Computational optimization of an optical sensor design

Abstract

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mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} It is interesting for the food industry to determine the microstructure of food products. Although several equipments already exist which can determine this microstructure, they’re only applicable to ‘simple’ structures (powders, emulsions or suspensions). An interesting technique to derive information over biological tissues is Vis/NIR spectroscopy. When light propagates through a biological tissue, photons will interact with the existing microstructure. The absorption of photons gives an idea about the chemical composition. Variations in the microstructure can however result into erroneous concentration estimations with classical Vis/NIR spectroscopy. This is the result of light scattering due to the microstructure. This light scattering is a dominant effect in biological tissues. In classical Vis/NIR spectroscopy one evaluates how light is fading away in the tissue, as a consequence of the interaction with the biological tissue. This results in a single measurements: reflection or transmission. It does not allow, however, to make a distinction between information about the chemical composition (absorption) and the microstructure (scattering). Advanced methods have arose, which perform multiple measurements, resolved over time or space. These methods employ light propagation models which allow to simulate the reflection or transmission of a sample with specific optical properties. Optical properties of a tissue can be estimated by iteratively comparing simulated spectra with measured ones. When determining the optical properties of a complex biological tissue, one needs an adapted sensor. The most efficient probe is therefore the result of an iterative development procedure, where improvements are being made after testing a previous prototype. Becauseof the significant investment necessary for building the prototypes,every step of this iterative process implies an increase in time andmoney. As a result, one can only justify building a small number of different prototypes. The result is a suboptimal probe design. If onewould be able to do this process computationally, this would be a large improvement. Light propagation models are a necessary tool for this computational sensor design. This research is subdivided into 4 parts. At first, a light propagation model will be developed. Starting from optical parameters, one should be able to derive the light distribution in a biological tissue. In the next step, an inverted algorithm will be developed. Starting from SRS-measurements, the optical properties of tissues will be estimated. Finally, a connection will be made between the optical properties – which characterize a tissue on a mesoscale – and the microstructure of the tissue. This will be done by estimating the particle size distribution of the tissue. Starting from this research, one will develop a computational optimization of the sensor design. This algorithm will make usage of the light propagation model, in combination with the inverse algorithm.Preface – Voorwoord i Samenvatting iii Abstract – Summary ix List of Symbols xiii Table of Contents xvii Chapter 1: General introduction 1 1.1 Importance of quality in food industry 1 1.2 Importance of food microstructure and composition 2 1.3 Applications of Vis/NIR spectroscopy in the food industry 4 1.4 The study of Vis/NIR light propagation in biological media 5 1.5 Problem statement and research objectives 6 Chapter 2: Light Propagation in Biomaterials: state of the art 9 2.1 Introduction 11 2.2 Electromagnetic spectrum 11 2.3 Theoretical principles of light propagation 12 2.3.1 Reflection and refraction 12 2.3.2 Absorption 14 2.3.3 Scattering 20 2.3.4 Bulk optical properties 23 2.4 Modeling propagation of electromagnetic radiation in turbid media 26 2.4.1 Radiative transfer theory 26 2.4.2 Adding-Doubling 29 2.5 Monte Carlo modeling of the light propagation in biomaterials 33 2.5.1 Introduction 33 2.5.2 Tracing photons through a biomaterial 35 2.5.3 Improving computational speed 44 2.5.4 Improving accuracy 49 2.6 Spectral fitting in tissue optics 51 2.7 Measurement of the bulk optical properties of turbid media 52 2.7.1 Unscattered transmittance measurements 52 2.7.2 Nephelometer measurements 54 2.7.3 Double integrating sphere measurement and inverse adding-doubling 55 2.7.4 Spatially resolved reflectance spectroscopy 58 2.7.5 Hyperspectral scatter imaging 60 2.8 Summary 61 Chapter 3: Estimation of optical properties – robust estimation using prior scattering information 63 3.1 Introduction 65 3.2 Materials and methods 68 3.2.1 Optical characterization of liquid phantoms 68 3.2.2 Metamodeling approximation of light propagation models 69 3.2.3 Light propagation metamodel 79 3.2.4 Inverse light propagation model 81 3.2.5 Validation of estimator 85 3.2.6 Wavelength-dependency 85 3.3 Results and discussion 87 3.3.1 Bulk optical properties of liquid phantoms 87 3.3.2 Visualization of the metamodel 88 3.3.3 Results of the estimation procedure on the calibration and validation set 91 3.3.4 Results for the estimation in the wavelength dependency test 95 3.4 Conclusions 97 Chapter 4: Computational optimization of spatially resolved spectroscopy sensor configuration design 99 4.1 Introduction 101 4.2 Materials and methods 102 4.2.1 Optical characterization of milk samples 102 4.2.2 Metamodeling 102 4.2.3 Simulating realistic SRS “measurements” of milk samples 103 4.2. 4 (Inverse) light propagation model 103 4.2.5 Optimization of sensor configuration: definition of a cost function 105 4.2.6 Genetic algorithm for optimizing a milk sensor configuration 106 4.3 Results 108 4.3.1 Bulk optical properties of milk samples 108 4.3.2 Estimation of milk BOP: the 30 fiber case 109 4.3.3 Optimization of a milk sensor design: overview of the different cases 110 4.3.4 Optimization of a milk sensor design: the optimal number of fibers 113 4.4 Conclusion and future perspectives 115 Chapter 5: Microscale light propagation modeling – linking microstructural information to optical properties in Monte Carlo simulations 119 5.1 Introduction 121 5.2 Materials and methods 122 5.2.1 Phase functions in MC simulations 122 5.2.2 Classical computation of the HG phase function 123 5.2.3 Example of a modified HG phase function 124 5.2.4 Simulating the bulk optical properties of polydisperse spherical particles in an absorbing host medium 125 5.2.5 Incorporating alternative phase functions in MC simulations 138 5.2.6 Testing the fpf-MC code 141 5.2.7 Comparing different MC algorithms: statistical analysis 144 5.3 Results 146 5.3.1 Effect of phase function resolution on accuracy of fpf-MC 146 5.3.2 Comparison with MCML 148 5.3.3 Effect of the second moment in the modified HG phase function 150 5.3.4 Introducing arbitrary phase functions derived from particle size distributions 150 5.4 Conclusions 151 Chapter 6: Microscale light propagation modeling – Monte Carlo modeling in realistic tissue structures 153 6.1. Introduction 155 6.2. Materials and methods 156 6.2.1 MMC-fpf algorithm 156 6.2.2 In silico validation 160 6.2.3 Experimental validation 164 6.3 Results and discussion 168 6.3.1 In silico validation 168 6.3.2 Experimental validation on tomato leaves 171 6.3.3 Absorption profiles of tomato leaf tissues 172 6.4 Discussion 174 6.5 Conclusions 177 Chapter 7: General conclusions and future perspectives 179 7.1 General conclusions 181 7.2 Future perspectives 183 7.2.1 Improving (inverse) light propagation modeling 183 7.2.2 Improving sensor design computation 186 7.2.3 Advanced chemometrics to predict composition 188 7.2.4 Inverse microscale models 188 Reference List 191 Curriculum vitae 209 Publication List 211 Appendix A: Mie expansion coefficients 213nrpages: 217status: publishe