Abstract

Endoscopic optical coherence tomography (OCT) catheters comprise a transparent tube to separate the imaging instrument from tissues. This tube acts as a cylindrical lens, introducing astigmatism into the beam. In this report, we quantified this negative effect using optical simulations of OCT catheter devices, and discuss possible compensation strategies. For esophageal imaging, the astigmatism is aggravated by the long working distance. For intracoronary imaging, the beam quality is degraded due to the liquid imaging environment. A nearly circular beam profile can be achieved by a curved focusing optics. We also consider the method of matching refractive indices, and it is shown to successfully restore a round beam.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef]
  2. M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
    [CrossRef]
  3. S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
    [CrossRef]
  4. H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
    [CrossRef]
  5. G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
    [CrossRef]
  6. X. Li, C. Chudoba, T. Ko, C. Pitris, and J. G. Fujimoto, “Imaging needle for optical coherence tomography,” Opt. Lett. 25, 1520–1522 (2000).
    [CrossRef]
  7. G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. 21, 543–545 (1996).
    [CrossRef]
  8. B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
    [CrossRef]
  9. E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
    [CrossRef]
  10. F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
    [CrossRef]
  11. G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
    [CrossRef]
  12. E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
    [CrossRef]
  13. B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
    [CrossRef]
  14. P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
    [CrossRef]
  15. G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
    [CrossRef]
  16. G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
    [CrossRef]
  17. M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
    [CrossRef]
  18. A. R. Tumlinson, L. P. Hariri, U. Utzinger, and J. K. Barton, “Miniature endoscope for simultaneous optical coherence tomography and laser-induced fluorescence measurement,” Appl. Opt. 43, 113–121 (2004).
    [CrossRef]
  19. P. Meemon, K. S. Lee, S. Murali, and J. Rolland, “Optical design of a dynamic focus catheter for high-resolution endoscopic optical coherence tomography,” Appl. Opt. 47, 2452–2457 (2008).
    [CrossRef]
  20. J. Xi, L. Huo, Y. Wu, M. J. Cobb, J. H. Hwang, and X. Li, “High-resolution OCT balloon imaging catheter with astigmatism correction,” Opt. Lett. 34, 1943–1945 (2009).
    [CrossRef]
  21. W. Kang, H. Wang, Y. Pan, M. W. Jenkins, G. A. Isenberg, A. Chak, M. Atkinson, D. Agrawal, Z. Hu, and A. M. Rollins, “Endoscopically guided spectral-domain OCT with double-balloon catheters,” Opt. Express 18, 17364–17372(2010).
    [CrossRef]
  22. W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008), pp. 397–400.
  23. E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).
  24. Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
    [CrossRef]
  25. Y. Mao, S. Chang, S. Sherif, and C. Flueraru, “Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging,” Appl. Opt. 46, 5887–5894 (2007).
    [CrossRef]
  26. W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
    [CrossRef]
  27. W. T. Silfvast, Laser Fundamentals (Cambridge University, 2003), pp. 402–432.
  28. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).
  29. C. W. Reno, “Laser astigmatism compensation,” U.S. Patent 5239414 (24August1993).

2011 (3)

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

2010 (4)

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

W. Kang, H. Wang, Y. Pan, M. W. Jenkins, G. A. Isenberg, A. Chak, M. Atkinson, D. Agrawal, Z. Hu, and A. M. Rollins, “Endoscopically guided spectral-domain OCT with double-balloon catheters,” Opt. Express 18, 17364–17372(2010).
[CrossRef]

2009 (2)

J. Xi, L. Huo, Y. Wu, M. J. Cobb, J. H. Hwang, and X. Li, “High-resolution OCT balloon imaging catheter with astigmatism correction,” Opt. Lett. 34, 1943–1945 (2009).
[CrossRef]

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

2008 (2)

P. Meemon, K. S. Lee, S. Murali, and J. Rolland, “Optical design of a dynamic focus catheter for high-resolution endoscopic optical coherence tomography,” Appl. Opt. 47, 2452–2457 (2008).
[CrossRef]

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

2007 (4)

Y. Mao, S. Chang, S. Sherif, and C. Flueraru, “Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging,” Appl. Opt. 46, 5887–5894 (2007).
[CrossRef]

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

2006 (4)

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
[CrossRef]

2004 (1)

2003 (1)

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

2000 (1)

1996 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Agrawal, D.

Ahmad, A.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Aretz, H. T.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Atkinson, M.

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Barlis, P.

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

Barton, J. K.

Benalcazar, W.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Bisaillon, C. E.

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Bisaillon, C.-E.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

Boppart, S. A.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. 21, 543–545 (1996).
[CrossRef]

Bouma, B. E.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. 21, 543–545 (1996).
[CrossRef]

Brezinski, M. E.

Brown, E. N.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Bruining, N.

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

Burris, N. S.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Chak, A.

Chan, R. C.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Chang, S.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Chudoba, C.

Cilesiz, I.

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

Cobb, M. J.

J. Xi, L. Huo, Y. Wu, M. J. Cobb, J. H. Hwang, and X. Li, “High-resolution OCT balloon imaging catheter with astigmatism correction,” Opt. Lett. 34, 1943–1945 (2009).
[CrossRef]

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

D’Amours, F.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

de Boer, J. F.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

de Smet, M. D.

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

DeJoseph Gauthier, D.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Desjardins, A. E.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Drexler, W.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008), pp. 397–400.

Dufour, M.

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Dufour, M. L.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

Evans, J. A.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Faber, D. J.

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Flueraru, C.

Fu, H. L.

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

Fujimoto, J. G.

X. Li, C. Chudoba, T. Ko, C. Pitris, and J. G. Fujimoto, “Imaging needle for optical coherence tomography,” Opt. Lett. 25, 1520–1522 (2000).
[CrossRef]

G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. 21, 543–545 (1996).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008), pp. 397–400.

Gauthier, B.

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Goderie, T.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

Goderie, T. P. M.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Gonzalo, N.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Gu, J.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Halpern, E. F.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Hariri, L. P.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Heng, X.

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

Hewko, M.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Houser, S. L.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Hsu, K.

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

Hu, Z.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Huo, L.

Hwang, J. H.

J. Xi, L. Huo, Y. Wu, M. J. Cobb, J. H. Hwang, and X. Li, “High-resolution OCT balloon imaging catheter with astigmatism correction,” Opt. Lett. 34, 1943–1945 (2009).
[CrossRef]

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

Isenberg, G. A.

Jang, I. K.

G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
[CrossRef]

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Jang, I.-K.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Jenkins, M. W.

Jung, W.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Kallam, S.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Kang, W.

Kauffman, C. R.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Kelly, D. L.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Ko, T.

Koljenovic, S.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

Kon, Z. N.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Laird, P.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Lamouche, G.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Lamport, R. B.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Lee, K. S.

Leng, Y.

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

Li, X.

Ligthart, J.

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

MacNeill, B. D.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Mao, Y.

McDowell, E. J.

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

McNamaram, E.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Meemon, P.

Monchalin, J. P.

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Murali, S.

Nishioka, N. S.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Oh, W. Y.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Oh, W.-Y.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

Okamura, T.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

Oosterhuis, J. W.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

Padioleau, C.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

Pan, Y.

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Petersen, C. L.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Pitris, C.

Poston, R. S.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Regar, E.

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

Reno, C. W.

C. W. Reno, “Laser astigmatism compensation,” U.S. Patent 5239414 (24August1993).

Rolland, J.

Rollins, A. M.

Schmitt, J. M.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Serruys, P. W.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

Sharma, U.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Sherif, S.

Shishko, M.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

Shishkov, M.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Silfvast, W. T.

W. T. Silfvast, Laser Fundamentals (Cambridge University, 2003), pp. 402–432.

Southern, J. F.

Sowa, M.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

Sowa, M. G.

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Suter, M. J.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Swanson, E.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Tang, C. M.

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

Tearney, G. J.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. 21, 543–545 (1996).
[CrossRef]

Tu, H.

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Tumlinson, A. R.

Utzinger, U.

Vakoc, B. J.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

van der Meer, F. J.

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

van der Steen, A. F.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

van der Steen, A. F. W.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

van Gemert, M. J.

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

van Leenders, G. J. L. H.

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

van Leenders, G. L.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

van Leeuwen, T. G.

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

van Noorden, S.

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

van Soest, G.

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

van Velthoven, M. E. J.

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

Verbraak, F. D.

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

Vergnole, S.

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Wang, H.

Weissman, N. J.

Wu, J.

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

Wu, Y.

Xi, J.

Yabushita, H.

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Yang, C.

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

Yaqoob, Z.

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

Yun, S. H.

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Appl. Opt. (3)

Expert Rev. Med. Devices (1)

P. Barlis, G. van Soest, P. W. Serruys, and E. Regar, “Intracoronary optical coherence tomography and the evaluation of stents,” Expert Rev. Med. Devices 6, 157–167(2009).
[CrossRef]

Gastrointestinal endoscopy (1)

B. J. Vakoc, M. Shishko, S. H. Yun, W.-Y. Oh, M. J. Suter, A. E. Desjardins, J. A. Evans, N. S. Nishioka, G. J. Tearney, and B. E. Bouma, “Comprehensive esophageal microscopy by using optical frequency–domain imaging (with video),” Gastrointestinal endoscopy 65, 898–905 (2007).
[CrossRef]

Heart (1)

B. E. Bouma, G. J. Tearney, H. Yabushita, M. Shishkov, C. R. Kauffman, D. DeJoseph Gauthier, B. D. MacNeill, S. L. Houser, H. T. Aretz, E. F. Halpern, and I. K. Jang, “Evaluation of intracoronary stenting by intravascular optical coherence tomography,” Heart 89, 317–320 (2003).
[CrossRef]

Herz (1)

E. Regar, J. Ligthart, N. Bruining, and G. van Soest, “The diagnostic value of intracoronary optical coherence tomography,” Herz 36, 417–429 (2011).
[CrossRef]

J. Am. Coll. Cardiol. Img. (1)

G. van Soest, E. Regar, T. P. M. Goderie, N. Gonzalo, S. Koljenović, G. J. L. H. van Leenders, P. W. Serruys, and A. F. W. van der Steen, “Pitfalls in plaque characterization by OCT: image artifacts in native coronary arteries,” J. Am. Coll. Cardiol. Img. 4, 810–813 (2011).
[CrossRef]

J. Biomed. Opt. (8)

G. van Soest, T. Goderie, E. Regar, S. Koljenovic, G. L. van Leenders, N. Gonzalo, S. van Noorden, T. Okamura, B. E. Bouma, G. J. Tearney, J. W. Oosterhuis, P. W. Serruys, and A. F. van der Steen, “Atherosclerotic tissue characterization in vivo by optical coherence tomography attenuation imaging,” J. Biomed. Opt. 15, 011105 (2010).
[CrossRef]

F. J. van der Meer, D. J. Faber, I. Cilesiz, M. J. van Gemert, and T. G. van Leeuwen, “Temperature-dependent optical properties of individual vascular wall components measured by optical coherence tomography,” J. Biomed. Opt. 11, 041120 (2006).
[CrossRef]

G. J. Tearney, I. K. Jang, and B. E. Bouma, “Optical coherence tomography for imaging the vulnerable plaque,” J. Biomed. Opt. 11, 021002 (2006).
[CrossRef]

E. N. Brown, N. S. Burris, J. Gu, Z. N. Kon, P. Laird, S. Kallam, C. M. Tang, J. M. Schmitt, and R. S. Poston, “Thinking inside the graft: applications of optical coherence tomography in coronary artery bypass grafting,” J. Biomed. Opt. 12, 051704(2007).
[CrossRef]

H. L. Fu, Y. Leng, M. J. Cobb, K. Hsu, J. H. Hwang, and X. Li, “Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter,” J. Biomed. Opt. 13, 060502 (2008).
[CrossRef]

G. Lamouche, M. Dufour, M. Hewko, S. Vergnole, B. Gauthier, C. E. Bisaillon, J. P. Monchalin, and M. G. Sowa, “Intravascular optical coherence tomography on a beating heart model,” J. Biomed. Opt. 15, 046023 (2010).
[CrossRef]

Z. Yaqoob, J. Wu, E. J. McDowell, X. Heng, and C. Yang, “Methods and application areas of endoscopic optical coherence tomography,” J. Biomed. Opt. 11, 063001 (2006).
[CrossRef]

W. Jung, W. Benalcazar, A. Ahmad, U. Sharma, H. Tu, and S. A. Boppart, “Numerical analysis of gradient index lens-based optical coherence tomography imaging probes,” J. Biomed. Opt. 15, 066027 (2010).
[CrossRef]

Nat. Med. (1)

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I.-K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12, 1429–1433 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (1)

M. L. Dufour, C.-E. Bisaillon, G. Lamouche, S. Vergnole, M. Hewko, F. D’Amours, C. Padioleau, and M. Sowa, “Tools for experimental characterization of the non-uniform rotational distortion in intravascular OCT probes,” Proc. SPIE 7883, 788339 (2011).
[CrossRef]

Prog. Retinal Eye Res. (1)

M. E. J. van Velthoven, D. J. Faber, F. D. Verbraak, T. G. van Leeuwen, and M. D. de Smet, “Recent developments in optical coherence tomography for imaging the retina,” Prog. Retinal Eye Res. 26, 57–77 (2007).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Other (5)

W. T. Silfvast, Laser Fundamentals (Cambridge University, 2003), pp. 402–432.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

C. W. Reno, “Laser astigmatism compensation,” U.S. Patent 5239414 (24August1993).

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008), pp. 397–400.

E. Swanson, C. L. Petersen, E. McNamaram, R. B. Lamport, and D. L. Kelly, “Ultra-small optical probes, imaging optics, and methods for using same,” U.S. Patent 6445939 (3September2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of imaging catheter tip, shown in (a) side view; (b) top view. n1: index of inner medium, n2: index of tube, n3: index of outer medium, R1: inner radius of tube, R2: outer radius of tube, d: thickness of tube, zw: working distance (zwx in azimuthal direction, zwy in longitudinal direction).

Fig. 2.
Fig. 2.

Schematic diagram of the simulation model of a GRIN lens–based OCT probe with a reflector;n1: index of inner medium, n2: index of tube, n3: index of outer medium.

Fig. 3.
Fig. 3.

Schematic diagram of simulation mode for a GRIN lens–based OCT probe with a prism;n1: index of inner medium, n2: index of tube, n3: index of outer medium.

Fig. 4.
Fig. 4.

Dependence of the spot size at the target focal plane in the azimuthal direction on the thickness of the tube for different inner radius (R1). (a) and (b): Short working distance (zw=2.0mm); (c) and (d): long working distance (zw=10mm). (a) and (c): Fluorinated ethylene propylene (FEP) tube (n2=1.34); (b) and (d): polyethylene (PE) tube (n2=1.50). The beam waist was set to be w0=20μm; n1=n3=1.0.

Fig. 5.
Fig. 5.

Plot of spot size at focal plane in azimuthal direction versus refractive index of medium with various inner radius (R1) of tube, made of 0.1 mm thickness FEP (n=1.34). zw=2.0mm; w0=20μm.

Fig. 6.
Fig. 6.

The irradiance profile of the astigmatic beam emitting from the tube with spot profile at target working distance. The scale bar is 50 μm; x: azimuthal direction, y: longitudinal direction.

Fig. 7.
Fig. 7.

(a) Schematic of Gaussian beam inside the tube, back-propagated from the focal plane, for a long working distance catheter: the interfaces of the mirror and lens are located at plane A (the reflector) and plane B (the distal lens surface) respectively; (b) Spot sizes of the Gaussian beam in azimuthal direction and the desired light beam varying with distance from the internal surface of the tube. The distances from the tube to the compensation planes are: A, 0.75 mm; B, 1.75 mm.

Fig. 8.
Fig. 8.

Schematic diagrams of simulation mode for a GRIN lens probe with (a) a cylindrical mirror and (b) a cylindrical lens. Near-perfect correction is achieved using a cylindrical mirror in plane A. GRIN lens diameter: 1 mm; lg: 0.7 mm; g: 0.636mm1; glass spacer ls: 3.7 mm; ns: 1.5. Rc: Curvature Radius.

Fig. 9.
Fig. 9.

Plot of spot size in Visipaque of the backpropagated light beam versus distance to internal surface of tube. The distance from the prism exit surface to the tube is 0.225 mm.

Fig. 10.
Fig. 10.

Schematic diagrams of simulation mode for a GRIN lens probe with a cylindrical lens mounted on the prism. The integral reaches its minimum value when the curvature radius is 0.75 mm. The parameters of GRIN lens and spacer are the same as Fig. 7. Rc: Curvature Radius.

Tables (3)

Tables Icon

Table 1. Beam Characteristics for an Esophageal Imaging Probe, and Two Compensation Methodsa

Tables Icon

Table 2. Spot Shape with Various Distances (z) from Optical Axis in Air, Saline, and Visipaquea

Tables Icon

Table 3. Characteristics of Light Beam after Compensation Showed as Spot Shapes in Visipaquea

Equations (7)

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

(10n2n3R2n3n2n3)(1d01)(10n1n2R1n2n1n2)=(1+dn1n2R1n2dn1n2n2n3R2n3+d(n2n3)(n1n2)R1R2n2n3+n1n2R1n3n1n3+dn1(n2n3)n2n3R2).
(100n2n3)(1d01)(100n1n2)=(1dn1n20n1n3).
q1=Z+ZRi=Z+πnmw02λi,
q2=Aq1+BCq1+D.
(ABCD)=(1f01)(100ngnm)(cos(glg)sin(glg)ggsin(glg)cos(glg))(100nsng)(1ls01)(100nfns).
Δw=zwzRzw+zR|wx(z)/wy(z)1|dz,
n2n3R1n2+d(n2n3)(n1n2)R1R2n2n3+n1n2R1n3=0.

Metrics