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H.P. Urbach

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Doctoral thesis (2026) - H. Shangguan, H.P. Urbach, J. Kalkman
Digital holography (DH) is a full-field, three-dimensional optical imaging technique for high-speed industrial inspection. By retrieving the complex optical field, DH provides quantitative phase information that enables three-dimensional measurement of surface topography. This thesis is motivated by the demands of advanced semiconductor manufacturing and assembly, where centimeter-scale depth ranges and large field-of-views must be achieved at high throughput. A lensless configuration is used to keep the optical system compact and integration-friendly, while numerical propagation enables refocusing. Within this framework, three key challenges of DH-based metrology are addressed: limited unambiguous depth range due to phase wrapping, pixel-size-limited lateral resolution in lensless DH configurations, and the trade-off between depth range and depth precision.

Industrial samples often exhibit large and abrupt height variations. In singlewavelength DH, the unambiguous depth range of half a wavelength is insufficient to unambiguously determine the height of micrometer to millimeter-scale structures. Chapter 2 describes the development of a dual-wavelength off-axis lensless DH configuration with spatial-frequency multiplexing to enable single-shot acquisition at two discrete wavelengths. By leveraging the beat frequency of the two wavelengths, the system generates a synthetic wavelength, which extends the unambiguous depth range to half the synthetic wavelength. A model for shot-noiselimited phase-precision is derived and experimentally validated. Measurements on calibrated targets and representative industrial samples demonstrate reliable threedimensional reconstruction over extended depth ranges, confirming the suitability of single-shot dual-wavelength DH for high-speed metrology.

When DH is implemented in a lensless configurations, the lateral resolution is constrained by sensor pixel size, which limits the maximum spatial frequencies and thus restricts the detection of fine features such as micro-defects. To overcome this limitation, Chapter 3 introduces an expanding wavefront illumination scheme that increases the available angular spectrum of the object field while maintaining system compactness. A background aberration compensation algorithm is developed to correct global aberrations using locally sampled regions, thereby retaining singleshot operation. By incorporating a tunable external-cavity diode laser, the system achieves a centimeter-scale depth range in combination with micrometer-scale lateral resolution.

Besides a large depth range, industrial metrology also demands high depth precision over the accessible depth span. In conventional dual-wavelength DH, increasing the synthetic wavelength enlarges the unambiguous range but proportionally amplifies phase noise when converted to height, which leads to degraded precision. Chapter 4 addresses this trade-off by developing a multi-wavelength DH technique based on discrete wavelength sampling. In multi-wavelength DH, the surface height is retrieved via multi-point phase fitting in the wavenumber domain, thereby combining Fourier-based coarse depth localization with linear regression. The utilized self-calibration strategy, based on pairwise beat-phase analysis, removes the need for auxiliary high-precision wavelength-monitoring instruments. This approach mitigates noise amplification and improves depth precision over a large depth range, broadening the feasibility of DH for large-scale, high-precision industrial inspection.

In summary, this thesis demonstrates that coordinated advances in optical system design and computational reconstruction can alleviate key limitations of DH in industrial metrology. By extending the depth range, enhancing lateral resolution, and improving depth precision, the proposed methods broaden the applicability of DH while maintaining its intrinsic advantages of full-field imaging and quantitative phase retrieval.
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Designing Freeform lenses for illumination applications using algorithmic differentiation

Doctoral thesis (2025) - A.N.M. Heemels, M. Möller, H.P. Urbach, A.J.L. Adam

How to design a nanostructure to scatter light in the direction you want

Doctoral thesis (2025) - T.P.S. Kotte, H.P. Urbach, A.J.L. Adam
This thesis investigates how light can be manipulated through directional scattering by nanostructures, as an alternative to traditional methods such as lenses, mirrors, and diffraction gratings. Thanks to modern nanofabrication techniques, light scattering can be controlled by carefully designed nanostructures. In this work, a design method was developed for nanoparticles that scatter light preferentially in a specific direction by combining absorbing and non-absorbing materials, introducing a phase difference in the scattered field. Experimental results with silica–gold particles confirm the theoretical predictions. The theory was subsequently applied to transmission diffraction gratings, in which glass structures combined with metals or semiconductors were fabricated using techniques such as electron-beam lithography. Although metallic gratings exhibited reduced efficiency due to absorption, gratings made with titanium nitride showed the expected performance improvements. ...
Doctoral thesis (2025) - Z. Zhu, H.P. Urbach, X.C. Yuan, A.J.L. Adam
Optical trapping of metallic nanoparticles has diverse applications because metallic nanoparticles have unique properties. One significant advantage is that the optical force exerted on metallic nanoparticles is considerably larger than that on dielectric nanoparticles of the same size and shape. This results in a significantly deeper optical potential well compared to the optical trapping of dielectric nanoparticles.
In this thesis, our central objective is to delve into the underlying physical mechanisms behind an exceptional and enhanced optical trapping phenomenon that is referred to as"nonlinear optical trapping". To achieve this, we extensively investigated the third-order nonlinear effects that come into play in this intriguing optical trapping behavior. This investigation aimed to shed light on the underlying principles and mechanisms that enable the manipulation of nanoparticles beyond the diffraction limit, opening up exciting possibilities for various applications in nanotechnology and beyond.... ...

For the optimisation of size, mass and cost-critical optical systems

Doctoral thesis (2025) - A.M. Boyd, H.P. Urbach, F. Bociort
Within the optics industry, there is a continuous drive to reduce the size, weight, power consumption and cost of optical systems (known as SWAP-C). A new generation of fabrication technologies for GRadient-INdex (GRIN) materials promise the capability to manufacture GRIN media of arbitrary refractive index distribution (within index variation and spatial resolution limits). This represents an opportunity to further optimise the SWAP-C of lens systems, yet also presents challenges for the optical designer. The necessary optical design tools for arbitary GRINs are not widely implemented, and the potential applications where arbitrary GRINs provide a benefit are not widely explored.

This work addresses these design challenges via two routes. In the first body of work we explore the necessary design tools for generalised GRIN lenses, including efficient mathematical representations for GRIN distributions and tools for the generation of starting points for further optimisation. A powerful new tool is devised that can convert conventional homogeneous lens constructions to generalised GRIN media, which allows the GRIN lens designer to leverage the vast archive available of homogeneous lens solutions as starting points. We also address the aberration correction potential of GRIN lenses with planar surfaces.

In the second body of work we explore the applications that directly benefit from GRIN optics. We demonstrate that layered polymer GRIN lenses of spherical distribution enabled by new extrusion-based manufacture technologies can show comparable performance to conventional cemented doublets and hybrid refractive-diffractive lenses. We also explore the application of a freeform-GRIN distribution to the design of a head-mounted display (HMD), showing that GRIN can significantly reduce the optical complexity of a baseline homogeneous HMD design. Finally, we demonstrate that GRIN can be a powerful tool in the optical design of optical systems with very wide, multispectral infrared wavebands. A short-wave to long-wave (SWIR-LWIR) infrared design study shows a GRIN-based solution can dramatically reduce lens count, size and mass while reducing sensitivity to manufacturing tolerances.

We conclude that the required design infrastructure for arbitrary GRIN lenses is feasible and emerging, and that there are technological challenges in modern optical design that justify ongoing research into GRIN optics. Progress in the optical design of generalised GRINs must be accompanied by refinement in manufacture, metrology, and environmental qualification to enable widespread adoption and deployment. ...
Doctoral thesis (2025) - S. Weerdenburg, W.M.J.M. Coene, H.P. Urbach
With the continuously growing transistor density in the semiconductor industry, where smaller features and tighter tolerances in the nanometer scale are the norm, there is a growing demand for more advanced metrology tools during manufacturing. While optical metrology in the visible range is the main workhorse, such as scatterometry, its performance is limited by the wavelength. Moving beyond the visible spectrum to extreme ultraviolet (EUV) and soft X-ray (SXR) wavelengths promises higher resolutions, but not without challenges. In this wavelength regime traditional microscopy struggles due to the non-availability of high numerical aperture optics for EUV and SXR at reasonable costs, failing to fully make use of the potential benefits of the shorter wavelength.

This thesis covers an alternative route to traditional microscopy through advanced lensless imaging or coherent diffractive imaging (CDI) techniques, particularly focusing on ptychography within the EUV and soft X-ray ranges demonstrated on a designed EUV beamline. Before we go into details about the setup we start with the basics of diffraction, coherent imaging, and ptychography in chapter 2. In chapter 3 we cover the generation of coherent EUV and SXR light from various sources, ranging from large scale facilities like synchrotrons to table-top High Harmonic Generation (HHG) setups.

From this point we cover the design and construction of a table-top EUV lensless imaging beamline in chapter 4, which has been designed and built from scratch at the Optics Research Group at the Delft University of Technology as part of this thesis. This section covers the design, optimization, and assembly of the beamline tailored for lensless imaging of industry relevant samples in a reflection configuration using EUV and soft X-rays from HHG sources. The beamline is split into several subsystems, a high intensity femtosecond fiber laser, the HHG EUV source, optical components for spectral filtering and illumination, and optomechanical systems required for ptychography which are individually covered in the chapter.

In chapter 5 we demonstrate one of the first ptychography reconstructions obtained on the EUV beamline, as presented in chapter 4, by illuminating an object with EUV light at 17.3 nm and 17.9 nm in a grazing reflection orientation of 20 degrees. The object, a silicon substrate which has been patterned with a 20 nanometer thick gold layer with feature sizes from a few microns down to 15 nanometers, has been reconstructed. This reconstruction has been generated with an in-house developed ptychography algorithm, based on automatic differentiation, for the ptychography reconstruction process. The experimental results demonstrate the feasibility of achieving high resolution reconstructions.

Line features down to 50 nanometers were retrieved with this method, close to the diffraction limit given an imaging NA of 0.17 at 18 nm wavelength. A reconstructed structure height of 23.6 ± 0.62 nm agrees well with the 20 nm nominal design value and the height retrieved from an atomic force microscope (AFM) measurement of 22.8 ± 1.45 nm.

The results in chapter 5 are quite promising, though there are certain challenges which need to be solved to further improve the reconstruction quality. One of these challenges are intensity stability issues which are typically associated with EUV sources based on high harmonic generation. Chapter 6 proposes a simple computational method to mitigate intensity fluctuations during ptychography scans by introducing a scanning position dependent multiplication factor. The algorithm effectively corrects for power fluctuations, enabling object reconstruction even in the presence of significant intensity variations up to 50 percent during the overall scan.

Chapter 7 presents a compact schlieren (from the German word ’streak’) imaging system integrated within the HHG EUV source, enabling quantitative density retrieval of the gas jet used to drive the high harmonic generation process. Schlieren imaging provides a straightforward alternative to vibration sensitive techniques like interferometry and can be used as a standardized tool for HHG sources, allowing for a better comparison among different HHG setups and for the optimization of HHG light sources.

In summary, this thesis does not only cover the field of lensless EUV microscopy but also covers the design process of such a beamline and the challenges associated with HHG EUV sources. This work presents a starting point for experimental EUV metrology within the Optics Research Group at the Delft University of Technology and enables future academic research relevant for the semiconductor industry.
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Doctoral thesis (2022) - X. Wei, H.P. Urbach, O. El Gawhary
This thesis addresses new methods and applications of ptychography which is a scanning Coherent Diffraction Imaging(CDI) method for reconstructing a complex valued object function from intensity measurements recorded in the Fraunhofer or Fresnel diffr- action region. The technique provides a solution to the so-called 'phase problem' and is found to be very suitable for Extreme Ultraviolet (EUV) and X-ray imaging applications due to its high fidelity and its minimum requirement on optical imaging elements. Moreover, abundant studies show that ptychography is able to provide a wide field-of-view and retrieve the illumination probe also. During the last two decades, ptychography has been successfully demonstrated with X-ray radiation sources, electron beams and visible light sources.

Chapter 1 is an introductory chapter which gives an overview of CDI techniques. The goal is to provide the necessary knowledge so that readers with different background can easily understand the following chapters. This chapter contains three parts. For the first part we introduce the problem statement of CDI, the approximations that are commonly used in CDI, i.e. the projection approximation, the Fraunhofer approximation, and the required conditions of these approximations. This part also includes the introduction about the discrete Fourier transform, the chirp-Z transform, the issue of sampling and the coherence requirements. The second part of this chapter gives a brief introduction about iterative and non-iterative phase retrieval methods in CDI. For the final part of this chapter, we discuss the fundamental of ptychography which is the main topic of this thesis. We first derive an iterative ptychographic algorithm based on the steepest descent method, then explain the extended field-of-view and the ambiguities in ptychography. Some of the recent developments of ptychography are included in this part as well.


For performing phase retrieval in the EUV regime more efficiently, developing polychromatic ptychography is desirable. As an alternative to the existing ptychographic information multiplexing method, we present in Chapter 2 an another scheme where all monochromatic exit waves are expressed in terms of the amplitude of the transmission function and the thickness function of the object. Our proposed algorithm is a gradient based method and its validity is studied numerically. In addition, the sampling issue which appears in the polychromatic ptychography scheme and its influence to the reconstruction quality are discussed.

In Chapter 3 we investigate the performance of ptychography with noisy data by analyzing the Cram\'{e}r Rao Lower Bound (CRLB). The lower bound of ptychography is derived and numerically computed for both top-hat plane wave and structured illumination. The influence of Poisson noise on the ptychography reconstruction is discussed. The computation result shows that, if the estimator is unbiased, the minimum variance for Poisson noise is mostly determined by the illumination power and the transmission function of the object. Monte Carlo analysis is conducted to validate our calculation results for different photon flux numbers. Furthermore, the performance of the maximum likelihood method and the approach of amplitude-based cost function minimization is studied in the Monte Carlo analysis.

In Chapter 4 we present a parameter retrieval method which combines ptychography and additional prior knowledge about the object. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the chapter. The CRLB in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.

The thesis is concluded with Chapter 5 where the main contribution of this thesis is listed. Furthermore, the unfinished work during my PhD and the possible extensions of the topics discussed in this thesis are addressed in this last chapter. ...

The study of coherence, aberration, and optimization

Doctoral thesis (2021) - Y. Shao, H.P. Urbach, F. Bociort
In this thesis we try to provide novel solutions to key problems related to imaging and imaging system. Imaging is usually referred to as the technique for reproducing the information of the object. In optics, we usually refer the object information to the light field in the object plane due to the interaction of the illumination field and the object. Imaging technique allows the reproduced object information to be recorded by detectors such as human eye, photo resist, or CCD/CMOS sensor. In order to image an object, there must be light. We consider only un polarized quasi-monochromatic light illuminating the object and we approximate the field in the object plane by the multiplication of the transmittance / reflectance of the object and the illumination field (the first Born approximation). However, the results in this thesis can also be generalized to situations beyond the above scope. Here we mainly focus on two aspects: the aberrations, the errors of the imaging system, and the spatial coherence of the light field. In a typical imaging scenario, we consider the object plane field as a source consisting a series of point sources. The field generated by each point source propagates independently to the image plane through the imaging system. Ideally, these fields should all identically have the correct distribution and be centered at the correct location. However, this is not the case in presence of the aberrations. As a result, the image will become blurred. ...
Doctoral thesis (2021) - J. Chang, H.P. Urbach, Val Zwiller
In the past decades, generating single photons on demand with well defined quantum states and detecting them after photon-photon or photon-matter interaction are central to the area of quantum optics and quantum information science. The ability to detect light efficiently at the single photon level offers unprecedented opportunities for a wide range of applications, including long-distance quantum key distribution, light detection and ranging, photonic quantum computing, weak light detection for astronomy and bio-imaging. ...

Solving the problem of divergent Born perturbation series by Padé approximants

Master thesis (2020) - T.A. van der Sijs, O. El Gawhary, H.P. Urbach
In many optical measurement methods one aims to retrieve the shape or physical properties of an unknown object by measuring how it scatters an incident optical field. Such an inverse problem is often approached by solving the corresponding direct scattering problem iteratively. Despite the existence of numerical methods, a perturbation approach could be a powerful way to solve those direct problems. In such an approach the field is expressed as a series, known as the Born series, in which the higher-order corrections represent multiplescattering effects. This approach has the advantage that each term of the series has a clear physical meaning and that it can unveil much more about the scattering process than a purely numerical approach. Under (very) weak-scattering conditions the Born series converges and then often the first or first few terms of the series are sufficient to model the scattering. However, except under very special circumstances such as for x-rays where optical contrasts are extremely low, multiple scattering effects are very important and the Born series in general does not converge. Although multiple scattering could, in principle, allow resolving subwavelength details of the unknown object, this is in practice impeded by the divergent nature of the Born series.

In this thesis, we show how Padé approximation can be employed in electromagnetic problems to retrieve an accurate evaluation of the scattered field even under strong-scattering conditions. Padé approximants are rational functions that can offer improvements in two ways, namely, accelerating the rate of convergence of (already) converging series and analytic continuation of series outside its region of convergence. We apply the method to three scalar scattering problems. In one dimension we consider an infinitely thin slab and a slab of finite thickness, and in two dimensions an infinitely long cylinder. In particular, we study cases in the strong-scattering regime for which the Born series diverges. It will be shown that for all cases studied, Padé approximation retrieves an accurate result.

The presented method integrates multiple-scattering effects one by one and can therefore represent an important building block to the application of the Born series to direct and inverse problems, with potential applications in superresolution, optical metrology, and phase retrieval. ...
Bachelor thesis (2020) - Jeroen Schmits, Paul Urbach
Dipoles are all around us and the extent to which it is possible to distinguish two dipoles next to each other is a very important criterion for optical resolution. This report proposes that the resolution can be enhanced by placing a substrate with a film underneath the dipoles. This report specifically looks at the effect on the near and far field using a coupling of the field radiated by the dipole and a guided mode in the film. In an integral over reflected plane waves, in case a guided wave occurs, the integrand has a singularity which has to be dealt with using the Cauchy Principle value technique. Other singularities are dealt with using multiple first order Taylor expansions. With the singularities dealt with, a Matlab function has been constructed that can compute the reflected field of a single dipole. The substrate underneath the dipole has a significant effect on the total field, both in the near and far field areas. Due to the reflection, the polarizability is represented more in the intensity and can be determined more easily. Although the influence of the film on enhancing the resolution requires to investigate to what extent two dipoles can be distinguished better when a film is present, due to lack of time, this report considers the computation of the field of a single dipole only. The extension to the case of two dipoles is in principle easy however. ...
Doctoral thesis (2020) - A. Ezerskaia, H.P. Urbach, S.F. Pereira
Skin is one of the most significant parts of the human body. It connects us with the environment and has a vast number of functions, among which defensive function is of a high importance. Skin structure and its layers may vary with a number of factors such as sight, age, sex, race and the overall health state of the individuals. The latter affects skin water to lipids ratio and their depth profile in the skin. Smaller changes in the water to lipids ratio may result in skin type variations. In both cases, skin appearance will change along with variations of skin conditions. Given the great importance of the state of the skin, a number of methods and devices for measuring water and lipids content were developed over the years. The research presented in this thesis proposes methods to achieve simultaneous measurements of water and lipids content of the skin and their ratio. We also analysed the impact of these measurements on determining the skin condition. Skin appearance is also addressed through measurement of the skin gloss, using several methods such as the ratio of specular to diffuse component of the image, the slope of the gradient intensity of the image from specular to the diffuse component, and an approached based on number of weighted pixels. The method proposed for simultaneous water and lipids content measurement is described in the Chapter 2, and is based on light measurements, comprising 3 wavelengths that are sensitive to primarily lipids, primarily water and equally sensitive to both, these wavelengths are: 1720 nm, 1770 nm, and 1750 nm, respectively. We benchmarked our measurement with those obtained with a corneomenter and sebumeter – benchmark devices, on induced skin conditions corresponding to combinations of high, low and neutral levels of water and lipids content in the skin. The study showed good agreement. The state of the protective function of stratum corneum (SC) and distribution as function of depth of skin lipids and water are addressed by means of short wave infrared spectroscopy. The method does not give information as a function of depth. This obstacle was overcome by tape stripping of one SC layer at a time. Comparative measurement was performed with Raman confocal microscopy and is described in the Chapter 3. Our proposed method showed similar pattern of the depth profile for water as obtained with the corneometer and with Raman confocal microscopy, while trans epidermal water loss measurement indicated the point of the barrier breaking point. Lipids measurements obtained with our method also showed similar trends as Raman confocal microscopy. As expected, water concentration increased and lipids concentration decreased with increasing depth into the stratum corneum. Additionally, a low-cost method for quantifying skin appearance by measuring skin gloss is proposed in Chapter 4. The method has proven to be reliable for skin gloss measurements via comparison with benchmark devices, and it also shows a great potential for other gloss measurements in a wide range, i.e., from an almost absolutely matte surface to a mirror like one. The proposed method comprises surface imaging by hand-held low-cost camera with ring-illumination along with image post processing based on weighting specular and diffuse components of the image. A gloss value is assigned as the result of the processing. Looking ahead, we discuss in Chapter 5 how the methods developed in this thesis could potentially be combined in one hand-held device. There will be several challenges such as the presence of other chromophores in the skin along with the low absorption coefficient of water and lipids in the spectral region suitable for the camera. The abovementioned obstacles can be solved by measuring absorption and scattering coefficients separately by means of illumination with spatial frequency modulation. The presence of several chromophores will as well require separating their impact on the absorption coefficient, potentially using more extensive data processing algorithms than those used in this research. ...

Spectral Imaging and Surface Manipulation on Liquid Lenses

Doctoral thesis (2020) - Matthias Strauch, Paul Urbach, Florian Bociort
This thesis focusses on two aspects of tunable optics: Fabry-Pérot interferometers with a variable distance between their mirrors and electrowetting liquid lenses. The need for a device to detect child abuse has motivated us to design and build a camera that can detect the chemical composition of the upper skin layers of a bruise using a self-made Fabry-Pérot interferometer. The research described in the first part of this thesis has shown that wide-angle spectral imaging can be achieved with compact and cost-effective cameras using Fabry-Pérot interferometers. Designs with a full field of 90◦ in which the Fabry-Pérot interferometer is mounted either in front of an imaging system or behind a telecentric lens system are presented and analysed. The dependency of the spectral resolution on the numerical aperture of the lens system is derived and its value as a design criterion is shown. It is shown that the telecentric camera design is preferable over the collimated design for bruise imaging with a Fabry-Pérot interferometer.
The idea to use a liquid lens for spectral imaging has directed the research towards a new concept of controlling surface waves on the surface of a liquid lens. We investigate and model surface waves because they decrease the imaging quality during fast focal switching. We propose a model that describes the surface modes appearing on a liquid lens and that predicts the resonance frequencies. The effects of those surface modes on a laser beam are simulated using geometrical optics and Fresnel propagation, and the model is verified experimentally. The model of the surface oscillations is used to develop a technique to create aspheric surface shapes on commercially available electrowetting liquid lenses. The surface waves on the liquid lens are described by Bessel functions of which a linear combination can be used to create any circularly symmetrical aspheric lens shape at an instant of time. With these surface profiles, one can realise a large set of circularly symmetrical wavefronts and hence intensity distributions of beams transmitted by the lens. The necessary liquid lens actuation to achieve a desired shape is calculated via a Hankel transform and confirmed experimentally. The voltage signal can be repeated at video rate. Measurements taken with a Mach-Zehnder interferometer confirm the model of the surface waves. The capabilities and limitations of the proposed method are demonstrated using the examples of a Bessel surface, spherical aberration, an axicon, and a top hat structure. ...

With Natural-Materials and Meta-Materials

Doctoral thesis (2019) - Ying Tang, Paul Urbach, Aurele Adam
The beauty of optical birefringence lies in the fact that it provides an independent control of light over different polarization directions, which leads to many important applications in today's optical systems. This thesis describes the applications of existing naturally-occurring birefringent materials as well as the engineered formed-birefringent meta-materials via nano-fabrication. In particular the application of birefringent materials in optical trapping, waveguide engineering and imaging are discussed. The investigation methods include numerical simulation, nano-fabrication and experimental validation. ...

Non-iterative methods, Ptychography, and Diffractive Shearing Interferometry

Doctoral thesis (2019) - Sander Konijnenberg, Wim Coene, Paul Urbach
In this thesis, several phase retrieval methods are discussed. Since the focus will mainly be on theory rather than experiment, the structure has been determined by the similarities and differences of the mathematics of these methods. For example, a distinction is made between non-iterative and iterative methods, and between single-shot iterative phase retrieval and multiple-shot iterative phase retrieval (ptychography). However, it must be noted that phase retrieval methods that are mathematically similar, are suitable for fundamentally different experimental setups. For example, one can consider setups for lensless imaging, of which an interesting application is metrology using Extreme Ultraviolet (EUV) radiation. In such setups, no focusing optics are used, and one typically computes an image from far-field intensity patterns. On the other hand, there are setups for aberrated imaging. In these setups, one does use focusing optics to form images, but by introducing some sort of variations or perturbations, one can generate a set of images from which a complex-valued field can be computed. For example, regular ptychography and Fourier ptychography are mathematically the same, but the former is used for lensless imaging, while the latter is used for aberrated imaging. Mathematically, the only difference between these two ptychographic approaches is that the roles of object space and Fourier space are interchanged. ...
In the search for new non-invasive diagnostic methods, healthcare researchers have turned their attention to exhaled human breath. Breath consists of thousands of molecular compounds in very low concentrations, in the order of parts per million by volume (ppmv), parts per billion by volume (ppbv) and parts per trillion by volume (pptv). They are the result of the different biological process taking place inside the body. When a disease is present the production of specific molecules is altered. In this work in particular, we investigate two cases. One being the concentration of acetone on minors with type 1 diabetes (T1D). In the second case we compare the breath of three groups to establish
significant differences and to identify relevant molecules. The groups under study are healthy children, children with asthma and children with cystic fibrosis (CF). 
The main challenges in human breath research are the detection of concentration changes in small quantities and the establishment of a direct relation between specific molecules and particular diseases. We use quantum cascade lasers (QCLs), a multipass cell and Mercury Cadmium Telluride (MCT) detectors to study the absorption of the molecular components of breath. We improve the identification of molecules by applying a multiline fitting algorithm. 
The different molecules present in breath have a strong absorption signature in the mid-infrared. For this reason we use QCLs emitting in the region between 832 and 1262.55 cm-1. In this region each molecular species has a unique absorption fingerprint that allows its identification. The absorption is magnified by increasing the interaction distance between the light of the QCLs and the gas sample. We use a multipass cell with two astigmatic mirrors. The multiple reflections in the mirrors provide an effective interaction distance of 54.36 meters inside a volume of only 0.6 liters. For the detection we use MCT detectors directly because the QCLs emit a very specific wavenumber at a time. The absorption spectra are built by scanning the wavenumber of the QCLs twice: first with the multipass cell empty, to build a reference, and then with the breath sample to measure the absorption. 
The scan of the QCLs eliminates the need of extra elements to separate the wavenumbers to build the absorption spectra. However, scanning over a broad wavenumber region introduces a new challenge: to guarantee its repeatability. This includes the assurance that the QCLs emit the same wavenumbers with the same intensities in every single scan. Only by minimizing the variability between independent scans we can create reliable absorption spectra and improve the sensitivity of the setup. We use two MCT detectors to monitor the intensity fluctuations. One detector is dedicated to monitor the intensity fluctuations of the QCLs while the other detector measures the intensity of the QCLs after the light has crossed the multipass cell. The variation of the wavenumber emission produces that independent scans are warped and uncorrelated with respect to each other. We implement two methods to correlate the measurements taken with the empty multipass cell and the measurements with the breath samples: a scan correlation using selected wavenumbers and a scan correlation using semiparametric time warping. Both methods are successful in obtaining a meaningful absorption spectrum. The selection of wavenumbers is more adequate to study molecules with a smooth profile and the semiparametric time warping method is more suitable for molecules with sharp absorption features. The result of the wavenumber and intensity corrections give the system a noise equivalent absorption sensitivity (NEAS) of 2.99×10−7cm−1Hz−1/2. With this NEAS we can detect ppbv concentrations of acetone in presence of 2% of water in the same wavenumber region. The complexity of the gas mixture in breath makes the identification of specific molecular components difficult. We implement a multiline fitting algorithm to analyze specific molecules and determine their concentrations. We use this method to study the concentration of acetone and methane in the exhaled breath of healthy children. For acetone we use its absorption signature in the 1150 - 1250 cm-1 region. Our results show that the production of acetone in healthy children is below the standard range established for healthy adults, between 0.39 and 1.09 ppmv. But the information and studies in this regard are limited and therefore more studies should be performed. In the case of methane we use its absorption fingerprint between 1258 and 1262.5 cm-1. The methane concentration in the breath of the participants is below 1 ppmv, which classifies them as non-producers. Given the small number of participants, eleven, this result is in accordance with previous reports establishing that only 10% to 20% of the children are methane producers. We perform a specific study to investigate the acetone concentration in the exhaled breath of T1D patients. We analyze the breath of two minors and one adult T1D patient, and the breath of one healthy volunteer. Simultaneously, we measure the blood glucose and ketone concentrations in blood to inspect their relation with acetone in exhaled breath. For each volunteer, we performed a series of measurements over a period of time, including overnight fasting of 11 ± 1 hours and during ketosis-hyperglycemia events for the minors. The results highlight the importance of performing personalized studies because the response of the minors to the presence of ketosis was consistent but unique for each individual. As in the case of healthy children mentioned above, we also find that the acetone concentration in the breath of T1D minors in stable conditions is lower than the standard range for healthy adults. This emphasizes the need to perform more studies with children and specifically with T1D minors. We strongly believe that a better understanding of the production of acetone in exhaled breath can help to develop new diagnostic methods. For example, it can be used to detect chronic ketosis, which is a condition that many children present in the early stages of T1D. In many cases children live with chronic ketosis for years before being diagnosed with T1D. By detecting abnormal concentrations of acetone we can help to diagnose T1D earlier. In a separate study we explore the clinical applicability of our spectroscopic setup by comparing the exhaled breath of 35 healthy children, 39 children with stable asthma and 15 with stable CF. Their age range is 6 – 18 years. We collect two to four exhaled breath samples in Tedlar bags and obtain their absorption spectrum in the region between 832 and 1262.55 cm-1. The results show a poor repeatability (Spearman’s ρ = 0.36 to 0.46) and agreement of the complete profiles. However, we identify wavenumber regions where the profiles are significantly different. Using these regions and the information from two molecular databases we present a list of molecules that can be used to discriminate between healthy children and children with asthma or CF. Our suggestion is to perform more studies and use the identified molecules as basis to understand the underlying inflammatory processes of asthma and CF. This study shows that the identification of the molecular components of exhaled breath is important and may be useful to develop new personalized treatments. Because scientists like to dream about the future, we also explore the future possibilities in exhaled breath research. We strongly believe the next generation of exhaled breath systems will be a hybrid between optical detection systems, electrochemical methods and nanotechnology. This idea is firmly supported by the latest developments in small hollow waveguides for lasers and the most advanced pre-concentration and filtering methods for gas samples. Furthermore, the growing interest in new, non-invasive medical systems is making exhaled breath research a very important player in the global economy. We cannot foresee all the benefits exhaled breath research can offer to society but without doubt its value is immense. ...