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Chapter 3:
Elements of Diffraction Theory
Under the premise of geometrical optics a point object would give rise to a sharp-point image. In reality no optical system can form a point image. Even if we could create a point source, the image is a halo of light centered at the geometrical image point. This blurring arises because light does not truly travel rectilinearly. Its wave nature compels it to bend around corners and obstructions to a small but finite degree. Such bending governs phenomena including Gaussian beam propagation and imaging of objects whose dimensions are comparable to or smaller than the wavelength. This latter scenario is frequently encountered in optical lithography, where details of intensity changes at aperture edges are significant. In this chapter we develop diffraction theory (also called physical optics) that describes light propagation in situations where the language of geometry is insufficient. Since the wave equations [Eq. (1.18)] are linear, we can rely on the principle of superposition and restrict our analysis to a basic time-harmonic spherical or plane wave. The total diffracted field is a linear combination of different basic waves, with each constituent wave satisfying the diffraction equations. By establishing reciprocity for electromagnetic fields, we shall formulate equations for Fresnel-Kirchhoff diffraction of an aperture in which the distance between the image region and the aperture is large compared with the wavelength, and for Fraunhofer diffraction in which the distance is large compared with both the wavelength and the aperture dimension. The former is germane to contact printing, while the latter is applicable to projection optical lithography.
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