# Nt1310 Unit 7 Lab 1

explanatory Essay
545 words
545 words

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…

#### In this essay, the author

• Explains that $gamma$ is the light extinction coefficient of the liquid, determined via calibration; $i_0 (x, z)$ is back-light intensity, measured from the dry test section.
• Explains that the method developed as a point-wise technique, using photodiodes or photomultipliers as light receivers, and later became 3d using digital video cameras and image processing.
• Explains that light absorption is enhanced by diluting in the liquid small concentration of colorant dye whose absorbance spectrum matches the emission spectrum of the light source.
• Illustrates the measurement test section in fig.refla_s. the light source is a 4x4 textscled array with $90%$ emittance.
• Explains how the synchronization ensures a time invariant reference image. the camera controls the leds so that the light flash occurs when the rolling shutter exposes the whole sensor.
• Explains the calibration step, which consists in evaluating the scaling factor and measuring the global extinction coefficient.
• Explains that the absorbance profile is computed from the gray scale reference video $i_0(x,y,t)$, taken with an empty vat, and the grey scale transmittance video
• Explains that 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 zero gradient components.
• Explains how the absorption coefficient is retrieved from the vat slope $s_x=tan (alpha)$, the slope of the absorption profile in the image and image scaling factor $m=x/p$.

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.