Erratum

In the third paragraph of section 3 of the original manuscript [1], it is specified that the actual area of the surface element under evaluation, $A_{\mathrm {r}}$, corresponds to the area of the field of view of a pixel of the CCD on the sample plane, $A_\mathrm {fov}$. Nevertheless, this is an errata since $A_{\mathrm {r}}=A_\mathrm {fov}/\cos {\theta _{\mathrm {r}}}$, as it is shown in Fig. S1. When the radiance is collected at $\theta _{\mathrm {r}}=0^{\circ}$ it is fulfilled $A_{\mathrm {r}}=A_\mathrm {fov}$, but when the radiance is collected at an arbitrary $\theta _{\mathrm {r}}$ the field of view of each pixel is projected through the sample surface and, therefore, $A_{\mathrm {r}}$ changes by $1/\cos {\theta _{\mathrm {r}}}$.

 

Fig. 1. Diagram of the relation between $A_\mathrm {fov}$ and $A_{\mathrm {r}}$.

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According to the statement given above, the Eq. (5) of the original manuscript must be rearranged as follows:

This term also disappears in the measurement equation, Eq. (7) of the original manuscript, becoming:

Thus, the acquisitions at this condition of the BSSRDF should have a lower position number than the acquisitions at $\theta _{\mathrm {r}}=0^{\mathrm {o}}$. Nevertheless, through the algorithm used for the coordinate system transformation from the camera reference system to the sample reference system, the observed positions that are missed in the measurements at higher $\theta _{\mathrm {r}}$ are interpolated based on the acquired data.

By applying Eqs. (S2) and (S3), the results showed in Fig. 7 of the original manuscript barely vary, as it is observed in Fig. S2, since the plotted values correspond to a collection polar angle $\theta _{\mathrm {r}}=10^{\mathrm {o}}$. Regarding the uncertainty, it is slightly lower now due to the absence of the contribution from the cosine of the collection polar angle.

 

Fig. 2. Same representation as in Fig. 7 of the original manuscript but having applied the corrected measurement equation. BSSRDF (up) and relative standard uncertainty (down) profiles of every sample at the measurement geometry with $\phi _\mathrm {i}=0^\mathrm {o}$, $\theta _\mathrm {i}=15^\mathrm {o}$, $\theta _\mathrm {r}=10^\mathrm {o}$ and $\phi _\mathrm {r}=0^\mathrm {o}$, irradiated with $\lambda =550$ nm.

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Nevertheless, the results showed in Fig. 8 of the original manuscript change considerably as it is shown in Fig. S3. It is seen that the previously observed increase of the BSSRDF values at higher collection polar angles was completely caused by the $\cos {\theta _{\mathrm {r}}}$ factor and is no longer observed, while the increasing trend at collection azimuth angles coinciding with the polar coordinate of the sample surface, $\alpha$, is still slightly observed. This could mean that, although low-order scattering events seem to dominate, high-order scattering events are also present and observable.

 

Fig. 3. Same representation as in Fig. 8 of the original manuscript but having corrected the represented values. Angular distribution of the BSSRDF of five different positions on the surface of the sample S6 when it is being irradiated at $\theta _{\rm {r}}=15^{\rm {o}}$ with $\lambda =550$ nm.

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The objective of this paper is to show a primary facility developed to provide with BSSRDF traceable measurements. Thus, the results showed in the paper are not the main goal of the work, but they serve as a demonstration of the capability of the measuring system, and the conclusions of the original manuscript are completely valid even taking into account this erratum.