diff --git a/ex-6/plot.py b/ex-6/plot.py index 90fc7bc..5ab7515 100755 --- a/ex-6/plot.py +++ b/ex-6/plot.py @@ -2,15 +2,14 @@ from pylab import * import sys -import matplotlib.pyplot as plt -plt.rcParams['font.size'] = 20 +rcParams['font.size'] = 12 a, b, f = loadtxt(sys.stdin, unpack=True) -suptitle('Fraunhofer diffraction') title(sys.argv[1] if len(sys.argv) > 1 else "", loc='right') -hist(a, np.insert(b, 0, a[0]), weights=f/sum(f), - color='#dbbf0d', edgecolor='#595856', linewidth=0.5) +hist(a, np.insert(b, 0, a[0]), weights=100*f/sum(f), + histtype='stepfilled', color='#e3c5ca', edgecolor='#92182b') xlabel(r'$\theta$ (radians)') ylabel(r'$I(\theta)$ (a.u.)') +tight_layout() show() diff --git a/notes/images/deco-fft-0.05.pdf b/notes/images/deco-fft-0.05.pdf deleted file mode 100644 index f419f8f..0000000 Binary files a/notes/images/deco-fft-0.05.pdf and /dev/null differ diff --git a/notes/images/deco-fft-0.5.pdf b/notes/images/deco-fft-0.5.pdf deleted file mode 100644 index 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b/notes/sections/6.md index 304b20d..e1a148f 100644 --- a/notes/sections/6.md +++ b/notes/sections/6.md @@ -1,6 +1,6 @@ # Exercise 6 -## Generating points according to Fraunhofer diffraction +## Generating points according to Fraunhöfer diffraction The diffraction of a plane wave thorough a round slit must be simulated by generating $N =$ 50'000 points according to the intensity distribution @@ -16,7 +16,7 @@ where: - $E$ is the electric field amplitude, default set $E = \SI{1e4}{V/m}$; - $a$ is the radius of the slit aperture, default set $a = \SI{0.01}{m}$; - $\theta$ is the angle specified in @fig:slit; -- $J_1$ is the Bessel function of first order; +- $J_1$ is a Bessel function of first kind; - $k$ is the wavenumber, default set $k = \SI{1e-4}{m^{-1}}$; - $L$ default set $L = \SI{1}{m}$. @@ -46,7 +46,7 @@ where: \node [cyclamen] at (5.5,-0.4) {$\theta$}; \node [rotate=-90] at (10.2,0) {screen}; \end{tikzpicture} -\caption{Fraunhofer diffraction.}\label{fig:slit} +\caption{Fraunhöfer diffraction.}\label{fig:slit} } \end{figure} @@ -88,8 +88,7 @@ omitted: The sample was binned and stored in a histogram with a customizable number $n$ of bins default set $n = 150$. In @fig:original an example is shown. -![Example of sorted points according to - $I(\theta)$.](images/6_original.pdf){#fig:original} +![Example of an intensity histogram.](images/fraun-original.pdf){#fig:original} ## Gaussian noise convolution {#sec:convolution} @@ -417,41 +416,41 @@ On the other hand, the Richardson-Lucy routine is less affected by this further complication being already inaccurate in itself.
-![Convolved signal.](images/noise-0.05.pdf){width=12cm} +![Convolved signal.](images/fraun-conv-0.05.pdf){width=12cm} -![Deconvolved signal with FFT.](images/deco-fft-0.05.pdf){width=12cm} +![Deconvolved signal with FFT.](images/fraun-fft-0.05.pdf){width=12cm} -![Deconvolved signal with RL.](images/deco-rl-0.05.pdf){width=12cm} +![Deconvolved signal with RL.](images/fraun-rl-0.05.pdf){width=12cm} Results for $\sigma = 0.05 \Delta \theta$, where $\Delta \theta$ is the bin width.
-![Convolved signal.](images/noise-0.5.pdf){width=12cm} +![Convolved signal.](images/fraun-conv-0.5.pdf){width=12cm} -![Deconvolved signal with FFT.](images/deco-fft-0.5.pdf){width=12cm} +![Deconvolved signal with FFT.](images/fraun-fft-0.5.pdf){width=12cm} -![Deconvolved signal with RL.](images/deco-rl-0.5.pdf){width=12cm} +![Deconvolved signal with RL.](images/fraun-rl-0.5.pdf){width=12cm} Results for $\sigma = 0.5 \Delta \theta$, where $\Delta \theta$ is the bin width.
-![Convolved signal.](images/noise-1.pdf){width=12cm} +![Convolved signal.](images/fraun-conv-1.pdf){width=12cm} -![Deconvolved signal with FFT.](images/deco-fft-1.pdf){width=12cm} +![Deconvolved signal with FFT.](images/fraun-fft-1.pdf){width=12cm} -![Deconvolved signal with RL.](images/deco-rl-1.pdf){width=12cm} +![Deconvolved signal with RL.](images/fraun-rl-1.pdf){width=12cm} Results for $\sigma = \Delta \theta$, where $\Delta \theta$ is the bin width.
-![Deconvolved signal with FFT.](images/poisson-fft.pdf){width=12cm} +![Deconvolved signal with FFT.](images/fraun-noise-fft.pdf){width=12cm} -![Deconvolved signal withh RL.](images/poisson-rl.pdf){width=12cm} +![Deconvolved signal withh RL.](images/fraun-noise-rl.pdf){width=12cm} -Results for $\sigma = \Delta \theta$, poissoned data. +Results for $\sigma = \Delta \theta$, with Poisson noise.