Nt1310 Unit 7 Lab 1

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where $\gamma$ is the light extinction coefficient of the liquid, determined via calibration; $I_0 (x, z) $ is the back-light intensity, referred to as \emph{Reference Image}, measured from the dry test section; $I (x, z, t) $ is the transmitted light intensity trough the liquid film, referred to as \emph{Trasmittance Image}, measured during the experiment. The dimensionless quantity $A=\ln(I_0/I)$ is referred to as \emph{absorbance}.

Developed as a point-wise technique, using photodiodes or photomultipliers as light receivers \cite{LAB_0,LAB_1b}, the method has later become a 3D approach using digital video cameras and image processing \cite{LAB_2,LAB_3,LAB_4}.

The light absorption is enhanced diluting in the liquid small concentration …show more content…

The light source (1) consists of two arrays with 4x4 \textsc{LEDs} of $\approx 0.7\,W$ each, with $90\%$ emittance in the range $636\pm26\mu m$. These LEDs are placed $10\,cm$ behind a $3mm$ thick screen Opal \textregistered PLEXIGLAS (2), which diffuses the light over the test section, to which it is attached. The receiver (3) is a rolling shutter $16bits$ \textsc{CMOS} camera (Hamamatsu ORCA-Flash4.0), synchronized with the \textsc{LEDs}, to acquire at $200 Hz$ with a resolution of $500 x 2048 …show more content…

The scaling factor ($M=19.6pixel/mm\pm1\%$) is obtained by binarizing an image containing a pattern of circles and extracting the diameter via standard morphology operations. The extinction coefficient is measured using a calibrating vat and positioning the set up horizontally. Fig.\ref{fig:calibrator} sketches the calibration step and shows a typical absorbance curve.

The absorbance profile is computed from the gray scale reference video $I_0(x,y,t)$, taken with an empty vat, and the gray scale transmittance video $I(x,y,t)$, taken with the vat filled with liquid. The corresponding absorbance image $A=ln({\overline{I}_0}/{\overline{I}})$ is obtained from the time averages of the videos $\overline{I}_0$ and $\overline{I}$.
The absorption image is spatially filtered with a low-pass Gaussian and the average profile is fitted via linear regression. The camera alignment error is corrected by rotating the image to have a zero gradient component $\partial A /\partial y=0$.

The absorption coefficient is retrieved from the vat slope $s_x=\tan (\alpha)$, the slope of the absorption profile in the image $s_p$, and the image scaling factor $M=x/p$, using eq.

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