Researching | Multiframe full-field heterodyne digital holographic microscopy

Journals >Chinese Optics Letters >Volume 14 >Issue 5 >Page 050901 > Article

Chinese Optics Letters
Vol. 14, Issue 5, 050901 (2016)

Multiframe full-field heterodyne digital holographic microscopy

Xiaoyu Lv, Bin Xiangli^*, Wenxi Zhang^**, Zhou Wu, Yang Li, Xinxin Kong, and Zhiliang Zhou

Author Affiliations

Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing 100094, China

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DOI: 10.3788/COL201614.050901 Cite this Article Set citation alerts

Xiaoyu Lv, Bin Xiangli, Wenxi Zhang, Zhou Wu, Yang Li, Xinxin Kong, Zhiliang Zhou. Multiframe full-field heterodyne digital holographic microscopy[J]. Chinese Optics Letters, 2016, 14(5): 050901 Copy Citation Text

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Abstract

Digital holographic microscopy using multiframe full-field heterodyne technology is discussed in which two acousto-optic modulators are applied to generate low-frequency heterodyne interference and a high-speed camera is applied to acquire multiframe full-field holograms. We use a temporal frequency spectrum analysis algorithm to extract the object’s information. The twin-image problem can be solved and the random noise can be significantly suppressed. The relationship between the frame number and the reconstruction accuracy is discussed. The typical objects of microlenses and biology cells are reconstructed well with 100-frame holograms for illustration.

U_{O} (t) = a_{O} e^{j (ω_{O} t + φ_{O})} .

(1)

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U_{R} (t) = a_{R} e^{j (ω_{R} t + φ_{R})} .

(2)

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s (t) = (U_{O} + U_{R}) {(U_{O} + U_{R})}^{*} .

(3)

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ω_{H} = ω_{O} - ω_{R} = 2 π f_{H} .

(4)

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s (t) = a_{O}^{2} + a_{R}^{2} + a_{O} a_{R} e^{j (ω_{H} t + φ_{O} - φ_{R})} + a_{O} a_{R} e^{- j (ω_{H} t + φ_{O} - φ_{R})} .

(5)

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s_{total} (t) = a_{o}^{2} + a_{R}^{2} + a_{o} a_{R} e^{j (ω_{H} t)} e^{j (φ_{o} - φ_{R})} e^{j φ_{Noise} (t)} + a_{o} a_{R} e^{- j (ω_{H} t)} e^{- j (φ_{o} - φ_{R})} e^{- j φ_{Noise} (t)} .

(6)

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N_{period} = f_{H} t .

(7)

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N_{step} = \frac{f_{D}}{f_{H}} .

(8)

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N_{total} = f_{D} t = N_{period} N_{step} .

(9)

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O (x, y) = a_{O} a_{R} e^{j (φ_{O} - φ_{R})} .

(10)

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S (ω_{H}) = \frac{1}{T} \int_{0}^{T} s_{total} (t) e^{- j (ω_{H} t)} d t .

(11)

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S (ω_{H}) = a_{O} a_{R} e^{j (φ_{O} - φ_{R})} \frac{1}{T} \int_{0}^{T} e^{j φ_{Noise} (t)} d t .

(12)

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\frac{1}{T} \int_{0}^{T} e^{j φ_{Noise} (t)} d t = E (e^{j φ_{Noise}}) .

(13)

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p (φ_{Noise}) = \frac{1}{\sqrt{2 π} σ} e^{- \frac{φ_{Noise}^{2}}{2 σ^{2}}},

(14)

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F (n) = \int_{- \infty}^{+ \infty} e^{j φ_{Noise} n} p (φ_{Noise}) d φ_{Noise} = e^{- \frac{n^{2} σ^{2}}{2}} .

(15)

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E (e^{j φ_{Noise}}) = F (1) = e^{- \frac{σ^{2}}{2}} .

(16)

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S (ω_{H}) = e^{- \frac{σ^{2}}{2}} a_{O} a_{R} e^{j (φ_{O} - φ_{R})} .

(17)

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e^{- \frac{σ^{2}}{2}} a_{O} a_{R} = | S (ω_{H}) | = \sqrt{{Re [S (ω_{H})]}^{2} + {Im [S (ω_{H})]}^{2}} .

(18)

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φ_{O} - φ_{R} = \tan^{- 1} \frac{Im [S (ω_{H})]}{Re [S (ω_{H})]} .

(19)

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\emptyset = \tan^{- 1} (\frac{I_{3} - I_{1}}{I_{0} - I_{2}}),

(20)

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RMSE = \sqrt{\frac{\sum_{i = 1}^{N} {(φ_{i} - φ_{s})}^{2}}{N}},

(21)

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References (31)

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Xiaoyu Lv, Bin Xiangli, Wenxi Zhang, Zhou Wu, Yang Li, Xinxin Kong, Zhiliang Zhou. Multiframe full-field heterodyne digital holographic microscopy[J]. Chinese Optics Letters, 2016, 14(5): 050901

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