Abstract

We report a Talbot bands-based optical coherence tomography (OCT) system capable of producing longitudinal B-scan OCT images and en-face scanning laser ophthalmoscopy (SLO) images of the human retina in-vivo. The OCT channel employs a broadband optical source and a spectrometer. A gap is created between the sample and reference beams while on their way towards the spectrometer’s dispersive element to create Talbot bands. The spatial separation of the two beams facilitates collection by an SLO channel of optical power originating exclusively from the retina, deprived from any contribution from the reference beam. Three different modes of operation are presented, constrained by the minimum integration time of the camera used in the spectrometer and by the galvo-scanners’ scanning rate: (i) a simultaneous acquisition mode over the two channels, useful for small size imaging, that conserves the pixel-to-pixel correspondence between them; (ii) a hybrid sequential mode, where the system switches itself between the two regimes and (iii) a sequential “on-demand” mode, where the system can be used in either OCT or SLO regimes for as long as required. The two sequential modes present varying degrees of trade-off between pixel-to-pixel correspondence and independent full control of parameters within each channel. Images of the optic nerve and fovea regions obtained in the simultaneous (i) and in the hybrid sequential mode (ii) are presented.

© 2014 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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2013 (2)

2012 (3)

2011 (3)

2010 (3)

2009 (3)

A. Bradu, L. Ma, J. W. Bloor, and A. Gh. Podoleanu, “Dual optical coherence tomography/fluorescence microscopy for monitoring of Drosophila melanogaster larval heart,” J. Biophotonics 2, 380–388 (2009).
[Crossref] [PubMed]

R. B. Rosen, M. Hathaway, J. A. Rogers, J. Pedro, P. Garcia, P. Laissue, G. M. Dobre, and A. Gh. Podoleanu, “Multidimensional en-face OCT imaging of the retina,” Opt. Express 17, 4112–4133 (2009).
[Crossref] [PubMed]

M. Hughes, D. Woods, and A. Gh. Podoleanu, “Control of visibility profile in spectral low-coherence interferometry,” Electron. Lett. 45, 182–183 (2009).
[Crossref]

2008 (4)

D. Woods and A. Gh. Podoleanu, “Controlling the shape of Talbot bands’ visibility,” Opt. Express 16, 9654–9670 (2008).
[Crossref] [PubMed]

B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, “Ultrahigh speed spectral/Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second,” Opt. Express 16, 15149–15169 (2008).
[Crossref] [PubMed]

A. Gh. Podoleanu and R. B. Rosen, “Combinations of techniques in imaging the retina with high resolution,” Prog. Retin. Eye Res. 27, 464–499 (2008).
[Crossref] [PubMed]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

2007 (4)

2006 (1)

2003 (3)

2002 (1)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography.” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

1999 (2)

T. Mitsui, “Dynamic Range of Optical Reflectometry with Spectral Interferometry,” Jpn. J. Appl. Phys. 38, 6133–6137 (1999).
[Crossref]

A. Gh. Podoleanu and D. A. Jackson, “Noise Analysis of a Combined Optical Coherence Tomograph and a Confocal Scanning Ophthalmoscope,” Appl. Opt. 38, 2116 (1999).
[Crossref]

1998 (1)

A. Gh. Podoleanu and D. A. Jackson, “Combined optical coherence tomograph and scanning laser ophthalmoscope,” Electron. Lett. 34, 1088–1090 (1998).
[Crossref]

1993 (1)

S. Taplin, A. Gh. Podoleanu, D. Webb, and D. Jackson, “Displacement sensor using channelled spectrum dispersed on a linear CCD array,” Electron. Lett. 29, 896 (1993).
[Crossref]

1979 (1)

L. D. Harris, R. A. Robb, T. S. Yuen, and E. L. Ritman, “Display and visualization of three-dimensional reconstructed anatomic morphology: experience with the thorax, heart, and coronary vasculature of dogs.” J. Comput. Assist. Tomogr. 3, 439–446 (1979).
[Crossref] [PubMed]

Adler, D. C.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

Arathorn, D. W.

Bajraszewski, T.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography.” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

Baumann, B.

Biedermann, B. R.

Bloor, J. W.

A. Bradu, L. Ma, J. W. Bloor, and A. Gh. Podoleanu, “Dual optical coherence tomography/fluorescence microscopy for monitoring of Drosophila melanogaster larval heart,” J. Biophotonics 2, 380–388 (2009).
[Crossref] [PubMed]

Bouchal, P.

Bouma, B.

Braaf, B.

Bradu, A.

P. Bouchal, A. Bradu, and A. Gh. Podoleanu, “Gabor fusion technique in a Talbot bands optical coherence tomography system,” Opt. Express 20, 5368–5383 (2012).
[Crossref] [PubMed]

A. Bradu and A. Gh. Podoleanu, “Attenuation of mirror image and enhancement of the signal-to-noise ratio in a Talbot bands optical coherence tomography system,” J. Biomed. Opt. 16, 076010 (2011).
[Crossref] [PubMed]

A. Bradu, L. Ma, J. W. Bloor, and A. Gh. Podoleanu, “Dual optical coherence tomography/fluorescence microscopy for monitoring of Drosophila melanogaster larval heart,” J. Biophotonics 2, 380–388 (2009).
[Crossref] [PubMed]

Cable, A.

Chen, N.

Chen, Y.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, “Ultrahigh speed spectral/Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second,” Opt. Express 16, 15149–15169 (2008).
[Crossref] [PubMed]

Choma, M.

Dai, C.

C. Dai, X. Liu, and S. Jiao, “Simultaneous optical coherence tomography and autofluorescence microscopy with a single light source,” J. Biomed. Opt. 17, 080502 (2012).
[Crossref] [PubMed]

de Boer, J.

de Boer, J. F.

K. V. Vienola, B. Braaf, C. K. Sheehy, Q. Yang, P. Tiruveedhula, D. W. Arathorn, J. F. de Boer, and A. Roorda, “Real-time eye motion compensation for OCT imaging with tracking SLO.” Biomed. Opt. Express 3, 2950–2963 (2012).
[Crossref] [PubMed]

J. F. de Boer, “Spectral/Fourier Domain Optical Coherence Tomography,” in “Opt. Coherence Tomogr. - Technol. Appl.”,W. Drexler and J. Fujimoto, eds. (Springer, 2008), Biological and Medical Physics, Biomedical Engineering.
[Crossref]

Dobre, G. M.

Duker, J. S.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

Duma, V.-F.

Duncan, J. L.

Eigenwillig, C. M.

Farsiu, S.

Fercher, A. F.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, and Others, “Performance of Fourier domain xvs. time domain optical coherence tomography,” Opt. Express 11, 889–894 (2003).
[Crossref] [PubMed]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography.” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

Ferguson, R. D.

D. X. Hammer, N. V. Iftimia, T. E. Ustun, J. C. Magill, and R. D. Ferguson, “Dual OCT/SLO Imager with Three-Dimensional Tracker,in Ophthalmic Technol. XV,”, vol. 5688, F. Manns, P. G. Soederberg, A. Ho, B. E. Stuck, and M. Belkin, eds. (Proceedings of SPIE Vol. 5688, 2005), vol. 5688, pp. 33–44.
[Crossref]

Fujimoto, J. G.

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, “Ultrahigh speed spectral/Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second,” Opt. Express 16, 15149–15169 (2008).
[Crossref] [PubMed]

Garcia, P.

Gorczynska, I.

B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Jiang, A. Cable, and J. G. Fujimoto, “Ultrahigh speed spectral/Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second,” Opt. Express 16, 15149–15169 (2008).
[Crossref] [PubMed]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

Götzinger, E.

Hammer, D. X.

D. X. Hammer, N. V. Iftimia, T. E. Ustun, J. C. Magill, and R. D. Ferguson, “Dual OCT/SLO Imager with Three-Dimensional Tracker,in Ophthalmic Technol. XV,”, vol. 5688, F. Manns, P. G. Soederberg, A. Ho, B. E. Stuck, and M. Belkin, eds. (Proceedings of SPIE Vol. 5688, 2005), vol. 5688, pp. 33–44.
[Crossref]

Harris, L. D.

L. D. Harris, R. A. Robb, T. S. Yuen, and E. L. Ritman, “Display and visualization of three-dimensional reconstructed anatomic morphology: experience with the thorax, heart, and coronary vasculature of dogs.” J. Comput. Assist. Tomogr. 3, 439–446 (1979).
[Crossref] [PubMed]

Hathaway, M.

Hitzenberger, C. K.

Hu, Z.

Huber, R.

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second.” Opt. Express 18, 14685–14704 (2010).
[Crossref] [PubMed]

V. J. Srinivasan, D. C. Adler, Y. Chen, I. Gorczynska, R. Huber, J. S. Duker, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-speed optical coherence tomography for three-dimensional and en face imaging of the retina and optic nerve head.” Invest. Ophthalmol. Vis. Sci. 49, 5103–5110 (2008).
[Crossref] [PubMed]

Hughes, M.

M. Hughes, D. Woods, and A. Gh. Podoleanu, “Control of visibility profile in spectral low-coherence interferometry,” Electron. Lett. 45, 182–183 (2009).
[Crossref]

Iftimia, N. V.

D. X. Hammer, N. V. Iftimia, T. E. Ustun, J. C. Magill, and R. D. Ferguson, “Dual OCT/SLO Imager with Three-Dimensional Tracker,in Ophthalmic Technol. XV,”, vol. 5688, F. Manns, P. G. Soederberg, A. Ho, B. E. Stuck, and M. Belkin, eds. (Proceedings of SPIE Vol. 5688, 2005), vol. 5688, pp. 33–44.
[Crossref]

Izatt, J.

Izatt, J. A.

Jackson, D.

S. Taplin, A. Gh. Podoleanu, D. Webb, and D. Jackson, “Displacement sensor using channelled spectrum dispersed on a linear CCD array,” Electron. Lett. 29, 896 (1993).
[Crossref]

Jackson, D. A.

A. Gh. Podoleanu and D. A. Jackson, “Noise Analysis of a Combined Optical Coherence Tomograph and a Confocal Scanning Ophthalmoscope,” Appl. Opt. 38, 2116 (1999).
[Crossref]

A. Gh. Podoleanu and D. A. Jackson, “Combined optical coherence tomograph and scanning laser ophthalmoscope,” Electron. Lett. 34, 1088–1090 (1998).
[Crossref]

Jiang, J.

Jiao, S.

C. Dai, X. Liu, and S. Jiao, “Simultaneous optical coherence tomography and autofluorescence microscopy with a single light source,” J. Biomed. Opt. 17, 080502 (2012).
[Crossref] [PubMed]

Klein, T.

Komar, K.

Kowalczyk, A.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography.” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

Laissue, P.

Larocca, F.

Lee, K.-s.

Leitgeb, R.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, and Others, “Performance of Fourier domain xvs. time domain optical coherence tomography,” Opt. Express 11, 889–894 (2003).
[Crossref] [PubMed]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography.” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

Liu, L.

Liu, X.

C. Dai, X. Liu, and S. Jiao, “Simultaneous optical coherence tomography and autofluorescence microscopy with a single light source,” J. Biomed. Opt. 17, 080502 (2012).
[Crossref] [PubMed]

Ma, L.

A. Bradu, L. Ma, J. W. Bloor, and A. Gh. Podoleanu, “Dual optical coherence tomography/fluorescence microscopy for monitoring of Drosophila melanogaster larval heart,” J. Biophotonics 2, 380–388 (2009).
[Crossref] [PubMed]

Magill, J. C.

D. X. Hammer, N. V. Iftimia, T. E. Ustun, J. C. Magill, and R. D. Ferguson, “Dual OCT/SLO Imager with Three-Dimensional Tracker,in Ophthalmic Technol. XV,”, vol. 5688, F. Manns, P. G. Soederberg, A. Ho, B. E. Stuck, and M. Belkin, eds. (Proceedings of SPIE Vol. 5688, 2005), vol. 5688, pp. 33–44.
[Crossref]

Markowitz, S. N.

S. N. Markowitz and S. V. Reyes, “Microperimetry and clinical practice: an evidence-based review,” Can. J. Ophthalmol. / J. Can. d’Ophtalmologie (2012).

Meemon, P.

Merino, D.

Mitsui, T.

T. Mitsui, “Dynamic Range of Optical Reflectometry with Spectral Interferometry,” Jpn. J. Appl. Phys. 38, 6133–6137 (1999).
[Crossref]

Motoczynska, M.

Nankivil, D.

Pan, Y.

Park, B.

Pedro, J.

Pircher, M.

Podoleanu, A. Gh.

P. Bouchal, A. Bradu, and A. Gh. Podoleanu, “Gabor fusion technique in a Talbot bands optical coherence tomography system,” Opt. Express 20, 5368–5383 (2012).
[Crossref] [PubMed]

A. Bradu and A. Gh. Podoleanu, “Attenuation of mirror image and enhancement of the signal-to-noise ratio in a Talbot bands optical coherence tomography system,” J. Biomed. Opt. 16, 076010 (2011).
[Crossref] [PubMed]

A. Bradu, L. Ma, J. W. Bloor, and A. Gh. Podoleanu, “Dual optical coherence tomography/fluorescence microscopy for monitoring of Drosophila melanogaster larval heart,” J. Biophotonics 2, 380–388 (2009).
[Crossref] [PubMed]

M. Hughes, D. Woods, and A. Gh. Podoleanu, “Control of visibility profile in spectral low-coherence interferometry,” Electron. Lett. 45, 182–183 (2009).
[Crossref]

R. B. Rosen, M. Hathaway, J. A. Rogers, J. Pedro, P. Garcia, P. Laissue, G. M. Dobre, and A. Gh. Podoleanu, “Multidimensional en-face OCT imaging of the retina,” Opt. Express 17, 4112–4133 (2009).
[Crossref] [PubMed]

D. Woods and A. Gh. Podoleanu, “Controlling the shape of Talbot bands’ visibility,” Opt. Express 16, 9654–9670 (2008).
[Crossref] [PubMed]

A. Gh. Podoleanu and R. B. Rosen, “Combinations of techniques in imaging the retina with high resolution,” Prog. Retin. Eye Res. 27, 464–499 (2008).
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A. Gh. Podoleanu, “Unique interpretation of Talbot Bands and Fourier domain white light interferometry,” Opt. Express 15, 9867–9876 (2007).
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Figures (7)

Fig. 1
Fig. 1

Dual channel Sp-OCT/SLO set-up. C1-6: fiber collimators; SLD: super-luminescent diode; DC: fiber-based directional coupler; DCB: dispersion compensation block (adjustable, depending on the sample being imaged); TS1-3: translation stages; SXY: pair of orthogonal galvo-scanners; TG: transmission grating; L1-3: achromatic lenses; BS: bulk beam-splitter; MMF: multimode fiber; CMOS: line camera; APD: avalanche photo-diode; IMAQ: Camera Link-based image acquisition board; DAQ: multi-function data acquisition board. Region delimited by the red box: detail of the Talbot bands set-up. Cross-sections of the beams incident on the TG (OCT) and on the fiber collimator C6 (SLO) are shown for the sample beam in red and for the reference beam in blue. Note the gap present between the two beams as they are directed towards the OCT channel, which ensures a higher sensitivity at nonzero OPDs.

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Fig. 2
Fig. 2

Schematic diagram of the control system of the OCT/SLO set-up to achieve the three modes of operation. The multi-function data acquisition card (DAQ) and the External Function Generator deliver signals to the X-scanner and the Y-scanner via the Scanner driver box. The Switch box is used in the sequential modes only. The detected spectra from the CMOS camera are sent through a Camera Link bus to the image acquisition (IMAQ) card while the analog SLO signal is sent to the DAQ card.

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Fig. 3
Fig. 3

Schematic description of the various modes of operation implemented. (i) and (ii) Sequence of frames in the three modes of operation, where the green shadows show the frame refresh period, and the orange glow shows the instants when the system switches between the two regimes, if applicable. (i) Simultaneous mode of acquisition: the two frames, OCT and SLO are acquired and refreshed at the same time: illustration of different vertical positions in the SLO image where the OCT B-scan is selected from by varying Ysc[DC]: a single OCT B-scan is captured, even though more can be buffered if necessary; (ii) Hybrid sequential and sequential “on-demand”: the system is toggled between the two regimes (SLO and OCT), and signal is acquired in each regime on separate time intervals; the toggle is automatic in the hybrid sequential mode or performed manually in the sequential “on-demand” mode. In the hybrid mode the two images are refreshed at the same time, even though they are not acquired simultaneously. (iii) and (iv): Scanner waveforms (x and y) and illustration of integration time on pixels within the spectral acquisition events, δtOCT, (orange rectangles) each leading to an A-scan and integration time on pixels within a T-scan, δtSLO (brown rectangles) in all three modes. (iii) Simultaneous mode of acquisition; (iv) Hybrid sequential and sequential “on-demand” modes of acquisition.

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Fig. 4
Fig. 4

Relation between the number of pixels, Nx, determining the lateral image size and the mode of operation applicable. The red shaded region corresponds to the settings which allow pixel-to-pixel correspondence between the OCT and SLO images, which is limited at Nx = NS. Lateral image size is calculated using Nx · D0, with D0 ≈ 10 μm.

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Fig. 5
Fig. 5

(i) OCT channel sensitivity. Black squares: conventional Sp-OCT, beams coincide spatially; Red circles: launcher moved laterally by ∼ 0.25 mm to produce Talbot bands; Green triangles: launcher moved laterally by ∼ 0.25 mm to produce Talbot bands and screen (TS2) placed on the edge of the laterally-shifted reference arm beam); (ii) Relative sensitivity for the Talbot bands configurations in respect to the conventional Sp-OCT for: launcher shifted laterally (red solid line), launcher shifted laterally and screen in place (green dashed line).

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Fig. 6
Fig. 6

Retinal images obtained while running the system in the simultaneous mode of operation at a frame rate of ≈ 3 Hz. SLO frames (top image in each frame) are 100 × 280 pixels and OCT frames (bottom image in each frame) are 100 × 512 pixels (here cropped to 100 × 150 pixels to emphasize the region under analysis). (i) edge of the optic nerve head, lateral size ≈ 500 × 500 μm2; (ii) region between the optic nerve and the fovea, in an area featuring larger photo-receptors (≈ 10 μm), lateral size ≈ 500 × 500 μm2; (iii) pair of SLO and OCT images (lateral size ≈ 500 × 500 μm2) featuring a blood vessel; the choriod (yellow arrow) is visible below the nerve fiber layer; (iv) optically under-sampled OCT image of the area between the foveal region and the optic nerve, lateral image size ≈ 2 × 2.5 mm2; (v) optically under-sampled OCT image of the optic nerve, the region in focus is the shallower retinal layer, lateral size ≈ 1.5 × 0.8 mm2. The OCT B-scans correspond to the location of the horizontal lines overlaid on the SLO C-scans.

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Fig. 7
Fig. 7

Images obtained with the OCT/SLO set-up operating in hybrid sequential mode (SLO top, OCT bottom). The images in (i), (ii) and (iii) have sufficient sampling whilst the images in (iv) and (v) are under-sampled. (i) and (ii): area between the optic nerve and the shallower retinal tissue (lateral size 2.6 × 5.2 mm2); (i): focus on shallow layers; (ii): focus at the lamina cribrosa’s depth; (iii): area located in the vicinity of the optic nerve, the OCT B-scan cut intercepts a blood vessel along its course (yellow arrows), lateral size 2.6 × 5.2 mm2; (iv): detail of the optic nerve region (5 × 6 mm2 lateral size) emphasizing several positions of the cursor with varying features selecting the associated OCT B-scans; (v): fovea region, lateral size 5 × 5 mm2. The OCT B-scans are obtained from an average of Λ = 4 OCT frames. The positions of the OCT cuts along the Y-axis correspond to the location of the horizontal lines overlaid on the SLO C-scans.

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Equations (2)

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V ( OPD ) = C T B ( OPD )   ( sin ξ ξ ) 2 ,
Z max = M λ 0 2 4 Δ λ .

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