Fourier Domain Optical Coherence Microscopy with Extended Depth of Field

Fourier Domain Optical Coherence Tomography (FDOCT) is a high speed biomedical imaging modality which extracts the sample structure in depth. The axial resolution is given by the coherence length of the employed light source. The lateral resolution on the other hand is determined by the numerical aperture (NA) of the objective. The parallel detection of the depth information has the drawback of loosing transverse resolution along the optical axis, limiting the depth of field (DOF) and the use of FDOCT in the field of microscopy. The principle idea to overcome this problem is to illuminate the sample with a cylindrically symmetric interference pattern. Such Bessel beam illumination creates a laterally highly confined needle extending several 100μm along the optical axis in depth.

Multiple scattering in wide-field optical coherence tomography

Boris Karamata

Optical Coherence Tomography (OCT), a well-established imaging method based on low-coherence interferometry, provides cross-sectional images of the internal structure of biological samples with a resolution in the micrometer range. OCT was successfully applied on various tissues such as for instance the retina, the skin or a tooth. In highly scattering tissues like the skin, probing depth is limited to approximately 2mm, mainly due to insufficient rejection of multiply scattered light. Presently, the contribution of multiple scattering in OCT is not fully understood. Therefore, there is a strong and urgent need to develop models allowing a reliable evaluation of the system's limitations as well as the improvement of the imaging capabilities. It is generally believed that a relevant model should account for loss of correlation between the reference and the sample field due to multiple scattering. We developed a new comprehensive model of OCT. Our preliminary study revealed that the reference and sample fields are actually fully correlated. This important result allowed us to model the OCT signal as a sum of stationary random phasors and treated it as a statistical signal. The mean of this signal can be calculated thanks to classical results of statistical optics and to a Monte Carlo simulation. Unlike other existing models, our model accounts for the source autocorrelation function. The model proved to be in excellent agreement with a whole range of experimental data gathered in a comprehensive study of cross-talk in wide-field OCT. Moreover, our results put in question the applicability of widely used models of OCT based on the "extended Huygens-Fresnel principle", which assume a partial correlation between interfering fields due to multiple scattering. The construction of conventional OCT images is based on lateral scanning of a beam focused within the sample. To increase image acquisition speed and eliminate the need for lateral scanning, wide-field OCT was recently developed. Our experimental and theoretical investigations of the potential and limitations of wide-field OCT revealed the crucial role played by the spatial coherence of the light source. Spatially coherent illumination generates considerable coherent optical cross-talk, which prevents shot-noise-limited detection and diffraction-limited imaging in scattering samples. The dependence on several parameters of the optical system and of the sample properties was investigated in a comprehensive study. Cross-talk increases with the wide-field diameter, numerical aperture, source coherence length, and sample optical density; and strongly depends on sample anisotropy. We showed that spatially incoherent illumination realized with a thermal light source permits cross-talk suppression in wide-field OCT, i.e. rejection of multiply scattered light to a level comparable to that of point scanning OCT. We performed a theoretical study which revealed that the power per spatial mode radiated by thermal light sources is too low to permit a high signal-to-noise ratio while maintaining a fast acquisition speed. Therefore, wide-field OCT realized with either spatially coherent or spatially incoherent illumination suffers from inherent fundamental limitation. This led us to investigate the possibility of exploiting a spatially incoherent light source brighter than a thermal light source. We came to the conclusion that such a "pseudothermal" light source can potentially lead to wide-field OCT systems devoid of cross-talk and an image acquisition speed higher than that of a point scanning OCT system. However, the attractive properties of pseudothermal light sources could be gained at the expense of the simplicity and the economical advantages offered by thermal light sources. Furthermore, fast acquisition speed also relies on a performing "smart pixel detector array". Presently, such detectors do not have sufficient sensitivity and their frequency readout is too low as shown in our feasibility study. We performed a theoretical investigation of the potential of thermal light sources in terms of axial resolution and power per mode. The former revealed that the maximum power per mode is radiated at a wavelength higher than the spectral peak of a blackbody radiator. This led to the important practical conclusion that, at 6000 K, the maximum power is collected in the therapeutic spectral window in OCT (600 - 1300 nm), while at 3000 K this peak is shifted out of the therapeutic window leading to significant power losses. More generally, our work provides a design tool for choosing the optimal thermal light source for a given therapeutic window in terms of signal-to-noise ratio. Currently available sources at 6000 K consist of high pressure gas arc lamps providing a spectrum endowed with spectral lines deleterious for OCT. By suppressing a portion of the spectrum devoid of spectral lines of a mercury arc lamp, we obtained amongst the highest axial resolution so far reported in OCT. Furthermore, the importance of the speckle statistics in OCT incited us to clarify the origin of a difference between two theoretical results reported in the literature. Indeed, two calculations of the amplitude distribution of speckles in OCT, each of them based on a different mathematical formulation, yield different results. We showed that a modification of an initial assumption in one of the formulation leads to equivalent results. In conclusion, this thesis provides a deeper understanding of the potential and limitations of widefield OCT, leading to important design rules. Moreover, it presents a new comprehensive model of OCT putting in question other widely used models.

EPFL2004

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

Longitudinally polarized fields in near-field imaging systems

The evolution path of nanotechnologies moves through the domain of microscopy. Among all the kinds of imaging tools available today, optical imaging systems are of primary importance. When using optical imaging systems, we take profit of the information remotely delivered by light to the detector, after interaction with the sample. Nevertheless, as light moves away from the place of interaction, a part of this information is inevitably lost. With the help of suitable probes, light in close proximity of the illuminated sample can be detected. In this way, an extraordinary richness of information about the sample becomes accessible and we can manage to "see the invisible". Light confined in proximity of the sample is called near-field and near-field microscopy is the branch of microscopy dealing with the detection of such an optical field. In the domain of near-field microscopy, the rigorous electromagnetic and the optical description of light meet together. When images are formed by detecting optical fields close to illuminated samples, the vectorial and electromagnetic nature of light can not be neglected. In this thesis we focused our attention on the special case of electromagnetic fields oriented parallel to the optical axis (longitudinal fields). The subject is particularly intriguing, as longitudinally polarized fields cannot be detected using standard microscope devices. We mainly considered the interaction of longitudinal fields with microfabricated, fully metal-coated quartz nano-probes, and managed to give a description of their role in the near-field imaging process. The work will be presented as follows. In the first chapter, an introduction to Scanning Near-field Optical Microscopy (SNOM) is given. Starting from the concept of super-resolution in paraxial imaging systems, we introduce the concept of near-field microscopy. For two of the best known SNOM techniques we demonstrate that a resolution beyond the capabilities of classical microscopes can be, in principle, achieved. Moreover, we present a rigorous electromagnetic description of a simplified SNOM system, and stress the necessity of adequate tools for the understanding and the interpretation of near-field images. The second chapter is devoted to the description of the SNOM system with which the main part of the experimental work has been performed. The near-field microscope is particularly interesting since it employs an innovative kind of probes: microfabricated, metal-coated quartz probes with no aperture at their apex. The presence of a full metal coating has strong effects in the near-field imaging characteristics of the probes. Results form standard imaging tests are also presented in this chapter. We demonstrate that fully-metalized probes can actually couple evanescent fields and are capable to attain super-resolution. Microfabricated probes can be used either as light sources or as light collectors. In the third chapter we study their optical response when 3D-oriented fields are collected. We find a non trivial selective collection behavior for longitudinally and transversely polarized fields. Moreover, the lateral resolution of our system shows a clear dependence on the polarization state of the collected field. A phenomenological explanation of this effect, involving a polarization-dependent coupling mechanism of light into the probes, is proposed. In the fourth chapter we study the behavior of fully-coated transparent probes as light emitters. With the help of a three-dimensional numerical model, we characterize the guiding properties of the probes and analyzed the near-field and far-field emitted patterns. A set of experimental measurements confirms the results expected by simulations and validates our phenomenological model describing the interaction of light with the probes. In addition, the essential role of longitudinal fields in an illumination-mode near-field scanning system is underlined. We managed to directly measure the longitudinally-polarized, ultra-small hot spot produced at the metallic apex, after injection of a radially polarized mode into the probe. An alternative way of producing longitudinally polarized light source for near-field imaging is proposed in the fifth chapter. With a set of theoretical calculations, we demonstrate that Surface Plasmon Polaritons (SPP) excited on structured metallic thin films can be exploited as non-radiating, strongly localized light sources. The study presented in this chapter is purely computational: no practical implementation of the proposed device has been performed yet. A conclusive summary of this work is presented in the sixth chapter.

Institut de Microtechnique, Université de Neuchâtel2006