All Figures

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg01.eps}\end{figure}$ Figure 1: A schematic view of the creation of the observed surface brightness of scattered light (see text). The figure shows an inhomogeneous cloud with arrows indicating the flow of photons. In the first phase external radiation is transported onto a selected line of sight where it is scattered toward the observer. Photons reach this line possibly after several scatterings and preferably through regions of low density. In the second phase radiation propagates out from the cloud along the selected sightline.
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In the text

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{5164fg02.eps}\end{figure}$ Figure 2: Examples of the structure seen in the model clouds. The frames a-d show column density maps of models A, C, D, and E, respectively. The colour scales are logarithmic and independent for each frame.
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In the text

$\begin{figure} \par\includegraphics[width=7.85cm,clip]{5164fg03.eps}\end{figure}$ Figure 3: Histograms of $A_{\rm V}$ values in the six model clouds with average visual extinction $\langle A_{\rm V} \rangle$ = 1.6 mag. For model C the distributions are plotted for three orthogonal directions of observations. For the other models distributions are shown only for one direction.
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In the text

$\begin{figure} \par\includegraphics[width=8.15cm,clip]{5164fg04.eps}\end{figure}$ Figure 4: A map of the difference between the simulated surface brightness and the prediction based on a curve fitted according to Eq. (1). The cloud is model C with $\langle A_{\rm V} \rangle$ = 1.6. The figure shows the shadowing effects that are caused by regions of moderate optical depth.
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In the text

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{5164fg05.eps}\end{figure}$ Figure 5: Relative rms-variation between between the simulated H-band surface brightness and the average curve based on Eq. (1), for models A, C, D, and E, where the mean visual extinction is scaled to either $A_{\rm }=1.6$ (thin lines) or $A_{\rm }=3.2$ (thick lines). For each model separate curves are shown corresponding to observations from three different directions (X, Y, and D1). This plot illustrates the amount of variation in the surface brightness of scattered light for a given line-of-sight column density.
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In the text

$\begin{figure} \par\includegraphics[width=8.15cm,clip]{5164fg06.eps}\end{figure}$ Figure 6: Curves of Eq. (1) fitted to data from selected models (models as in Fig. 5). The lower curve is for the K band and the upper curve for the J band. Each curve is drawn for the range of $A_{\rm V}$ values found in the corresponding model and direction of observations.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5164fg07.eps}\end{figure}$ Figure 7: Scatter plots of surface brightness versus $A_{\rm V}$ . The plot combines data from all six model clouds and three directions of observation (X, Y, and D1). The two frames correspond to average visual extinction $\langle A_{\rm V} \rangle$ = 1.6 and 3.2. The colour scale is linear with respect to the density of points.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg08.eps}\end{figure}$ Figure 8: Maps of relative error of column density estimates in the case of the models shown in Fig. 2. The average extinction is 1.6 mag (see Fig. 3), the input maps are convolved with a beam with fwhm equal to two pixels, and no observational noise is added. The contours are drawn at the levels of $\pm$ 5% and $\pm$ 10%. The plots show the total projected area of model clouds.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg09.eps}\end{figure}$ Figure 9: Rms-error of column density estimates as a function of the line-of-sight visual extinction. The plot includes results for all six model clouds, for three different directions of observation (X, Y, and D1). The frames correspond to the two values of average visual extinction.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg10.eps}\end{figure}$ Figure 10: Rms-error of column density estimates as a function of $A_{\rm }$ . The plot includes results for all six model clouds and for three different directions of observation (X, Y, and D1). Observational noise was added to the input maps (see text). The frames correspond to the two values of average visual extinction.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg11.eps}\end{figure}$ Figure 11: Estimated column density maps of the four models (A, C, D, and E) of Fig. 2. The column densities are calculated based on surface brightness maps where observational noise is included (see text). The images show the logarithm of the column density, transformed into $A_{\rm V}$ . The frames a, b, and d share a common colour scale. The model D has a much smaller range of column densities (see Fig. 3), and the frame c has a different colour scale.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg12.eps}\end{figure}$ Figure 12: The errors of the estimated column densities when model F is discretized into 64³, 125³, or 256³ cells. The estimates are based on average parameters derived from all models with $\langle A_{\rm V} \rangle$ = $1.6^{\rm m}$ and $\langle A_{\rm V} \rangle$ = $3.2^{\rm m}$ . The points show the average bias in different $A_{\rm V}$ intervals and the errorbars correspond to the 1- $\sigma$ variation within each interval. At low $A_{\rm V}$ part of the differences is caused by the Monte Carlo noise of the simulations, which was higher for models of higher resolution.
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In the text

$\begin{figure} \par\includegraphics[width=8.15cm,clip]{5164fg13.eps}\end{figure}$ Figure 13: Effect of a change in dust properties and/or field strength on the column density estimates. The plots show the bias and scatter in the estimates when dust properties are assumed to correspond to $R_{\rm V}=4.0$ , while they in reality correspond to either $R_{\rm V}=3.1$ or $R_{\rm V}=5.5$ . In frame b the radiation field is also 30% higher than assumed in the column density derivation, and the parameter a_K is re-estimated based on the maximum surface brightness. The small circles show the result in the case of $R_{\rm V}=3.1$ without re-evaluation of parameter a_K.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg14.eps}\end{figure}$ Figure 14: Upper frame: errors in the simulated extinction map. Plots are shown for two versions of model C, with average visual extinction 1.6 (circles) or 3.2 mag (squares). The resolution of the extinction map corresponds to a FWHM equal to seven map pixels. Lower frame: accuracy of the column density estimates based on NIR scattering. Results are shown for the two versions of the model C. The parameters are either the average values from all models (six clouds, three viewing directions and two scalings of average column density; open symbols) or were determined by correlating surface brightness against column densities estimated using the colour excess method (solid symbols).
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In the text

$\begin{figure} \par\includegraphics[width=16.5cm,clip]{5164fg15.eps}\end{figure}$ Figure 15: Model containing variable dust properties, $R_{\rm V}=3.1$ in low density regions and $R_{\rm V}=5.5$ in high density regions. The frames are: a. True $A_{\rm V}$ , b. $A_{\rm V}$ based on colour excesses of $\sim$ 2000 background stars, and c. $A_{\rm V}$ based on scattered surface brightness. All maps have been smoothed to a resolution of six map pixels.
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In the text

$\begin{figure} \par\includegraphics[width=16.5cm,clip]{5164fg16.eps}\end{figure}$ Figure 16: Frames a)- c): H-band surface brightness maps for each of the three point sources that were added to model cloud C. Frame d)- f): column density estimates for model C containing three point sources. The maps show the true column density, estimates based on NICER method and estimates based on scattered surface brightness. Note that the colour scale is logarithmic in the upper frames and linear in the lower frames.
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In the text

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{5164fg17.eps}\end{figure}$ Figure A.1: Comparison of the accuracy of column density estimates obtained with the analytical method (open symbols) and with detailed radiative transfer modelling (solid symbols). Results are shown for model D with $\langle A_{\rm V} \rangle$ = $3.2^{\rm m}$ and for model F with $\langle A_{\rm V} \rangle$ = $1.6^{\rm m}$ . The plot shows the bias and the scatter with respect to the true column densities.

In the text

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{5164fg18.eps}\end{figure}$ Figure A.2: Relative errors in the column densities obtained for model C, $\langle A_{\rm V} \rangle$ = $1.6^{\rm m}$ , with iterative radiative transfer modelling. The model assumed Gaussian density distribution along the line-of-sight.

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg19.eps}\end{figure}$ Figure A.3: Accuracy of column density estimates in the case of model C, $\langle A_{\rm V} \rangle$ = $1.6^{\rm m}$ , when three different methods are used. Upper frame: original method using Eq. (1) (open circles), iterative modelling with Gaussian line-of-sight density distribution (solid circles), and iterative modelling with Gaussian line-of-sight density distribution with width taken as a free parameter for each sightline (solid triangles). Lower frame: results from iterative modelling with clumpy density distribution (squares), and the same after a simple correction based on the error in the predicted J-band intensity (triangles).

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg20.eps}\end{figure}$ Figure B.1: Ratio of column density estimates and true column density when the analysis ignores an existing background surface brightness. In the plot the column densities are derived based on K-band data and using the average parameters obtained from the numerical models. The background intensity is 1.64 $\times$ 10^-19 erg/s/cm²/Hz/sr (see text).

In the text

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{5164fg02.eps}\end{figure}$	Figure 2: Examples of the structure seen in the model clouds. The frames a-d show column density maps of models A, C, D, and E, respectively. The colour scales are logarithmic and independent for each frame.
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$\begin{figure} \par\includegraphics[width=7.85cm,clip]{5164fg03.eps}\end{figure}$	Figure 3: Histograms of $A_{\rm V}$ values in the six model clouds with average visual extinction $\langle A_{\rm V} \rangle$ = 1.6 mag. For model C the distributions are plotted for three orthogonal directions of observations. For the other models distributions are shown only for one direction.
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$\begin{figure} \par\includegraphics[width=8.15cm,clip]{5164fg04.eps}\end{figure}$	Figure 4: A map of the difference between the simulated surface brightness and the prediction based on a curve fitted according to Eq. (1). The cloud is model C with $\langle A_{\rm V} \rangle$ = 1.6. The figure shows the shadowing effects that are caused by regions of moderate optical depth.
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$\begin{figure} \par\includegraphics[width=8.15cm,clip]{5164fg06.eps}\end{figure}$	Figure 6: Curves of Eq. (1) fitted to data from selected models (models as in Fig. 5). The lower curve is for the K band and the upper curve for the J band. Each curve is drawn for the range of $A_{\rm V}$ values found in the corresponding model and direction of observations.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{5164fg07.eps}\end{figure}$	Figure 7: Scatter plots of surface brightness versus $A_{\rm V}$ . The plot combines data from all six model clouds and three directions of observation (X, Y, and D1). The two frames correspond to average visual extinction $\langle A_{\rm V} \rangle$ = 1.6 and 3.2. The colour scale is linear with respect to the density of points.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg08.eps}\end{figure}$	Figure 8: Maps of relative error of column density estimates in the case of the models shown in Fig. 2. The average extinction is 1.6 mag (see Fig. 3), the input maps are convolved with a beam with fwhm equal to two pixels, and no observational noise is added. The contours are drawn at the levels of $\pm$ 5% and $\pm$ 10%. The plots show the total projected area of model clouds.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg09.eps}\end{figure}$	Figure 9: Rms-error of column density estimates as a function of the line-of-sight visual extinction. The plot includes results for all six model clouds, for three different directions of observation (X, Y, and D1). The frames correspond to the two values of average visual extinction.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{5164fg10.eps}\end{figure}$	Figure 10: Rms-error of column density estimates as a function of $A_{\rm }$ . The plot includes results for all six model clouds and for three different directions of observation (X, Y, and D1). Observational noise was added to the input maps (see text). The frames correspond to the two values of average visual extinction.
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$\begin{figure} \par\includegraphics[width=16.5cm,clip]{5164fg15.eps}\end{figure}$	Figure 15: Model containing variable dust properties, $R_{\rm V}=3.1$ in low density regions and $R_{\rm V}=5.5$ in high density regions. The frames are: a. True $A_{\rm V}$ , b. $A_{\rm V}$ based on colour excesses of $\sim$ 2000 background stars, and c. $A_{\rm V}$ based on scattered surface brightness. All maps have been smoothed to a resolution of six map pixels.
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