Incoming inclination factor for scalar imaging theory

Abstract

The conventional scalar imaging theories that are represented in the Fresnel-Kirchhoff diffraction formula or the RayleighSommerfeld diffraction formulae involve contradictions. By introducing incoming inclination factors not only for the diffraction surface but also for the image plane, we propose a new equation that fulfills both the selfconsistency and the reciprocity theorem. We also confirm the validity of this new equation by both theoretical discussions and numerical calculations.

Study on the Reduction Effect of Stereo Depth Caused by Lens Aberration in Lenticular-Based Autostereoscopic Displays

“…However, in most cases, the wave from the pixel to the viewing point is slant, which makes Equation 1invalid. To solve this problem, an inclination factor [24] is introduced into Equation 1, which is related to the viewing angle θ view , as expressed by:…”

Theoretical study for aerial image intensity in resist in high numerical aperture projection optics and experimental verification with one-dimensional patterns

“…Several researchers have proposed some advanced arguments and useful theories. [1][2][3][4][5][6][7][8][9] These previous studies, however, involve ambiguity in the treatments of emerging inclination factor from object and incoming inclination factor onto image in terms of the scalar imaging theory. In addition, we point out paradoxical phenomenon between electric intensity and photon number on the image plane in terms of the vector imaging theory.…”

“…(1) Correspondence principle between wave optics and geometrical optics: When λ is limitedly equal to zero, the wave optical point spread function (PSF) should be equal to the spot diagram. 8 (2) Reciprocity: When the object and the image are exchanged with each other, the PSF is perfectly similar to the original one. 7,8 (3) Parseval theorem: 12 Even in the case of high numerical aperture (NA), this mathematical theory for Fourier transform is physically satisfied as energy conservation between the pupil and the image.…”

“…8 (2) Reciprocity: When the object and the image are exchanged with each other, the PSF is perfectly similar to the original one. 7,8 (3) Parseval theorem: 12 Even in the case of high numerical aperture (NA), this mathematical theory for Fourier transform is physically satisfied as energy conservation between the pupil and the image. 7 In this paper, we reconsider the imaging theory in detail and compare theoretical aerial image intensity with experimental pattern width in resist of one-dimensional (1-D) pattern in optical lithography.…”

“…We introduce the illuminating inclination factor onto the object (mask), the emerging inclination factor from the object, and the incoming inclination factor onto the image (wafer). [7][8][9][10][11]13 As in previous papers, 2,7,9 we also introduce well-known factor of radiometric correction (RC), which is due to the ratio between the cross-section area of the exit plane wave from the object and that of the entrance plane wave onto the image in projection optics. Moreover, in this paper, considering the change of the cross-section area of the inclined illuminating plane wave, we point out scaling factor of amplitude of incoming illuminating plane waves, which is introduced for the first time, to the best of our knowledge.…”