Abstract

A dual-channel lateral shearing beam splitter was used in a Fourier transform imaging spectrometer, forming a dual-channel imaging spectrometer, to investigate the usability of this technique for large field-of-view (FOV) spectral detection. The large FOV obtained by stitching together the different channels’ individual FOVs greatly improved the spectral detection efficiency for large-area targets. This report describes the principle of the dual-rectangle lateral shearing beam splitter and the analysis of the lateral shearing distance, FOV, modulation, and method of dual-channel stitching. Large-FOV spectral images of a scene were acquired experimentally at visible wavelengths, confirming the effectiveness of this technique.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (1)

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
[Crossref]

2014 (2)

X. Lin, G. Wetzstein, Y. Liu, and Q. Dai, “Dual-coded compressive hyperspectral imaging,” Opt. Lett. 39(7), 2044–2047 (2014).
[Crossref] [PubMed]

R. O. Green, “Lessons and key results from 30 years of imaging spectroscopy,” Proc. SPIE 9222, 92220B (2014).
[Crossref]

2012 (2)

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

2011 (3)

2009 (1)

A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: A personal view,” Remote Sens. Environ. 113, S5–S16 (2009).
[Crossref]

2008 (2)

2005 (1)

2004 (1)

2002 (1)

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
[Crossref]

1998 (1)

M. Q. Xue, B. Xiangli, and B. Q. An, “Optical systems of imaging interferometers,” Proc. SPIE 3482, 474–483 (1998).
[Crossref]

1996 (7)

1995 (1)

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

1994 (1)

D. Loiseaux, A. Michel, C. Babolat, and Y. Delclaud, “MERIS camera optics development: particular processes for an original concept,” Proc. SPIE 2209, 252–261 (1994).
[Crossref]

1993 (1)

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

1991 (1)

1989 (1)

A. H. Vaughan, “Imaging Michelson spectrometer for Hubble space telescope,” Proc. SPIE 1036, 2–14 (1989).
[Crossref]

1985 (1)

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228(4704), 1147–1153 (1985).
[Crossref] [PubMed]

1954 (1)

Akagi, J.

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
[Crossref]

An, B. Q.

M. Q. Xue, B. Xiangli, and B. Q. An, “Optical systems of imaging interferometers,” Proc. SPIE 3482, 474–483 (1998).
[Crossref]

Anger, C. D.

S. K. Babey and C. D. Anger, “A compact airborne spectrographic imager (CASI),” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 1989), pp. 1028–1031.

Babey, S. K.

S. K. Babey and C. D. Anger, “A compact airborne spectrographic imager (CASI),” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 1989), pp. 1028–1031.

Babolat, C.

D. Loiseaux, A. Michel, C. Babolat, and Y. Delclaud, “MERIS camera optics development: particular processes for an original concept,” Proc. SPIE 2209, 252–261 (1994).
[Crossref]

Bai, C.

Barducci, A.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

Boreman, G. D.

Buckwald, R. A.

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

Budney, C.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Butcher, S. D.

Cabib, D.

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

Castagnoli, F.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

Castellini, G.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

Chavel, P.

Chen, D. T.

Corson, M.

Coudrain, C.

Craven-Jones, J.

Crites, S. T.

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
[Crossref]

Dai, Q.

Davis, C. O.

Delclaud, Y.

D. Loiseaux, A. Michel, C. Babolat, and Y. Delclaud, “MERIS camera optics development: particular processes for an original concept,” Proc. SPIE 2209, 252–261 (1994).
[Crossref]

Dereniak, E. L.

Deschamps, J.

Dybwad, P.

Ferrec, Y.

Fienup, J. R.

Fischer, H.

Fletcher-Holmes, D.

Fournet, P.

Garini, Y.

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

Goetz, A. F. H.

A. F. H. Goetz, “Three decades of hyperspectral remote sensing of the Earth: A personal view,” Remote Sens. Environ. 113, S5–S16 (2009).
[Crossref]

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228(4704), 1147–1153 (1985).
[Crossref] [PubMed]

Green, R. O.

Guizar-Sicairos, M.

Guzzi, D.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

Hammer, P. D.

Harvey, A.

Hinck, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Horton, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Ichioka, Y.

Inoue, T.

Itoh, K.

Jacquinot, P.

Jim, K. T. C.

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
[Crossref]

Korb, A. R.

Korwan, D. R.

Kudenov, M. W.

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
[Crossref]

J. Craven-Jones, M. W. Kudenov, M. G. Stapelbroek, and E. L. Dereniak, “Infrared hyperspectral imaging polarimeter using birefringent prisms,” Appl. Opt. 50(8), 1170–1185 (2011).
[Crossref] [PubMed]

Lastri, C.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

Li, J.

Li, R. R.

Lin, X.

Liu, Y.

Loiseaux, D.

D. Loiseaux, A. Michel, C. Babolat, and Y. Delclaud, “MERIS camera optics development: particular processes for an original concept,” Proc. SPIE 2209, 252–261 (1994).
[Crossref]

Lucey, P. G.

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
[Crossref]

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Lucke, R. L.

Maione, B.

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
[Crossref]

Malik, Z.

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

Marcoionni, P.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

McGlothlin, N. R.

Michel, A.

D. Loiseaux, A. Michel, C. Babolat, and Y. Delclaud, “MERIS camera optics development: particular processes for an original concept,” Proc. SPIE 2209, 252–261 (1994).
[Crossref]

Mouroulis, P.

Nardino, V.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

Oelhaf, H.

Pantalone, B.

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
[Crossref]

Pfeiffer, J.

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
[Crossref]

Pippi, I.

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
[Crossref]

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, P. Marcoionni, and I. Pippi, “ALISEO on MIOSAT: an aerospace imaging interferometer for Earth observation,” in Proceedings of IEEE Conference on International Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. II-464–II-467.
[Crossref]

Primot, J.

Rafert, B.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Rock, B. N.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228(4704), 1147–1153 (1985).
[Crossref] [PubMed]

Roy, S. G.

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
[Crossref]

Rusk, T. B.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Salisbury, J. W.

Sauer, H.

Self, V. A.

V. A. Self and P. A. Sermon, “Fourier transform infrared cell for surface studies at controlled temperatures and in controlled atmospheres with time resolution and spatial resolution,” Rev. Sci. Instrum. 67(6), 2096–2099 (1996).
[Crossref]

Sellar, R. G.

Sermon, P. A.

V. A. Self and P. A. Sermon, “Fourier transform infrared cell for surface studies at controlled temperatures and in controlled atmospheres with time resolution and spatial resolution,” Rev. Sci. Instrum. 67(6), 2096–2099 (1996).
[Crossref]

Shen, Y.

Shepherd, G. G.

Smith, W. H.

Snijders, B.

B. Snijders and H. Visser, “Imaging spectrometer with a large field of view,” Proc. SPIE 2830, 331–340 (1996).
[Crossref]

Snyder, W. A.

Soenkeson, D.

Z. Malik, D. Cabib, R. A. Buckwald, Y. Garini, and D. Soenkeson, “A novel spectral imaging system combining spectroscopy with imaging-applications for biology,” Proc. SPIE 2329, 180–184 (1995).
[Crossref]

Solomon, J. E.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228(4704), 1147–1153 (1985).
[Crossref] [PubMed]

Sparks, A.

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
[Crossref]

Stapelbroek, M. G.

Taboury, J.

Thurman, S. T.

Topping, M.

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
[Crossref]

Vane, G.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228(4704), 1147–1153 (1985).
[Crossref] [PubMed]

Vaughan, A. H.

A. H. Vaughan, “Imaging Michelson spectrometer for Hubble space telescope,” Proc. SPIE 1036, 2–14 (1989).
[Crossref]

Visser, H.

B. Snijders and H. Visser, “Imaging spectrometer with a large field of view,” Proc. SPIE 2830, 331–340 (1996).
[Crossref]

Wadsworth, W.

Wetzstein, G.

Williams, T.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
[Crossref]

Wilson, D. W.

Wood, D. L.

Wood, M.

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
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Xiangli, B.

M. Q. Xue, B. Xiangli, and B. Q. An, “Optical systems of imaging interferometers,” Proc. SPIE 3482, 474–483 (1998).
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Xue, M. Q.

M. Q. Xue, B. Xiangli, and B. Q. An, “Optical systems of imaging interferometers,” Proc. SPIE 3482, 474–483 (1998).
[Crossref]

Yoon, D.

M. Topping, J. Pfeiffer, A. Sparks, K. T. C. Jim, and D. Yoon, “Advanced airborne hyperspectral imaging system(AAHIS),” Proc. SPIE 4816, 1–11 (2002).
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Zhou, J.

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A. R. Korb, P. Dybwad, W. Wadsworth, and J. W. Salisbury, “Portable Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” Appl. Opt. 35(10), 1679–1692 (1996).
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R. L. Lucke, M. Corson, N. R. McGlothlin, S. D. Butcher, D. L. Wood, D. R. Korwan, R. R. Li, W. A. Snyder, C. O. Davis, and D. T. Chen, “Hyperspectral Imager for the Coastal Ocean: instrument description and first images,” Appl. Opt. 50(11), 1501–1516 (2011).
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Opt. Eng. (1)

A. Barducci, F. Castagnoli, G. Castellini, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Developing a new hyperspectral imaging interferometer for earth observation,” Opt. Eng. 51(11), 111706 (2012).
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Proc. SPIE (11)

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[Crossref]

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[Crossref]

P. G. Lucey, M. Wood, S. T. Crites, and J. Akagi, “A LWIR hyperspectral imager using a Sagnac interferometer and cooled HgCdTe detector array,” Proc. SPIE 8390, 83900Q (2012).
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[Crossref]

M. W. Kudenov, S. G. Roy, B. Pantalone, and B. Maione, “Ultraspectral imaging and the snapshot advantage,” Proc. SPIE 9467, 94671X (2015).
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P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, B. Rafert, and T. B. Rusk, “SMIFTS: A cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–141 (1993).
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[Crossref]

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Figures (18)

Fig. 1
Fig. 1 (a) Schematic diagram of the dual-channel FOV stitching imaging spectrometer. Two-dimensional spatial intensity distributions from two different FOVs that are superimposed with the fringe pattern can be obtained by CCD1 and CCD2. (b) Dual-rectangle lateral shearing beam splitter. M1, M2, M3, and M4 are reflectors, and BS1 and BS2 are beam splitters.
Fig. 2
Fig. 2 Unfolded optical layout of dual-rectangle lateral shearing beam splitter. The dotted lines are the positions of M3 and M4 after translation.
Fig. 3
Fig. 3 Schematic diagram of the obtaining of different FOVs. L1 is the objective lens. L2 is the collimator. L3 and L4 indicate imaging lenses. CCD1 and CCD2 acquire images with different FOVs. (a) Obtaining of the down-FOV. (b) Obtaining of the up-FOV.
Fig. 4
Fig. 4 Extraction of the interferogram of a point. Interferometric images are acquired using the push-broom technique. A1, A2, A3, …, An are the positions of point A from the scene, which has different coordinates in different images. A1, A2, A3, …, An have the same coordinates after image registration, and the interferogram of point A can be acquired by extracting the same point from all of the images.
Fig. 5
Fig. 5 Schematic diagram of the beam shearing principle. Lines B′C′ and AB cross at point O. Line OB and the dotted line cross at point R. The auxiliary line RT is perpendicular to M4. Line OP is perpendicular to line BC. Line OQ is parallel to line CC′.
Fig. 6
Fig. 6 Schematic diagram of the overlap of two Airy disks. The shaded area represents the region in which the two Airy disks overlap.
Fig. 7
Fig. 7 Schematic diagram of image stitching.
Fig. 8
Fig. 8 Experimental setup. The dual-channel lateral shearing beam splitter was composed of BS1, BS2, M1, M2, M3, and M4. The imaging plane of the objective lens L1 coincided with the focal plane of the collimator L2. L3 and L4 indicate imaging lenses. CCD1 and CCD2 acquired images with different FOVs.
Fig. 9
Fig. 9 OPD linearity analysis of the system. (a) Part of the fringe pattern along with the experimental estimations of the OPD and a reference OPD curve obtained with theoretical analysis. (b) Nonlinear deviation of the experimental OPD.
Fig. 10
Fig. 10 Simulation results of spectrum reconstruction for a signal of 638 nm under the linear and nonlinear conditions.
Fig. 11
Fig. 11 Target and interference images from two channels. (a) Experimental target scene. (b) Interference images from the up-FOV. (c) Interference images from the down-FOV.
Fig. 12
Fig. 12 Interference images after registration. (a) Interference images from the up-FOV. (b) Interference images from the down-FOV.
Fig. 13
Fig. 13 Spectral reconstruction of point A. (a) Interference images after registration. (b) Interferogram of point A extracted from the interference images. (c) Spectrum of point A reconstructed by the proposed method and the USB4000.
Fig. 14
Fig. 14 Reconstructed spectral images. (a) Reconstructed images of the up-FOV. (b) Reconstructed images of the down-FOV.
Fig. 15
Fig. 15 Wide-format spectral images obtained by stitching together the spectral images of the two FOVs.
Fig. 16
Fig. 16 Schematic diagram of the most compact configuration of the lateral shearing splitter. M1 and M2 cross at point A. M3 and M4 cross at point B.
Fig. 17
Fig. 17 Unfolded optical layout of the path reflected by M1 and M2. M1′, M2′, BS1′, and BS2′ are the positions of M1, M2, BS1, and BS2, respectively, after unfolding. D′ is the position of the right endpoint of BS1 after unfolding. Beams 1 and 2 go through the incident plane at points F and G, respectively.
Fig. 18
Fig. 18 Unfolded optical layout of the path reflected by M3 and M4. M4′ and BS2′ are the positions of M4 and BS2, respectively, after unfolding, and O′ is the position of the right endpoint of BS2 after unfolding. Beams 1 and 2 go through the incident plane at points I and J, respectively.

Equations (33)

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I Δ ( δ ) = σ min σ max B Δ ( σ ) K Δ cos ( 2 π σ δ ) d σ
I ( δ ) = σ min σ max B ( σ ) K cos ( 2 π σ δ ) d σ ,
δ = d sin θ x .
B Δ ( σ ) = - + I Δ ( θ x ) exp ( 2 π σ d sin θ x ) d θ x
B ( σ ) = + I ( θ x ) exp ( 2 π σ d sin θ x ) d θ x ,
d = ( L A A + L R T / cos θ B R T ) cos θ P O B sin θ P O Q = 2 d ( 1 / sin α + 1 / cos α ) sin 2 α 2 sin ( π / 4 α )
K Δ 1 = 2 r B S 1 - s 1 r B S 1 s 2 r M 1 s r M 2 s r M 3 s r M 4 s r B S 2 s 1 r B S 2 s 2 + 2 r B S 1 p 1 r B S 1 p 2 r M 1 p r M 2 p r M 3 p r M 4 p r B S 2 p 1 r B S 2 p 2 r B S 1 s 2 r M 1 s 2 r M 2 s 2 ( 1 r B S 2 s 2 ) + ( 1 r B S 1 s 2 ) r M 3 s 2 r M 4 s 2 r B S 2 s 2 + r B S 1 p 2 r M 1 p 2 r M 2 p 2 ( 1 r B S 2 p 2 ) + ( 1 r B S 1 p 2 ) r M 3 p 2 r M 4 p 2 r B S 2 p 2
K 1 = 2 r B S 1 - s 1 r B S 1 s 2 r M 1 s r M 2 s r M 3 s r M 4 s r B S 2 s 1 r B S 2 s 2 + 2 r B S 1 p 1 r B S 1 p 2 r M 1 p r M 2 p r M 3 p r M 4 p r B S 2 p 1 r B S 2 p 2 r B S 1 s 2 r M 1 s 2 r M 2 s 2 r B S 2 s 2 + ( 1 r B S 1 s 2 ) r M 3 s 2 r M 4 s 2 ( 1 r B S 2 s 2 ) + r B S 1 p 2 r M 1 p 2 r M 2 p 2 r B S 2 p 2 + ( 1 r B S 1 p 2 ) r M 3 p 2 r M 4 p 2 ( 1 r B S 2 p 2 )
K Δ 1 r B S 1 s = K Δ 1 r B S 2 s = K Δ 1 r B S 1 p = K Δ 1 r B S 2 p = 0 ,
ε max = min ( arc tan ( tan θ Δ R / f ) θ Δ 2 , arc tan ( tan θ R / f ) θ 2 )
I 2 ( x , y ) = I 1 ( x x 0 , y y 0 ) .
F 2 ( u , v ) = F 1 ( u , v ) exp ( j ( u x 0 + v y 0 ) ) .
C ( u , v ) = F 1 ( u , v ) F 2 ( u , v ) | F 1 ( u , v ) F 2 ( u , v ) | = exp ( j ( u x 0 + v y 0 ) )
x ˜ 0 = x 0 + Δ x 0 / k y ˜ 0 = y 0 + Δ y 0 / k .
K = | ( E 1 ( x , y ) E 2 ( x , y ) + E 2 ( x , y ) E 1 ( x , y ) ) d x d y | 2 I A ,
E ( x , y ) = 2 E 0 J 1 ( π D σ ( x x 0 ) 2 + ( y y 0 ) 2 / l ) π D σ ( x x 0 ) 2 + ( y y 0 ) 2 / l ,
I A = 2 0 2 π 0 R ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l ) 2 d x ¯ d ϕ ,
| ( E 1 ( x , y ) E 2 ( x , y ) + E 2 ( x , y ) E 1 ( x , y ) ) d x d y | = 0 Γ 0 R s 2 + 2 R s cos ϕ Y ( x ¯ , s ) d x ¯ d ϕ ,
Y ( x ¯ , s ) = ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l + 2 J 1 ( π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) 2 ,
K = 0 Γ 0 R 2 + s 2 - 2 R s cos ϕ ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l + 2 J 1 ( π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) 2 d x ¯ d ϕ 2 0 2 π 0 R ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l ) 2 d r d ϕ .
s Δ = f | ( tan θ Δ tan ( θ Δ + 2 ε ) ) |
s = f | ( tan θ tan ( θ + 2 ε ) ) | .
K Δ 2 = 0 Γ Δ 0 R 2 + s Δ 2 - 2 R s Δ cos ϕ ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l + 2 J 1 ( π D σ x ¯ 2 + s Δ 2 2 x ¯ s Δ cos ϕ / l ) π D σ x ¯ 2 + s Δ 2 2 x ¯ s Δ cos ϕ / l ) 2 d x ¯ d ϕ 2 0 2 π 0 R ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l ) 2 d x ¯ d ϕ
K 2 = 0 Γ 0 R 2 + s 2 - 2 R s cos ϕ ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l + 2 J 1 ( π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) π D σ x ¯ 2 + s 2 2 x ¯ s cos ϕ / l ) 2 d x ¯ d ϕ 2 0 2 π 0 R ( 2 J 1 ( π D σ x ¯ / l ) π D σ x ¯ / l ) 2 d x ¯ d ϕ ,
L C F > 2 H tan β 1 ,
L E G > 3 2 2 H tan β 2 ,
L F G = 2 2 H 2 H tan β 1 3 2 2 H tan β 2 > 0 ,
2 2 H 5 2 2 H tan U 1 > 0 ,
L E D = L E F sin ( π / 2 U 1 ) sin ( π / 4 U 1 )
L P I > 2 2 H tan γ 1 ,
L K J > 3 2 2 H tan γ 2 ,
L I J = 2 2 H 2 2 H tan γ 1 3 2 2 H tan γ 2 > 0 ,
2 2 H 7 2 2 H tan U 2 > 0 ,

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