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The effect of water dispersion and absorption on axial resolution in ultrahigh-resolution optical coherence tomography

Timothy R. Hillman and David D. Sampson

Open Access Open Access

Abstract

We examine the effects of dispersion and absorption in ultrahigh-resolution optical coherence tomography (OCT), particularly the necessity to compensate for high dispersion orders in order to narrow the axial point-spread function envelope. We present a numerical expansion in which the impact of the various dispersion orders is quantified; absorption effects are evaluated numerically. Assuming a Gaussian source spectrum (in the optical frequency domain), we focus on imaging through water as a first approximation to biological materials. Both dispersion and absorption are found to be most significant for wavelengths above ~1µm, so that optimizing the system effective resolution (ER) requires choosing an operating wavelength below this limit. As an example, for 1-µm source resolution (FWHM), and propagation through a 1-mm water cell, if up to third-order dispersion compensation is applied, then the optimal center wavelength is 0.8µm, which generates an ER of 1.5µm (in air). The incorporation of additional bandwidth yields no ER improvement, due to uncompensated high-order dispersion and long-wavelength absorption.

©2005 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Time-domain OCT schematic, showing transfer function representations of the sample and reference arms.

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Fig. 2.
Fig. 2. Absorption (blue curve) and refractive index (black curve) spectrum of water, due to Segelstein [21]. The red curve shows the refractive index spectrum due to the formulation of Harvey et al. [23], extrapolated beyond the specified wavelength range of 0.2–2.5 µm (asymptote shown as dotted line).

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Fig. 3.
Fig. 3. Envelope broadening factor (EBF) plotted as a function of source center wavelength, for z=1mm, taking absorption into account (top row), and ignoring it (bottom row), for given source resolutions (SRs).

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Fig. 4.
Fig. 4. Comparison between the different broadening factor definitions, for source resolutions of 1µm and 3µm. EBFNS: Unsquared RMS; EBFV: Visibility; EBFFWHM: FWHM.

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Fig. 5.
Fig. 5. Plots of interferograms due to the effects of dispersion and absorption. The source resolution is 1µm. Top row: Red curve represents undistorted source power spectral density; black curve represents absorption-distorted power spectral density. Centre row: Normalized interferogram envelopes (legend given in right panel). Bottom row: As center row, but absorption neglected. Center wavelengths are labelled by column; propagation distance z=1mm in each instance.

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Fig. 6.
Fig. 6. Plots of envelope broadening factor (EBF) vs. single-pass propagation distance z, presented in rows according to source resolution (SR), and columns according to center wavelength. The legend corresponding to the four different dispersion-compensation approaches is given in the bottom-center panel.

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Fig. 7.
Fig. 7. Plots of effective resolution (ER) vs. center wavelength. The dispersion-compensation conditions for each plot are given, and the propagation distance z=1mm. Multiple curves reflect different source resolutions (SRs), with the legend in the lower-left panel applicable to all plots.

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Equations (12)

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I ˜ = 2 ℜ [ ∫ − ∞ ∞ H S ( ν ) H R * ( ν ) G 0 ( ν ) d ( ν − ν ̅ ) ] ,
I ˜ = 2 ℜ [ ∫ − ∞ ∞ G 0 ( ν ) exp { 2 z [ 1 2 α ( ν ) + j β ( ν ) ] d ( ν − ν ̅ ) } ] ,
2 β ( ν ) z = ∑ k = 0 ∞ β k ( ν − ν ̅ ) k ,
β 2 = − 2 π z ν ̅ 2 G D = − 2 π z c ν ̅ 2 D λ = 2 π z D ν = 2 π 2 D ω .
I ˜ c = exp ( j 2 π ν ̅ τ p ) 𝓕 { g ( u ) } ,
G ( τ g ) = 𝓕 { g ( u ) } = ∫ − ∞ ∞ g ( u ) exp { j 2 π u τ g } d u .
σ τ g = ∫ − ∞ ∞ τ g 2 E ( τ g ) d τ g ∫ − ∞ ∞ E ( τ g ) d τ g − [ ∫ − ∞ ∞ τ g E ( τ g ) d τ g ∫ − ∞ ∞ E ( τ g ) d τ g ] 2 ,
σ τ g = K 2 + β 2 2 2 π 2 K = σ 0 1 + ( β 2 K ) 2 ,
[ E ( τ g ) ] 2 = ∣ 𝓕 { g ( u ) } ∣ 2 = 𝓕 { ∫ − ∞ ∞ g ( w ) g * ( w − u ) d w } .
σ τ g ′ = 1 2 π [ N ′ ( 0 ) N ( 0 ) ] 2 − N ″ ( 0 ) N ( 0 ) ,
σ τ g ′ = σ τ g , ND ′ 1 + ∑ t = 2 ∞ ∑ s = t ∞ C s , t β s β t ,
C s , t = { 8 ( 2 − δ s , t ) s t ( 8 K ) ( s + t ) ⁄ 2 ( s + t − 2 ) ! ( s + t − 2 2 ) ! , if s , t even ; 8 ( 2 − δ s , t ) s t ( 8 k ) ( s + t ) ⁄ 2 [ ( s + t − 2 ) ! ( s + t − 2 2 ) ! − ( s − 1 ) ! ( t − 1 ) ! ( s − 1 2 ) ! ( t − 1 2 ) ! ] if s , t odd ; 0 , otherwise,
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