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Principles of Biophotonics: Linear systems and the Fourier transform in optics aims to teach students, instructors and professionals the basis of optical techniques for biomedical investigation. It is a book for experimentalists who are active at the interface between biology, medicine and optics (i.e. biological optics, biomedical optics and biophotonics), and it presents the unifying optics principles employed in this broad and interdisciplinary field. With the format of a classical textbook, this work contains the underlying theory of biological optics and applications to real laboratory problems via exercises and homework. While maintaining mathematical rigor, the theory is presented with emphasis on the physical phenomena, and heavy use of the linear systems approach and frequency domain representation. The text stresses the similarity between various techniques, thus reducing the number of governing concepts as much as possible.
1. Superposition principle
2. Linear Systems
3. Spatial and temporal frequencies
4. 1D Fourier transform
5. 2D Fourier transform
6. 3D Fourier transform
7. Complex signals
8. The uncertainty relation
9. Linear systems with random inputs
10. Fourier transform of vector-valued functions
11. The Laplace transform
Appendix A. Complex variables
Appendix B. Vector algebra
Appendix C. Useful trigonometric formulas
Appendix D. Useful integrals