Commit 7f51f864 authored by Turnhout, M.C. van's avatar Turnhout, M.C. van
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pics and scripts to own directory

parent 49456597
......@@ -20,7 +20,7 @@ The `LC' in LC-PolScope stands for `liquid crystal'. These liquid crystals can a
In the optical train we investigate, light passes a linear \gls*{polariser}, two liquid crystals or variable \gls*{retardance} plates, the sample, a \gls*{quarter wave plate} and finally a linear \gls*{analyser}, see figure \eqref{polscopetrain}.
\caption{Optical train of the LC-PolScope, adapted from Shribak and Oldenbourg \cite[figure 1b]{Shribak2003}. Monochromatic light passes a linear \gls*{polariser} \gls*{P}, a \gls*{quarter wave plate} \gls*{Q}, the sample \gls*{Ssample}, two liquid crystals or variable \gls*{retardance} plates \gls*{LB} and \gls*{LA} and finally a linear \gls*{analyser} \gls*{A}.}\label{polscopetrain}
......@@ -14,7 +14,7 @@ In the crossed \gls*{polariser}s set-up, light passed first a \gls*{polariser} w
\caption{Optical train of a conventional polarisation microscope. Monochromatic light passes a linear \gls*{polariser} \gls*{P}, the sample \gls*{Ssample}, and finally a linear \gls*{analyser} \gls*{A}. The orientations of the \gls*{polariser} and \gls*{analyser} differ by 90\,\degree.}\label{crossedtrain}
......@@ -43,11 +43,11 @@ And its intensity is therefore (figure \ref{fig:IASP}):
\caption{Observed intensity of a sample with \gls*{retardance} $\gls*{Delta}$ and \gls*{azimuth} $\gls*{phi}$ compared to the orientation of the \gls*{polariser} placed between crossed \gls*{polariser}s (equation \ref{IASP}). With \textbf{(a)} intensity for given \gls*{retardance} $\gls*{Delta}$ as a function of \gls*{azimuth} $\gls*{phi}$, the maximum intensity is $f(\gls*{Delta}) =\frac{1}{2} \sin^2\frac{\gls*{Delta}}{2}$; and
\textbf{(b)} intensity for given \gls*{azimuth} $\gls*{phi}$ as a function of \gls*{retardance} $\gls*{Delta}$, the maximum intensity is $f(\gls*{phi}) = \frac{1}{2}\sin^22\gls*{phi}$.
\label{fig:IASP} }
......@@ -125,7 +125,7 @@ Thus $\gls*{J0}$ is \gls*{linearly polarised} (no short axis: $b=0$), as is $\gl
\section{Analysis with quarter wave plate}
\caption{Observed intensity of a sample with \gls*{retardance} $\gls*{Delta} = \frac{\piup}{6}$\,[rad] and \gls*{azimuth} $\gls*{phi}$ placed between crossed \gls*{polariser}s without a \gls*{quarter wave plate} in the light path (black, equation \ref{IASP}, figure \ref{Ic_fphi}), and with a \gls*{quarter wave plate} at 45\,\degree\ in the light path (red, equation \ref{IASQP}). The dotted lines show the background, i.e.\ no sample/no \gls*{birefringence}, intensity.\label{fig:IASQP} }
......@@ -175,7 +175,7 @@ but, as we have seen, for a given \gls*{birefringence} \gls*{Deltaupn} and fibre
The observed colour in white light \gls*{PLM} is a mix of these three colours with their respective intensities, and therefore changes with changes in fibre or sample \gls*{retardance} (figure \ref{white2RGB}).
\caption{\gls*{PLM} response of different colours of light for a given \gls*{birefringence} \gls*{Deltaupn} and fibre thickness \gls*{d} (equations \ref{eq:retardance} and \ref{equivbirefringence}). The background shows how the different proportions of these three waves, when combined, form different colours in white light \gls*{PLM}.}\label{white2RGB}
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......@@ -11,14 +11,14 @@ For purposes of evaluating the behaviour of light in \gls*{PL} microscopy (\gls
With $A$ the amplitude of the light wave [-]; $f$ the frequency of the light wave [Hz]; $\omega=2 \piup f$ the angular frequency of the light wave [rad/s]; and $\gls*{varphi}$ the phase of the light wave [rad] (figure \ref{wave0}).
\caption{A `wave' of light with phase $\gls*{varphi} =\frac{\piup}{4}$\,[rad] and wavelength $\gls*{lambda} = 600$\,[nm]; and thus $f = \frac{\text{c}}{\gls*{lambda}} = 500$\,[THz]; $T = \frac{1}{f} = 2$\,[fs] and $\omega = 2\piup f = \piup$\,[P\,rad/s].}\label{wave0}
Light that propagates in a Cartesian coordinate system in $\vec{z}$-direction has an amplitude in the $\vec{x}\vec{y}$-plane. When the amplitude makes a certain, arbitrary, angle with our coordinate system, we can decompose this amplitude into two components that are in the $\vec{x}$- and $\vec{y}$-direction using ordinary vector calculus. Similarly, we can add the amplitudes of multiple waves to obtain the resulting wave orientation in the $\vec{x}\vec{y}$-plane (figure \ref{wave_xy}).
\caption{The black wave travelling in the $\vec{z}$-direction makes an angle of 45\,\degree\ with our coordinate system and can be decomposed in the dashed red and blue waves with orientations that correspond with the $\vec{x}$- and $\vec{y}$-direction of our coordinate system. Likewise, we can add the two waves (dashed red and dashed blue) to obtain the resulting black wave.}\label{wave_xy}
......@@ -31,12 +31,12 @@ We speak of \gls*{PL} when all the waves (of equal wavelength) in a `ray of ligh
\item for any other (arbitrary) phase difference, $\Deltaup \gls*{varphi} \neq k\frac{\piup}{2},$\,[rad] with $k \in \mathbb{Z}$, the light is \gls*{elliptically polarised} (figure \ref{polellipse_xyz}-\ref{polellipse_xy}).
\caption{Three types of \gls*{PL}. \textbf{(a)} and \textbf{(b)} \gls*{linearly polarised} light for a phase difference of $\Deltaup \gls*{varphi} = 0$\,[rad]; \textbf{(c)} and \textbf{(d)} \gls*{circularly polarised} light for a phase difference of $\Deltaup \gls*{varphi} = \frac{\piup}{2}$\,[rad]; and \textbf{(e)} and \textbf{(f)} \gls*{elliptically polarised} light for any other phase difference: $\Deltaup \gls*{varphi} \neq k\frac{\piup}{2},$\,[rad], with $k \in \mathbb{Z}$. \label{polthree}}
......@@ -45,7 +45,7 @@ The aspect ratio and long axis orientation of the amplitude ellipse in the $\vec
\section{PLM: crossed polarisers}
\caption{Polarised light microscopy is performed with crossed \gls*{polariser}s. Both \gls*{P} and \gls*{A} are \gls*{polariser}s that only transmit the component of the \gls*{PL} that is aligned with the orientation of the \gls*{polariser}. The \gls*{polariser} \gls*{P} that is positioned immediately after the (unpolarised) light source is called the `\gls*{polariser}'. The \gls*{polariser} \gls*{A} that is positioned just before the detector, eye piece or camera, is called the `\gls*{analyser}'. Because the light that is transmitted by the \gls*{polariser} $\gls*{P}(\alpha)$ has no component with orientation $\alpha+90$\,\degree , no light from the source reaches the detector when there is no sample between the two \gls*{polariser}s. }\label{crossed_train_nosample}
......@@ -57,9 +57,9 @@ Because the orientations of the two \gls*{polariser}s are mutually perpendicular
\caption{Birefringence. \textbf{(a)} A collagen fibre (grey) has two refractive indices that are aligned with the collagen fibre ({\color{blue}$\vec{n}_\text{o}$, blue}, `fast axis') and perpendicular to the collagen fibre ({\color{red}$\vec{n}_\text{e}$, red}, `slow axis'); and \textbf{(b)} two rays with parallel wave propagation directions but perpendicular polarisation passing through a \gls*{birefringent} material, c.s.\ a \gls*{birefringent} crystal, illustrating the different refractions of these two rays (by Mikael H{\"a}ggstr{\"o}m, \href{}{Wikimedia Commons}).}\label{birefringent}
......@@ -69,7 +69,7 @@ With \gls*{PLM} we look at \gls*{birefringent} samples. A \gls*{birefringent} ma
\caption{A sample $S$ with \gls*{retardance} $\gls*{Delta}$ and \gls*{azimuth} $\gls*{phi}$ between the \gls*{polariser} and \gls*{analyser} changes the polarisation state of the incident light from \gls*{linearly polarised} to \gls*{elliptically polarised}. The part of the \gls*{elliptically polarised} light that has the same orientation as the \gls*{analyser}, is transmitted to the detector.}\label{crossed_train_polstates}
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