chapter 19, Advanced Concepts

from: Optical Design of Microscopes

Author(s): George H. Seward

Published: 19 April 2010

Chapter DOI: http://dx.doi.org/10.1117/3.855480.ch19

Chapter Page Count: 13 pages

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Front Matter

1. Optical Design Concepts

2. Basic Microscope Concepts

3. Basic Geometric Optics

4. Aberrations

5. Basic Physical Optics

6. Fluorescence

7. Optical Design Metrics

8. Image Contrast

9. Microlens Formats

10. Illumination Systems

11. Cover Strata

12. Objective Lenses

13. Tube Elements

14. Ocular Lenses

15. Sensors

16. Human Vision

17. Optical Materials

18. Composition and Spectra of Materials

19. Advanced Concepts

20. Prescriptions

Back Matter

Preview

Chapter Contents

19.1 Wave Equation
19.2 Refractive Index
19.3 Relative Partial Dispersion
19.4 Emission
19.5 Coherence
19.6 Gaussian Beam P
19.7 Transfer Functions
19.8 Scatter
19.9 Interference Filters
19.10 Shot Noise

Excerpt

19.1 Wave Equation

An electromagnetic wave is governed by three important features: the spatial curvature of the electric field ∇²E, the temporal curvature of the electric field Ë, and the temporal slope of electric current density J, which may also be considered the acceleration of electric current density. These parameters are expressed in the wave equation as follows:

∇E = μ(ε₀ Ë, + J),

where μ is the magnetic permeability and ε₀ is the electric permittivity.

The ∇ operator defines the gradient as

∇ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k

where i, j, and k are unit vectors. The ∇² operator defines the Laplacian as

∇² = (∂²/∂x²)i + (∂²/∂y²)j + (∂²/∂z²)k.