Abstract

We present a class of novel system characterization methods for spectral-domain optical coherence tomography (SD-OCT) particularly on getting optimized axial resolution performance. Our schemes uniquely utilize the autocorrelation interference response, also known as the self-interference product, which is generated by the optical fields from the imaging sample in automatic interferences. In our methods, an autocorrelation-inducing calibration sample was prepared which was made by sandwiching glass plates. OCT images of the calibration sample were captured by an SD-OCT system under testing. And the image data were processed to find various system characteristics based on the unique properties of autocorrelation interferograms, free of dispersion- and polarization-involved modulations. First, we could analyze the sampling characteristic of the SD-OCT’s spectrometer for spectral calibration that enables accurate linear-k resampling of detected spectral fringes. Second, we could obtain the systematic polarization properties for quantifying their impact on the achieved axial resolutions. We found that our methods based on the autocorrelation response provide an easy way of self-characterization and self-validation that is useful in optimizing and maintaining axial resolution performances. It was found very attractive that a variety of system characteristics can be obtained in a single-shot measurement without any increased system complexity.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express 15(23), 15129–15146 (2007).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
    [Crossref] [PubMed]
  9. M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
    [Crossref] [PubMed]
  10. X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express 18(23), 24331–24343 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  14. M. Szkulmowski, S. Tamborski, and M. Wojtkowski, “Spectrometer calibration for spectroscopic Fourier domain optical coherence tomography,” Biomed. Opt. Express 7(12), 5042–5054 (2016).
    [Crossref] [PubMed]
  15. B. Park, M. C. Pierce, B. Cense, S.-H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13(11), 3931–3944 (2005).
    [Crossref] [PubMed]
  16. Y. Chen, Z. Li, N. Nan, Y. Bu, X. Wang, L. Pan, and X. Wang, “Automatic spectral calibration for polarization-sensitive optical coherence tomography,” Opt. Express 25(20), 23605–23618 (2017).
    [Crossref] [PubMed]
  17. Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. 32(24), 3525–3527 (2007).
    [Crossref] [PubMed]
  18. E. Z. Zhang, W.-Y. Oh, M. L. Villiger, L. Chen, B. E. Bouma, and B. J. Vakoc, “Numerical compensation of system polarization mode dispersion in polarization-sensitive optical coherence tomography,” Opt. Express 21(1), 1163–1180 (2013).
    [Crossref] [PubMed]
  19. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (1)

2016 (1)

2015 (2)

2013 (1)

2011 (2)

M. Jeon, J. Kim, U. Jung, C. Lee, W. Jung, and S. A. Boppart, “Full-range k-domain linearization in spectral-domain optical coherence tomography,” Appl. Opt. 50(8), 1158–1163 (2011).
[Crossref] [PubMed]

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

D. J. Faber and T. G. van Leeuwen, “Doppler calibration method for Spectral Domain OCT spectrometers,” J. Biophotonics 2(6-7), 407–415 (2009).
[Crossref] [PubMed]

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (4)

2006 (2)

R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006).
[Crossref] [PubMed]

J. M. Lerner, “Imaging spectrometer fundamentals for researchers in the biosciences-A tutorial,” Cytometry A 69(8), 712–734 (2006).
[Crossref] [PubMed]

2005 (2)

B. Park, M. C. Pierce, B. Cense, S.-H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13(11), 3931–3944 (2005).
[Crossref] [PubMed]

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

2004 (1)

Ahn, Y. C.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Bajraszewski, T.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Balicki, M.

Boppart, S. A.

Bouma, B.

Bouma, B. E.

Bu, Y.

Carney, P. S.

Cense, B.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

B. Park, M. C. Pierce, B. Cense, S.-H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13(11), 3931–3944 (2005).
[Crossref] [PubMed]

Chen, L.

Chen, T. C.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Chen, Y.

Chen, Z.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

S. Moon, S.-W. Lee, and Z. Chen, “Reference spectrum extraction and fixed-pattern noise removal in optical coherence tomography,” Opt. Express 18(24), 24395–24404 (2010).
[Crossref] [PubMed]

Davis, B. J.

de Boer, J.

de Boer, J. F.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

DeRose, P.

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

Ding, Z. H.

Duker, J.

Eom, T. J.

M. G. Hyeon, H.-J. Kim, B.-M. Kim, and T. J. Eom, “Spectral domain optical coherence tomography with balanced detection using single line-scan camera and optical delay line,” Opt. Express 23(18), 23079–23091 (2015).
[Crossref] [PubMed]

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Faber, D. J.

D. J. Faber and T. G. van Leeuwen, “Doppler calibration method for Spectral Domain OCT spectrometers,” J. Biophotonics 2(6-7), 407–415 (2009).
[Crossref] [PubMed]

Fujimoto, J.

Gaigalas, A. K.

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

Gorczynska, I.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Han, J. H.

He, H. J.

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

Hu, Z.

Hyeon, M. G.

Jeon, M.

Jeong, J.

Jung, U.

Jung, W.

Kang, J. U.

Kim, B.-M.

Kim, C. S.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Kim, D. Y.

Kim, H.-J.

Kim, J.

Kim, J. H.

Ko, T.

Kowalczyk, A.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

Lee, C.

Lee, S.-W.

Lerner, J. M.

J. M. Lerner, “Imaging spectrometer fundamentals for researchers in the biosciences-A tutorial,” Cytometry A 69(8), 712–734 (2006).
[Crossref] [PubMed]

Li, Z.

Liu, X.

Ma, Z.

R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006).
[Crossref] [PubMed]

Marks, D. L.

Moon, S.

Mujat, M.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

B. Park, M. C. Pierce, B. Cense, S.-H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13(11), 3931–3944 (2005).
[Crossref] [PubMed]

Nan, N.

Oh, W.-Y.

Pan, L.

Park, B.

Park, B. H.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Pierce, M. C.

Radzewicz, C.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Ralston, T. S.

Rollins, A. M.

Srinivasan, V.

Szkulmowski, M.

M. Szkulmowski, S. Tamborski, and M. Wojtkowski, “Spectrometer calibration for spectroscopic Fourier domain optical coherence tomography,” Biomed. Opt. Express 7(12), 5042–5054 (2016).
[Crossref] [PubMed]

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Tamborski, S.

Targowski, P.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Taylor, R. H.

Tearney, G.

Vakoc, B. J.

van Leeuwen, T. G.

D. J. Faber and T. G. van Leeuwen, “Doppler calibration method for Spectral Domain OCT spectrometers,” J. Biophotonics 2(6-7), 407–415 (2009).
[Crossref] [PubMed]

Villiger, M. L.

Wang, K.

Wang, L.

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

Wang, R. K.

R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006).
[Crossref] [PubMed]

Wang, X.

Wasilewski, W.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Wojtkowski, A.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Wojtkowski, M.

Yun, S.-H.

Zhang, E. Z.

Appl. Opt. (1)

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

Cytometry A (1)

J. M. Lerner, “Imaging spectrometer fundamentals for researchers in the biosciences-A tutorial,” Cytometry A 69(8), 712–734 (2006).
[Crossref] [PubMed]

J. Biomed. Opt. (2)

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

J. Biophotonics (1)

D. J. Faber and T. G. van Leeuwen, “Doppler calibration method for Spectral Domain OCT spectrometers,” J. Biophotonics 2(6-7), 407–415 (2009).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

J. Res. Natl. Inst. Stand. Technol. (1)

A. K. Gaigalas, L. Wang, H. J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4-6), 569–578 (2005).
[Crossref]

Opt. Express (8)

M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004).
[Crossref] [PubMed]

B. Park, M. C. Pierce, B. Cense, S.-H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13(11), 3931–3944 (2005).
[Crossref] [PubMed]

M. G. Hyeon, H.-J. Kim, B.-M. Kim, and T. J. Eom, “Spectral domain optical coherence tomography with balanced detection using single line-scan camera and optical delay line,” Opt. Express 23(18), 23079–23091 (2015).
[Crossref] [PubMed]

E. Z. Zhang, W.-Y. Oh, M. L. Villiger, L. Chen, B. E. Bouma, and B. J. Vakoc, “Numerical compensation of system polarization mode dispersion in polarization-sensitive optical coherence tomography,” Opt. Express 21(1), 1163–1180 (2013).
[Crossref] [PubMed]

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express 18(23), 24331–24343 (2010).
[Crossref] [PubMed]

S. Moon, S.-W. Lee, and Z. Chen, “Reference spectrum extraction and fixed-pattern noise removal in optical coherence tomography,” Opt. Express 18(24), 24395–24404 (2010).
[Crossref] [PubMed]

S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express 15(23), 15129–15146 (2007).
[Crossref] [PubMed]

Y. Chen, Z. Li, N. Nan, Y. Bu, X. Wang, L. Pan, and X. Wang, “Automatic spectral calibration for polarization-sensitive optical coherence tomography,” Opt. Express 25(20), 23605–23618 (2017).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Med. Biol. (1)

R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Illustrative description of the extraction process for a fringe component by using a spatial filter of Π (z).
Fig. 2
Fig. 2 AC-producing calibration sample made of glass plates used in our SD-OCT system characterizations (a) and its partial OCT images (b).
Fig. 3
Fig. 3 Computational procedure of finding a peak amplitude of an AC response for a given set of parameters, {a2, a3, a4}, from a spectral signal of I(P) acquired with the calibration sample.
Fig. 4
Fig. 4 Map of peak powers, μ2, in two-dimensional space of parameters (a) and the OCT image of our calibration sample at the best parameters of the spectrometer calibration (b).
Fig. 5
Fig. 5 OCT images of a rabbit’s cornea, ex vivo, from the raw data (a), the linear-k resampled data (b), and the dispersion-compensated linear-k resampled data (c).
Fig. 6
Fig. 6 Polarization match factor of γ (a) and the effective sample fields’ spectra (b) retrieved from the filtered fringes of the XC and AC responses. The reference spectrum, IR,,was separately measured. Each trace has a different vertical scale in (b).
Fig. 7
Fig. 7 Dispersion-compensative phase function with a multi-order WP placed in the reference arm (a) and the plot of the polarization match factor γ as a function of normalized k (b), compared to no WP in place.
Fig. 8
Fig. 8 Schematic of the camera-equipped spectrometer with a large field curvature (a), an exemplary fringe acquisition in the presence of position-dependent optical aberrations (b), and the polarization match factors retrieved from different combinations of the acquired correlation responses (c).

Tables (2)

Tables Icon

Table 1 FOM analysis of the spectrometer calibration

Tables Icon

Table 2 FOM analysis of the axial resolution performance

Equations (14)

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

I= | E R + E S | 2 = I R + I S +( E R * E S + E R E S * )
I= I R + I S +2Re{ E R * E n + E R * E m + E n * E m }
I= I R + I S + A n cos ϕ n + A m cos ϕ m + A nm cosΔϕ
A n =2γ I R I n
A m =2γ I R I m
A nm =2 I n I m
A ˜ η (k)=2 F 1 { F{ I(k) } Π η (z) }
γ(k)= A n A m 2 I R A nm
I η (k)=( 1 4 γ 2 I R ) A η 2 =Γ(k) A η 2 (k)
I AC (p) 1 2 A 12 (p) e +iΔϕ(p) = F 1 { F{ I(p) } Π AC ( z ) }
K=( 1 a 2 a 3 a 4 )P+ a 2 P 2 + a 3 P 3 + a 4 P 4
J(z)=F{ I(k) e iΦ(k) }
Φ(K)=( b 2 3 4 b 3 )K+ b 2 K 2 + b 3 K 3
FOM η = δz δ z 0 = W[ | F { A ˜ η (k) } | ] W[ | F { A η (k) } | ]

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