In [1]:
%pylab inline
import emcee
import triangle
import pandas as pd
import seaborn as sns
from astroML.decorators import pickle_results
In [2]:
sns.set_context("paper", font_scale=4.0, rc={"lines.linewidth": 2.5})
sns.set(style="ticks")
Import all the local models, saved locally as etalon.py. See the paper for derivations of these equations.
In [3]:
from etalon import *
np.random.seed(78704)
Read in the data. We want "VG09-12" from February 2015
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df = pd.read_csv('../data/VG09_12_gap_20150206.csv', index_col=0)
df.head()
Out[4]:
The step interval is 2.0 mm. There are 26 steps.
In [5]:
# Introduce the Real data, decimate the data.
x = df.index.values
N = len(x)
# Define T_DSP for the model
T_DSP = T_gap_Si(x, 0.0)
n1 = sellmeier_Si(x)
# Define uncertainty
yerr = 0.0002*np.ones(N)
yerr[(x > 1350) & (x < 1420)] = 0.0005 #higher noise in this region
iid_cov = np.diag(yerr ** 2)
# Select the spectrum of interest
# Normalize the spectrum by measured DSP Si wafer.
y = df['VG09-12_1_14'].values
Plot the data. This is the original plot.
In [6]:
plt.plot(df.index, df['VG09-12_1_4'], label='On-mesh- 4 mm')
plt.plot(df.index, df['VG09-12_1_6'], label='On-mesh- 6 mm')
plt.plot(df.index, df['VG09-12_1_8'], label='On-mesh- 8 mm')
plt.plot(df.index, df['VG09-12_1_10'], label='On-mesh- 10 mm')
plt.plot(df.index, df['VG09-12_1_12'], label='On-mesh- 12 mm')
plt.plot(df.index, df['VG09-12_1_14'], label='On-mesh- 14 mm')
plt.plot(df.index, df['VG09-12_1_16'], 'k.', label='Mesh Boundary')
plt.plot(df.index, df['VG09-12_1_18'], 'b-.', label='Off-mesh- 18 mm')
fit1 = T_gap_Si_withFF_fast(x, 43, 0.5, n1)/T_DSP
fit2 = T_gap_Si_withFF_fast(x, 55, 0.5, n1)/T_DSP
fit2_label = 'Model with $d_M={:.0f}\pm{:.0f}$ nm, $\epsilon={:.0f}$'.format(49, 6, 0)
plt.fill_between(x, fit1, fit2, alpha=0.6, color=sns.xkcd_rgb["green apple"])
plt.plot([-10, -9], [-10, -9],"-", alpha=0.85, color=sns.xkcd_rgb["green apple"], label=fit2_label)
plt.plot([-1000, 9000], [1,1], 'k--')
plt.legend(loc='best')
plt.ylim(0.85, 1.05)
plt.xlim(1250, 1780)
plt.ylabel("$T_{gap}$")
plt.xlabel("$\lambda$ (nm)");
plt.savefig("VG0912_STA_scan.pdf", bbox_inches='tight')
In [7]:
sns.set_context("paper", font_scale=1.5, rc={"lines.linewidth": 2.0})
In [9]:
plt.step(df.index, df['VG09-12_1_4'], label='On-mesh- 4 mm')
plt.step(df.index, df['VG09-12_1_6'], label='On-mesh- 6 mm')
plt.step(df.index, df['VG09-12_1_8'], label='On-mesh- 8 mm')
plt.step(df.index, df['VG09-12_1_10'], label='On-mesh- 10 mm')
plt.step(df.index, df['VG09-12_1_12'], label='On-mesh- 12 mm')
plt.step(df.index, df['VG09-12_1_14'], label='On-mesh- 14 mm')
#plt.plot(df.index, df['VG09-12_1_16'], 'k.', label='Mesh Boundary')
plt.plot(df.index, df['VG09-12_1_18'], 'b.', label='Off-mesh- 18 mm')
fit1 = T_gap_Si_withFF_fast(x, 43, 0.3, n1)/T_DSP
fit2 = T_gap_Si_withFF_fast(x, 55, 0.75, n1)/T_DSP
fit2_label = 'Model with $d_M={:.0f}\pm{:.0f}$ nm, ${:.1f}<f<{:.2f}$'.format(49, 6, 0.30, 0.75)
plt.fill_between(x, fit1, fit2, alpha=0.6, color='#cccccc')
plt.plot([-10, -9], [-10, -9],"-", alpha=0.0, color='#cccccc', label=fit2_label)
plt.plot([-1000, 9000], [1,1], 'k--')
plt.legend(loc='best')
# Complete hack to get a shaded band in the legend.
plt.fill_between([1390, 1440], [0.825, 0.825], [0.845,0.845], alpha=0.6, color='#cccccc')
plt.ylim(0.82, 1.02)
plt.xlim(1250, 1780)
plt.ylabel("$T_{gap}$")
plt.xlabel("$\lambda$ (nm)");
plt.savefig("../figs/VG0912_STA_scan_coarse.pdf", bbox_inches='tight')
Sample VG09-12 has a single coarse mesh. The mesh is composed of boxes plasma-etched to a depth of $49\pm6\;$nm. The boxes have an edge length of 1.5 mm. The edges of adjacent boxes are spaced 0.62 mm apart, to yield an overall fill factor of 50%. The Cary5000 measurement beam size is $\sim$1 mm $\times$ 10 mm. Since the beam size is comparable to the mesh size, the fill factor at the position of the measurement will will differ from 50%. The slit measurement was aligned with the mesh grid. The highest fill factor acheivable is about 75%, assuming the slit fit perfectly within a column of boxes. The slit is larger than 0.62 mm, so the measurement cannot exhibit a 0% fill factor of voids. The precise value of the minimum fill factor depends on the details of the slit width, which is not known precisely. We assume that a minimum fill factor of 30%, but caution that this boundary is fuzzy.
The end.