## The influence of non-imaging detector design on heralded ghost-imaging and ghost-diffraction examined using a triggered ICCD camera |

Optics Express, Vol. 21, Issue 25, pp. 30460-30473 (2013)

http://dx.doi.org/10.1364/OE.21.030460

Acrobat PDF (3682 KB)

### Abstract

Ghost imaging and ghost diffraction can be realized by using the spatial correlations between signal and idler photons produced by spontaneous parametric down-conversion. If an object is placed in the signal (idler) path, the spatial correlations between the transmitted photons as measured by a single, non-imaging, “bucket” detector and a scanning detector placed in the idler (signal) path can reveal either the image or diffraction pattern of the object, whereas neither detector signal on its own can. The details of the bucket detector, such as its collection area and numerical aperture, set the number of transverse modes supported by the system. For ghost imaging these details are less important, affecting mostly the sampling time required to produce the image. For ghost diffraction, however, the bucket detector must be filtered to a single, spatially coherent mode. We examine this difference in behavour by using either a multi-mode or single-mode fibre to define the detection aperture. Furthermore, instead of a scanning detector we use a heralded camera so that the image or diffraction pattern produced can be measured across the full field of view. The importance of a single mode detection in the observation of ghost diffraction is equivalent to the need within a classical diffraction experiment to illuminate the aperture with a spatially coherent mode.

© 2013 Optical Society of America

## 1. Introduction

7. R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. **15**, 073032 (2013). [CrossRef]

8. P. H. S. Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Controlling the degree of visibility of Young’s fringes with photon coincidence measurements,” Phys. Rev. A **49**, 4176–4179 (1994). [CrossRef] [PubMed]

11. J. O. de Almeida, S. P. Walborn, P. H. Souto Ribeiro, and M. Hor-Meyll, “Fourth-order coherence induced by spatial mode parity selection,” Phys. Rev. A **86**, 033839 (2012). [CrossRef]

7. R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. **15**, 073032 (2013). [CrossRef]

12. R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Real-time imaging of quantum entanglement,” Sci. Rep. **3**, 1914 (2013). [CrossRef] [PubMed]

13. C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A **57**, 3123–3126 (1998). [CrossRef]

17. M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. **282**, 1154–1159 (2009). [CrossRef]

## 2. Theoretical background

*camera arm*and the

*object arm*, respectively. An imaging system characterized by magnification

*M*is placed in both arms. Considering only the case where the photons are split at the BS, the propagated transverse mode function of the two-photon field can be written as where

*ρ*

_{1}= (

*x*

_{1},

*y*

_{1}) and

*ρ*

_{2}= (

*x*

_{2},

*y*

_{2}) are the transverse coordinates in the object and camera arm, respectively, and a 50 : 50 beam splitter is assumed. Note that the inversion of the horizontal coordinate,

*x*, caused by the reflection at the BS is neglected, as it is compensated for by further reflections in the optical system. The two terms in Eq. (3) represent the two possibilities in which signal and idler photons are split into different paths at the BS.

*A*(

*ρ*

_{1}). A microscope objective lens collects the photons diffracted from the SLM, and is adjusted to focus a collimated light beam onto the input facet of a single- or multi-mode optical fibre. When using a single-mode fibre in the detection system, the photons diffracted from the SLM are projected into a single transverse spatial mode

*ψ*that can be selected by the use of different holograms on the SLM [21

_{mn}21. E. Yao, S. Franke-Arnold, J. Courtial, M. J. Padgett, and S. M. Barnett, “Observation of quantum entanglement using spatial light modulators,” Opt. Express **14**, 13089–13094 (2006). [CrossRef] [PubMed]

23. M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-Gauss modes,” Phys. Rev. A **87**, 012326 (2013). [CrossRef]

*ϕ*〉 is written as Here

_{mn}*ψ*is a square-integrable two-dimensional function whose indices

_{mn}*m*and

*n*are associated with orthogonal transverse degrees of freedom such as the cartesian coordinates

*x*and

*y*or the polar coordinates given by the azimuthal angle and the radial position.

*ψ*} being a complete set of orthogonal functions described by discrete indices

_{mn}*m*and

*n*spanning the transverse mode space of the photons. In this case, the heralded photon in the camera arm is prepared in a mixed state

*ς̂*

_{2}given by [24

24. N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, and P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. **94**, 150502 (2005). [CrossRef] [PubMed]

_{1}is the partial trace with respect to the photon 1 in the object arm. In the following we will calculate the detection probabilities for the heralded states (8) and (10) in the camera arm.

### 2.1. Detection probabilities on the ICCD camera

7. R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. **15**, 073032 (2013). [CrossRef]

*M*, is equivalent to that of the object arm, whereas the Fourier system is characterized by an effective focal length

*f*. In both configurations, the ICCD provides a multi-pixel detection system capable of measuring the full transverse field of the down-converted light in the camera arm.

_{e}*Ã*|

^{2}is only visible when using a single-mode detection at the object arm. The detection probability (12) is given by the convolution of the Fourier transform of the object’s aperture function and the Gaussian distribution of the detection mode. This is a typical diffraction pattern generated by a single-mode illumination of an aperture. On the other hand, the detection probability (14) is equivalent to the diffraction pattern of an aperture illuminated with an incoherent superposition of multiple transverse spatial modes. The resulting detection probability in this case is the sum of the diffraction patterns generated from each transverse mode.

## 3. Experimental setup

32. P. H. S. Ribeiro, C. H. Monken, and G. A. Barbosa, “Measurement of coherence area in parametric downconversion luminescence,” Appl. Opt. **33**, 352–355 (1994). [CrossRef] [PubMed]

*μ*m. The SLM is programmed to produce an amplitude modulation with the shape of a chess board,

*i.e.*a pattern of alternate opaque and transparent squares. The aperture function

*A*(

*ρ*

_{1}) associated with this modulation assumes only the values “0” or “1”, such that

*A*

^{2}=

*A*=

*A*

^{*}. The side length of each square is 300

*μ*m, corresponding to 15 pixels of the SLM. The output light of the SLM is collected by a ×4 microscope objective lens and focused onto the input facet of an optical fibre connected to a single-photon avalanche diode (SPAD).

*M*= 3 or a Fourier system with an effective focal length of

*f*≈ 167mm. Using the ICCD camera, we recorded images of the down-converted light in the image plane and the far-field of the SPDC source, as shown in Fig. 2. These images were acquired using the internal trigger of the ICCD to gate the intensifier continuously (10 acquisitions of 1s each), thus revealing the intensity pattern of the SPDC light. As shown in Fig. 2, the diameter of the down-converted beam as seen on the ICCD is approximately the same in both configurations. The illumination pattern used to probe the SLM in the object arm is equivalent to the distribution shown in Fig. 2(a).

_{e}## 4. Experimental results

*τ*= 2s exposure, resulting in a total acquisition time of 1 hour. We work with a region of interest (ROI) on the ICCD comprising 600×600 pixels operating in the single-photon counting regime; applying a binary threshold to the pixel outputs of each acquisition [7

**15**, 073032 (2013). [CrossRef]

33. E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. **386**, 2262–2270 (2008). [CrossRef]

34. D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A **88**, 013816 (2013). [CrossRef]

*μ*m, the field of view of the selected ROI is (7.8 × 7.8)mm

^{2}. Figure 3 shows the resulting images using the single-mode fibre (3-a and 3-b) and multi-mode fibre (3-c and 3-d). Horizontal cross-sections of the acquired images are shown in Fig. 4. The displayed cross-sections were averaged over the 20 central rows for the images taken in the image plane and over the 120 central rows for the images taken in the far-field.

### 4.1. Heralding efficiencies of the camera arm

*τ*= 2s are assigned a value “0” or “1”, where “1” correspond to a photo-detection or a noise event [33

33. E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. **386**, 2262–2270 (2008). [CrossRef]

34. D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A **88**, 013816 (2013). [CrossRef]

**15**, 073032 (2013). [CrossRef]

12. R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Real-time imaging of quantum entanglement,” Sci. Rep. **3**, 1914 (2013). [CrossRef] [PubMed]

**15**, 073032 (2013). [CrossRef]

*N̄*, from the 1800 images taken with the single- or multi-mode trigger detection system with the ICCD in the image plane and far-field of the SPDC source. These numbers are summarized in table 1. We note that although a photo-event island is counted as a single detected photon, all excited pixels on the CCD chip contributed to the generated images in Figs. 3 and 5.

_{e}*N̄*, we subtract the predicted number of noise events

_{e}*N̄*to obtain an estimation of the average number of detected heralded photons. The noise probabilities in a single-photon sensitive CCD can be estimated from a series of images acquired with the shutter of the camera closed [33

_{n}33. E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. **386**, 2262–2270 (2008). [CrossRef]

34. D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A **88**, 013816 (2013). [CrossRef]

*η*of the triggered detection system in the camera arm as where

_{H}*S*and

_{T}*S*are the trigger and background count rate of the SPAD in the object arm, respectively. The difference of these count rates in the denominator of the heralding efficiency (15) represents the average number of trigger photons per second. As these count rates are expressed in units of s

_{BG}^{−1}, we multiply them by the exposure time

*τ*of the images to obtain the number of trigger events during an exposure of the ICCD. The measured values of these quantities along with the calculated heralding efficiency are summarized in table 1.

*η*≈ 3% for the single-mode detection system and

_{H}*η*≈ 1% for the multi-mode detection system (see table 1). It is perhaps surprising to notice the lower heralding efficiencies obtained for the multi-mode case. This difference, however, is attributed to the higher mean number of photons per image and limitations both in the detection mechanism of the camera and our photon counting methodology. As a photo-event manifest itself as a multi-pixel island of photo-detections on the CCD chip [12

_{H}12. R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Real-time imaging of quantum entanglement,” Sci. Rep. **3**, 1914 (2013). [CrossRef] [PubMed]

35. C. H. Sequin, “Blooming suppression in charge coupled area imaging devices,” Bell Syst. Tech. J. **51**, 1923 (1972). [CrossRef]

*η*obtained with the data for the single-mode fibre is a better estimate of the heralding efficiency of our system. We note that the significantly higher heralding efficiencies achieved in this work as compared to [7

_{H}**15**, 073032 (2013). [CrossRef]

## 5. Conclusions

**15**, 073032 (2013). [CrossRef]

**3**, 1914 (2013). [CrossRef] [PubMed]

10. S. P. Walborn, P. H. Souto Ribeiro, and C. H. Monken, “Interference effects induced by non-local spatial filtering,” Opt. Express **19**, 17308–17317 (2011). [CrossRef] [PubMed]

11. J. O. de Almeida, S. P. Walborn, P. H. Souto Ribeiro, and M. Hor-Meyll, “Fourth-order coherence induced by spatial mode parity selection,” Phys. Rev. A **86**, 033839 (2012). [CrossRef]

13. C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A **57**, 3123–3126 (1998). [CrossRef]

17. M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. **282**, 1154–1159 (2009). [CrossRef]

25. M. A. Solís-Prosser and L. Neves, “Remote state preparation of spatial qubits,” Phys. Rev. A **84**, 012330 (2011). [CrossRef]

26. Y. Kang, K. Cho, J. Noh, D. L. P. Vitullo, C. Leary, and M. G. Raymer, “Remote preparation of complex spatial states of single photons and verification by two-photon coincidence experiment,” Opt. Express **18**, 1217–1233 (2010). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A |

2. | D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. |

3. | A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. |

4. | F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. |

5. | T. Iskhakov, A. Allevi, D. A. Kalashnikov, V. G. Sala, M. Takeuchi, M. Bondani, and M. Chekhova, “Intensity correlations of thermal light,” Eur. Phys. J. Special Topics |

6. | G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A |

7. | R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. |

8. | P. H. S. Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Controlling the degree of visibility of Young’s fringes with photon coincidence measurements,” Phys. Rev. A |

9. | P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A |

10. | S. P. Walborn, P. H. Souto Ribeiro, and C. H. Monken, “Interference effects induced by non-local spatial filtering,” Opt. Express |

11. | J. O. de Almeida, S. P. Walborn, P. H. Souto Ribeiro, and M. Hor-Meyll, “Fourth-order coherence induced by spatial mode parity selection,” Phys. Rev. A |

12. | R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Real-time imaging of quantum entanglement,” Sci. Rep. |

13. | C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A |

14. | M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. |

15. | A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. |

16. | I. F. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A |

17. | M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. |

18. | S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. |

19. | S. P. Walborn, A. N. de Oliveira, S. Padua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. |

20. | C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. |

21. | E. Yao, S. Franke-Arnold, J. Courtial, M. J. Padgett, and S. M. Barnett, “Observation of quantum entanglement using spatial light modulators,” Opt. Express |

22. | V. D. Salakhutdinov, E. R. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett. |

23. | M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-Gauss modes,” Phys. Rev. A |

24. | N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, and P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett. |

25. | M. A. Solís-Prosser and L. Neves, “Remote state preparation of spatial qubits,” Phys. Rev. A |

26. | Y. Kang, K. Cho, J. Noh, D. L. P. Vitullo, C. Leary, and M. G. Raymer, “Remote preparation of complex spatial states of single photons and verification by two-photon coincidence experiment,” Opt. Express |

27. | A. M. Brańczyk, T. C. Ralph, W. Helwig, and C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. |

28. | F. M. Miatto, H. D. L. Pires, S. M. Barnett, and M. P. van Exter, “Spatial Schmidt modes generated in parametric down-conversion,” Eur. Phys. J. D |

29. | F. M. Miatto, T. Brougham, and A. M. Yao, “Cartesian and polar Schmidt bases for down-converted photons: How high dimensional entanglement protects the shared information from non-ideal measurements,” Eur. Phys. J. D |

30. | S. P. Walborn and A. H. Pimentel, “Generalized Hermite–Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion,” J. Phys. B: At. Mol. Opt. Phys. |

31. | J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. |

32. | P. H. S. Ribeiro, C. H. Monken, and G. A. Barbosa, “Measurement of coherence area in parametric downconversion luminescence,” Appl. Opt. |

33. | E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. |

34. | D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A |

35. | C. H. Sequin, “Blooming suppression in charge coupled area imaging devices,” Bell Syst. Tech. J. |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(040.1490) Detectors : Cameras

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: September 23, 2013

Revised Manuscript: November 4, 2013

Manuscript Accepted: November 4, 2013

Published: December 4, 2013

**Citation**

D. S. Tasca, R. S. Aspden, P. A. Morris, G. Anderson, R. W. Boyd, and M. J. Padgett, "The influence of non-imaging detector design on heralded ghost-imaging and ghost-diffraction examined using a triggered ICCD camera," Opt. Express **21**, 30460-30473 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-25-30460

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### References

- T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A52, R3429–R3432 (1995). [CrossRef] [PubMed]
- D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett.74, 3600–3603 (1995). [CrossRef] [PubMed]
- A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett.93, 093602 (2004). [CrossRef] [PubMed]
- F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett.94, 183602 (2005). [CrossRef] [PubMed]
- T. Iskhakov, A. Allevi, D. A. Kalashnikov, V. G. Sala, M. Takeuchi, M. Bondani, and M. Chekhova, “Intensity correlations of thermal light,” Eur. Phys. J. Special Topics199, 127–138 (2011). [CrossRef]
- G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, and I. R. Berchera, “Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light,” Phys. Rev. A83, 063807 (2011). [CrossRef]
- R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys.15, 073032 (2013). [CrossRef]
- P. H. S. Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Controlling the degree of visibility of Young’s fringes with photon coincidence measurements,” Phys. Rev. A49, 4176–4179 (1994). [CrossRef] [PubMed]
- P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A54, 3489–3492 (1996). [CrossRef] [PubMed]
- S. P. Walborn, P. H. Souto Ribeiro, and C. H. Monken, “Interference effects induced by non-local spatial filtering,” Opt. Express19, 17308–17317 (2011). [CrossRef] [PubMed]
- J. O. de Almeida, S. P. Walborn, P. H. Souto Ribeiro, and M. Hor-Meyll, “Fourth-order coherence induced by spatial mode parity selection,” Phys. Rev. A86, 033839 (2012). [CrossRef]
- R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Real-time imaging of quantum entanglement,” Sci. Rep.3, 1914 (2013). [CrossRef] [PubMed]
- C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A57, 3123–3126 (1998). [CrossRef]
- M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett.87, 013602 (2001). [CrossRef]
- A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett.93, 213903 (2004). [CrossRef] [PubMed]
- I. F. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A72, 033802 (2005). [CrossRef]
- M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun.282, 1154–1159 (2009). [CrossRef]
- S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep.495, 87–139 (2010). [CrossRef]
- S. P. Walborn, A. N. de Oliveira, S. Padua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003). [CrossRef] [PubMed]
- C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett.92, 127903 (2004). [CrossRef] [PubMed]
- E. Yao, S. Franke-Arnold, J. Courtial, M. J. Padgett, and S. M. Barnett, “Observation of quantum entanglement using spatial light modulators,” Opt. Express14, 13089–13094 (2006). [CrossRef] [PubMed]
- V. D. Salakhutdinov, E. R. Eliel, and W. Löffler, “Full-field quantum correlations of spatially entangled photons,” Phys. Rev. Lett.108, 173604 (2012). [CrossRef] [PubMed]
- M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-Gauss modes,” Phys. Rev. A87, 012326 (2013). [CrossRef]
- N. A. Peters, J. T. Barreiro, M. E. Goggin, T.-C. Wei, and P. G. Kwiat, “Remote state preparation: Arbitrary remote control of photon polarization,” Phys. Rev. Lett.94, 150502 (2005). [CrossRef] [PubMed]
- M. A. Solís-Prosser and L. Neves, “Remote state preparation of spatial qubits,” Phys. Rev. A84, 012330 (2011). [CrossRef]
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