computational on-chip microscopy technique that can detect individual sub-100 nm particles and viruses across an ultralarge FOV of 20.5 mm2, that is, more than two orders of magnitude larger than other nanoimaging techniques. Through a wetting film-based method that induces self-assembled liquid nanolenses around individual particles, we reconstruct both amplitude and phase images of single nanoparticles that are otherwise undetectable with on-chip microscopy. The enhancement provided by the self-assembled nanolenses is well understood through analytical models of the liquid meniscus shape and numerical models of its contribution to the optical diffraction signal.
Samples were received as concentrated nanoparticle solutions (polystyrene beads, Corpuscular) as well as cultured influenza A (H1N1) viral particles and adenoviruses, which were fixed using 1.5% formaldehyde. The virus specimens, with an initial density of 100,000 μl−1, were centrifuged at ~25,000g, and the supernatant was separated and filtered using a syringe filter with a pore size of 0.2 μm to remove larger contaminations and clusters. Small volumes of concentrated nanobead or virus solutions were then diluted at room temperature using 0.1 M Tris-HCl with 10% PEG 600 buffer (Sigma Aldrich), and were sonicated for ~2 min so that the final concentration was >20,000 μl−1. We then prepared a hydrophilic substrate by cleaning a 22 mm × 22 mm glass coverslip (Fisher Scientific) with isopropanol and distilled water, then plasma-treating it using a portable and lightweight plasma generator (Electro-Technic Products, BD-10AS) for ~5 min.
Lensfree holographic image acquisition was performed using only the green pixels of a 16-megapixel colour (RGB) CMOS chip (Sony) or a monochrome 39-megapixel CCD chip (Kodak). The sample was illuminated with a quasi-monochromatic light source with a central wavelength of 480 nm and a spectral bandwidth of ~3 nm, coupled to a multimode fibre (core size, 0.1 mm), the end of which was located at Z1 = 8–12 cm above the sensor array, as shown in Fig. 1a.
For details regarding image processing, see Supplementary section, ‘Computational Methods’.
Supplementary Figure 1 | Ultra-wide field CCD-based lensfree detection of 200 nm particles using self-assembled nano-lenses. We illustrate lensfree microscopy of 200 nm particles over a wide FOV of 37 mm × 25 mm, that is approximately one-half of the active area of a 39 megapixel CCD chip (KAF-39000, Kodak, 6.8 μm pixel size). The black marks within this FOV (top left) are placed to ease finding the corresponding 60X objective lens (NA=0.85) images of the nano-particles. This FOV is more than 45 fold larger than the CMOS sensor-array (5.2 mm × 3.9 mm) used in the main text. However the larger pixel size, i.e., 6.8 μm (CCD) vs. 1.1 μm (CMOS), also makes it more challenging to sample and detect the lensfree signatures of nano-particles. The reconstruction process here is similar to that used with the CMOS sensor with minor adjustments because the CCD is monochrome, while the CMOS has a Bayer colour pattern. The implementation of pixel super-resolution results in an effective pixel count of more than 0.75 gigapixels across this FOV. a1 and b1 were digitally cropped from A and B, respectively, which were also cropped from the much larger image FOV (37 mm × 25 mm). Lensfree raw holographic images as well as their pixel super-resolved counterparts for a1 and b1 are shown together with their amplitude and phase reconstructions. Iterative twin image (TI) elimination algorithm described in [1,2] was utilized to suppress the TI noise of reconstructed particles. Arrows point out the locations of 200 nm particles in holographic reconstructions as well as their corresponding objective lens images. Note that some of the stationary particles visible in microscope comparison images are located on the objective lens, not on the samples. Red scale bars in a1 and b1 are 20 μm.
Supplementary Figure 2 | CCD-based lensfree detection of 100–150 nm particles using self-assembled nano-lenses. Similar to Supplementary Figure 1, various nanoparticles with sizes ranging for example between 100 nm and 150 nm are imaged using a wide-field CCD chip (KAF-39000, Kodak, 6.8 μm pixel size, full field-of-view: ~18 cm2). The much larger pixel size (~6.8 μm) when compared to the CMOS imager (which has ~1.1 μm wide pixels) makes it more difficult to detect lensfree images of individual nanoparticles; however, the reconstructed images, especially the phase image, provide a decent contrast for these nanoparticles. Same as in Supplementary Figure 1, some of the stationary particles visible in the microscope comparison image are located on the objective lens, not on the samples. To digitally clean such objective lens artefacts, we also show a background subtracted microscope image to better illustrate the locations of the nanoparticles on the sample, providing a decent match to our lensfree reconstructions. SEM comparisons are also provided for some of the particles within the same field of view; unless otherwise mentioned, all the numbers noted in these SEM images refer to the diameter of the corresponding nanoparticle. White scale bars: 20 μm; Blue scale bars: 5 μm.
Supplementary Figure 3 | Additional reconstructions and corresponding SEM verifications from the same heterogeneous nano-bead sample as in Figs. 2 and and33 of the main text. Red arrows are used to locate the ≤ 100 nm beads, whereas blue arrows point out the beads having diameters between 100 nm and 150 nm. Please also note that the lensfree reconstructed image was digitally cropped from a much larger field of view (i.e., > 20 mm2 – active area of the CMOS sensor-array).
Supplementary Figure 4 | Additional reconstructions and corresponding SEM verifications from the same heterogeneous nano-bead sample as in Figs. 2 and and33 of the main text. Red arrows are used to locate the ≤ 100 nm beads, whereas blue arrows point out the beads having diameters between 100 nm and 150 nm. This region of interest partially overlaps with that of Supplementary Figure 3 (overlapping regions are denoted with asterisks). Please also note that this lensfree reconstructed image was digitally cropped from a much larger field of view (i.e., >20 mm2 - active area of the CMOS sensor-array).
Supplementary Figure 5 | Additional reconstructions and corresponding SEM verifications from the same heterogeneous nano-bead sample as in Figs. 2 and and33 of the main text. Red arrows are used to locate the ≤ 100 nm beads, whereas blue arrows point out the beads having diameters between 100 nm and 150 nm. The holographic artefact of an out-of-focus object is also seen within the reconstructed image, although it does not cause issues for visualization of the nano-particles at the image plane. Please also note that this lensfree reconstructed image was digitally cropped from a much larger field of view (i.e., >20 mm2 - active area of the CMOS sensor-array).
Supplementary Figure 6 | Additional reconstructions and corresponding SEM verifications from the same heterogeneous nano-bead sample as in Figure 2 of the main text. This region of interest is an enlarged and rotated version of that presented in Figure 2 of the main text. Red arrows are used to locate the ≤ 100 nm beads, whereas blue arrows point out the beads having diameters between 100 nm and 150 nm. Please also note that this lensfree reconstructed image was digitally cropped from a much larger field of view (i.e., >20 mm2 - active area of the CMOS sensor-array).
Supplementary Figure 7 | SNR and contrast enhancement via pixel super-resolution. Lensfree pixel super-resolution images of 198 nm beads are synthesized using sub-pixel shifted lower resolution holographic frames. Refer to Fig. 3 of the main text for similar results on 95 nm particles.
Supplementary Figure 8 | On-chip detection of nano-particles using liquid nano-lenses. 198 nm and 95 nm beads are imaged on a CMOS chip using self-assembled liquid nano-lenses.
Supplementary Figure 9 | Simulated optical fields for a 95 nm particle with surrounding nano-lens. (a) Under the thin-lens model, the object does not introduce any amplitude modulation. (b) The large phase modulation from the bead and the more subtle modulation from the surrounding nano-lens are indicated. A 20 nm grid resolution is used to numerically model the system. (c) and (d) Amplitude and phase of the thin-lens object after a free-space propagation of 3 μm. (e) and (f) FDTD-modelled amplitude and phase recorded 3 μm after the glass-air interface, within the air gap between the sample and the sensor. Because of the limited FDTD domain, the fields are truncated at a radius of 6.5 μm. Within this region, there is very good agreement between FDTD and the thin-lens models. (g–j) Simulated amplitude and phase reconstructions from the two models agree very well. These reconstructions are a subset of those presented in Fig. 5 of the main text, and are obtained by propagating the fields to z = 300 μm, adding Gaussian noise with standard deviation 1% of the mean hologram intensity, quantizing to 10-bit intensity levels, downsampling to a super-resolved pixel size of 0.28 μm, and finally back-propagating −300 μm to z = 0 μm.
Supplementary Figure 10 | Experimental and theoretical phase profiles of nano-lenses. (a) shows the comparison between the experimentally reconstructed phase profiles (thin lines) and two different models (thick lines), based on the SEM bead size measurements in Supplementary Figure 3. Beads in the range 60 nm to 140 nm (mean value 110 nm) are coloured red. Beads in the range 160 nm to 245 nm (mean value 200 nm) are coloured green. Beads in the range 310 nm to 360 nm (mean value 330 nm) are coloured blue. Thick dashed lines show the thin-lens phase profile predicted by the Nano-lens Equation (Eq. 4 in main text) using contact angles θp = 50°, θs = 2.5° (θs is an adjustable parameter here, but is consistent with the very small macroscopic contact angle measured using a sessile drop). Thick solid lines show the theoretically propagated and reconstructed thin-lens phase profiles. Propagation and reconstruction (solid lines) reduce the axial phase value when compared to the Nano-lens equation (thick dashed lines) near the centre of the particle due to diffraction; however, the phase profiles in the wings of the nano-lenses are maintained as illustrated in this figure. The theoretically predicted reconstructions agree well with experimental curves, validating the mathematical form of the Nano-lens Equation (Eq. 4 in main text). (b) shows a comparison between the theoretically propagated and reconstructed bead + nano-lens profiles from (a) (solid thick lines) and the much weaker theoretically propagated and reconstructed profiles for beads alone “without” the nano-lenses (thin dot-dashed lines).
Supplementary Figure 11 | Theoretical effects of nano-lens properties and illumination wavelength on particle detectability. (a) Nano-lenses composed of absorbing or scattering films can increase the signal-to-noise ratio (SNR), making particles with surrounding nano-lenses (NL) easier to detect via both amplitude and phase reconstructions. (b) When the nano-lens is more wetting (smaller contact angle), larger lenses form, making particles easier to detect. (c) Higher refractive nano-lenses generate a stronger signal, making particle detection easier. All amplitude reconstructions without nano-lenses show SNR < 2dB here. (d) Shorter wavelength illumination provides better SNR on average due to improved resolution. Background shading indicates particle detectability with a detection threshold between 9 and 12 dB. The insets in (b) show the amplitude reconstructions for three points in the vicinity of this detection threshold. (a) and (b) assume a polystyrene particle size of 50 nm, while (c) and (d) assume a particle size of 75 nm. For all data in a given subplot, an identical, randomly-generated 1% Gaussian noise field is added at the hologram plane. In (a–c), this noise field results in identical noise fields at the reconstructed image plane and therefore smooth curves, as the reconstruction distance (z2 = 100 μm here) and wavelength (λ = 480 nm) are the same for each data point. In (d), however, the wavelength is different for each data point, resulting in different reconstructed noise fields and the large scatter in SNR. Unless a parameter is being explicitly varied, all simulations assume a purely real film refractive index of 1.35, and a substrate contact angle of 10°.
Ozcan Research Lab acknowledges the support of the Army Research Office Young Investigator Award, the Presidential Early Career Award for Scientists and Engineers (PECASE), an NSF CAREER Award, an Office of Naval Research Young Investigator Award and the National Institutes of Health (NIH) Director’s New Innovator Award (DP2OD006427) from the Office of The Director, NIH. The work at CEA-Leti was supported by the Carnot Institutes Network. The authors thank Hangfei Qi and Ren Sun of UCLA for H1N1 and adenovirus specimens.
Author contributionsO.M. performed the experiments and processed the resulting data. E.M. developed the theory and conducted numerical simulations and the related analysis. E.M., W.L., A.G and A.F.C. assisted in conducting the experiments and data analysis. O.M., E.M., Y.H., C.P.A. and A.O. planned the research and O.M., E.M. and A.O. wrote the manuscript.
A.O. supervised the project.
Supplementary information is available in the online version of the paper.
Reprints and permissions information is available online at www.nature.com/reprints.
Competing financial interests
Aydogan Ozcan is the co-founder of a start-up company that aims to commercialize lensfree microscopy tools.