Search results for "Kirchhoff's diffraction formula"
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Chapter 1 The Resolution Challenge in 3D Optical Microscopy
2009
Publisher Summary This chapter discusses the theoretical principles of 3D microscopy with the widespread realizations of 3D microscopy.Based on the paraxial diffraction equations, it has been shown that conventional microscopes, when dealing with 3D fluorescent samples, provide sets of 2D images. These images of the different transverse sections of the 3D object contain, in addition to the sharp image of the in focus section, the blurred images of the rest of the specimen. The paraxial formalism has been generalized in a very simple way to a non-paraxial context, showing that the equations that govern non-paraxial imaging are similar to those that govern paraxial imaging. The only differenc…
Three-dimensional behavior of apodized nontelecentric focusing systems.
2002
The scalar field in the focal volume of nontelecentric apodized focusing systems cannot be accurately described by the Debye integral representation. By use of the Fresnel–Kirchhoff diffraction formula it is found that, if the aperture stop is axially displaced, the focal-volume structure is tuned. We analyze the influence of the apodizing function and find that, whereas axially superresolving pupil filters are highly sensitive to the focal-volume reshaping effect, axially apodizing filters are more inclined to the focal-shift effect.
Debye representation of dispersive focused waves
2006
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matri…