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N-slit interferometer

December 15, 2023

The N-slit interferometer is an extension of the double-slit interferometer also known as Young's double-slit interferometer. One of the first known uses of N-slit arrays in optics was illustrated by Newton.[1] In the first part of the twentieth century, Michelson[2] described various cases of N-slit diffraction.

Feynman[3] described thought experiments the explored two-slit quantum interference of electrons, using Dirac's notation.[4] This approach was extended to N-slit interferometers, by Duarte and colleagues in 1989,[5] using narrow-linewidth laser illumination, that is, illumination by indistinguishable photons. The first application of the N-slit interferometer was the generation and measurement of complex interference patterns.[5][6] These interferograms are accurately reproduced, or predicted, by the N-slit interferometric equation for either even (N = 2, 4, 6,...), or odd (N = 3, 5, 7,...), numbers of slits.[6]

N-slit laser interferometer edit

 
Top view schematics of the N-slit interferometer: TBE is a telescopic beam expander, MPBE is a multiple-prism beam expander. The N-slit array is at j (with the slits perpendicular to the beam expansion) and the interferometric plane is at x where the digital detector is positioned.[6][7][8][9] The intra interferometric distance D has been reported to be as large as 527 m. Note: N-slit interferometers include three-slit interferometers (or triple-slit interferometers), four-slit interferometers, etc.[7][8]

The N-slit laser interferometer, introduced by Duarte,[5][6][10] uses prismatic beam expansion to illuminate a transmission grating, or N-slit array, and a photoelectric detector array (such as a CCD or CMOS) at the interference plane to register the interferometric signal.[6][10][11] The expanded laser beam illuminating the N-slit array is single-transverse-mode and narrow-linewidth. This beam can also take the shape, via the introduction of a convex lens prior to the prismatic expander, of a beam extremely elongated in the propagation plane and extremely thin in the orthogonal plane.[6][10] This use of one-dimensional (or line) illumination eliminates the need of point-by-point scanning in microscopy and microdensitometry.[6][10] Thus, these instruments can be used as straight forward N-slit interferometers or as interferometric microscopes.

The disclosure of this interferometric configuration introduced the use of digital detectors to N-slit interferometry.[5][11]

Applications edit

Secure optical communications edit

 
Interferogram for N = 3 slits with diffraction pattern superimposed on the right outer wing. This particular interferogram corresponds to the interferometric character "b".[9]
 
The diffraction pattern over the interferogram shown above, corresponding to N = 3 slits, was generated using a single spider silk fiber with a diameter of about 25 μm.[9]

These interferometers, originally introduced for applications in imaging,[6] are also useful in optical metrology and have been proposed for secure optical communications in free space,[7][12] between spacecraft. This is due to the fact that propagating N-slit interferograms suffer catastrophic collapse from interception attempts using macroscopic optical methods such as beam splitting.[7] Recent experimental developments include terrestrial intra-interferometric path lengths of 35 meters[8] and 527 meters.[9]

These large, and very large, N-slit interferometers are used to study various propagation effects including microscopic disturbances on propagating interferometric signals. This work has yielded the first observation of diffraction patterns superimposed over propagating interferograms.[9]

These diffraction patterns (as shown in the first photograph) are generated by inserting a spider web fiber (or spider silk thread) into the propagation path of the interferogram. The position of the spider web fiber is perpendicular to the propagation plane.[9]

Clear air turbulence edit

N-slit interferometers, using large intra interferometric distances, are detectors of clear air turbulence.[8][9] The distortions induced by clear air turbulence upon the interferometric signal are different, in both character and magnitude, from the catastrophic collapse resulting from attempted interception of optical signals using macroscopic optical elements.[13]

Expanded beam interferometric microscopy edit

The original application of the N-slit laser interferometer was interferometric imaging.[6][10][14] In particular, the one dimensionally expanded laser beam (with a cross section 25-50 mm wide by 10-25 μm high) was used to illuminate imaging surfaces (such as silver-halide films) to measure the microscopic density of the illuminated surface. Hence the term interferometric microdensitometer.[10] Resolution down to the nano regime can be provided via the use of interinterferometric calculations.[6] When used as a microdensitometer the N-slit interferometer is also known as a laser microdensitometer.[14]

The multiple-prism expanded laser beam is also described as an extremely elongated laser beam. The elongated dimension of the beam (25-50 mm) is in the propagation plane while the very thin dimension (in the μm regime) of the beam is in the orthogonal plane. This was demonstrated, for imaging and microscopy applications, in 1993.[6][10] Alternative descriptions of this type of extremely elongated illumination include the terms line illumination, linear illumination, thin light sheet illumination (in light sheet microscopy), and plane illumination (in selective plane illumination microscopy).

Other applications edit

N-slit interferometers are of interest to researchers working in atom optics,[15] Fourier imaging,[16] optical computing,[17] and quantum computing.[18]

See also edit

References edit

  1. ^ I. Newton, Opticks (Royal Society, London, 1704).
  2. ^ A. A. Michelson, Studies in Optics (Chicago University, Chicago, 1927).
  3. ^ R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. III (Addison Wesley, Reading, 1965).
  4. ^ P. A. M. Dirac, The Principles of Quantum Mechanics, 4th Ed. (Oxford, London, 1978).
  5. ^ a b c d F. J. Duarte and D. J. Paine, Quantum mechanical description of N-slit interference phenomena, in Proceedings of the International Conference on Lasers '88, R. C. Sze and F. J. Duarte (Eds.) (STS, McLean, Va, 1989) pp. 42–47.
  6. ^ a b c d e f g h i j k Duarte, F.J. (1993). "On a generalized interference equation and interferometric measurements". Optics Communications. Elsevier BV. 103 (1–2): 8–14. Bibcode:1993OptCo.103....8D. doi:10.1016/0030-4018(93)90634-h. ISSN 0030-4018.
  7. ^ a b c d Duarte, F J (2004-12-11). "Secure interferometric communications in free space: enhanced sensitivity for propagation in the metre range". Journal of Optics A: Pure and Applied Optics. IOP Publishing. 7 (1): 73–75. doi:10.1088/1464-4258/7/1/011. ISSN 1464-4258.
  8. ^ a b c d Duarte, F J; Taylor, T S; Clark, A B; Davenport, W E (2009-11-25). "TheN-slit interferometer: an extended configuration". Journal of Optics. IOP Publishing. 12 (1): 015705. Bibcode:2010JOpt...12a5705D. doi:10.1088/2040-8978/12/1/015705. ISSN 2040-8978. S2CID 121521124.
  9. ^ a b c d e f g Duarte, F J; Taylor, T S; Black, A M; Davenport, W E; Varmette, P G (2011-02-03). "N-slit interferometer for secure free-space optical communications: 527 m intra interferometric path length". Journal of Optics. IOP Publishing. 13 (3): 035710. Bibcode:2011JOpt...13c5710D. doi:10.1088/2040-8978/13/3/035710. ISSN 2040-8978. S2CID 6086533.
  10. ^ a b c d e f g F. J. Duarte, Electro-optical interferometric microdensitometer system, US Patent 5255069 (1993) 2017-10-13 at the Wayback Machine.
  11. ^ a b F. J. Duarte, in High Power Dye Lasers (Springer-Verlag, Berlin, 1991) Chapter 2.
  12. ^ Duarte, F.J. (2002). "Secure interferometric communications in free space". Optics Communications. Elsevier BV. 205 (4–6): 313–319. Bibcode:2002OptCo.205..313D. doi:10.1016/s0030-4018(02)01384-6. ISSN 0030-4018.
  13. ^ F. J. Duarte, Interferometric imaging, in Tunable Laser Applications, 2nd Edition (CRC, New York, 2009) Chapter 12.
  14. ^ a b F. J. Duarte, Interferometric imaging, in Tunable Laser Applications (Marcel-Dekker, New York, 1995) Chapter 5.
  15. ^ L-B. Deng, Theory of atom optics: Feynman path integral approach, Frontiers Phys. China 1, 47-53 (2006).
  16. ^ Liu, Honglin; Shen, Xia; Zhu, Da-Ming; Han, Shensheng (2007-11-07). "Fourier-transform ghost imaging with pure far-field correlated thermal light". Physical Review A. American Physical Society (APS). 76 (5): 053808. Bibcode:2007PhRvA..76e3808L. doi:10.1103/physreva.76.053808. ISSN 1050-2947.
  17. ^ F. J. Duarte, Tunable Laser Optics, 2nd Edition (CRC, New York, 2015) Chapter 10.
  18. ^ Clauser, John F.; Dowling, Jonathan P. (1996-06-01). "Factoring integers with Young's N-slit interferometer". Physical Review A. American Physical Society (APS). 53 (6): 4587–4590. arXiv:0810.4372. Bibcode:1996PhRvA..53.4587C. doi:10.1103/physreva.53.4587. ISSN 1050-2947. PMID 9913434. S2CID 34750766.

December 15, 2023
slit, interferometer, extension, double, slit, interferometer, also, known, young, double, slit, interferometer, first, known, uses, slit, arrays, optics, illustrated, newton, first, part, twentieth, century, michelson, described, various, cases, slit, diffrac. The N slit interferometer is an extension of the double slit interferometer also known as Young s double slit interferometer One of the first known uses of N slit arrays in optics was illustrated by Newton 1 In the first part of the twentieth century Michelson 2 described various cases of N slit diffraction Feynman 3 described thought experiments the explored two slit quantum interference of electrons using Dirac s notation 4 This approach was extended to N slit interferometers by Duarte and colleagues in 1989 5 using narrow linewidth laser illumination that is illumination by indistinguishable photons The first application of the N slit interferometer was the generation and measurement of complex interference patterns 5 6 These interferograms are accurately reproduced or predicted by the N slit interferometric equation for either even N 2 4 6 or odd N 3 5 7 numbers of slits 6 Contents 1 N slit laser interferometer 2 Applications 2 1 Secure optical communications 2 2 Clear air turbulence 2 3 Expanded beam interferometric microscopy 2 4 Other applications 3 See also 4 ReferencesN slit laser interferometer edit nbsp Top view schematics of the N slit interferometer TBE is a telescopic beam expander MPBE is a multiple prism beam expander The N slit array is at j with the slits perpendicular to the beam expansion and the interferometric plane is at x where the digital detector is positioned 6 7 8 9 The intra interferometric distance D has been reported to be as large as 527 m Note N slit interferometers include three slit interferometers or triple slit interferometers four slit interferometers etc 7 8 The N slit laser interferometer introduced by Duarte 5 6 10 uses prismatic beam expansion to illuminate a transmission grating or N slit array and a photoelectric detector array such as a CCD or CMOS at the interference plane to register the interferometric signal 6 10 11 The expanded laser beam illuminating the N slit array is single transverse mode and narrow linewidth This beam can also take the shape via the introduction of a convex lens prior to the prismatic expander of a beam extremely elongated in the propagation plane and extremely thin in the orthogonal plane 6 10 This use of one dimensional or line illumination eliminates the need of point by point scanning in microscopy and microdensitometry 6 10 Thus these instruments can be used as straight forward N slit interferometers or as interferometric microscopes The disclosure of this interferometric configuration introduced the use of digital detectors to N slit interferometry 5 11 Applications editSecure optical communications edit nbsp Interferogram for N 3 slits with diffraction pattern superimposed on the right outer wing This particular interferogram corresponds to the interferometric character b 9 nbsp The diffraction pattern over the interferogram shown above corresponding to N 3 slits was generated using a single spider silk fiber with a diameter of about 25 mm 9 These interferometers originally introduced for applications in imaging 6 are also useful in optical metrology and have been proposed for secure optical communications in free space 7 12 between spacecraft This is due to the fact that propagating N slit interferograms suffer catastrophic collapse from interception attempts using macroscopic optical methods such as beam splitting 7 Recent experimental developments include terrestrial intra interferometric path lengths of 35 meters 8 and 527 meters 9 These large and very large N slit interferometers are used to study various propagation effects including microscopic disturbances on propagating interferometric signals This work has yielded the first observation of diffraction patterns superimposed over propagating interferograms 9 These diffraction patterns as shown in the first photograph are generated by inserting a spider web fiber or spider silk thread into the propagation path of the interferogram The position of the spider web fiber is perpendicular to the propagation plane 9 Clear air turbulence edit N slit interferometers using large intra interferometric distances are detectors of clear air turbulence 8 9 The distortions induced by clear air turbulence upon the interferometric signal are different in both character and magnitude from the catastrophic collapse resulting from attempted interception of optical signals using macroscopic optical elements 13 Expanded beam interferometric microscopy edit The original application of the N slit laser interferometer was interferometric imaging 6 10 14 In particular the one dimensionally expanded laser beam with a cross section 25 50 mm wide by 10 25 mm high was used to illuminate imaging surfaces such as silver halide films to measure the microscopic density of the illuminated surface Hence the term interferometric microdensitometer 10 Resolution down to the nano regime can be provided via the use of interinterferometric calculations 6 When used as a microdensitometer the N slit interferometer is also known as a laser microdensitometer 14 The multiple prism expanded laser beam is also described as an extremely elongated laser beam The elongated dimension of the beam 25 50 mm is in the propagation plane while the very thin dimension in the mm regime of the beam is in the orthogonal plane This was demonstrated for imaging and microscopy applications in 1993 6 10 Alternative descriptions of this type of extremely elongated illumination include the terms line illumination linear illumination thin light sheet illumination in light sheet microscopy and plane illumination in selective plane illumination microscopy Other applications edit N slit interferometers are of interest to researchers working in atom optics 15 Fourier imaging 16 optical computing 17 and quantum computing 18 See also editBeam expander Clear air turbulence Diffraction from slits Double slit experiment Free space optical communication Laser communication in space Microscopy Microdensitometer N slit interferometric equation List of laser articlesReferences edit I Newton Opticks Royal Society London 1704 A A Michelson Studies in Optics Chicago University Chicago 1927 R P Feynman R B Leighton and M Sands The Feynman Lectures on Physics Vol III Addison Wesley Reading 1965 P A M Dirac The Principles of Quantum Mechanics 4th Ed Oxford London 1978 a b c d F J Duarte and D J Paine Quantum mechanical description of N slit interference phenomena in Proceedings of the International Conference on Lasers 88 R C Sze and F J Duarte Eds STS McLean Va 1989 pp 42 47 a b c d e f g h i j k Duarte F J 1993 On a generalized interference equation and interferometric measurements Optics Communications Elsevier BV 103 1 2 8 14 Bibcode 1993OptCo 103 8D doi 10 1016 0030 4018 93 90634 h ISSN 0030 4018 a b c d Duarte F J 2004 12 11 Secure interferometric communications in free space enhanced sensitivity for propagation in the metre range Journal of Optics A Pure and Applied Optics IOP Publishing 7 1 73 75 doi 10 1088 1464 4258 7 1 011 ISSN 1464 4258 a b c d Duarte F J Taylor T S Clark A B Davenport W E 2009 11 25 TheN slit interferometer an extended configuration Journal of Optics IOP Publishing 12 1 015705 Bibcode 2010JOpt 12a5705D doi 10 1088 2040 8978 12 1 015705 ISSN 2040 8978 S2CID 121521124 a b c d e f g Duarte F J Taylor T S Black A M Davenport W E Varmette P G 2011 02 03 N slit interferometer for secure free space optical communications 527 m intra interferometric path length Journal of Optics IOP Publishing 13 3 035710 Bibcode 2011JOpt 13c5710D doi 10 1088 2040 8978 13 3 035710 ISSN 2040 8978 S2CID 6086533 a b c d e f g F J Duarte Electro optical interferometric microdensitometer system US Patent 5255069 1993 Archived 2017 10 13 at the Wayback Machine a b F J Duarte in High Power Dye Lasers Springer Verlag Berlin 1991 Chapter 2 Duarte F J 2002 Secure interferometric communications in free space Optics Communications Elsevier BV 205 4 6 313 319 Bibcode 2002OptCo 205 313D doi 10 1016 s0030 4018 02 01384 6 ISSN 0030 4018 F J Duarte Interferometric imaging in Tunable Laser Applications 2nd Edition CRC New York 2009 Chapter 12 a b F J Duarte Interferometric imaging in Tunable Laser Applications Marcel Dekker New York 1995 Chapter 5 L B Deng Theory of atom optics Feynman path integral approach Frontiers Phys China 1 47 53 2006 Liu Honglin Shen Xia Zhu Da Ming Han Shensheng 2007 11 07 Fourier transform ghost imaging with pure far field correlated thermal light Physical Review A American Physical Society APS 76 5 053808 Bibcode 2007PhRvA 76e3808L doi 10 1103 physreva 76 053808 ISSN 1050 2947 F J Duarte Tunable Laser Optics 2nd Edition CRC New York 2015 Chapter 10 Clauser John F Dowling Jonathan P 1996 06 01 Factoring integers with Young s N slit interferometer Physical Review A American Physical Society APS 53 6 4587 4590 arXiv 0810 4372 Bibcode 1996PhRvA 53 4587C doi 10 1103 physreva 53 4587 ISSN 1050 2947 PMID 9913434 S2CID 34750766 Retrieved from https en 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