Abstract

We present a collinear, common-path image-inversion interferometer using the polarization channels of a single optical beam. Each of the channels is an imaging system of unit magnification, one positive and the other negative (inverted). Image formation is realized by means of a set of anisotropic lenses, each offering refractive power in one polarization and none in the other. The operation of the interferometer as a spatial-parity analyzer is demonstrated experimentally by separating even- and odd-order orbital angular momentum modes of an optical beam. The common-path configuration overcomes the stability issues present in conventional two-path interferometers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

M. Tsang, “Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment,” Phys. Rev. A 97, 023830 (2018).
[Crossref]

L. De Sio, D. E. Roberts, Z. Liao, J. Hwang, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Beam shaping diffractive wave plates,” Appl. Opt. 57, A118 (2018).
[Crossref]

2017 (7)

W. K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s Curse by imaging using phase information,” Phys. Rev. Lett. 118, 1–6 (2017).
[Crossref]

S. Zheng and J. Wang, “Measuring orbital angular momentum (OAM) states of vortex beams with annular gratings,” Sci. Reports 7, 1–9 (2017).

A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos. Transactions Royal Soc. A: Math. Phys. Eng. Sci. 375, 20150436 (2017).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

S. V. Serak, D. E. Roberts, J.-Y. Hwang, S. R. Nersisyan, N. V. Tabiryan, T. J. Bunning, D. M. Steeves, and B. R. Kimball, “Diffractive waveplate arrays,” J. Opt. Soc. Am. B 34, B56–B63 (2017).
[Crossref]

2016 (5)

2015 (6)

2014 (2)

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

2013 (1)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

2012 (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

2011 (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161 (2011).
[Crossref]

A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Angular and radial mode analyzer for optical beams,” Opt. Lett. 36, 4683 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

2007 (3)

K. Wicker and R. Heintzmann, “Interferometric resolution improvement for confocal microscopes,” Opt. Express 15, 12206–12216 (2007).
[Crossref] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

2004 (1)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

1995 (1)

1975 (1)

1974 (1)

1972 (1)

1966 (1)

Abouraddy, A. F.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Reports 5, 15333 (2015).
[Crossref]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Angular and radial mode analyzer for optical beams,” Opt. Lett. 36, 4683 (2011).
[Crossref] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

Anwar, A.

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Atia, G. K.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Babovsky, H.

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer,” Opt. Commun. 342, 102–108 (2015).
[Crossref]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Boyd, R. W.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

Breckinridge, J. B.

Bunning, T. J.

Cottrell, D. M.

Courtial, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Davis, J. A.

De Sio, L.

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

Dorsch, R. G.

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

Durak, K.

Ferretti, H.

W. K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s Curse by imaging using phase information,” Phys. Rev. Lett. 118, 1–6 (2017).
[Crossref]

Forbes, A.

A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos. Transactions Royal Soc. A: Math. Phys. Eng. Sci. 375, 20150436 (2017).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Gangi Reddy, S.

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), 3rd ed.

Hagerott, E. C.

Heintzmann, R.

Hwang, J.

Hwang, J.-Y.

Igarashi, K.

Jahromi, A. K.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Kagalwala, K. H.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Reports 5, 15333 (2015).
[Crossref]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

Kiessling, A.

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer,” Opt. Commun. 342, 102–108 (2015).
[Crossref]

D. Weigel, A. Kiessling, and R. Kowarschik, “Aberration correction in coherence imaging microscopy using an image inverting interferometer,” Opt. Express 23, 20505–20520 (2015).
[Crossref] [PubMed]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

Kimball, B. R.

Kondakci, H. E.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Reports 5, 15333 (2015).
[Crossref]

Konforti, N.

Kowarschik, R.

D. Weigel, A. Kiessling, and R. Kowarschik, “Aberration correction in coherence imaging microscopy using an image inverting interferometer,” Opt. Express 23, 20505–20520 (2015).
[Crossref] [PubMed]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer,” Opt. Commun. 342, 102–108 (2015).
[Crossref]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

Lal, N.

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Larson, W. D.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Lavery, M. P. J.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

Leach, J.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Liao, Z.

Ling, A.

Lohmann, A. W.

Malhotra, T.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Malik, M.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

Mardani, D.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Martin, L.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

McLaren, M.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

Mendlovic, D.

Mirhosseini, M.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

Moreno, I.

Murty, M. V. R. K.

Nair, R.

R. Nair and M. Tsang, “Interferometric superlocalization of two incoherent optical point sources,” Opt. Express 24, 3684 (2016).
[Crossref] [PubMed]

R. Nair and M. Tsang, “Far-field superresolution of thermal electromagnetic sources at the quantum limit,” Phys. Rev. Lett. 117, 1–13 (2016).
[Crossref]

Nersisyan, S. R.

Padgett, M. J.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161 (2011).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Perumangatt, C.

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Roberts, D. E.

Ruiz, I.

Saleh, B. E.

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

Saleh, B. E. A.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Reports 5, 15333 (2015).
[Crossref]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Angular and radial mode analyzer for optical beams,” Opt. Lett. 36, 4683 (2011).
[Crossref] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

Serak, S. V.

Shabahang, S.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

Sindbert, S.

Singh, R. P.

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

Souma, D.

Steeves, D. M.

Steinberg, A. M.

W. K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s Curse by imaging using phase information,” Phys. Rev. Lett. 118, 1–6 (2017).
[Crossref]

Tabiryan, N.

Tabiryan, N. V.

Takeshima, K.

Tang, Z. S.

Teich, M. C.

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

Tham, W. K.

W. K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s Curse by imaging using phase information,” Phys. Rev. Lett. 118, 1–6 (2017).
[Crossref]

Tsang, M.

M. Tsang, “Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment,” Phys. Rev. A 97, 023830 (2018).
[Crossref]

R. Nair and M. Tsang, “Far-field superresolution of thermal electromagnetic sources at the quantum limit,” Phys. Rev. Lett. 117, 1–13 (2016).
[Crossref]

R. Nair and M. Tsang, “Interferometric superlocalization of two incoherent optical point sources,” Opt. Express 24, 3684 (2016).
[Crossref] [PubMed]

M. Tsang, “Quantum limits to optical point-source localization,” Optica 2, 646 (2015).
[Crossref]

Tsuritani, T.

Vamivakas, A. N.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Wang, J.

S. Zheng and J. Wang, “Measuring orbital angular momentum (OAM) states of vortex beams with annular gratings,” Sci. Reports 7, 1–9 (2017).

Weigel, D.

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer,” Opt. Commun. 342, 102–108 (2015).
[Crossref]

D. Weigel, A. Kiessling, and R. Kowarschik, “Aberration correction in coherence imaging microscopy using an image inverting interferometer,” Opt. Express 23, 20505–20520 (2015).
[Crossref] [PubMed]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

Wicker, K.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161 (2011).
[Crossref]

Yarnall, T.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

Yarnall, T. M.

Zalevsky, Z.

Zeldovich, B. Y.

Zheng, S.

S. Zheng and J. Wang, “Measuring orbital angular momentum (OAM) states of vortex beams with annular gratings,” Sci. Reports 7, 1–9 (2017).

Adv. Opt. Photonics (2)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200 (2016).
[Crossref]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3, 161 (2011).
[Crossref]

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nat. Commun. (3)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Single-photon three-qubit quantum logic using spatial light modulators,” Nat. Commun. 8, 739 (2017).
[Crossref] [PubMed]

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 1–7 (2014).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 1–6 (2013).
[Crossref]

Nat. Photonics (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2012).
[Crossref]

Opt. Commun. (2)

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Imaging properties of different types of microscopes in combination with an image inversion interferometer,” Opt. Commun. 332, 301–310 (2014).
[Crossref]

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, “Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer,” Opt. Commun. 342, 102–108 (2015).
[Crossref]

Opt. Express (9)

D. Weigel, A. Kiessling, and R. Kowarschik, “Aberration correction in coherence imaging microscopy using an image inverting interferometer,” Opt. Express 23, 20505–20520 (2015).
[Crossref] [PubMed]

K. Igarashi, D. Souma, K. Takeshima, and T. Tsuritani, “Selective mode multiplexer based on phase plates and Mach-Zehnder interferometer with image inversion function,” Opt. Express 23, 183 (2015).
[Crossref] [PubMed]

R. Nair and M. Tsang, “Interferometric superlocalization of two incoherent optical point sources,” Opt. Express 24, 3684 (2016).
[Crossref] [PubMed]

Z. S. Tang, K. Durak, and A. Ling, “Fault-tolerant and finite-error localization for point emitters within the diffraction limit,” Opt. Express 24, 22004 (2016).
[Crossref] [PubMed]

K. Wicker and R. Heintzmann, “Interferometric resolution improvement for confocal microscopes,” Opt. Express 15, 12206–12216 (2007).
[Crossref] [PubMed]

K. Wicker, S. Sindbert, and R. Heintzmann, “Characterisation of a resolution enhancing image inversion interferometer,” Opt. Express 17, 15491–15501 (2009).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, I. Ruiz, and D. M. Cottrell, “Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating,” Opt. Express 18, 7173 (2010).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Y. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24, 7091 (2016).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses of switchable focal length - new generation in optics,” Opt. Express 23, 25783 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Opt. Photonics News (1)

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The Promise of diffractive waveplates,” Opt. Photonics News 21, 40 (2010).
[Crossref]

Optica (1)

Philos. Transactions Royal Soc. A: Math. Phys. Eng. Sci. (1)

A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos. Transactions Royal Soc. A: Math. Phys. Eng. Sci. 375, 20150436 (2017).
[Crossref]

Phys. Lett. Sect. A: Gen. At. Solid State Phys. (1)

C. Perumangatt, N. Lal, A. Anwar, S. Gangi Reddy, and R. P. Singh, “Quantum information with even and odd states of orbital angular momentum of light,” Phys. Lett. Sect. A: Gen. At. Solid State Phys. 381, 1858–1865 (2017).
[Crossref]

Phys. Rev. A (1)

M. Tsang, “Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment,” Phys. Rev. A 97, 023830 (2018).
[Crossref]

Phys. Rev. Lett. (6)

W. K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s Curse by imaging using phase information,” Phys. Rev. Lett. 118, 1–6 (2017).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[Crossref]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 4 (2004).
[Crossref]

T. Yarnall, A. F. Abouraddy, B. E. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

R. Nair and M. Tsang, “Far-field superresolution of thermal electromagnetic sources at the quantum limit,” Phys. Rev. Lett. 117, 1–13 (2016).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 4 (2002).
[Crossref]

Sci. Reports (3)

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Reports 5, 15333 (2015).
[Crossref]

S. Zheng and J. Wang, “Measuring orbital angular momentum (OAM) states of vortex beams with annular gratings,” Sci. Reports 7, 1–9 (2017).

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Reports 7, 1–11 (2017).

Other (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), 3rd ed.

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Figures (5)

Fig. 1
Fig. 1 Schematic of a conventional image inversion interferometer. An image inverter (INV) is placed in one branch and 1 and 2 are linear systems used for various applications.
Fig. 2
Fig. 2 (a) Shift-invariant amplitude impulse response function of the systems 1 and 2. (b) Shift-variant point spread function of the interferometric system incoherent illumination.
Fig. 3
Fig. 3 A set of six anisotropic doublets used as a common-path polarization-based interferometric spatial parity analyzer. Right-circular polarization sees a cascade of four Fourier-transforming imaging systems made of the lenses labled “R”, creating an uninverted image in the output plane. Meanwhile, left-circular polarization sees a cascade of two Fourier-transforming imaging systems made of the lenses labled “L”, creating an inverted image in the output plane. A polarization analyzer (not shown) generates the sum and difference of the two images, thereby separating the even and odd spatial parities of the input image.
Fig. 4
Fig. 4 Powers PV and PH of the vertically and horizontally polarized outputs of the polarization analyzer for an input spatial distribution containing a superposition of even and odd functions with amplitudes cos 2 ϕ 2 and sin 2 ϕ 2 as a function of ϕ, the phase difference between the faces of the SLM. At each value of ϕ, PV and PH are divided by their sum to normalize for the effect of variations of the SLM reflectance at different values of ϕ.
Fig. 5
Fig. 5 Powers PV and PH of the vertically and horizontally polarized outputs of the polarization analyzer for OAM modes of order . As alternates between even and odd, the power switches between the vertical- and horizontal-polarization channels. For each mode, the sum of these powers have been normalized to unity in order to account for variation in the strength of the vortex singularity on the face of the SLM that generates these modes.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

g ± ( x ) = 1 2 [ 1 f ( x ) ± 2 f ( x ) ] .
g ± ( x ) = 1 2 [ f ( x ) ± f ( x ) ]
α ± = 1 2 d x h ( x ) [ f ( x ) ± f ( x ) ] = d x h ± ( x ) f ( x ) ,
g + ( x ) = 1 2 d x [ f ( x ) + f ( x ) ] e i k x = d x f ( x ) cos ( k x ) ,
g ( x ) = 1 2 d x [ f ( x ) f ( x ) ] e i k x = i d x f ( x ) sin ( k x ) .
g ± ( x ) = 1 2 d x [ h 1 ( x ; x ) f ( x ) ± h 2 ( x ; x ) f ( x ) ] = d x h ± ( x ; x ) f ( x ) ,
h ± ( x , x ) = 1 2 [ h 1 ( x ; x ) ± h 2 ( x ; x ) ] .
I ± ( x ) = | g ± ( x ) | 2 = d x | h ± ( x ; x ) | 2 I i ( x ) .
I o ( x ) = d x h i ( x ; x ) I i ( x ) ,
h i ( x ; x ) = Re { h 1 * ( x ; x ) h 2 ( x ; x ) }
h i ( x ; x ) = Re { h * ( x x ) h ( x + x ) } .
h i ( x ; x ) = e 2 x 2 / σ 2 e 2 x 2 / σ 2 .
h i ( x ; x ) = cos ( 2 π x x / λ d ) ,
I o ( x ) = Re d x d x h 1 * ( x ; x ) h 2 ( x ; x ) Γ ( x , x ) .
I o ( x ) = Re d x d x e i 2 π x ( x + x ) / λ d Γ ( x , x )
E 1 ( x ) = f ( x ) 1 2 ( e ^ R + e ^ L ) ,
E 2 ( x ) = 1 2 [ f ( x ) e ^ R + f ( x ) e ^ L ] ,
E 2 ( x ) = f o ( x ) e ^ H + f e ( x ) e ^ V ,
f ( x ) = cos ( ϕ 2 ) Φ e ( x ) + i sin ( ϕ 2 ) Φ o ( x )

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