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Multimodal imaging polarimeter
The instrument that has been developed in the context of this Ph.D. is based in the conoscopic configuration in order to profit the advantages of the absence of moving parts and the fact that multiple scattering angles can be accessed in a single measurement run. These characteristics contribute to improve the accuracy of the polarimetric measurements, and the measurement time. As it will be discussed in detail in a further section, the optical configuration of this instrument consists of an improvement of the standard configuration of a conoscopic scatterometer by adding the possibility of accessing the full polarimetric properties of the optical response of the sample, and also, the possibility of switching between different imaging modes, i.e. real plane and Fourier plane imaging by a minimal change in the optical configuration of the system, which can be easily done by the user of the instrument, in the framework of the development of imaging Muller polarimeters based on liquid crystals30–32 combined with the switching-image-plane approach33–35 in the laboratory LPICM. In real space mode, as the name suggest, the instrument provides the image of the object with a magnification that can be controlled with the choice of lenses used before and after the sample used to illuminate and to image it respectively. The real imaging mode allows the visualization of the area of the sample to be analyzed by eventually selecting the size and position of the zone of interest. Moreover, this imaging mode allows a spatially resolved measurement of the polarimetric response of the sample with a very good resolution which is in principle limited by the diffraction of light inside of the instrument. In Fourier imaging mode, instruments provide angle resolved images which correspond to the angular distribution of light intensity (and polarization) emitted (or scattered) by the studied sample. Switching between the two imaging modes is done by the insertion (or removal) of a lens, called a Bertrand lens for historical reasons, in the optical train of the instrument. The insertion of the Bertrand lens in the instrument, if done properly, does not affect the alignment of the beam. In Figure 6, there is shown a schematic representation of the trajectories of rays imaged in the real mode configuration and the Fourier mode configuration, respectively. Moreover, a representative image is included for the two configurations to illustrate how the measurements look like. The image in the real plane corresponds to the total transmittance image from the surface of the semi-transparent plastic tape which has the rough surface, and the image in the Fourier plane corresponds to the total transmittance from the same sample but it illustrates the angular distribution of the light scattered by the plastic tape. A more detailed discussion about the information that can be gathered from polarimetric measurements in both imaging modes is provided in the first part of chapter 5 of this manuscript by measuring a thin film of translucent scotch tape. (b) The Fourier plane imaging mode shows the angular distribution of light transmitted or scattered through the sample. In Fourier mode the image is interpreted in terms or two circular coordinates: the polar angle, θ, related to the direction of propagation respect to the axis of the imager, and the azimuth, ϕ, which relates to the orientation of the light respect to a given direction normal to the optic axis of the imager.
The full polarization measurement of the instrument is done by the incorporation of two sophisticated polarization control units. The first one is inserted in the illumination part of the instrument, and the second one in the imaging part. They allow to measure the Mueller matrix of the sample, and from which, as will be discussed further in the manuscript, all the fundamental properties of the sample (diattenuation, birefringence and depolarization) can be measured. Standard conoscopic instruments are usually used to access the diattenuation properties of the samples and only in some cases this information is completed with the birefringence of the sample because it requires a complicated manipulation of the instrument and an elaborated data analysis. In any case in standard instruments it is not possible to access information related to circular diattenuation and birefringence which can be eventually be present in the optical response of the samples. This drawback is not present in the instrument discussed in this work. An example will be given in chapter 4.
This instrument can thus be considered as a generalization of the classical conoscopic scatterometers and for this reason it has been called Multimodal polarimetric imager coupled to a microscope (or Multimodal polarimetric imager to make it shorter in the manuscript).
Polarimetric instrumentation
Different types of polarimeter have been developed and they can be categorized depending on their applications and measurement techniques.36,37 The most basic concept of polarimeter is a Stokes polarimeter. Generally speaking, Stokes polarimeters consist of single optical arm which is equipped with a polarization state analyzer (PSA) and a detector to measure the Stokes vector components (I, Q, U, and V). In the most general configuration, the PSA is made of succession of retarders, used to get access to the different types of retardation (linear and circular) as well as their orientation, followed by a linear and polarizer, used to determine the diattenuation properties of the beam as well as its orientation. Since the Stokes polarimeters do not have an illumination arm to control the incident polarization states, they are applicable in the areas such as astronomy, remote sensing, or characterization of light sources.38–40 The first type of polarimeters are usually referred as Stokesmeters. In the second type of polarimeter, the polarization of both, the illumination and the analysis part can be controlled. In general, the second type of polarimeters are made of two arms and the sample to be studied is placed between them. Each one of the arms is equipped with optical elements to control the polarization of the light. In the first arm polarization states are generated, and in the second arm polarization states are analyzed. In normal operation, the sample is sequentially illuminated with a set of well-defined polarization states. Then, each one of these states, after being modified by the sample, is analyzed by the optical elements in the second arm. As a result, a collection of measurements is retrieved which allows to characterize the optical response of the sample. In general, the set of measurements are presented (or arranged) to form a matrix. Depending on the physical properties of the sample, and the instrumentation used to build the polarimeter, the formalism used to write the matrices will be different. If the interaction with the sample modifies the polarization state of the incoming light but preserves the polarization purity (or polarization degree) then by convention there is tendency to refer to the instrument used to do the measurements as an ellipsometer, and the technique, whose goal is to characterize the optical properties of the sample is called ellipsometry. Thanks to their fast, accurate, and precise properties, the spectroscopic ellipsometers have achieved great success in semiconductor industries or other in-situ real-time characterization in the process of a glass fabrication. However, they remain as an incomplete characterization technique since the Jones vectors are defined only for fully polarized states, so they cannot use conveniently to explore situations in which the interaction of the light beam with the sample and the instrument itself modifies to a given point its degree of polarization. A Mueller polarimeter, in contrast to an ellipsometer, is an instrument which is able to measure light which is partially polarized. Since a Mueller polarimeter can be also used as an ellipsometer to measure fully polarized light, a Mueller polarimeter can be understood as the most general and complete form of an ellipsometer. When working with partially polarized light, it is common to use a mathematical formalism representing polarization as a four-dimensional vector, the Stokes vector, and consequently the optical properties of the sample in the form of a 4 by 4 matrix, called the Mueller matrix.
Regarding Mueller polarimeters, they can be sub-divided into two great categories: spectroscopic polarimeters or imaging polarimeters. The spectroscopic polarimeters give a multi-wavelength approach on the sample. The polarimetric imagers measure the spatial information of the sample. The spatial information can be a real surface of the sample when the system measures the real plane of the imaging lens. Another capability of the polarimetric imager is that it measures a spatial distribution of the scattered, transmitted, or reflected light when it focuses on Fourier plane of the imaging lens. As we discussed in the previous section, the measurement in Fourier plane corresponds to the angle resolved measurement or the conoscopic measurement.
Applications of polarimetry
In the past decades, there have been plenty of applications and researches using the polarimeter. Astronomy is one of the applications.41 The light from the Sun through a telescope is polarized and is related with the magnetic fields in the Sun following a Zeeman effect.40 The structure of the magnetic field between stars has been acquired by measuring the polarization properties of the starlight42,43 , which can be useful to study a distance to external galaxies44 and planetary atmosphere45. The great success of ellipsometry in the multidisciplinary areas is a matter of course.46 The Mueller polarimeter has been applied in optical metrology, materials science, atmospheric remote sensing, and target detection.47–49 In biomedical imaging, the polarimeter has been considered as a useful technique to characterize biological tissues since the biological tissue itself has a nature that it shows polarimetric properties such as birefringence, diattenuation, and depolarization because of its specific structure.50,51 Moreover, it can be extended to the applications for the freshness and quality control in food industries.
Motivation and goal of thesis
Why should we need to know the polarimetric properties of scattered light? Because the scattered light intensity is a function of polarization. It is well-known that sunglasses decrease the glare of reflected light because the reflected glare light has a much dominant horizontal polarization component than the vertical polarization component. So, the sunglasses which have vertically oriented polarizers block the horizontal component of reflected light. We can also find that the brightness is different when we see the blue sky by rotating the sunglasses between 0° and 90° since the light comes from the blue sky undergoes scattering so that it has more vertical polarization component. As it was already discussed in section 1.1, all the activities of transmitted or reflected light are the results from the scattering phenomena; light-matter interactions. Those two simple examples with sunglasses in our real-life show that the scattered light has a polarization property. When we analyze a desired sample which shows scattering, this polarization property can depend on the form of the sample, material indices, and the properties of incident light; an initial polarization, a wavelength, an amplitude (or number of rays), and an angle of incidence (AoI). Moreover, the polarization property accompanies a depolarization property depending on the measurement condition and this depolarization property will be illustrated in the following chapter. So, if the conditions of incident light are well controllable, the analysis of polarization and depolarization properties of scattered light can be useful to characterize the sample properties. The goal of this thesis is i) to design and describe an innovative multimodal Mueller polarimetric imager, ii) to introduce possible applications discovering an optical response with applicable parameters, iii) to explain the optical response from the studied sample with a proper theory and modelling.
Extraction of polarimetric properties
The Mueller matrix itself is too complex to illustrate the polarimetric properties at a glance. Some ways have been proposed to extract the polarimetric properties from the Mueller matrix, called Mueller matrix decomposition. The decomposition has been classified and needs to be considered properly depending on the type of studied samples. In other words, the choice of a given decomposition is mainly determined by the structure of the sample.47,55 In this section, three different types of the Mueller matrix decompositions will be discussed.
Product decomposition
Product decompositions need to be selected when the layers of different polarimetric properties are distinguishable in the plane parallel to the plane of incidence. The most widely-used product decomposition was proposed by Lu and Chipman52. In the product decompositions, the light interacts sequentially with different parts of the sample, each of which being characterized by a well-defined fundamental polarization property showing a random and complex Mueller matrix as a product of elementary Mueller matrices which are diattenuators, retarders, and depolarizers.
There are three kinds of Mueller matrices comprising a diattenuator, a retarder, and a depolarizer. The one way of ordering them is represented as below, = (Eq. 46) , where MδP is a Mueller matrix for a depolarizer, the MR is a Mueller matrix for a retarder, and the MD is a Mueller matrix for a diattenuator. When the diattenuator and the retarder are in the ideal forms, then the depolarizer cannot be an ideal form since the Mueller matrix, M, should not show the polarizance as shown in Figure 12.a. Consequently, the depolarizer has the non-zero polarizance and its Mueller matrix is illustrated as below,
Table of contents :
ACKNOWLEDGEMENTS
RESUME
ABSTRACT
CHAPTER 1. INTRODUCTION
1.1. SCATTERING OF LIGHT
1.2. ANALYSIS OF SCATTERED LIGHT
1.3. POLARIMETRIC INSTRUMENTATION
1.4. MOTIVATION AND GOAL OF THESIS
1.5. OVERVIEW OF THESIS
CHAPTER 2. FUNDAMENTALS OF POLARIZATION OF LIGHT
2.1. MUELLER FORMALISM
2.2. BASIC POLARIMETRIC PROPERTIES
2.3. EXTRACTION OF POLARIMETRIC PROPERTIES
2.4. CONCLUSION
CHAPTER 3. INSTRUMENTATION
3.1. ORIGINAL PROTOTYPES
3.2. MULTIMODAL IMAGING POLARIMETRIC MICROSCOPE
3.3. GENERAL CALIBRATION METHOD
3.4. VERIFICATION OF SYSTEM
3.5. CONCLUSION
CHAPTER 4. POLARIMETRIC IMAGING IN OBLIQUE INCIDENCE AND GEOMETRIC PHASES
4.1. SCATTERING CONFIGURATION IN OBLIQUE INCIDENCE
4.2. VECTORIAL RAY TRACING AND POLARIZATION TRANSFORMATION BY HIGH NA LENSES
4.3. VECTORIAL POLARIMETRY APPLIED TO LINEAR RADIATING DIPOLE
4.4. VECTORIAL POLARIMETRY APPLIED TO SPHERICAL PARTICLES
4.5. VECTORIAL POLARIMETRY APPLIED TO CHARACTERIZE SPHERICAL AND SPHEROIDAL PARTICLES
4.6. CONCLUSION
CHAPTER 5. IMAGING OF COMPLEX MEDIA AND BIOMEDICAL TISSUES
5.1. INTRODUCTION
5.2. ANISOTROPIC TURBID MEDIA: SCOTCH TAPE ANALYSIS
5.3. EX-VIVO ANALYSIS
5.4. CONCLUSION
CHAPTER 6. OTHER APPLICATIONS
6.1. OPTICAL PROPERTIES OF NANO-PATTERNED SAMPLES
6.2. OPTICAL PROPERTIES OF SAMPLES MODIFIED BY FEMTOSECOND LASER DIRECT WRITING
6.3. OPTICAL PROPERTIES OF CYLINDRICAL MICROPARTICLES
CHAPTER 7. GENERAL CONCLUSIONS AND PERSPECTIVES
LIST OF PUBLICATIONS
REFERENCES
