Analysis of Off-Axial Optical Systems (2) |
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Authors: | Keisuke Araki |
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Affiliation: | (1) Optics Research Dept. 31, Optics Technology Research Laboratory, Canon Inc., 3-30-2, Shimomaruko, Ohta-ku, Tokyo 146-8501, Japan |
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Abstract: | The extended 4×4 Gaussian bracket matrix Gij represents the lowest order quantity of “aberration coefficient tensor quantities” which are defined to as the peculiarity of off-axial optical systems and are independent of azimuths. We newly confirmed this extended 4×4 Gaussian bracket matrix of deflection (refraction or reflection), transmission and “twisting.” The result determined by use of a new representative method of asymmetrical surfaces and a method of paraxial expansion along the folded reference axis shows that the 4×4 Gaussian bracket matrix is the extended form of the 2x2 Gaussian bracket matrix which is used in co-axial rotational symmetric optical systems. Furthermore, we analyze and formalize the crossterm effects, which are the most serious problem in optical systems having multiple off-axial surfaces, using the concept of a chain of “optical systems divided into former and latter” and the vector-tensor analysis method. The result of this analysis reveals the structure of the cross-term effects and proves the usefulness of the vector-tensor analysis method in general image analysis. |
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Keywords: | off-axial optical system paraxial expansion along the folded reference axis 4× 4 Gaussian bracket matrix deflection transmission twisting 4-element vectors cross-term effects tensor algebra chain of “ optical systems divided into former and latter” |
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