Ebook: Mathematical Models in Photographic Science

th Although photography has its beginning in the 17 century, it was only in the 1920’s that photography emerged as a science. And as with other s- ences, mathematics began to play an increasing role in the development of photography. The mathematical models and problems encountered in p- tography span a very broad spectrum, from the molecular level such as the interaction between photons and silver halide grains in image formation, to chemical processing in ?lm development and issues in manufacturing and quality control. In this book we present mathematical models that arise in today’s p- tographic science. The book contains seventeen chapters, each dealing with oneareaofphotographicscience.Eachchapter,exceptthetwointroductory chapters, begins with general background information at a level understa- able by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as Ordinary Di?erential Equations, Partial Di?erential Equations, and Stochastic Processes. Next, some mathematical results are mentioned, often providing a partial solution to problemsraisedby the model.Finally,mostchaptersinclude problems.By the nature of the subject, there is quite a bit ofdisparity in the mathematical level of the various chapters.

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This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters and the last one, begins with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains "Modeling and Applied Mathematics" exercises based on the material presented in the earlier chapters.These exercises are intended primarily for graduate students and advanced undergraduates.

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This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters and the last one, begins with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains "Modeling and Applied Mathematics" exercises based on the material presented in the earlier chapters.These exercises are intended primarily for graduate students and advanced undergraduates.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-2
History of Photography....Pages 3-6
Front Matter....Pages 7-7
An Overview....Pages 9-11
Crystal Growth — Ostwald Ripening....Pages 12-26
Crystal Growth-Sidearm Precipitation....Pages 27-38
Gelatin Swelling....Pages 39-44
Gelation....Pages 45-52
Polymeric Base....Pages 53-64
Front Matter....Pages 65-66
Limited Coalescence....Pages 67-74
Measuring Coalescence....Pages 75-83
Front Matter....Pages 85-86
Newtonian Coating Flows....Pages 87-98
Coating Configurations....Pages 99-108
Curtain Coating....Pages 109-130
Shear Thinning....Pages 131-140
Front Matter....Pages 141-141
Latent Image Formation....Pages 143-151
Granularity....Pages 152-157
Front Matter....Pages 159-159
A Reaction-Diffusion System....Pages 161-175
Parameter Identification....Pages 176-182
Back Matter....Pages 183-184

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This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters and the last one, begins with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains "Modeling and Applied Mathematics" exercises based on the material presented in the earlier chapters.These exercises are intended primarily for graduate students and advanced undergraduates.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-2
History of Photography....Pages 3-6
Front Matter....Pages 7-7
An Overview....Pages 9-11
Crystal Growth — Ostwald Ripening....Pages 12-26
Crystal Growth-Sidearm Precipitation....Pages 27-38
Gelatin Swelling....Pages 39-44
Gelation....Pages 45-52
Polymeric Base....Pages 53-64
Front Matter....Pages 65-66
Limited Coalescence....Pages 67-74
Measuring Coalescence....Pages 75-83
Front Matter....Pages 85-86
Newtonian Coating Flows....Pages 87-98
Coating Configurations....Pages 99-108
Curtain Coating....Pages 109-130
Shear Thinning....Pages 131-140
Front Matter....Pages 141-141
Latent Image Formation....Pages 143-151
Granularity....Pages 152-157
Front Matter....Pages 159-159
A Reaction-Diffusion System....Pages 161-175
Parameter Identification....Pages 176-182
Back Matter....Pages 183-184
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