Super-Resolution Imaging of a Dielectric Microsphere Is Governed by the Waist of Its Photonic Nanojet

Dielectric microspheres with appropriate refractive index can image objects with super-resolution, that is, with a precision well beyond the classical diffraction limit. A microsphere is also known to generate upon illumination a photonic nanojet, which is a scattered beam of light with a high-intensity main lobe and very narrow waist. Here, we report a systematic study of the imaging of water immersed nanostructures by barium titanate glass microspheres of different size. A numerical study of the light propagation through a microsphere points out the light focusing capability of microspheres of different size and the waist of their photonic nanojet. The former correlates to the magnification factor of the virtual images obtained from linear test nanostructures, the biggest magnification being obtained with microspheres of similar to 6-7 mu m in size. Analyzing the light intensity distribution of microscopy images allows determining analytically the point spread function of the optical system and thereby quantifies its resolution. We find that the super-resolution imaging of a microsphere is dependent on the waist of its photonic nanojet, the best resolution being obtained with a 6 mu m empty set microsphere, which generates the nanojet with the minimum waist. This comparison allows elucidating the super-resolution imaging mechanism.

Super-resolution fluorescence microscopy based on physical models

François Aguet

This thesis introduces a collection of physics-based methods for super-resolution in optical microscopy. The core of these methods constitutes a framework for 3-D localization of single fluorescent molecules. Localization is formulated as a parameter estimation problem relying on a physically accurate model of the system's point spread function (PSF). In a similar approach, methods for fitting PSF models to experimental observations and for extended-depth-of-field imaging are proposed. Imaging of individual fluorophores within densely labeled samples has become possible with the discovery of dyes that can be photo-activated or switched between fluorescent and dark states. A fluorophore can be localized from its image with nanometer-scale accuracy, through fitting with an appropriate image function. This concept forms the basis of fluorescence localization microscopy (FLM) techniques such as photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which rely on Gaussian fitting to perform the localization. Whereas the image generated by a single fluorophore corresponds to a section of the microscope's point spread function, only the in-focus section of the latter is well approximated by a Gaussian. Consequently, applications of FLM have for the most part been limited to 2-D imaging of thin specimen layers. In the first section of the thesis, it is shown that localization can be extended to 3-D without loss in accuracy by relying on a physically accurate image formation model in place of a Gaussian approximation. A key aspect of physically realistic models lies in their incorporation of aberrations that arise either as a consequence of mismatched refractive indices between the layers of the sample setup, or as an effect of experimental settings that deviate from the design conditions of the system. Under typical experimental conditions, these aberrations change as a function of sample depth, inducing axial shift-variance in the PSF. This property is exploited in a maximum-likelihood framework for 3-D localization of single fluorophores. Due to the shift-variance of the PSF, the axial position of a fluorophore is uniquely encoded in its diffraction pattern, and can be estimated from a single acquisition with nanometer-scale accuracy. Fluroescent molecules that remain fixed during image acquisition produce a diffraction pattern that is highly characteristic of the orientation of the fluorophore's underlying electromagnetic dipole. The localization is thus extended to incorporate the estimation of this 3-D orientation. It is shown that image formation for dipoles can be represented through a combination of six functions, based on which a 3-D steerable filter for orientation estimation and localization is derived. Experimental results demonstrate the feasibility of joint position and orientation estimation with accuracies of the order of one nanometer and one degree, respectively. Theoretical limits on localization accuracy for these methods are established in a statistical analysis based on Cramér-Rao bounds. A noise model for fluorescence microscopy based on a shifted Poisson distribution is proposed. In these localization methods, the aberration parameters of the PSF are assumed to be known. However, state-of-the-art PSF models depend on a large number of parameters that are generally difficult to determine experimentally with sufficient accuracy, which may limit their use in localization and deconvolution applications. A fitting algorithm analogous to localization is proposed; it is based on a simplified PSF model and shown to accurately reproduce the behavior of shift-variant experimental PSFs. Finally, it is shown that these algorithms can be adapted to more complex experiments, such as imaging of thick samples in brightfield microscopy. An extended-depth-of-field algorithm for the fusion of in-focus information from frames acquired at different focal positions is presented; it relies on a spline representation of the sample surface and as a result yields a continuous and super-resolved topography of the specimen.

EPFL2009

Extended Focus Optical Coherence Microscopy

Martin Villiger

Optical coherence tomography (OCT) is an interferometric imaging technique that can provide depth resolved cross-sectional views of biological tissue. OCT employs light with low temporal and yet high spatial coherence. The sample is illuminated point by point and raster scanned in the lateral directions. Part of the incident light is back-scattered by differences in the tissue refractive index and combined with a strong reference signal. The detection in the Fourier, or frequency domain (FDOCT), separates the interference signal spectrally and records the resulting pattern with a line camera. Processing of this pattern extracts the sample structure along the axial direction but without axial scanning and in parallel with high resolution of 2-3 µm. The interferometric detection conveys a very high sensitivity that allows imaging several hundred micrometers deep into the tissue. A single two dimensional scan thus can extract the three dimensional structure of the object, resulting in very high volume acquisition rates and offering an exceptional speed advantage over other optical imaging methods. Combined with its ability to measure an intrinsic sample property without the need of adding extrinsic labels or contrasting agents, FDOCT has become a confirmed tool for minimally invasive in vivo measurements and comprehensive volumetric imaging. While the axial resolution in OCT is defined by the coherence length of the employed light source, it is the optical focusing that specifies the resolution in the lateral direction, which reaches in general only approximately 10 µm. To improve the resolution, classical optical coherence microscopy (OCM) uses higher numerical apertures. However, this implies a reduction of the lateral dimension of the focal spot which leads to a dramatic decrease in the depth of field (DOF). This imposes a severe limitation on FDOCT's parallel depth extraction. Therefore, the motivation behind this thesis work was to circumvent the compromise between the lateral resolution and the depth of field by engineering an extended focal volume (xf). Combining FDOCT's assets of speed and sensitivity with the high lateral resolution of microscopy provided a very promising tool for rapid in vivo imaging at close to cellular resolution. To study the mechanisms limiting the DOF and to investigate what impact they have on the tomogram reconstruction process, we developed a model for image formation in FDOCT. Generally, the tomogram is reconstructed from the two dimensional interference patterns in the individual spectral channels of the detection. By making use of the coherent transfer functions (CTF), the spatial frequency content made accessible by each channel, was analyzed. This provided a novel perspective on the entire tomogram formation. We were able to show that the out-of-focus structures suffer from two signal degrading mechanisms. First, a de-focusing effect, induced by additional phase arguments in the spatial frequency domain provokes a lateral blurring. Second, the setup's reduced transmission efficiency for out-of-focus structures results in an amplitude scaling. The application of the CTF enabled us to illustrate the intrinsic link between these two effects and to develop optical design strategies and novel configurations to circumvent their detrimental impact on the quality of the tomogram. It is known that with the use of a conical lens, it is possible to produce a so-called diffraction-less beam. Close to the optical axis, the radial envelope of its field amplitude follows a Bessel function of order zero and is maintained upon propagation over a long axial range. We could show that a combination of such a Bessel-like beam with a Gaussian detection indeed limits both the de-focusing and amplitude scaling phenomenon, all the while improving the lateral resolution. The price to pay is a reduced signal amplitude also at the in-focus position, as compared to a Gaussian focal volume of a classical confocal setting. Another possibility is to combine the Bessel-like illumination with a Bessel-like detection, although with differently spaced side lobes in its envelope. These different combinations were evaluated both analytically and with computer simulations. Several of the proposed solutions were implemented in practice to confirm the theoretical predictions. Considering that the theoretical analysis was performed in the spatial frequency domain and in terms of the CTF, the corresponding system parameters had to be measured. Lacking an adequate technique, we developed and validated a method which derived characteristic parameters of the optical system's CTF from the measurement of a simple rubber surface. The tomogram of this sample consists of a fully developed speckle field. Although generally disfavored for degrading the tomogram quality, in this case the speckle shape provided information on the system characteristics because it was imposed by the illumination and detection apertures of the system in question. Since the principal interest behind the development of xfOCM was its amenability to live imaging, we used this novel concept to visualize individual islets of Langerhans in a mouse pancreas. These endocrine islets are assemblies of insulin-secreting beta cells contained within the exocrine tissue of the organ. They are of primary importance in the research on diabetes, but their large diversity in size, down to the micrometer scale, and their localization in the pancreas have so far hindered their observation in vivo. To meet the conditions for successful live imaging, we implemented the xfOCM into a specially designed setup that could provide enough mechanical robustness to allow for measurements over long periods. In addition, the set up was equipped with a fast beam scanning device to achieve high volume acquisition rates. The signal processing and the user interface were conceived in such a way that they offered a rapid visualization of the tomograms, providing an instantaneous feedback and facilitating sample handling. With the developed architecture we achieved label-free in vivo visualization of pancreatic lobules, ducts, blood vessels and individual islets of Langerhans and could demonstrate the potential of the xfOCM in diabetes research for high resolution studies on live animals. Besides the aim of an extended focal volume, the control over the design of the CTF also enabled the realization of a dark field configuration. Signals with low spatial frequencies are suppressed in this configuration, which enabled the measurement of the weak scattering signature of near transparent live cell samples. In conclusion, this thesis provides a better understanding of the image formation involved in the FDOCT. Several strategies to increase the trade-off between lateral resolution and DOF were proposed and validated experimentally. The suitability and potential of this approach for small animal in vivo imaging was demonstrated in the context of a relevant biological question.

EPFL2010

Optical microscopy for imaging through scattering media

Xin Yang

Optical microscopy has been widely used in the life sciences and biological research for several decades. It possesses many advantages over x-ray radiography, computed tomography, ultrasound imaging and magnetic resonance imaging, in terms of being low cost, high resolution, harmless and capable of multiple contrast mechanism, etc. However, the weakness of optical microscopy is the inability to perform deep tissue imaging. Owing to the short wavelength of optical waves, it experiences much more scattering than longer waves in inhomogeneous materials such as biological tissues. Scattering scrambles the wavefront and limits the penetration depth of optical microscopy to only hundreds of microns. We explore in this thesis, novel optical approaches to image through scattering media. There are two main categories of the state of art techniques: imaging with ballistic photons, which requires separation of ballistic photons from the sneak or multiple scattered ones; and imaging with scattered photons, which relies on manipulation of the scattered photons according to the specific scattering properties. We primarily focus on the second category in this thesis. Taking advantage of the reversibility of light, phase conjugation has a long history in aberration compensation. A deterministic wave is incident on a scattering medium and results in a random scattered field. If we record the full information of the scattered field (amplitude and phase) and generate a phase conjugated replica of it, the phase conjugated wave can follow the same path and reconstruct the original deterministic wave after passing back through the scattering medium. In this work, phase conjugation is achieved using digital method, called digital phase conjugation. The scattered field is recorded through digital holography, and a spatial light modulator is applied to construct the phase conjugated wave. Second harmonic radiation imaging probes are used as the original light source, rendering the generation of a focus behind the scattering medium. The memory effect, which indicates the correlation between speckles with different incident angles, is exploited to move the focus around and obtain three-dimensional scanning microscopy behind scattering medium. Speckle scanning microscopy is the second method demonstrated in this thesis for imaging through turbid media. In contrast to digital phase conjugation, which requires access from both sides of the scatterers to measure the scattered field, in speckle scanning microscopy, excitation and collection can be achieved from the same side. The specific scattering events are not taken into account, instead, the statistic property of the scatterers plays a major role. This technique makes full use of two facts: 1. The statistically averaged autocorrelation of speckle fields approaches a delta function; 2. When a speckle pattern scans across a fluorescence object, the collected fluorescence intensity is proportional to the convolution of the speckle field and the object. Linking these two facts with delicate calculation, we can eventually minimize the influence of the speckle, and reconstruct two-dimensional images of objects behind turbid medium. Encouraged by the success of two-dimensional speckle scanning microscopy, we investigate more advanced possibilities by simulation, including three-dimensional speckle scanning and reference based speckle scanning techniques. [...]

EPFL2014