Abstract

Polarization imaging can reveal orthogonal information with respect to color about the structural composition of biological tissue, and with the advance of superior polarimeters its use for biomedical applications has proliferated in the last decade. Polarimetry can be used in pre-clinical and clinical settings for the early detection of cancerous tissue. Polarization-based endoscopy with the complementary near-infrared fluorescence imaging modality improves the early diagnosis of flat cancerous lesions in colorectal tumor models. With the development of new polarization sensors the need to use standard laboratory optics to create custom imaging systems increases. These additional optics can behave as polarization filters effectively degrading and modifying the original tissue’s polarization signatures leading to erroneous judgments. Here, we present a framework to characterize the spectral and polarization properties of rigid endoscopes for polarization-based endoscopic imaging. We describe and evaluate two calibration schemes based on Mueller calculus to reconstruct the original polarization information. Optical limitations of the endoscopes and minimum polarimeter requirements are discussed that may be of interest to other researchers working with custom polarization-based imaging systems.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (1)

2016 (1)

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

2015 (5)

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

W.-L. Hsu, J. Davis, K. Balakrishnan, M. Ibn-Elhaj, S. Kroto, N. Brock, and S. Pau, “Polarization microscope using a near infrared full-Stokes imaging polarimeter,” Opt. Express 23(4), 4357–4368 (2015).
[Crossref] [PubMed]

2014 (4)

W.-L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22(3), 3063–3074 (2014).
[Crossref] [PubMed]

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (2)

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

J. Qi, C. Barrière, T. C. Wood, and D. S. Elson, “Polarized multispectral imaging in a rigid endoscope based on elastic light scattering spectroscopy,” Biomed. Opt. Express 3(9), 2087–2099 (2012).
[Crossref] [PubMed]

2010 (2)

2009 (1)

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107(6), 884–890 (2009).
[Crossref]

2008 (3)

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[Crossref]

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

2006 (2)

2005 (1)

2002 (1)

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7(3), 359–371 (2002).
[Crossref] [PubMed]

1996 (2)

J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, “Target detection in optically scattering media by polarization-difference imaging,” Appl. Opt. 35(11), 1855–1870 (1996).
[Crossref] [PubMed]

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

1970 (1)

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24(111), 647–656 (1970).
[Crossref]

Achilefu, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Akers, W. J.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Akiyama, Y.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Alavi, K.

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

Balakrishnan, K.

Barrière, C.

Bloch, S.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Bouma, B.

Brock, N.

Cadeddu, J. A.

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

Cappabianca, P.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Cariou, J.

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Cavallo, L. M.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Charanya, T.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Chenault, D. B.

Colao, A.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Cronin, T. W.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Davis, J.

de Boer, E.

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

de Boer, J.

de Boer, J. F.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7(3), 359–371 (2002).
[Crossref] [PubMed]

de Divitiis, O.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

de Erausquin, I.

Doradla, P.

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

Doronin, A.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Eccles, M.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Edmiston, C.

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

Eliès, P.

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Elson, D. S.

Engheta, N.

Esposito, F.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Gagnon, Y. L.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

Gao, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

Garcia, M.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

M. Garcia and V. Gruev, “Optical characterization and polarization calibration for rigid endoscopes,” in Proc. of SPIE (SPIE, 2017), 1004008.

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

Garcia, N. M.

Garcia-Allende, P. B.

Giles, R.

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

Glatz, J.

Goldstein, D. L.

Greten, F. R.

J. Glatz, J. Varga, P. B. Garcia-Allende, M. Koch, F. R. Greten, and V. Ntziachristos, “Concurrent video-rate color and near-infrared fluorescence laparoscopy,” J. Biomed. Opt. 18(10), 101302 (2013).
[Crossref] [PubMed]

Gruev, V.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010).
[Crossref] [PubMed]

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

M. Garcia and V. Gruev, “Optical characterization and polarization calibration for rigid endoscopes,” in Proc. of SPIE (SPIE, 2017), 1004008.

Hancock, E.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarisation images,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (IEEE, 2010), 1229–1236.
[Crossref]

Harlaar, N. J.

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

Hartmans, E.

Hirano, M.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Horita, Y.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Hsu, W.-L.

Huynh, C. P.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarisation images,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (IEEE, 2010), 1229–1236.
[Crossref]

Ibn-Elhaj, M.

Jacques, S.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Jeune, B. L.

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Jiang, L.

Johnsen, S.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

Joseph, C.

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

Kahan, L.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Kimachi, A.

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[Crossref]

Koch, M.

Komatsu, K.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Kroto, S.

Kunnen, B.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Lake, S. P.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Liang, K.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Lin, S.-S.

Lotrian, J.

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Macdonald, C.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Marshall, J.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Marshall, N. J.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

Meglinski, I.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

Mikami, T.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Mikuni, N.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Milner, T. E.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7(3), 359–371 (2002).
[Crossref] [PubMed]

Myhre, G.

Nagatani, T.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Nagengast, W. B.

Nakahara, N.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Nassif, N.

Neel, V.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107(6), 884–890 (2009).
[Crossref]

Nishihata, T.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Ntziachristos, V.

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

P. B. Garcia-Allende, J. Glatz, M. Koch, J. J. Tjalma, E. Hartmans, A. G. Terwisscha van Scheltinga, P. Symvoulidis, G. M. van Dam, W. B. Nagengast, and V. Ntziachristos, “Towards clinically translatable NIR fluorescence molecular guidance for colonoscopy,” Biomed. Opt. Express 5(1), 78–92 (2013).
[Crossref] [PubMed]

J. Glatz, J. Varga, P. B. Garcia-Allende, M. Koch, F. R. Greten, and V. Ntziachristos, “Concurrent video-rate color and near-infrared fluorescence laparoscopy,” J. Biomed. Opt. 18(10), 101302 (2013).
[Crossref] [PubMed]

Otaki, S.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Park, B.

Pau, S.

Perkins, R.

Pierce, M.

Powell, S.

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

Powell, S. B.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Pugh, E. N.

Qi, J.

Raman, B.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Raman, J. D.

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

Rane, A.

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

Rao, P.

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

Roberts, N. W.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Robles-Kelly, A.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarisation images,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (IEEE, 2010), 1229–1236.
[Crossref]

Rosenthal, E. L.

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

Rowe, M. P.

Roy-Bréhonnet, F. L.

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Rubin, D.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Saha, D.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Salomatina-Motts, E.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107(6), 884–890 (2009).
[Crossref]

Shanno, D. F.

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24(111), 647–656 (1970).
[Crossref]

Shaw, J. A.

Shishkov, M.

Solari, D.

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Sudlow, G.

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

Suzuki, K.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Symvoulidis, P.

Takebayashi, S.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Tanei, T.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Taruttis, A.

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

Tearney, G.

Terwisscha van Scheltinga, A. G.

Tjalma, J. J.

Tominaga, S.

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[Crossref]

Tu, X.

Tyo, J. S.

van Dam, G. M.

Varga, J.

J. Glatz, J. Varga, P. B. Garcia-Allende, M. Koch, F. R. Greten, and V. Ntziachristos, “Concurrent video-rate color and near-infrared fluorescence laparoscopy,” J. Biomed. Opt. 18(10), 101302 (2013).
[Crossref] [PubMed]

Wakabayashi, T.

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Wanibuchi, M.

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Wood, T. C.

Yaroslavskaya, A.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107(6), 884–890 (2009).
[Crossref]

Yemelyanov, K. M.

York, T.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010).
[Crossref] [PubMed]

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

Appl. Opt. (2)

Biomed. Opt. Express (3)

BJU Int. (1)

J. D. Raman, J. A. Cadeddu, P. Rao, and A. Rane, “Single-incision laparoscopic surgery: initial urological experience and comparison with natural-orifice transluminal endoscopic surgery,” BJU Int. 101(12), 1493–1496 (2008).
[Crossref] [PubMed]

Br. J. Surg. (1)

E. de Boer, N. J. Harlaar, A. Taruttis, W. B. Nagengast, E. L. Rosenthal, V. Ntziachristos, and G. M. van Dam, “Optical innovations in surgery,” Br. J. Surg. 102(2), e56–e72 (2015).
[Crossref] [PubMed]

Curr. Biol. (1)

S. Johnsen, Y. L. Gagnon, N. J. Marshall, T. W. Cronin, V. Gruev, and S. Powell, “Polarization vision seldom increases the sighting distance of silvery fish,” Curr. Biol. 26(16), R752–R754 (2016).
[Crossref] [PubMed]

J. Biomed. Opt. (4)

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19(8), 080501 (2014).
[Crossref] [PubMed]

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7(3), 359–371 (2002).
[Crossref] [PubMed]

J. Glatz, J. Varga, P. B. Garcia-Allende, M. Koch, F. R. Greten, and V. Ntziachristos, “Concurrent video-rate color and near-infrared fluorescence laparoscopy,” J. Biomed. Opt. 18(10), 101302 (2013).
[Crossref] [PubMed]

T. Charanya, T. York, S. Bloch, G. Sudlow, K. Liang, M. Garcia, W. J. Akers, D. Rubin, V. Gruev, and S. Achilefu, “Trimodal color-fluorescence-polarization endoscopy aided by a tumor selective molecular probe accurately detects flat lesions in colitis-associated cancer,” J. Biomed. Opt. 19(12), 126002 (2014).
[Crossref] [PubMed]

J. Biophotonics (1)

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref] [PubMed]

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

J. Phys. D Appl. Phys. (1)

F. L. Roy-Bréhonnet, B. L. Jeune, P. Eliès, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D Appl. Phys. 29(1), 34–38 (1996).
[Crossref]

Math. Comput. (1)

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24(111), 647–656 (1970).
[Crossref]

Neurol. Med. Chir. (Tokyo) (1)

T. Tanei, N. Nakahara, S. Takebayashi, M. Hirano, T. Nagatani, T. Nishihata, and T. Wakabayashi, “Endoscopic biopsy for lesions located in the parenchyma of the brain: preoperative planning based on stereotactic methods. Technical note,” Neurol. Med. Chir. (Tokyo) 52(8), 617–621 (2012).
[Crossref] [PubMed]

Neurol. Res. (1)

Y. Akiyama, M. Wanibuchi, T. Mikami, Y. Horita, K. Komatsu, K. Suzuki, S. Otaki, and N. Mikuni, “Rigid endoscopic resection of deep-seated or intraventricular brain tumors,” Neurol. Res. 37(3), 278–282 (2015).
[Crossref] [PubMed]

Opt. Eng. (1)

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[Crossref]

Opt. Express (6)

Opt. Spectrosc. (1)

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc. 107(6), 884–890 (2009).
[Crossref]

Pituitary (1)

P. Cappabianca, L. M. Cavallo, O. de Divitiis, D. Solari, F. Esposito, and A. Colao, “Endoscopic pituitary surgery,” Pituitary 11(4), 385–390 (2008).
[Crossref] [PubMed]

Proc IEEE Inst Electr Electron Eng (1)

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Other (7)

P. Doradla, K. Alavi, C. S. Joseph, and R. H. Giles, “Development of terahertz endoscopic system for cancer detection,” in SPIE OPTO (International Society for Optics and Photonics, 2016), paper 97470F.

D. H. Goldstein, Polarized light (CRC press, 2016).

M. Garcia, S. Gao, C. Edmiston, T. York, and V. Gruev, “A 1300× 800, 700 mW, 30 fps spectral polarization imager,” in IEEE International Symposium on Circuits and Systems (ISCAS), (IEEE, 2015), 1106–1109.
[Crossref]

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarisation images,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (IEEE, 2010), 1229–1236.
[Crossref]

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” in Computer Vision and Pattern Recognition, 2006 IEEE Computer Society Conference on, (IEEE, 2006), 1984–1991.
[Crossref]

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M. Garcia and V. Gruev, “Optical characterization and polarization calibration for rigid endoscopes,” in Proc. of SPIE (SPIE, 2017), 1004008.

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Figures (13)

Fig. 1
Fig. 1 Gray scale image (left) and a polarization image (right) in a linear false-color map for an in vivo polarization endoscopy of an adenomatous tumor in a mouse. Red areas indicate a higher degree of polarization while dark blue areas indicate a lower degree of polarization. A higher polarization is associated with healthy tissue while lower polarization signatures indicate possible tumor locations.
Fig. 2
Fig. 2 Optical setup for polarization characterization.
Fig. 3
Fig. 3 Optical setup for spectral characterization.
Fig. 4
Fig. 4 Data plotted on the Poincaré sphere. Input Stokes vector data (a) and output Stokes vector data for the 5 mm (b) and 10 mm (c) endoscopes. Three-dimensional representation (left) and two-dimensional profiles (right). The data is clustered into 10 groups of color-coded data points with the purpose of visually identifying the polarization migration of the initial input Stokes vectors (a) caused by the rigid endoscopes to the final output Stokes vectors (b and c); i.e., this color coding indicates corresponding pairs of input and output Stokes vectors.
Fig. 5
Fig. 5 Output AoP vs. input AoP, with DoLP = 1, for the 5 mm (left) and 10 mm endoscope (right).
Fig. 6
Fig. 6 Output DoLP vs. input DoLP, with DoLP = 0 & AoP = 0, for the 5 mm (left) and 10 mm endoscope (right).
Fig. 7
Fig. 7 Output DoLP, and output DoCP vs. input AoP, for the 5 mm (left) and 10 mm endoscope (right).
Fig. 8
Fig. 8 Input Stokes vector data (red cubes) and reconstructed input Stokes vector data (green spheres) on the Poincaré sphere (top) with error histograms (bottom) for the 5 mm (left) and the 10 mm (right) endoscopes using the double rotated retarder model.
Fig. 9
Fig. 9 Input Stokes vector data (red cubes) and reconstructed input Stokes vector data (green spheres) on the Poincaré sphere (top) for one cross-validation iteration with error histograms (bottom) for the 5 mm (left) and the 10 mm (right) endoscope using the linear regression model.
Fig. 10
Fig. 10 Spectral response as a function of wavelength for the 5 mm (left) and 10 mm (right) endoscope.
Fig. 11
Fig. 11 DOF target images for the 5 mm (a) and 10 mm (b) endoscopes.
Fig. 12
Fig. 12 Sample images used to calculate the MTF curve for the 5 mm (a) and 10 mm (b) endoscope and MTF curve plots for the 5 mm and 10 mm endoscope (c).
Fig. 13
Fig. 13 1951 USAF resolution chart images for the 5 mm (a) and 10 mm (b) endoscope and magnified versions (right).

Tables (2)

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Table 1 Double rotated retarder model calibration results.

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Table 2 Linear regression model calibration results.

Equations (7)

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I( θ,ϕ )= 1 2 ( S 0 + S 1 cos2θ+ S 2 sin2θcosϕ+ S 3 sin2θsinϕ )
S out =M S in
M( ϕ,2θ )=( 1 0 0 0 0 cos 2 2θ+cosϕ sin 2 2θ ( 1cosϕ )sin2θcos2θ sinϕsin2θ 0 ( 1cosϕ )sin2θcos2θ sin 2 2θ+cosϕ cos 2 2θ sinϕcos2θ 0 sinϕsin2θ sinϕcos2θ cosϕ )
S * out =M( ϕ 1 * ,2 θ 1 * )M( ϕ 2 * ,2 θ 2 * ) S in = M endoscope S in
error= i=1 n S 1,i S 2,i n , for n data points
M * = S out_train S in_train p
S * in_test = ( M * ) p S out_test

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