Consistent scalar imaging theory

Since scalar imaging theory treats propagating waves as being scalar, it does not completely describe their physical properties. However, it plays an important role in the field of optical design and applications, such as semiconductor exposure projection optics. Therefore, we establish an accurate and meaningful scalar imaging theory, applicable even for high numerical aperture optics. We call this the consistent scalar imaging theory and consider the following three criteria for consistency. (1) When the wavelength of light becomes close to zero, the point spread function of wave optics coincides with the spot diagram (correspondence principle). (2) When considering point imaging, the total energy incident on the pupil equals that on the image. (3) The reciprocity theorem holds between object and image. These conditions are simultaneously fulfilled by introducing appropriate outgoing and incoming inclination factors. We emphasize that the pupil coordinates should be defined as the direction cosine of the ray.