Ghost Imaging Technology in Sensing Applications

1. Ghost Imaging Technology in Sensing Applications 18th NPA Conference, College Park, MD, USA July 6-9, 2011 Sanjit Karmakarand Yanhua Shih Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250 S. Karmakar and Y. Shih, Phys. Rev. A 81, 033845 (2010)

2. Outline • Introduction • Objective • Experiment • Analysis & Discussion • Conclusion

3. Introduction

4. Classical Imaging Fig. 1: Experimental Set up for classical imaging • Gaussian thin lens equation : • Corresponding image point of an object point is due to constructive interference. • A perfect image : • Because of Diffraction effect: whereandis the 1st order Bessel function M. D'Angelo, A. Valencia, M.H. Rubin, and Y. H. Shih, Phys. Rev. A., Vol. 72,013810, (2005).

5. Ghost Imaging Fig: Object & Image • “Ghost” Imaging => peculiar feature of imaging Fig. : Schematic setup of ghost imaging experiment T. B. Pittman et. al., Phys. Rev. A, Vol. 52, R3429, (1995)

6. In EPR’s Language • The “ghost” image is a realization of the 1935 EPR gedakenexperiment. • The EPR -functions, and in transverse dimension, are the key to understand the ghost imaging phenomenon. • The geometric rays in the fig. actually represent the two-photon amplitudes of a signal-idler photon pair. • The point-to-point correspondence is the result of the superposition of these two-photon amplitudes. • A “click-click” joint measurement at two detectors is the result of the coherent superposition of all these two-photon amplitudes. T. B. Pittman et. al., Phys. Rev. A, Vol. 52, R3429, (1995)

7. Fig. 1: Unfolded quantum imaging experimental set-up with imaging lens on the signal photon arm • According to Glauber theory of photo-detection, M. D'Angelo, A. Valencia, M.H. Rubin, and Y. H. Shih, Phys. Rev. A., Vol. 72,013810, (2005)

8. Now calculate for the above experimental setup where and • Gaussian thin-lens equation: or Y.H. Shih, An Introduction to Quantum Optics, Taylor & Francis (2011)

9. This ‘bucket’ detector collects all that passes through the object aperture function as a joint photo-detection event. and • Because of finite size of lens (radius R), • This somb function describes point-to-spot relation. • Minimum resolving angle: where is the diameter of the imaging lens and is the wavelength corresponds to where the detector D2 scans the image on the image plane Y.H. Shih, An Introduction to Quantum Optics, Taylor & Francis (2011)

10. Two-color Ghost Imaging Two-photon quantum imaging has so far demonstrated two peculiar features (1) reproducing nonlocal images in “ghost” imaging type experiments. (2) improving imaging spatial resolution beyond the classical limit in quantum lithography type measurements. Recently resolution of non-degenerate ghost imaging was theoretically studied by Rubin et al. and Chan et al. T. B. Pittman et al., Phys. Rev. A 53, 2804 (1996); Phys. Rev. A, Vol. 52, R3429, (1995). A.N. Boto et al., Phys. Rev. Lett. 85, 2733 (2000); M.D'Angelo et al., Phys. Rev. Lett. 87, 013603 (2001). M.H. Rubin et. Al., Phys. Rev. A 78, 033836 (2008); K. C. Chan et al., Phys. Rev. A 79, 033808 (2009).

11. Objective

12. Two experimental configurations on two-color ghost imaging reproduce a ghost image + enhance the angular resolving power greater field of view or a greater imaging amplification compared to that of classical imaging. In one particular experimental configuration With the help of an entangled photon pair of observe a ghost image enhanced angular resolving power by a factor of a field of view which is times greater than that of the classical imaging setup

13. 2) In other experimental configuration With the help of an entangled photon pair possibility of reproducing a ghost image The enhancement of the angular resolving power a greater imaging amplification compared with that of classical imaging.

14. Experiment

15. Schematic of our experimental setup

16. Image of the double slit aperture The slit width and center-to-center distance between the slits of the double slit aperture are 1 mm and 2.75 mm respectively. In our experimental results, the slit width and center-to-center distance between the slits of the double slit image are 0.335 mm and 0.716 mm respectively.

17. Analysis & Discussion

18. 1st experimental Configuration Unfolded version of the schematic shown in Fig. 1

19. A modified Gaussian thin-lens equation for two colors where and In this experiment, we choose mm, mm, mm and mm. The observed field of view for this case is whereas the field of view for the degenerate case is . That means field of view is improved by a factor of 1.16. The angular resolving power is improved by a factor of

20. The two-photon effective wavefunction of this set up is The angular limit of spatial resolution is with magnification factor If we keep the same and , the object plane has to move closer to the imaging lens by factor of in order to form an image or

21. where and are the image and object distance from the imaging lens in degenerate ghost imaging set-up respectively. The same imaging magnification factor as that of degenerate case When forming this image, the opening angle of the object is enlarged by a factor of . That means field of view is improved by a factor of compared with that of degenerate case. When the object plane is moved, the resolving power is increased by a factor of .

22. 2nd experimental Configuration Unfolded version of the schematic of the experimental setup in which the imaging lens is on the arm of the signal beam.

23. Under the Approximation ( ): The two-photon effective wavefunction for this case Comparing with the degenerate ghost imaging system: An angular limit of resolution: where is the diameter of the imaging lens. (2) A different image-forming equation: Keeping and same, the image plane have to move away from the lens by a factor of in order to form an image

24. (3) The imaging magnification factor is still the same When the image plane moves away from the imaging lens by a factor of , the resolving power of two-color imaging system is improved by a factor of . When the image plane is moved away from the imaging lens by a factor of , the imaging amplification increases by a factor of .

25. Advantage of imaging in space under a specific condition In degenerate case , the angular resolution limit is Absorption of shorter wavelengths in the atmosphere creates problemThe Angular limit of Spatial Resolution isUnder specific case of Under this condition, one can send the longer wavelength signal to the target to achieve a better angular resolution limit with the shorter wavelength idler.

26. Conclusion

27. Although the same magnification factor of 0.26 as that of classical imaging, the angular resolving power and the field of view of this two-color ghost imaging are enhanced by the factor of 1.25 and 1.16 respectively compared with that of classical imaging. We have also studied another experimental configuration in which we can reproduce a ghost image and enhance the angular resolving power and imaging amplification compared with that of classical imaging. The reported experimental configurations are demonstrated here as a quantum mechanical two-photon geometrical effect for the non-degenerate case. From the fundamental point of view, the EPR correlation for the entangled signal-idler pair in the non-degenerate SPDC case is also demonstrated by these reported experimental configurations. The reported features of two-color ghost imaging move forward the progress of the imaging as well as the sensing technology .

28. ACKNOWLEDGMENTS T. B. Pittman, M. H. Rubin, R. Reno, J. P. Simon, Y. Zhou, H. Chen, T. Peng, H. You, M. Lai and N. Sharma

29. Thank you

30. With 1st experimental configuration Under the Approximation ( ): The two-photon effective wavefunction for this case Comparing with the degenerate ghost imaging system: An angular limit of resolution: where is the diameter of the imaging lens. (2) A different image-forming equation: Keeping and same, the object plane have to move closer to the lens by a factor of in order to form an image

31. (3) The imaging magnification factor is still the same When the object plane moves closer to the imaging lens by a factor of , the resolving power of two-color imaging system is improved by a factor of . When the object plane is moved closer to the imaging lens by a factor of , the imaging amplification increases by a factor of .

32. Advantage of imaging in space under a specific condition In degenerate case , the angular resolution limit is Absorption of shorter wavelengths in the atmosphere creates problemThe Angular limit of Spatial Resolution isUnder specific case of Under this condition, one can send the longer wavelength signal to the target to achieve a better angular resolution limit with the shorter wavelength idler.