# The Physics of Turbulence-Free Ghost Imaging

## Abstract

**:**

## 1. Introduction

## 2. Classical Imaging

## 3. “Noise” Produced Image

## 4. The Theory for Turbulence-Free Lensless Ghost Imaging

#### 4.1. An Interference Model Based on a Large Number of Random Radiation Subfields

#### 4.2. Quantum Theory of Lensless Light Ghost Imaging

## Acknowledgments

## Conflicts of Interest

## References

- Pittman, T.B.; Shih, Y.H.; Strekalov, D.V.; Sergienko, A.V. Optical Imaging by Means of Two-photon Quantum Entanglement. Phys. Rev. A
**1995**, 52. [Google Scholar] [CrossRef] - Strekalov, D.V.; Sergienko, A.V.; Klyshko, D.N.; Shih, Y.H. Observation of Two-Photon “Ghost” Interference and Diffraction. Phys. Rev. Lett.
**1995**, 74. [Google Scholar] [CrossRef] [PubMed] - Valencia, A.; Scarcelli, G.; D’Angelo, M.; Shih, Y.H. Two-photon Imaging with Thermal Light. Phys. Rev. Lett.
**2005**, 94. [Google Scholar] [CrossRef] [PubMed] - Cao, D.; Xiong, J.; Wang, K. Geometrical Optics in Coincidence Imaging System. 2005. Available online: https://arxiv.org/abs/quant-ph/0407065v1 (accessed on 6 December 2016).
- Cai, Y.J.; Zhu, S.Y. Ghost Imaging with Incoherent and Partially Coherent Light Radiation. Phys. Rev. E
**2005**, 71. [Google Scholar] [CrossRef] [PubMed] - Scarcelli, G.; Berardi, V.; Shih, Y.H. Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuation? Phys. Rev. Lett.
**2006**, 96. [Google Scholar] [CrossRef] [PubMed] - Bennink, R.S.; Bentley, S.J.; Boyd, R.W. “Two-photon” Coincidence imaging with a classical source. Phys. Rev. Lett.
**2002**, 89. [Google Scholar] [CrossRef] [PubMed] - Gatti, A.; Brambilla, E.; Bache, M.; Lugiato, L.A. Correlated Imaging, Quantum and Classical. Phys. Rev. A
**2004**, 70. [Google Scholar] [CrossRef] - Ferri, F.; Magatti, D.; Gatti, A.; Bache, M.; Brambilla, E.; Lugiato, L.A. High-Resolution Ghost Image and Ghost Diffraction Experiments with Thermal Light. Phys. Rev. Lett.
**2005**, 94. [Google Scholar] [CrossRef] [PubMed] - Meyers, R.E.; Deacon, K.S.; Shih, Y.H. Turbulence-free Ghost Imaging. Appl. Phys. Lett.
**2011**, 98. [Google Scholar] [CrossRef] - Hecht, E. Optics, 4th ed.; Addison Wesley: Boston, MA, USA, 2002; pp. 154–196. [Google Scholar]
- Shih, Y.H. An Introduction to Quantum Optics: Photon and Biphoton Physics, 1st ed.; Taylor & Francis: Oxfordshire UK, 2011; pp. 53–60. [Google Scholar]
- Einstein, A. On a heuristic viewpoint concerning the production and transformation of light. Annalen der Physik
**1905**, 17, 132. [Google Scholar] [CrossRef] - Chen, H.; Peng, T.; Shih, Y.H. 100% Correlation of Chaotic Thermal Light. Phys. Rev. A
**2013**, 88. [Google Scholar] [CrossRef] - Peng, T.; Chen, H.; Shih, Y.H.; Scully, M.O. Delayed-choice quantum eraser with thermal light. Phys. Rev. Lett.
**2014**, 112. [Google Scholar] [CrossRef] [PubMed] - Glauber, R.J. The Quantum Theory of Optical Coherence. Phys. Rev.
**1963**, 130. [Google Scholar] [CrossRef] - Scully, M.O.; Zubairy, M.S. Quantum Optics; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar]
- Hanbury-Brown, R.; Twiss, R.Q. Correlation Between Photons in Two Coherent Beams of Light. Nature
**1956**, 177. [Google Scholar] [CrossRef] - Hanbury-Brown, R.; Twiss, R.Q. A Test of A New Type of Stellar Interferometer on Sirius. Nature
**1956**, 178. [Google Scholar] [CrossRef] - Hanbury-Brown, R. Intensity Interferometer; Taylor and Francis Ltd.: London, UK, 1974. [Google Scholar]
- Scarcelli, G.; Valencia, A.; Shih, Y.H. Two-photon Interference with Thermal Light. Europhys. Lett.
**2004**, 68. [Google Scholar] [CrossRef] - Meyers, R.E.; Deacon, K.S.; Shih, Y.H. Ghost-Imaging Experiment by Measuring Reflected Photons. Phys. Rev. A
**2008**, 77. [Google Scholar] [CrossRef] - Martienssen, W.; Spiller, E. Coherence and Fluctuations in Light Beams. Am. J. Phys.
**1964**, 32. [Google Scholar] [CrossRef] - Glauber, R.J. Coherent and Incoherent States of the Radiation Field. Phys. Rev.
**1963**, 131. [Google Scholar] [CrossRef]

**Figure 1.**Optical imaging: a lens produces an image of an object in the plane defined by the Gaussian thin-lens equation $1/{s}_{i}+1/{s}_{o}=1/f$. Image formation is based on a point-to-point relationship between the object plane and the image plane. All radiation emitted from a point on the object plane will “collapse” to a unique point on the image plane.

**Figure 2.**Imaging from “noise”: an image of the target object, which is under the influence of atmospheric turbulence, is produced from the correlation measurement of $\langle \Delta n({\overrightarrow{\rho}}_{i1})\Delta n({\overrightarrow{\rho}}_{i2})\rangle $ or $\langle \Delta n({\overrightarrow{\rho}}_{i1})\int d{\overrightarrow{\rho}}_{i2}\Delta n({\overrightarrow{\rho}}_{i2})\rangle $. This figure illustrates the later measurement: the “bucket” detector (BD) sums over the fluctuations at all ${\overrightarrow{\rho}}_{i2}$, using the integrated fluctuations for the joint measurement paired with that of each element of the CCD (Charge-Coupled Device) array (${\overrightarrow{\rho}}_{i2}$). The classical images in $\langle {n}_{i1}\rangle $ and $\langle {n}_{i2}\rangle $ are both “blurred” due to the influence of atmospheric turbulence. However, the observed image in $\langle \Delta n({\overrightarrow{\rho}}_{i1})\Delta n({\overrightarrow{\rho}}_{i2})\rangle $, and/or $\langle \Delta n({\overrightarrow{\rho}}_{i1})\int d{\overrightarrow{\rho}}_{i2}\Delta n({\overrightarrow{\rho}}_{i2})\rangle $, are turbulence-free. In this setup the turbulence may appear either in the optical pass between the camera and the object or in the optical pass between the object and the light source, or appear in both passes.

**Figure 3.**Two-photon Young’s double-slit interference experiment. The interferometer is a standard Young’s double-slit interferometer, except the measurement is $\langle \Delta I({x}_{1})\Delta I({x}_{2})\rangle $ by means of the use of two point-like scannable photodetectors ${D}_{1}$ and ${D}_{2}$, as well as the PNFC (Photon Number Fluctuation Correlation) measurement circuit. The separation between the upper slit-A and the lower slit-B is much greater than the coherence length of the thermal field, $d\gg {l}_{c}$. Consequently, no first-order interferences are observable from $\langle I({x}_{1})\rangle $ and $\langle I({x}_{2})\rangle $. The question is: do we observe interference from $\langle \Delta I({x}_{1})\Delta I({x}_{2})\rangle $?

**Figure 4.**Lensless ghost imaging of chaotic-thermal light demonstrated by Meyers et al. in 2008. ${D}_{2}$ is a “bucket” photon counting detector that is used to collect and count all random scattered and reflected photons from the object. The photon number fluctuation correlation between the “bucket detector” (${D}_{2}$) and the CCD array (${D}_{1}$) is measured and calculated by a photon-counting-coincidence circuit, similar to the PNFC circuit described in the last section. The counting rate of ${D}_{2}$ and each element of the CCD array of ${D}_{1}$ were both monitored to be constants during the measurement (the consistent value is mainly determined by the source intensity). Surprisingly, a ghost image of the object was captured in the photon number fluctuation correlation $\langle \Delta n({\overrightarrow{\rho}}_{1})\int d{\overrightarrow{\rho}}_{2}\Delta n({\overrightarrow{\rho}}_{2})\rangle $ between the CCD and ${D}_{2}$, when taking ${z}_{1}={z}_{2}$. The images “blurred” when the CCD is moved away from ${z}_{1}={z}_{2}$, either to the direction of ${z}_{1}>{z}_{2}$ or ${z}_{1}<{z}_{2}$. There is no doubt that thermal radiation propagates to any transverse plane in a random and chaotic manner. In the lensless setup, there is no lens applied to force the thermal radiation to “collapse” to a point or speckle either. What is the cause of the point-to-point image-forming correlation?

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**MDPI and ACS Style**

Shih, Y.
The Physics of Turbulence-Free Ghost Imaging. *Technologies* **2016**, *4*, 39.
https://doi.org/10.3390/technologies4040039

**AMA Style**

Shih Y.
The Physics of Turbulence-Free Ghost Imaging. *Technologies*. 2016; 4(4):39.
https://doi.org/10.3390/technologies4040039

**Chicago/Turabian Style**

Shih, Yanhua.
2016. "The Physics of Turbulence-Free Ghost Imaging" *Technologies* 4, no. 4: 39.
https://doi.org/10.3390/technologies4040039