Machine vision methods for process measurements in pulping

The papermaking industry has been continuously developing intelligent solutions to characterize the raw materials it uses, to control the manufacturing process in a robust way, and to guarantee the desired quality of the end product. Based on the much improved imaging techniques and image-based analysis methods, it has become possible to look inside the manufacturing pipeline and propose more effective alternatives to human expertise. This study is focused on the development of image analyses methods for the pulping process of papermaking. Pulping starts with wood disintegration and forming the fiber suspension that is subsequently bleached, mixed with additives and chemicals, and finally dried and shipped to the papermaking mills. At each stage of the process it is important to analyze the properties of the raw material to guarantee the product quality. In order to evaluate properties of fibers, the main component of the pulp suspension, a framework for fiber characterization based on microscopic images is proposed in this thesis as the first contribution. The framework allows computation of fiber length and curl index correlating well with the ground truth values. The bubble detection method, the second contribution, was developed in order to estimate the gas volume at the delignification stage of the pulping process based on high-resolution in-line imaging. The gas volume was estimated accurately and the solution enabled just-in-time process termination whereas the accurate estimation of bubble size categories still remained challenging. As the third contribution of the study, optical flow computation was studied and the methods were successfully applied to pulp flow velocity estimation based on double-exposed images. Finally, a framework for classifying dirt particles in dried pulp sheets, including the semisynthetic ground truth generation, feature selection, and performance comparison of the state-of-the-art classification techniques, was proposed as the fourth contribution. The framework was successfully tested on the semisynthetic and real-world pulp sheet images. These four contributions assist in developing an integrated factory-level vision-based process control.

Brittleness of Paper

Brittleness is a well-known material characteristic but brittleness of paper is vaguely covered. The objective of this thesis was to characterize the phenomenon and causes around brittleness of paper and to clarify if it is a measurable property. Brittleness of paper was approached from the perspectives of paper physics and paper mills. Brittleness is a property of dry paper and it causes problems at the finishing stages of paper machine. According to paper physics, brittle materials fail in the elastic regime, while ductile materials can locally accumulate a plastic deformation prior to the fracture and they are often able to withstand higher stresses. Brittleness of paper is vastly affected by the surrounding conditions: paper as a hygroscopic material tries to get to the equilibrium. It is also affected by the quality of the pulp used. Measurement techniques can be divided into two categories: based on the viscoelastic behavior of paper and on the exposure to the mechanical stress of sort. The experimental part of the thesis was based on the trials with brittle and non-brittle mill-made LWC papers. It is divided into three parts: strength testing of the brittle and non-brittle papers, analysis of the conditions that may contribute the brittleness and the experimental methods to evaluate brittle behavior. The strength measurements confirmed the influence of the moisture content, but only tensile energy absorption and the fracture toughness measurements provided modest differences between the brittle and non-brittle papers. Versatile analysis of the possible contributing factors resulted into speculation, while the brittle papers contained higher amount of starch, triglycerides and steryl esters. The experimental research proved that the formation, the sensory impression and the variation of local strains may contain the crucial information of paper brittleness.

Influence of reactant absorption and dissolution in heterogeneous precipitation processes

In this research work, the aim was to investigate the volumetric mass transfer coefficient [kLa] of oxygen in stirred tank in the presence of solid particle experimentally. The kLa correlations as a function of propeller rotation speed and flow rate of gas feed were studied. The O2 and CO2 absorption in water and in solid-liquid suspensions and heterogeneous precipitation of MgCO3 were thoroughly examined. The absorption experiments of oxygen were conducted in various systems like pure water and in aqueous suspensions of quartz and calcium carbonate particles. Secondly, the precipitation kinetics of magnesium carbonate was also investigated. The experiments were performed to study the reactive crystallization with magnesium hydroxide slurry and carbon dioxide gas by varying the feed rates of carbon dioxide and rotation speeds of mixer. The results of absorption and precipitation are evaluated by titration, total carbon (TC analysis), and ionic chromatrography (IC). For calcium carbonate, the particle concentration was varied from 17.4 g to 2382 g with two size fractions: 5 µm and 45-63 µm sieves. The kLa and P/V values of 17.4 g CaCO3 with particle size of 5µm and 45-63 µm were 0.016 s-1 and 2400 W/m3. At 69.9 g concentration of CaCO3, the achieved kLa is 0.014 s-1 with particle size of 5 µm and 0.017 s-1 with particle size of 45 to 63 µm. Further increase in concentration of calcium carbonate, i.e. 870g and 2382g , does not affect volumetric mass transfer coeffienct of oxygen. It could be concluded from absorption results that maximum value of kLa is 0.016 s-1. Also particle size and concentration does affect the transfer rate to some extend. For precipitation experiments, the constant concentration of Mg(OH)2 was 100 g and the rotation speed varied from 560 to 750 rpm, whereas the used feed rates of CO2 were 1 and 9 L/min. At 560 rpm and feed rate of CO2 is 1 L/min, the maximum value of Mg ion and TC were 0.25 mol/litre and 0.12 mol/litre with the residence time of 40 min. When flow rate of CO2 increased to 9 L/min with same 560 rpm, the achieved value of Mg and TC were 0.3 mol/litre and 0.12 mol/L with shorter residence time of 30 min. It is concluded that feed rate of CO2 is dominant in precipitation experiments and it has a key role in dissociation and reaction of magnesium hydroxide in precipitation of magnesium carbonate.

Chart of a portion of North-West Greenland : altered according to the positions and measurements obtained by the Swedish expedition of 1870

Kartta kuuluu A. E. Nordenskiöldin kokoelmaan

NIR-Vis Up-Conversion Luminescence in the Yb3+,Er3+ Doped Y2O2S, ZrO2, and NaYF4 Nanomaterials

Since the discovery of the up-conversion phenomenon, there has been an ever increasing interest in up-converting phosphors in which the absorption of two or more low energy photons is followed by emission of a higher energy photon. Most up-conversion luminescence materials operate by using a combination of a trivalent rare earth (lanthanide) sensitizer (e.g. Yb or Er) and an activator (e.g. Er, Ho, Tm or Pr) ion in a crystal lattice. Up-converting phosphors have a variety of potential applications as lasers and displays as well as inks for security printing (e.g. bank notes and bonds). One of the most sophisticated applications of lanthanide up-conversion luminescence is probably in medical diagnostics. However, there are some major problems in the use of photoluminescence based on the direct UV excitation in immunoassays. Human blood absorbs strongly UV radiation as well as the emission of the phosphor in the visible. A promising way to overcome the problems arising from the blood absorption is to use a long wavelength excitation and benefit from the up-conversion luminescence. Since there is practically no absorption by the whole-blood in the near IR region, it has no capability for up-conversion in the excitation wavelength region of the conventional up-converting phosphor based on the Yb3+ (sensitizer) and Er3+ (activator) combination. The aim of this work was to prepare nanocrystalline materials with high red (and green) up-conversion luminescence efficiency for use in quantitative whole-blood immunoassays. For coupling to biological compounds, nanometer-sized (crystallite size below 50 nm) up-converting phosphor particles are required. The nanocrystalline ZrO2:Yb3+,Er3+, Y2O2S:Yb3+,Er3+, NaYF4:Yb3+,Er3+ and NaRF4-NaR’F4 (R: Y, Yb, Er) materials, prepared with the combustion, sol-gel, flux, co-precipitation and solvothermal synthesis, were studied using the thermal analysis, FT-IR spectroscopy, transmission electron microscopy, EDX spectroscopy, XANES/EXAFS measurements, absorption spectroscopy, X-ray powder diffraction, as well as up-conversion and thermoluminescence spectroscopies. The effect of the impurities of the phosphors, crystallite size, as well as the crystal structure on the up-conversion luminescence intensity was analyzed. Finally, a new phenomenon, persistent up-conversion luminescence was introduced and discussed. For efficient use in bioassays, more work is needed to yield nanomaterials with smaller and more uniform crystallite sizes. Surface modifications need to be studied to improve the dispersion in water. On the other hand, further work must be carried out to optimize the persistent up-conversion luminescence of the nanomaterials to allow for their use as efficient immunoassay nanomaterials combining the advantages of both up-conversion and persistent luminescence.

Two-phase flow measurements with spacer grid in a rod bundle geometry

Heat transfer effectiveness in nuclear rod bundles is of great importance to nuclear reactor safety and economics. An important design parameter is the Critical Heat Flux (CHF), which limits the transferred heat from the fuel to the coolant. The CHF is determined by flow behaviour, especially the turbulence created inside the fuel rod bundle. Adiabatic experiments can be used to characterize the flow behaviour separately from the heat transfer phenomena in diabatic flow. To enhance the turbulence, mixing vanes are attached to spacer grids, which hold the rods in place. The vanes either make the flow swirl around a single sub-channel or induce cross-mixing between adjacent sub-channels. In adiabatic two-phase conditions an important phenomenon that can be investigated is the effect of the spacer on canceling the lift force, which collects the small bubbles to the rod surfaces leading to decreased CHF in diabatic conditions and thus limits the reactor power. Computational Fluid Dynamics (CFD) can be used to simulate the flow numerically and to test how different spacer configurations affect the flow. Experimental data is needed to validate and verify the used CFD models. Especially the modeling of turbulence is challenging even for single-phase flow inside the complex sub-channel geometry. In two-phase flow other factors such as bubble dynamics further complicate the modeling. To investigate the spacer grid effect on two-phase flow, and to provide further experimental data for CFD validation, a series of experiments was run on an adiabatic sub-channel flow loop using a duct-type spacer grid with different configurations. Utilizing the wire-mesh sensor technology, the facility gives high resolution experimental data in both time and space. The experimental results indicate that the duct-type spacer grid is less effective in canceling the lift force effect than the egg-crate type spacer tested earlier.

Fluvio-morphological processes of meander bends - Combining conventional field measurements, close-range remote sensing and computational modelling

Meandering rivers have been perceived to evolve rather similarly around the world independently of the location or size of the river. Despite the many consistent processes and characteristics they have also been noted to show complex and unique sets of fluviomorphological processes in which local factors play important role. These complex interactions of flow and morphology affect notably the development of the river. Comprehensive and fundamental field, flume and theoretically based studies of fluviomorphological processes in meandering rivers have been carried out especially during the latter part of the 20th century. However, as these studies have been carried out with traditional field measurements techniques their spatial and temporal resolution is not competitive to the level achievable today. The hypothesis of this study is that, by exploiting e increased spatial and temporal resolution of the data, achieved by combining conventional field measurements with a range of modern technologies, will provide new insights to the spatial patterns of the flow-sediment interaction in meandering streams, which have perceived to show notable variation in space and time. This thesis shows how the modern technologies can be combined to derive very high spatial and temporal resolution data on fluvio-morphological processes over meander bends. The flow structure over the bends is recorded in situ using acoustic Doppler current profiler (ADCP) and the spatial and temporal resolution of the flow data is enhanced using 2D and 3D CFD over various meander bends. The CFD are also exploited to simulate sediment transport. Multi-temporal terrestrial laser scanning (TLS), mobile laser scanning (MLS) and echo sounding data are used to measure the flow-based changes and formations over meander bends and to build the computational models. The spatial patterns of erosion and deposition over meander bends are analysed relative to the measured and modelled flow field and sediment transport. The results are compared with the classic theories of the processes in meander bends. Mainly, the results of this study follow well the existing theories and results of previous studies. However, some new insights regarding to the spatial and temporal patterns of the flow-sediment interaction in a natural sand-bed meander bend are provided. The results of this study show the advantages of the rapid and detailed measurements techniques and the achieved spatial and temporal resolution provided by CFD, unachievable with field measurements. The thesis also discusses the limitations which remain in the measurement and modelling methods and in understanding of fluvial geomorphology of meander bends. Further, the hydro- and morphodynamic models’ sensitivity to user-defined parameters is tested, and the modelling results are assessed against detailed field measurement. The study is implemented in the meandering sub-Arctic Pulmanki River in Finland. The river is unregulated and sand-bed and major morphological changes occur annually on the meander point bars, which are inundated only during the snow-melt-induced spring floods. The outcome of this study applies to sandbed meandering rivers in regions where normally one significant flood event occurs annually, such as Arctic areas with snow-melt induced spring floods, and where the point bars of the meander bends are inundated only during the flood events.

Possibility Of Controlling The Atmosphere Inside A Package Using Microperforation

This work focuses on the study of the determination on the possibilities of controlling the required moisture within the inside of film sealed packages. The task is based on the challenges faced by fresh food producers in actualizing a longer product shelf-life coupled with the growing complex desires coming from consumers in the aspect of quality. One way to realize this is by proper evaluation on the use of the flexible plastic films through permeation measurements on the required amount of moisture penetrating through the plastic film with the application of microperforation. A packaging material requires proper interaction on moisture transmission, between the product and the outside environment. The plastic film material that stands between, fresh fruits, vegetables and the outside environment could have appropriate respiration rates through possible micro holes. This work simulates similar process with the aid of water vapor transmission rate (WVTR) experiment using anhydrous CaCl2 as the desiccant, in studying the WVTR values of various perforated film materials at different conditions of storage (standard, fridge, and tropical conditions). However, the results showed absorption rates of water vapor at various conditions in grams of H2O/m2/24h.

Influence of multi-phase phenomena on semibatch crystallization processes of aqueous solutions

Crystal properties, product quality and particle size are determined by the operating conditions in the crystallization process. Thus, in order to obtain desired end-products, the crystallization process should be effectively controlled based on reliable kinetic information, which can be provided by powerful analytical tools such as Raman spectrometry and thermal analysis. The present research work studied various crystallization processes such as reactive crystallization, precipitation with anti-solvent and evaporation crystallization. The goal of the work was to understand more comprehensively the fundamentals, phenomena and utilizations of crystallization, and establish proper methods to control particle size distribution, especially for three phase gas-liquid-solid crystallization systems. As a part of the solid-liquid equilibrium studies in this work, prediction of KCl solubility in a MgCl2-KCl-H2O system was studied theoretically. Additionally, a solubility prediction model by Pitzer thermodynamic model was investigated based on solubility measurements of potassium dihydrogen phosphate with the presence of non-electronic organic substances in aqueous solutions. The prediction model helps to extend literature data and offers an easy and economical way to choose solvent for anti-solvent precipitation. Using experimental and modern analytical methods, precipitation kinetics and mass transfer in reactive crystallization of magnesium carbonate hydrates with magnesium hydroxide slurry and CO2 gas were systematically investigated. The obtained results gave deeper insight into gas-liquid-solid interactions and the mechanisms of this heterogeneous crystallization process. The research approach developed can provide theoretical guidance and act as a useful reference to promote development of gas-liquid reactive crystallization. Gas-liquid mass transfer of absorption in the presence of solid particles in a stirred tank was investigated in order to gain understanding of how different-sized particles interact with gas bubbles. Based on obtained volumetric mass transfer coefficient values, it was found that the influence of the presence of small particles on gas-liquid mass transfer cannot be ignored since there are interactions between bubbles and particles. Raman spectrometry was successfully applied for liquid and solids analysis in semi-batch anti-solvent precipitation and evaporation crystallization. Real-time information such as supersaturation, formation of precipitates and identification of crystal polymorphs could be obtained by Raman spectrometry. The solubility prediction models, monitoring methods for precipitation and empirical model for absorption developed in this study together with the methodologies used gives valuable information for aspects of industrial crystallization. Furthermore, Raman analysis was seen to be a potential controlling method for various crystallization processes.

Photon Upconverting Nanophosphors: Unique Reporters for Optical Biosensing

Upconversion photoluminescence is a unique property of mostly certain inorganic materials, which are capable of converting low-energy infrared radiation into a higher-energy emission at visible wavelengths. This anti-Stokes shift enables luminescence detection without autofluorescence, which makes the upconverting materials a highly suitable reporter technology for optical biosensing applications. Furthermore, they exhibit long luminescence lifetime with narrow bandwidths also at the optical window of biomaterials enabling luminescence measurements in challenging sample matrices, such as whole blood. The aim of this thesis was to study the unique properties and the applicability of nano-sized upconverting phosphors (UCNPs) as reporters in biosensing applications. To render the inorganic nanophosphors water-dispersible and biocompatible, they were subjected to a series of surface modifications starting with silica-encapsulation and ending with a bioconjugation step with an analyte-recognizing biomolecule. The paramagnetism of the lanthanide dopants in the nanophosphors was exploited to develop a highly selective separation method for the UCNP-bioconjugates based on the magnetic selectivity of the high gradient magnetic separation (HGMS) system. The applicability of the nano-sized UCNPs as reporters in challenging sample matrices was demonstrated in two homogeneous sensing applications based on upconversion resonance energy transfer (UC-RET). A chemosensor for intracellular pH was developed exploiting UC-RET between the UCNP and a fluorogenic pH-sensitive dye with strongly increasing fluorescence intensity in decreasing pH. The pH-independent emission of the UCNPs at 550 nm was used for referencing. The applicability of the pH-nanosensor for intracellular pH measurement was tested in HeLa cells, and the acidic pH of endosomes could be detected with a confocal fluorescence microscope. Furthermore, a competitive UC-RET-based assay for red blood cell folic acid was developed for the measurement of folate directly from a whole blood sample. The optically transparent window of biomaterials was used in both the excitation and the measurement of the UC-RET sensitized emission of a near-infrared acceptor dye to minimize sample absorption, and the anti-Stokes detection completely eliminated the Stokes-shifted autofluorescence. The upconversion photoluminescence efficiency is known to be dependent on crystallite size, because the increasing surface-to-volume ratio of nano-sized UCNPs renders them more susceptible to quenching effects of the environment than their bulk counterpart. Water is known to efficiently quench the luminescence of lanthanide dopants. In this thesis, the quenching mechanism of water was studied using luminescence decay measurements. Water was found to quench the luminescence of UCNPs by increasing the non-radiative relaxation of the excited state of Yb3+ sensitizer ion, which had a very strong quenching effect on upconversion luminescence intensity.

Uncertainty of Efficiency Measurements in Electric Drives

The two central goals of this master's thesis are to serve as a guidebook on the determination of uncertainty in efficiency measurements and to investigate sources of uncertainty in efficiency measurements in the field of electric drives by a literature review, mathematical modeling and experimental means. The influence of individual sources of uncertainty on the total instrumental uncertainty is investigated with the help of mathematical models derived for a balance and a direct air cooled calorimeter. The losses of a frequency converter and an induction motor are measured with the input-output method and a balance calorimeter at 50 and 100 % loads. A software linking features of Matlab and Excel is created to process measurement data, calculate uncertainties and to calculate and visualize results. The uncertainties are combined with both the worst case and the realistic perturbation method and distributions of uncertainty by source are shown based on experimental results. A comparison of the calculated uncertainties suggests that the balance calorimeter determines losses more accurately than the input-output method with a relative RPM uncertainty of 1.46 % compared to 3.78 - 12.74 % respectively with 95 % level of confidence at the 93 % induction motor efficiency or higher. As some principles in uncertainty analysis are open to interpretation the views and decisions of the analyst can have noticeable influence on the uncertainty in the measurement result.

Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

The effect of cationic-anionic polyelectrolyte multilayer surface treatment on inkjet ink spreading and print quality

The focus of the work reported in this thesis was to study and to clarify the effect of polyelectrolyte multilayer surface treatment on inkjet ink spreading, absorption and print quality. Surface sizing with a size press, film press with a pilot scale coater, and spray coating, have been used to surface treat uncoated wood-free, experimental wood-free and pigmentcoated substrates. The role of the deposited cationic (polydiallydimethylammonium chloride, PDADMAC) and anionic (sodium carboxymethyl cellulose, NaCMC) polyelectrolyte layers with and without nanosilica, on liquid absorption and spreading was studied in terms of their interaction with water-based pigmented and dye-based inkjet inks. Contact angle measurements were made in attempt to explain the ink spreading and wetting behavior on the substrate. First, it was noticed that multilayer surface treatment decreased the contact angle of water, giving a hydrophilic character to the surface. The results showed that the number of cationic-anionic polyelectrolyte layers or the order of deposition of the polyelectrolytes had a significant effect on the print quality. This was seen for example as a higher print density on layers with a cationic polyelectrolyte in the outermost layer. The number of layers had an influence on the print quality; the print density increased with increasing number of layers, although the increase was strongly dependent on ink formulation and chemistry. The use of nanosilica clearly affected the rate of absorption of polar liquids, which also was seen as a higher density of the black dye-based print. Slightly unexpected, the use of nanosilica increased the tendency for lateral spreading of both the pigmented and dye-based inks. It was shown that the wetting behavior and wicking of the inks on the polyelectrolyte coatings was strongly affected by the hydrophobicity of the substrate, as well as by the composition or structure of the polyelectrolyte layers. Coating only with a cationic polyelectrolyte was not sufficient to improve dye fixation, but it was demonstrated that a cationic-anionic-complex structure led to good water fastness. A threelayered structure gave the same water fastness values as a five-layered structure. Interestingly, the water fastness values were strongly dependent not only on the formed cation-anion polyelectrolyte complexes but also on the tendency of the coating to dissolve during immersion in water. Results showed that by optimizing the chemistry of the layers, the ink-substrate interaction can be optimized.

On site measurements of DC link electrolytic capacitor bank of frequency converter using constant DC magnetization of the motor

Preventive maintenance of frequency converters has been based on pre-planned replace-ment of wearing or ageing components. Exchange intervals follow component life-time expectations which are based on empirical knowledge or schedules defined by manufac-turer. However, the lifetime of a component can vary significantly, because drives are used in very different operating environments and applications. The main objective of the research was to provide information on methods, i.e. how in-verter's operating condition can be measured reliably under field conditions. At first, the research focused on critical components such as current transducers, IGBTs and DC link capacitor bank, because these aging have already been identified. Of these, the DC link capacitor measurement method was selected for closer examination. With this method, the total capacitance and its total series resistance can be measured. The suitability of the measuring procedure was estimated on the basis of practical measurements. The research was made by using so called triangulation method, including a literature review, simulations and practical measurements. Based on the results, the new measu-rement method seems suitable with some reservations to practical measurements. How-ever, the measuring method should be further developed in order to improve its reliability.

Inverkan av indirekt rekombination på fotoinducerad absorption

I organiska halvledare påverkas mängden laddningsbärare kraftigt av indirekt rekombination, det vill säga processen då fria laddningsbärare försvinner genom att kombineras med orörliga laddningsbärare av motsatt laddning. De orörliga laddningsbärarna uppstår när laddningsbärare fastnar i fällor, som är energitillstånd med låg energi och densitet. Utöver indirekt rekombination sker även direkt rekombination mellan fria laddningsbärare. Då man tillverkar solceller av organiska halvledare påverkas effektiviteten av energidistributionen och rekombinationsprocesserna i materialen. Utveckling av olika metoder för undersökning av dessa egenskaper är således till nytta i jakten på bättre solcellsmaterial. Målet med detta arbete var att vidareutveckla dataanalysen för cwPA-mätningar(från engelska continuous-wave Photoinduced Absorption) för att ur resultaten få information om indirekt rekombination och fälldistributioner. I cwPA-mätningar studerar man fotoinducerad absorption, det vill säga förändringen i absorption hos ett prov då densiteten av fotogenererade laddningsbärare varierar. Laddningsbärarna genereras av ett pumpljus vars intensitet ges av en fyrkantsvåg som växlar mellan 0 och I med vinkelfrekvensen omega. Resultaten fås i form av i-fas-signal (PAI), som har samma frekvens och fas som pumpljuset, och kvadratur (PAQ), som har samma frekvens som pumpljuset men är fasförskjuten 90 grader. Fördelen med denna mätning är förutom känsligheten att den är kontaktlös, vilket gör att den visar egenskaperna hos det undersökta materialet utan att påverkas av elektriska kontakter. För att undersöka inverkan av indirekt rekombination på cwPA-mätningar simulerades mätresultat genom att använda numeriska beräkningar. Grunden för simuleringarna var att lösa differentialekvationer för densiteter av laddningsbärare i olika tillstånd. Beräkningarna använde en modell med transporttillstånd och fällor placerade så att energidistributionen var symmetrisk för elektroner och hål. Modellen antog att laddningsbärare inte kunde röra sig direkt mellan fällor utan endast via transporttillstånd. Från simuleringarna erhölls användbara samband mellan fotoinducerad absorption och olika fälldistributioner. Särskilt påverkade distributionerna i-fas-signalen för hög intensitet på pumpljuset och kvadraturen för låg frekvens på fyrkantsvågen. För en exponentiell fälldistribution hittades samband mellan mätresultat och distributionens karakteristiska energi (Ech) i förhållande till temperaturen (T). Dessa är för hög intensitet PAI~I^(1+Ech/kT) och för låg frekvens PAQ~omega^(kT/Ech). Resultaten visade att man kan skilja på en exponentiell fälldistribution, en gaussisk fälldistribution och ett system som domineras av direkt rekombination genom att göra cwPA-mätningar vid olika temperaturer.