Mathematical Models in Photographic Science

By: Avner Friedman, David Ross

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Hardcover | 11 December 2002

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Hardcover
184 Pages

Dimensions(cm)
23.5 x 15.5 x 1.27

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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.

Industry Reviews

This book provides an interesting and well documented presentation of mathematical topics related to photographic sciences. [...] This is an attractive and easy to read book, which is characterized by a valuable (in the reviewer?s opinion) feature: each chapter covers the whole path from the phenomenological analysis and interpretation of the real system, to modeling, statement of problems related to the application of models, an outline of qualitative analysis, and finally to perspectives and open problems.

This book is recommended to applied mathematicians interested in industrial mathematics and is intended for applications and the development of mathematical methods for problems generated from technology. It is also a good text for advanced university courses on mathematical modeling to be joined to courses on computational methods.

Applied mathematicians will find a description of open problems which are definitely challenging even for experienced mathematicians.

MathSciNet 2004. Nicola Bellomo (I-TRNP)

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Introduction	p. 1
History of Photography	p. 3
References	p. 6
The Components of a Film
An Overview	p. 9
Crystal Growth - Ostwald Ripening	p. 12
The Model	p. 12
Mathematical Analysis	p. 15
A More General Model	p. 17
Open Problems	p. 20
Ostwald Ripening in a Colloidal Dispersion	p. 21
Exercises	p. 25
References	p. 26
Crystal Growth-Sidearm Precipitation	p. 27
The Physical Model	p. 27
Mathematical Model for CSTR Mixer	p. 30
Mathematical Model for PFR Mixer	p. 34
Mathematical Analysis	p. 35
Open Problems	p. 37
Exercises	p. 37
References	p. 38
Gelatin Swelling	p. 39
Introduction	p. 39
A Mathematical Model	p. 40
Mathematical Results	p. 42
Open Problems	p. 44
References	p. 44
Gelation	p. 45
Introduction	p. 45
The Model	p. 46
Mathematical Analysis	p. 48
Open Problems	p. 51
Exercises	p. 51
References	p. 52
Polymeric Base	p. 53
Bending Recovery of Elastic Film	p. 53
Viscoelastic Material	p. 56
The Bending Recovery Function for t > t_w	p. 58
Exercises	p. 64
References	p. 64
The Role of Surfactants
Limited Coalescence	p. 67
Introduction	p. 67
The Model	p. 68
Mathematical Results	p. 70
Open Problems	p. 74
References	p. 74
Measuring Coalescence	p. 75
The Coalescence Problem	p. 75
Introducing Chemiluminescent Species	p. 77
Mathematical Results	p. 79
Open Problems	p. 82
References	p. 82
Coating
Newtonian Coating Flows	p. 87
The Mathematical Model	p. 87
The Dynamic Contact Angle	p. 92
Mathematical Results	p. 93
Open Problems	p. 96
Exercise	p. 97
References	p. 97
Coating Configurations	p. 99
An Extrusion Die	p. 99
The Basic Model	p. 101
Fluid Flow in the Slot	p. 102
Design Problems	p. 106
Exercise	p. 108
References	p. 108
Curtain Coating	p. 109
Reducing the Surface Tension	p. 109
Measuring DST	p. 115
Potential Flow Model of a Curtain	p. 120
Time-Dependent Liquid Curtains	p. 124
Open Problems	p. 128
Exercises	p. 128
References	p. 129
Shear Thinning	p. 131
Motivation	p. 131
Viscosity Divergence	p. 131
Brownian Dynamics	p. 133
Numerical Results	p. 136
Future Directions	p. 139
References	p. 140
Image Capture
Latent Image Formation	p. 143
The Physical Model	p. 143
Monte Carlo Simulation	p. 144
An Alternative Approach	p. 147
References	p. 151
Granularity	p. 152
Transmittance and Granularity	p. 152
Moments of the Transmission	p. 154
Open Problems	p. 157
References	p. 157
Development
A Reaction-Diffusion System	p. 161
The Development Process	p. 161
A Mathematical Model	p. 162
Homogenization	p. 165
Edge Enhancement	p. 170
Acutance	p. 172
Open Problems	p. 174
Exercises	p. 174
References	p. 175
Parameter Identification	p. 176
The Direct Problem	p. 176
The Inverse Problems	p. 178
A Solution to an Inverse Problem	p. 178
Open Problems	p. 181
Exercises	p. 181
References	p. 181
Index	p. 183
Table of Contents provided by Publisher. All Rights Reserved.

Mathematical Models in Photographic Science

At a Glance

Hardcover

Industry Reviews

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