On the Characteristics of Highly Confined Light Fields

The Investigation of highly confined light fields created by different mechanisms, such as refraction, diffraction, and scattering, are the main subject of this thesis. We distinguish a specific scattering phenomenon of dielectric microspheres from general definition of light scattering that includes refraction and diffraction. Light confinement has been studied by numerous researchers in theoretical ways. However, the experimental approaches for microstructures were always limited due to the lack of resolution and functionalities of the measurement system. To understand the characteristics of optical fields propagating in free space or emerging form microstructures, intensity is not always sufficient. It is therefore necessary to measure the phase of light. The main goal of this work was to set up an optical instrument that is able to measure the amplitude and phase of the light field in the real 3D object space. By combining an optical interferometer (Mach-Zehnder type) with an optical microscope, we have developed a multi-functional high-resolution interference microscope (HRIM). Phase shifting interferometry (PSI) and the five frame (Schwider-Hariharan) algorithm have been introduced in the HRIM in order to directly measure the phase. Auxiliary techniques have been applied for the first time to the experimental setup of the HRIM. For example, multiple-wavelengths light sources for the study of the spectral dependency, immersion of object space for an enhanced resolution and a phase telescope (Bertrand lens) to image and manipulating the Fourier plane (the back focal plane of the objective) have been demonstrated. In addition to a plane-wave illumination, the engineering of the illumination beams allows to broaden the range of experimental investigations for a given sample, such as wavefront management by focused Gaussian beams and focused Bessel beams, and polarization-induced beam shaping for particular shapes of localized illuminations to a small sample. Our main subject is the confinement of light. Three physical optical mechanisms are discussed in detail: refraction, diffraction and scattering. Discussion is done by examples. We have chosen effects that represent the different effects of physical optics at a microscale: highly focused Gaussian beam for refraction, the spot of Arago and Talbot effect for diffraction and photonic nanojets for scattering. Note that even though scattering in general includes refraction and diffraction, here we use the term "scattering" only for scattered hotspots, i.e., photonic nanojets, by dielectric microspheres. Our study contributes to the understanding of strong confinement in submicron or sub-wavelength dimensions by such effects and show for the first time experimental data on phase and amplitude fields. Basic physical principles, like the Gouy phase shift for focused light were demonstrated for the photonic nanojet, for a complex optical phenomenon where focusing is based on scattering rather than refraction. We present the capabilities of the HRIM system through a series of measurements of aforementioned problems for highly confined light fields. To meet the proper experimental conditions for each problem of interest, the HRIM employs several auxiliary techniques of conventional microscopy, e.g., multiple-wavelengths light sources, an immersion technique, and a manipulation of the Fourier plane (the back focal plane of the objective). Engineering of the illumination including polarization-induced beam shaping broadens the range of applications of the instrument and we illustrate this by examples. Furthermore, the HRIM can be operated in two distinguished modes for measurements of the axial phase evolution, "longitudinal-differential mode" or "propagation mode". The longitudinal differential mode directly visualizes peculiar phase evolutions along the optical axis used to prove the phase anomalies. The HRIM with auxiliary techniques therefore serves as a powerful tool for the investigation of highly confined light fields in small volumes.

Phase calibration of a basic bright-field microscope for 3D metrology of transparent samples at the nanoscale

Martinus Gijs, Daniel Migliozzi, Bingying Zhao

Optical retrieval of the structure of transparent objects at the nano-scale requires adapted methods capable of probing their interaction with suitable light. Scattering events, for instance, depend on the content and the arrangement of the medium encountered by the light along its propagation path. Physical models of scattering were used in the past to understand image formation and phase retrieval in transparent objects. Here, we considered one of them, which is based on the acquisition of defocused images obtained with partially coherent illumination, and explored its phase retrieval capability over a wide range of illumination angles. We used a basic transmission bright-field microscope with a bandpass filter and an adjustable illumination aperture. The bandpass filter was used to select a specific wavelength range to avoid light dispersion in the sample and maximize illumination capabilities. The adjustable illumination aperture was used to probe and assess the calibration over a wide range of illumination angles, which give access to different parts of the spatial frequency spectrum of the sample. We subsequently employed a computational algorithm to retrieve the local 3-dimensional phase-shift induced on the light field by the scattering through the sample. We imaged several types of samples to explore the calibration and the results in different experimental configurations. We employed: (1) commercial dielectric nanospheres to assess the phase calibration when measured along the optical axis, (2) custom-made nanosteps micropatterned in a glass substrate to assess the phase calibration when measured along the transversal axis. We first verified the model prediction in the spatial frequency domain for the scattering induced by our samples, and subsequently obtained a consistent and linear phase-calibration for illumination numerical apertures ranging from 0.1 to 0.5. This enabled us to calibrate a very simple optical system in a wide range of illumination angles to obtain quantitative 3D metrology of transparent samples at the nanoscale.

SPIE-INT SOC OPTICAL ENGINEERING2021

Distributed sensing using polarization sensitive optical low-coherence reflectometry and fiber gratings

Dragan Coric

Optical low coherence reflectometry (OLCR) is non-destructive interferometric technique that allows measuring amplitude and phase of the light reflected from the device under test. OLCR is a powerful tool for the characterization of the various optical devices such as fiber gratings and optical waveguides. This thesis work had explored possibilities to combine the OLCR technique with fiber gratings to perform distributed strain and temperature measurements, and to develop novel sensing techniques as an alternative to classical spectral methods. Special attention is devoted to polarization sensitive measurements and techniques, and OLCR techniques that use only amplitude information, as an alternative to more complicated phase sensitive measurements. Using a polarization sensitive system two methods for the measurement of local birefringence of fiber Bragg gratings (FBG) using OLCR were developed. The first technique uses oscillations in the OLCR amplitude signal to directly obtain the beat length and the birefringence. The second method is based on the measurement of the OLCR phase and inverse scattering algorithm. Both methods were compared with birefringence obtained from spectral measurements, and very good agreement was obtained. The indirect method, based on local Bragg grating determination requires two independent measurements and mathematical reconstruction, but provides a very high spatial resolution of ≈ 25 µm. The grating length limits the minimum measurable birefringence in the direct method, but a good sensitivity of 4×10-6 was obtained, which corresponds to a Bragg wavelength shift of 4 pm. The spatial resolution is in the millimeter range in this case. The novel methods were successfully applied for the distributed measurement of birefringence of FBG under diametric load. New types of tunable devices and sensors – fiber Bragg gratings written in high attenuation fibers (HAF) were developed. Active tuning by heating was achieved by optical pumping of a pure single mode fiber without any mechanical or electrical parts, or deposited light absorption coatings. Tuning can be controlled by the applied pump power, the position of the grating, the HAF attenuation level, and the pumping configuration. The proposed design assures a high repeatability and long lifetime. Using OLCR these devices were successfully applied to measure the liquid level with a spatial resolution of 100 micrometers. Liquid level measurements that use both phase and amplitude, or only amplitude were demonstrated. The same principles could be easily applied to design other fiber grating devices (long-period, tilted etc), and sensors based on hot-wire anemometry, like flow or vacuum sensors.

EPFL2007

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