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来源机构: Optics Express
来源目录: Optics Express
发布日期: Aug 13, 2019
资源类型: 293.33KB
资源性质: 科技论文
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Interferenceless and motionless method for recording digital holograms of coherently illuminated 3D objects by coded aperture correlation holography system

Equations (9). Equations on this page are rendered with MathJax. Learn more. (1) H O B J ( r ¯ ) = ∫ I O B J ( r ¯ , z ) ∗ t ( r ¯ , z ) d z , (2) I I M G ( r ¯ , z j ) = H O B J ( r ¯ ) ⊗ R ( r ¯ , z j ) , (3) A I n ( r ¯ ) ∗ f ( r ¯ ) 2 ≈ A I n ( r ¯ ) 2 ∗ q ( r ¯ ) , (4) A I n ( r ¯ ) ∗ ∑ k a k δ ( r ¯ − r ¯ k ) 2 = ∑ k a k A I n ( r ¯ − r ¯ k ) 2 = ∑ k a k 2 A I n ( r ¯ − r ¯ k ) 2 = A I n ( r ¯ ) 2 ∗ ∑ k a k 2 δ ( r ¯ − r ¯ k ) , (5) I k = O ( r ¯ R / r ¯ R M T M T ) 2 ∗ ∑ i = 1 N a i 2 δ ( r ¯ R − r ¯ k , i ) , (6) I I M G = H O B J ⊗ H P S H ′ = O ( r ¯ R / r ¯ R M T M T ) ∗ H P S F 2 ⊗ H P S H ′ = O ( r ¯ R / r ¯ R M T M T ) ∗ [ ∑ i = 1 N a i δ ( r ¯ R − r ¯ 1 , i ) − ∑ i = 1 N b i δ ( r ¯ R − r ¯ 2 , i ) ] 2 ⊗ H P S H ′ = O ( r ¯ R / r ¯ R M T M T ) 2 ∗ [ ∑ i = 1 N a i 2 δ ( r ¯ R − r ¯ 1 , i ) − ∑ i = 1 N b i 2 δ ( r ¯ R − r ¯ 2 , i ) ] ⊗ H P S H ′ = F − 1 { F [ O ( r ¯ R / r ¯ R M T M T ) 2 ] F [ ∑ i = 1 N a i 2 δ ( r ¯ R − r ¯ 1 , i ) − ∑ i = 1 N b i 2 δ ( r ¯ R − r ¯ 2 , i ) ] exp ⁡ ( − j φ ) } = F − 1 { F [ O ( r ¯ R / r ¯ R M T M T ) 2 ] h exp ⁡ ( j φ ) exp ⁡ ( − j φ ) } = O ( r ¯ R / r ¯ R M T M T ) 2 ∗ F − 1 { h } ≈ O ( r ¯ R / r ¯ R M T M T ) 2 , (7) F { ∑ i = 1 N a i 2 δ ( r ¯ R − r ¯ 1 , i ) − ∑ i = 1 N b i 2 δ ( r ¯ R − r ¯ 2 , i ) } = h exp ⁡ ( j φ ) . (8) H O B J = ∑ q = 1 P { O q ( r ¯ R / r ¯ R M T M T ) 2 ∗ ∑ p = 1 P [ ∑ i = 1 N a p , i g q , p ( r ¯ R − r ¯ 1 , p , i ) − ∑ i = 1 N b p , i g q , p ( r ¯ R − r ¯ 2 , p , i ) ] } , (9) I I M G = H O B J ⊗ H P S H , l ′ = ∑ q = 1 P { O q ( r ¯ R / r ¯ R M T M T ) 2 ∗ ∑ p = 1 P [ ∑ i = 1 N a p , i g q , p ( r ¯ R − r ¯ 1 , p , i ) − ∑ i = 1 N b p , i g q , p ( r ¯ R − r ¯ 2 , p , i ) ] } ⊗ H P S H , l ′ = ∑ q = 1 P O q ( r ¯ R / r ¯ R M T M T ) 2 ∗ [ ∑ i = 1 N a q , i δ ( r ¯ R − r ¯ 1 , q , i ) − ∑ i = 1 N b q , i δ ( r ¯ R − r ¯ 2 , q , i ) ] ⊗ H P S H , l ′ + ∑ q = 1 P ∑ p ≠ q P O q ( r ¯ R / r ¯ R M T M T ) 2 ∗ [ ∑ i = 1 N a p , i g q , p ( r ¯ R − r ¯ 1 , p , i ) − ∑ i = 1 N b p , i g q , p ( r ¯ R − r ¯ 2 , p , i ) ] ⊗ H P S H , l ′ ≈ O l ( r ¯ R / r ¯ R M T M T ) 2 + ∑ q ≠ l P O q ( r ¯ R / r ¯ R M T M T ) 2 ∗ g q , l ( r ¯ R ) . .

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