Elements of the theory of diffraction

Side lobe suppression of a Bessel beam for high aspect ratio laser processing

“…For comparison, the theoretical curves for the CFB and the GB -which have the same spot size -were calculated and are shown with black and blue lines, respectively. The theoretical curves for the CFB were obtained using the diffraction integral [14,15], and the curves for the GB were obtained from the paraxial Helmholtz equation [11]. The SBB maintains constant intensity over a wider range than either the CFB or the GB in Fig.…”

Incoming inclination factor for scalar imaging theory

“…Overall light propagation in optical systems is addressed by scalar imaging theory, which is based on the integral theorem of Helmholtz and Kirchhoff. 1 Although this theorem is mathematically rigorous, one needs to assume hypotheses to obtain practical formulae. Different hypotheses yield different formulae, such as the Fresnel-Kirchhoff diffraction formula and the Rayleigh-Sommerfeld diffraction formulae.…”

“…Different hypotheses yield different formulae, such as the Fresnel-Kirchhoff diffraction formula and the Rayleigh-Sommerfeld diffraction formulae. 1,2 It is well-known that there are some contradictions in these formulae. 1,[3][4][5] The reciprocity theorem is fulfilled in the theorem of Helmholtz and Kirchhoff.…”

“…1,2 It is well-known that there are some contradictions in these formulae. 1,[3][4][5] The reciprocity theorem is fulfilled in the theorem of Helmholtz and Kirchhoff. 1,3 The FresnelKirchhoff diffraction formula also fulfills the reciprocity theorem, even though this formula inherently involves a mathematical contradiction.…”

“…1,[3][4][5] The reciprocity theorem is fulfilled in the theorem of Helmholtz and Kirchhoff. 1,3 The FresnelKirchhoff diffraction formula also fulfills the reciprocity theorem, even though this formula inherently involves a mathematical contradiction. 2 Since the reciprocity theorem is one of the fundamental properties in optics, the scalar imaging theory should fulfill this theorem.…”