10-信息光学7-1.pdfVIP

#7-1 Wave-Optics Analysis of Coherent Optical Systems （Chapter 5） 1.A thin lens as a phase transformation y Δ(x,y) Δ x 0 φ(x, y) = knΔ(x, y) + k[Δ0 ? Δ(x, y)] where n is the refractive index of the lens material, knΔ(x,y) is the phase delay introduced by the lens, and k[Δ0-Δ(x,y)] is the phase delay introduced by the remaining region of free space between the two planes Δ(x,y) Δ0 Ul(x,y) Ul′(x,y) tl (x, y) = exp( jkΔ0 )exp[ jk(n ?1)Δ(x, y)] Ul (x, y) = tl (x, y)Ul (x, y) The problem remains to find the mathematical form of the thickness function Δ(x,y)in order that the effects of the lens may be understood. Δ(x,y) 2 2 2 2 Δ0 x + y x + y Δ(x, y) = Δ0 ? R1(1? 1? 2 ) + R2 (1? 1? 2 ) R1 R2 The paraxial approximation 2 2 2 2 x2 + y 2 x2 + y 2 x + y x + y 1? 2 =1? 2 1? 2 =1? 2 R2 2R2 R1 2R1 x2 + y 2 x2 + y 2 Δ(x, y) = Δ0 ? R1(1? 1? 2 ) + R2 (1? 1? 2 ) R1 R2 x2 + y 2 1 1 Δ(x, y) = Δ0 ? ( ? ) 2 R1 R2 The phase transformation and its physical meaning x2 + y 2 1 1 Δ(x, y) = Δ0 ? ( ? ) 2 R1 R2 tl (x, y) = exp( jkΔ0 )exp[ jk(n ?1)Δ(x, y)] Define the focal length f as Ignore the constant 1 1 1 phase factor ≡ (n ?1)( ? ) k 2 2