Abstract

Dispersive samples introduce a wavelength dependent phase distortion to the probe beam. This leads to a noticeable loss of depth resolution in high resolution OCT using broadband light sources. The standard technique to avoid this consequence is to balance the dispersion of the sample by arranging a dispersive material in the reference arm. However, the impact of dispersion is depth dependent. A corresponding depth dependent dispersion balancing technique is diffcult to implement. Here we present a numerical dispersion compensation technique for Partial Coherence Interferometry (PCI) and Optical Coherence Tomography (OCT) based on numerical correlation of the depth scan signal with a depth variant kernel. It can be used a posteriori and provides depth dependent dispersion compensation. Examples of dispersion compensated depth scan signals obtained from microscope cover glasses are presented.

© Optical Society of America

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References

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  1. A. F. Fercher and E. Roth, "Ophthalmic laser interferometry," Proc. SPIE 658, 48-51 (1986).
    [CrossRef]
  2. 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, J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  3. A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, H. Sattmann, "A thermal light source technique for optical coherence tomography," Opt. Commun. 185, 57-64 (2000).
    [CrossRef]
  4. C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, "Dispersion induced multiple signal peak splitting in partial coherence interferometry," Opt. Commun. 154, 179-185 (1998).
    [CrossRef]
  5. W. Drexler, U. Morgner, F. X. K�rtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, "In vivo ultra-high resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999).
    [CrossRef]
  6. A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, T. Lasser, "A new dispersion compensation technique for Partial Coherence Interferometry (PCI) and Optical Coherence Tomography (OCT)," Proc SPIE 4431 (to be published).
  7. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University Press, 1998).
  8. C.K. Hitzenberger, A. Baumgartner, W. Drexler, A.F. Fercher, "Dispersion effects in partial coherence interferometry: implications for intraocular ranging," J. Biomed. Opt. 4, 144-151, 1999.
    [CrossRef] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).
  10. A.-G.Van Engen, S. Diddams, T.-S.Clement, "Dispersion measurements of water with white-light interferometry," Appl. Opt. 37, 5679-5686, 1998.
    [CrossRef]
  11. T. Fuji, M. Miyata, S. Kawato, T. Hattori, H. Nakatsuka, "Linear propagation of light investigated with a white-light Michelson interferometer", J. Opt. Soc. Am. B 141074-1078 (1997).
    [CrossRef]
  12. SCHOTT'96 for Windows Catalog Optical Glass, Schott Glaswerke Mainz, Germany, 1996, http://us.schott.com/sgt/english/products/catalogs.html.
  13. J. M. Schmitt and G. Kumar, "Optical scattering properties of soft tissue: a discrete particle model," Appl. Opt. 37, 2788-2797, 1998.
    [CrossRef]

Other

A. F. Fercher and E. Roth, "Ophthalmic laser interferometry," Proc. SPIE 658, 48-51 (1986).
[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, J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, H. Sattmann, "A thermal light source technique for optical coherence tomography," Opt. Commun. 185, 57-64 (2000).
[CrossRef]

C. K. Hitzenberger, A. Baumgartner, A. F. Fercher, "Dispersion induced multiple signal peak splitting in partial coherence interferometry," Opt. Commun. 154, 179-185 (1998).
[CrossRef]

W. Drexler, U. Morgner, F. X. K�rtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, J. G. Fujimoto, "In vivo ultra-high resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999).
[CrossRef]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, T. Lasser, "A new dispersion compensation technique for Partial Coherence Interferometry (PCI) and Optical Coherence Tomography (OCT)," Proc SPIE 4431 (to be published).

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University Press, 1998).

C.K. Hitzenberger, A. Baumgartner, W. Drexler, A.F. Fercher, "Dispersion effects in partial coherence interferometry: implications for intraocular ranging," J. Biomed. Opt. 4, 144-151, 1999.
[CrossRef] [PubMed]

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).

A.-G.Van Engen, S. Diddams, T.-S.Clement, "Dispersion measurements of water with white-light interferometry," Appl. Opt. 37, 5679-5686, 1998.
[CrossRef]

T. Fuji, M. Miyata, S. Kawato, T. Hattori, H. Nakatsuka, "Linear propagation of light investigated with a white-light Michelson interferometer", J. Opt. Soc. Am. B 141074-1078 (1997).
[CrossRef]

SCHOTT'96 for Windows Catalog Optical Glass, Schott Glaswerke Mainz, Germany, 1996, http://us.schott.com/sgt/english/products/catalogs.html.

J. M. Schmitt and G. Kumar, "Optical scattering properties of soft tissue: a discrete particle model," Appl. Opt. 37, 2788-2797, 1998.
[CrossRef]

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Figures (1)

Fig. 1.
Fig. 1.

Resolution improvement obtained by dispersion compensation using depth-variant numerical correlation. Light of a filtered Hg high pressure lamp (λ 0≅710 nm; Δλ≅210 nm) is incident from left (thick arrow). The object has been synthesized using experimentally obtained non-dispersed front and dispersed back scattered depth scan signals of a single microscope cover slide. Shown are the (direct) auto- and cross-correlation depth scan signals (red) of the two front and the two back interfaces and the corresponding numerically dispersioncompensated correlation signals (black).

Equations (18)

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

l c = 4 ln 2 π λ 0 2 Δ λ
n s = c d k d ω = n λ d n d λ .
d n g d λ = λ d 2 n d λ 2 = λ 2 π v 3 c d 2 k d ω 2
f = 1 + 4 d 2 τ 0 4 ( d 2 k d ω 2 ) 2 ,
l C , dispersed = l C · f
G ( τ ) = E ( t ) · E ( t + τ ) = G ( ω ) e i ω π d ω ;
G ( τ + τ 0 ) = G ( ω ) e i Φ 0 e i ω τ d ω
G Disp ( τ + τ 0 ) = G ( ω ) e i ( Φ 0 + Φ Disp ) e i ω τ d ω .
Φ Disp ( ω ω 0 ) = k ( ω ω 0 ) z
= k ( ω 0 ) z + k ( 1 ) ( ω 0 ) ( ω ω 0 ) z + k ( 2 ) ( ω 0 ) ( ω ω 0 ) 2 2 z + k ( 3 ) ( ω 0 ) ( ω ω 0 ) 3 6 z +
v g = [ k ( 1 ) ( ω 0 ) ] 1
E ( t ) = E ̂ ( ω ) e i ω t d ω ,
I I T ( τ ) = G ( τ ) = E ( t + τ ) E * ( t ) = d ω G ( ω ) e i ω τ
I I T ( τ ) = E ( t + τ ) E * Disp ( t ) = d ω G ( ω ) e i ω τ e i Φ Disp ( ω ) .
I Comp ( τ ) = F T { I local ( ω ) exp ( i Φ local ( ω ) } .
I Comp ( τ ) = I local ( τ ) K local ( τ )
K ( t ) = a e t 2 τ 0 2 e i ω 0 t .
n ( λ ) = 1 + B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 + B 3 λ 2 λ 2 C 3

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