# Incoherent Digital Holography: A Review

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## Abstract

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## 1. Introduction

## 2. Principle of OSH

#### 2.1. Setup of OSH

#### 2.2. Mathematical Model of OSH

#### 2.3. Point Spread Function and Pupil Engineering

## 3. Principle of FINCH

#### 3.1. Setup of FINCH

#### 3.2. Mathematical Model of FINCH

#### 3.3. Point Spread Function

## 4. Special Topics and Applications

#### 4.1. Fluorescence Holography

#### 4.2. Optical Display of Incoherent Hologram

#### 4.3. Reduction of Scanning Speed and Recorded Data in OSH

#### 4.4. Single-Shot Imager for the Aim of Capturing High-Speed Incoherent 3D Objects

#### 4.5. Coded Aperture Correlation Holography (COACH)

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic setup of optical scanning holography (OSH). EOM: electro-magnetic modulator; PBS: polarizing beamsplitter; M’s: mirrors; BEs: beam expanders; HWP: half-wave plate; L’s: lenses; ${f}_{2}$ and ${f}_{3}$ are the focal lengths of lenses L2 and L3, respectively; PDs: photodetectors; BPF@Ω: band-pass filter tuned at frequency Ω.

**Figure 2.**Hologram of two coins recorded by optical scanning holography (OSH): (

**a**) real part, and (

**b**) imaginary part. (Reproduced with permission from [57], OSA publishing, 2015).

**Figure 3.**Reconstructed image at (

**a**) ${z}_{r}=90\text{\hspace{0.17em}}\mathrm{mm}$, and (

**b**) ${z}_{r}=115\text{\hspace{0.17em}}\mathrm{mm}$. The larger figures show the whole field of view, while the small figures are the zoom-in of selected regions (Reproduced with permission from [57], OSA publishing, 2015).

**Figure 5.**Setups of fluorescence holography: (

**a**) Fresnel incoherent correlation holography (FINCH), and (

**b**) optical scanning holography (OSH).

**Figure 6.**Experimental results of fluorescence holography. (

**a**) One of the phase-shifted holograms, (

**b**) intensity, and (

**c**) phase distributions on the image sensor plane. (

**d**) Reconstructed image on a specified depth, and (

**e**) three-dimensional (3D) mapping of fluorescent nanoparticles with incoherent digital holographic microscopy.

**Figure 8.**Single-shot in-line phase-shifting digital holography (DH) with Fresnel incoherent correlation holography (FINCH). (

**a**) Schematic of a constructed optical setup. (

**b**) Transitions of the states of polarizations.

**Figure 9.**Experimental results. (

**a**) Recorded hologram; (

**b**) magnified image of a part of (

**a**) four phase-shifted holograms, which are generated from (

**a**), with (

**c**) 0, (

**d**) $\pi /2$, (

**e**) $\pi $, and (

**f**) $3\pi /2$ phase shifts; (

**g**) amplitude, and (

**h**) phase images on the image sensor plane, which are extracted by phase-shifting interferometry; (

**i**) reconstructed image of a 1 mm aperture object illuminated by incoherent light.

**Table 1.**Comparison of optical scanning holography (OSH) and Fresnel incoherent correlation holography (FINCH).

OSH | FINCH | |
---|---|---|

1. Field of view | Large ^{1} | Small |

2. Pixel pitch | Very small ^{1} | Small |

3. System variety ^{2} | High | Low |

4. Recording time | Slow | Fast |

5. Imaging by natural light | No ^{3} | Yes ^{4} |

6. System complexity | High | Low |

^{1}The field of view and pixel pitch in OSH depends on the scanning setup.

^{2}This means that the system can be adapted to realize different applications of imaging.

^{3}Active scanning imaging.

^{4}Passive imaging.

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**MDPI and ACS Style**

Liu, J.-P.; Tahara, T.; Hayasaki, Y.; Poon, T.-C.
Incoherent Digital Holography: A Review. *Appl. Sci.* **2018**, *8*, 143.
https://doi.org/10.3390/app8010143

**AMA Style**

Liu J-P, Tahara T, Hayasaki Y, Poon T-C.
Incoherent Digital Holography: A Review. *Applied Sciences*. 2018; 8(1):143.
https://doi.org/10.3390/app8010143

**Chicago/Turabian Style**

Liu, Jung-Ping, Tatsuki Tahara, Yoshio Hayasaki, and Ting-Chung Poon.
2018. "Incoherent Digital Holography: A Review" *Applied Sciences* 8, no. 1: 143.
https://doi.org/10.3390/app8010143