In a nutshell¶

[1]:

import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.constrained_layout.use'] = True
%matplotlib notebook
import toolbox_scs as tb

Cupy is not installed in this environment, no access to the GPU

plot and fit a knife-edge run¶

[2]:

proposal = 4476
runNB = 130
fields = ['XRD_STZ', 'FastADC2_5raw']
run, ds = tb.load(proposal, runNB, fields, fadc2_bp='scs_ppl')

w0_x = tb.knife_edge(ds, axisKey='XRD_STZ',
                     signalKey='FastADC2_5peaks', plot=True)[0]

fitting function: a*erfc(np.sqrt(2)*(x-x0)/w0) + b
w0 = (653.5 +/- 0.4) um
x0 = (-7.327 +/- 0.000) mm
a = 1.135880e+05 +/- 1.950313e+01
b = -3.857367e+02 +/- 2.580742e+01

OL power measurement and fluence calibration¶

[3]:

# the following two arrays comes from laser power measurement
rel_powers = np.array([100, 75, 50, 25, 15, 12, 10, 8, 6, 4, 2, 1, 0.75, 0.5, 0.25, 0.1])
power_mW = np.array([505, 384, 258, 130, 81, 67, 56.5, 45.8, 35.6, 24.1, 14.1, 9.3, 8.0, 6.5, 4.8, 4.1]) #in mW
npulses = 336
# Here we assume that w0y = w0x
F, F_fit, E, E_fit = tb.fluenceCalibration(rel_powers, power_mW, npulses,
                                           w0x=w0_x*1e-3, fit_order=1)

Beam size versus scanning parameter (focus lens position, KB bending, …)¶

[4]:

proposal = 900291
runList = range(9, 16)
fields = ['chem_Y', 'HFM_BENDING', 'VFM_BENDING', 'FastADC9raw']
data = {}
for runNB in runList:
    run, ds = tb.load(proposal, runNB, fields, fadc_bp='sase3')
    data[runNB] = ds

chem_Y: only 70.3% of trains (4650 out of 6618) contain data.
HFM_BENDING: only 52.9% of trains (3499 out of 6618) contain data.
VFM_BENDING: only 52.9% of trains (3499 out of 6618) contain data.
FastADC9raw: only 12.9% of trains (852 out of 6618) contain data.
chem_Y: only 76.6% of trains (4748 out of 6201) contain data.
HFM_BENDING: only 52.8% of trains (3273 out of 6201) contain data.
VFM_BENDING: only 52.8% of trains (3273 out of 6201) contain data.
FastADC9raw: only 16.3% of trains (1011 out of 6201) contain data.
chem_Y: only 91.7% of trains (5284 out of 5762) contain data.
HFM_BENDING: only 52.9% of trains (3046 out of 5762) contain data.
VFM_BENDING: only 52.9% of trains (3046 out of 5762) contain data.
FastADC9raw: only 25.3% of trains (1458 out of 5762) contain data.
HFM_BENDING: only 53.1% of trains (3073 out of 5791) contain data.
VFM_BENDING: only 53.1% of trains (3073 out of 5791) contain data.
FastADC9raw: only 29.3% of trains (1698 out of 5791) contain data.
chem_Y: only 85.0% of trains (5136 out of 6040) contain data.
HFM_BENDING: only 53.0% of trains (3204 out of 6040) contain data.
VFM_BENDING: only 53.0% of trains (3204 out of 6040) contain data.
FastADC9raw: only 21.5% of trains (1299 out of 6040) contain data.
chem_Y: only 80.8% of trains (4850 out of 6005) contain data.
HFM_BENDING: only 54.3% of trains (3258 out of 6005) contain data.
VFM_BENDING: only 54.3% of trains (3258 out of 6005) contain data.
FastADC9raw: only 19.9% of trains (1196 out of 6005) contain data.
chem_Y: only 38.4% of trains (3200 out of 8333) contain data.
HFM_BENDING: only 73.6% of trains (6136 out of 8333) contain data.
VFM_BENDING: only 73.6% of trains (6136 out of 8333) contain data.
FastADC9raw: only 6.7% of trains (559 out of 8333) contain data.

[5]:

w0_vs_bender = []
for runNB, ds in data.items():
    w0 = tb.knife_edge(ds, signalKey='FastADC9peaks', axisKey='chem_Y')[0]
    w0_vs_bender.append([ds['VFM_BENDING'].mean().values, w0])
w0_vs_bender = np.array(w0_vs_bender)

[6]:

plt.figure()
plt.plot(w0_vs_bender[:,0], w0_vs_bender[:, 1]*1e3, 'o')
plt.ylabel('FEL radius @ 1/e^2 [$\mu$m]')
plt.xlabel('VFM BENDING')

[6]:

Text(0.5, 0, 'VFM BENDING')

Detailed notebook¶

The peak fluence of a Gaussian beam is defined as:

$F_0 = \frac{2 E_P}{\pi w_{0,x} w_{0,y}}$ with $E_P$ the pulse energy, $w_{0,x}$ and $w_{0,y}$ the beam radii at $1/e^2$ in $x$ and $y$ axes, respectively.

Demonstration¶

For a Gaussian beam at the waist position, the intensity distribution is defined as:

$I(x,y) = I_0 e^{\left(-\frac{2x^2}{w_{0,x}^2} -\frac{2y^2}{w_{0,y}^2}\right)}$

with $I_0$ the peak intensity of the Gaussian beam, $w_{0,x}$ and $w_{0,y}$ the beam radii at $1/e^2$ in $x$ and $y$ axes, respectively.

Let’s consider a knife-edge “corner” at position $(x,y)$ that blocks the beam for $x^\prime < x$ and $y^\prime < y$. The detected power behind the knife-edge is given by:

$P(x,y) = I_0 \int{x}^:nbsphinx-math:`infty `:nbsphinx-math:`int`{y}:sup::nbsphinx-math:infty e{\left`(-:nbsphinx-math:frac{2x^{prime 2}}{w_{0,x}^2}` -\frac{2y^{\prime 2}}{w_{0,y}^2}\right)} dx^{:nbsphinx-math:}prime dy:nbsphinx-math:`prime `$

Now let’s consider a purely vertical knife-edge. The power in the $y$ axis is integrated from $-\infty$ to $\infty$, thus:

$P(x) = I_0 \sqrt\frac{\pi}{2}w_{0,y}\int_x^\infty e^{\left(-\frac{2x^{\prime 2}}{w_{0,x}^2}\right)}dx^\prime$.

Similarly, for a purely horizontal knife-edge:

$P(y) = I_0 \sqrt\frac{\pi}{2}w_{0,x}\int_y^\infty e^{\left(-\frac{2y^{\prime 2}}{w_{0,y}^2}\right)}dy^\prime$

By fitting the knife edge scans to these functions, we extract the waist in $x$ and $y$ axes.

The total power of one pulse is then:

$P_{TOT} = \frac{I_0 \pi w_{0,x} w_{0,y}}{2}$

Hence, the peak fluence, defined as $F_0=I_0\tau$ with $\tau$ the pulse duration of the laser, is given as:

$F_0 = \frac{2 E_P}{\pi w_{0,x} w_{0,y}}$

where $E_P$ is the pulse energy.

Optical laser beam profile and fluence¶

Knife-edge measurement (OL)¶

The laser used in these knife-edge scans was the SCS backup laser, for which there was no bunch pattern table, so, whenever a function needs the bunch pattern as input argument, we set it to ‘None’. If the PP laser is used, then the corresponding bunch pattern key is ‘scs_ppl’.

[7]:

proposal = 900094
runNB = 384
fields = ["FastADC4raw", "scannerX"]
runX, dsX = tb.load(proposal, runNB, fields, laser_bp='None')

fields = ["FastADC4raw", "scannerY"]
runNB = 385
runY, dsY = tb.load(proposal, runNB, fields, laser_bp='None')

FastADC4raw: only 94.1% of trains (768 out of 816) contain data.

Using ‘show_all=True’ displays the entire trace and all integration regions. We can then zoom and pan in the interactive figure.

[8]:

paramsX = tb.check_peak_params(runX, 'FastADC4raw', show_all=True, bunchPattern='None')
print(paramsX)

Auto-find peak params: 118 pulses, 324 samples between two pulses

{'pulseStart': 5393, 'pulseStop': 5424, 'baseStart': 5371, 'baseStop': 5387, 'period': 324, 'npulses': 118}

using the default ‘show_all=False’ parameter only shows the first and last pulses of the trace

[9]:

tb.check_peak_params(runX, 'FastADC4raw', bunchPattern='None')

Auto-find peak params: 118 pulses, 324 samples between two pulses

[9]:

{'pulseStart': 5393,
 'pulseStop': 5424,
 'baseStart': 5371,
 'baseStop': 5387,
 'period': 324,
 'npulses': 118}

[10]:

w0_x = tb.knife_edge(dsX, axisKey='scannerX', plot=True)[0]*1e-3
w0_y = tb.knife_edge(dsY, axisKey='scannerY', plot=True)[0]*1e-3

print('X-FWHM [um]:', w0_x * np.sqrt(2*np.log(2))*1e6)
print('Y-FWHM [um]:', w0_y * np.sqrt(2*np.log(2))*1e6)

fitting function: a*erfc(np.sqrt(2)*(x-x0)/w0) + b
w0 = (131.9 +/- 0.1) um
x0 = (18.757 +/- 0.000) mm
a = 1.752229e+05 +/- 2.642387e+01
b = 5.670915e+03 +/- 3.665072e+01

fitting function: a*erfc(np.sqrt(2)*(x-x0)/w0) + b
w0 = (297.3 +/- 0.5) um
x0 = (12.093 +/- 0.000) mm
a = -1.737334e+05 +/- 1.014418e+02
b = 3.424424e+05 +/- 1.518455e+02
X-FWHM [um]: 155.33422804507632
Y-FWHM [um]: 350.08711535421213

Fluence calculation (OL)¶

[11]:

#measurement performed in Exp Hutch before in-coupling window
rel_powers = np.array([100, 75, 50, 25, 15, 12, 10, 8, 6, 4, 2, 1, 0.75, 0.5, 0.25, 0.1])
power_mW = np.array([505, 384, 258, 130, 81, 67, 56.5, 45.8, 35.6, 24.1, 14.1, 9.3, 8.0, 6.5, 4.8, 4.1]) #in mW
npulses = 336

Note that it is possible to change the polynomial order of the fit (for example to 2), which is useful if the output is SHG (400 nm) or THG (266 nm) but the power control is changing the 800 nm pump before conversion.

[12]:

F, F_fit, E, E_fit = tb.fluenceCalibration(rel_powers, power_mW, npulses,
                                           w0x=w0_x, w0y=w0_y, fit_order=1)