10-信息光学5.pdf

#5 Fresnel and Fraunhofer Diffraction（Chapter 4 ） Scalar Diffraction Theory Scalar Diffraction Theory Transfer function Point spread function representation (frequency representation (spatial domain) domain) Angular Spectrum Kirchoff/Rayleigh- Sommerfeld Approximations Fresnel Frauhofer Diffraction Diffraction Diffraction Equivalence (Huygen’s Principle) between the angular spectrum Spherica Quadratic and the First l Rayleigh Sommerfeld solution can be shown using the Weyl Expansion Diffraction Approximations Rayleigh-Sommerfeldλ ξ η Fresnel Approximation Fraunhofer Approximation 1 e jkr01 θ U (x, y) = U ( , ) cos dξdη j ∫∫ r Σ 01 can also be written as … λ ξ Rayleigh-Sommerfeldη diffraction Fresnel diffraction integral as a λ ξ integral as a convolution convolution η ξ ξ ξ jk z 2 +(x? )2 +( y?η )2 jkz ∞ k z e e j [](x? )2 +( y?η )2 U (x, y) = U ( , ) η dξdη U (x, y) = U ( , )e 2z dξdη ∫∫ 2 2 2 ∫∫ j Σ z + (x ? ) + (y ? ) j z ?∞ can also be written as … distance r is approximated as … distance r 01 ξ 01 ξ 2 2