Since the technical characteristics of the OCT setups at 1300 and 1600 nm imaging wavelengths are matched, only the optical properties of the sample determine the difference in the measured OCT imaging depth. In the determination of the OCT imaging depth, two sample parameters are of importance: the backscatter coefficient μb, which determines the initial magnitude of the OCT signal, and the attenuation coefficient μt, which determines how fast the OCT signal decays with depth to the noise floor.
The backscatter coefficient μb
is formally defined as the (total) scattering coefficient of an isotropically scattering particle with a phase function pISO
(θ) = p
(180), where p
(180) is the phase function of the original scatterer in the backward direction. This leads to
= 4πμs p
(180). In the OCT geometry the following interpretation of μb
is more appropriate: μb
θ, e.g. the phase function integrated over the numerical aperture (NA) of the OCT sample arm lens in the backscatter direction. From Eq. (1)
, the magnitude of the OCT signal immediately after the front glass-Intralipid boundary (z
= 0) is therefore proportional to the square root of the scattering coefficient μs
. shows that the OCT magnitude increases with Intralipid concentration, consistent with the observed increase in the scattering coefficient. In addition, the magnitudes of the OCT signal at 1300 and 1600 nm for the same Intralipid concentration are similar. This suggests that the difference in backscattering coefficient at these wavelengths is small. Since μs
is larger at 1300 nm compared to 1600 nm , we conclude that the Intralipid scattering phase function in the backscattering direction (180°) within the detection NA is higher at 1600 nm compared to 1300 nm. This observation is consistent with a reduced size parameter at 1600 nm compared to 1300 nm making the phase function more isotropic at 1600 nm compared to 1300 nm.
Our measurements are performed on samples with constant H2
O content. The reported scattering coefficients are calculated by subtracting a constant absorption from the measured attenuation coefficients . Using this method we obtain a μs
that approaches zero when no scattering is present [zero Intralipid concentration; see ]. In addition, the value of the scattering coefficient μs
at 1300 nm is in good agreement to those found in
]. For all Intralipid concentrations the scattering at 1600 nm is lower compared to 1300 nm. However, since the absorption is higher at 1600 nm, the OCT imaging depth is enhanced compared to 1300 nm only for Intralipid concentrations above 4 vol.%. For Intralipid concentrations lower than 4 vol.% the lower scattering coefficient at 1600 is compensated by the higher absorption, resulting in an increased imaging depth for 1300 nm. In the limit of very high Intralipid concentrations the H2
O absorption coefficient can be neglected and the difference between the scattering coefficients at the two wavelengths saturates at Δμs
. Consequently, the OCT imaging depth enhancement also reaches a plateau at a difference of 200 µm, i.e. 30% higher for 1600 nm compared to 1300 nm.
Recent work on the comparison of the performance of OCT systems with light sources centered at 1300 and 1650 nm [14
] showed that the ratio of the attenuation coefficients for 10 wt.% Intralipid at 1300 nm to 1650 nm is 1.24. This value is close to our result for this Intralipid concentration, which is 1.29 (with a minor difference in water absorption and central wavelength). However, because of the differences in setup characteristics and the fact that in the published work the attenuation coefficient was calculated without correction for the refractive index of Intralipid, it is difficult to compare our imaging depth measurements with these published results.
It is interesting to compare the scattering coefficient of Intralipid at 1300 and 1600 nm. For a polydisperse solution of particles, like Intralipid, and the absence of strong absorption, the wavelength dependency of the scattering coefficient is described empirically in the form of a power law: μs
, where a
and SP are the parameters for scattering amplitude and scattering power, respectively [24
]. The parameter a
is associated with the magnitude of the scattering, but does not depend on wavelength: tissues with high scattering coefficient µs
have high a
parameter and vice versa. The SP parameter determines how strong the scattering changes with wavelength. The value of SP is related to the average size of the scatterers: for particles with diameter d
much smaller than wavelength of light (d
<<λ) the parameter SP approaches 4 (Rayleigh scattering regime). With increasing particles size, the SP decreases (Mie scattering). From this simple model, changes in the scattering coefficient with wavelength (λ1
) can be described as follows:
shows the measured scattering coefficient at 1600 nm versus that at 1300 nm for all Intralipid concentrations. From a linear fit to the data points using Eq. (3)
SP = 2.8 ± 0.1, which is close to a previously reported value of SP for Intralipid SP = 2.4 [24
]. In addition, shows that the relative difference in the scattering coefficient at 1300 to 1600 nm remains approximately constant for all Intralipid concentrations. We can conclude that concentration dependent scattering effects are similar for the two wavelengths.
Fig. 5 Measured µs at 1600 nm versus 1300 nm. Sample points are marked according to the Intralipid concentration. From a linear fit to the data (solid line) we determine the SP value for Intralipid (indicated). The dashed lines indicate the 95% confidence (more ...)
Since the SP parameter describes the wavelength dependence of the scattering coefficient, this parameter can be used to predict changes in the OCT imaging depth with wavelength for biological tissues. From Eq. (3)
follows that for samples with a low SP the variation in scattering with wavelength is small. In this case, the increase of the OCT imaging depth with increasing wavelength is expected to be small. For samples with a high SP the scattering coefficient shows a strong variation with wavelength and a relatively large increase of the OCT imaging depth can be expected. Additionally, for samples with significant water content, the higher water absorption in the 1600 – 1800 nm spectral band is a counteracting factor. Therefore, we expect an increase of the OCT imaging depth for samples with high SP and low water content (e.g. enamel) and we do not expect an increase of the OCT imaging depth for samples with a low SP and high water content (e.g. skin). However, since the wavelength dependence of the backscattering coefficient is not known a priori, the procedures, as outlined in this paper, should be followed to determine the optimum OCT imaging wavelength.