Chapter 12: Quantum optics of synchrotron light

Below is a set of python codes associated with Chapter 12 of Daniele Pelliccia and David M. Paganin, “Synchrotron Light: A Physics Journey from Laboratory to Cosmos” (Oxford University Press, 2025).

In order to run any of these python codes, you will need to include the following header.

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import poisson

synchrotron_style = {
    'font.family': 'FreeSerif',
    'font.size': 30,
    'axes.linewidth': 2.0,
    'axes.edgecolor': 'black',
    'grid.color': '#5b5b5b',
    'grid.linewidth': 1.2,
}

import numpy as np

import matplotlib.pyplot as plt

from scipy.stats import poisson

synchrotron_style = {

'font.family': 'FreeSerif',

'font.size': 30,

'axes.linewidth': 2.0,

'axes.edgecolor': 'black',

'grid.color': '#5b5b5b',

'grid.linewidth': 1.2,

}

Poisson distribution

See Fig. 12.5

n = np.arange(0,80,1)
P = np.zeros_like(n).astype('float32')
linecol = ['r', 'g', 'b', 'm']
mk = ['ro','sg', 'db', '*m'] 
with plt.style.context(('seaborn-v0_8-whitegrid')):
    plt.rcParams.update(synchrotron_style)
    fig = plt.figure(figsize=(18,9.6))
    
    for k, mu in enumerate([2,5,10,50]):
        for i,j in enumerate(n):

            P[i] = poisson.pmf(j, mu)
        
        markerline, stemline, baseline = plt.stem(n, P, linefmt=linecol[k], basefmt =linecol[k], markerfmt=mk[k], label="$\mu = $"+str(mu))
        plt.setp(markerline, markersize = 10)  


        plt.xticks(fontsize = 28)
        plt.yticks(fontsize = 28)
    plt.legend(fontsize=30, frameon=True, framealpha=1)
    plt.show()

n = np.arange(0,80,1)

P = np.zeros_like(n).astype('float32')

linecol = ['r', 'g', 'b', 'm']

mk = ['ro','sg', 'db', '*m']

with plt.style.context(('seaborn-v0_8-whitegrid')):

plt.rcParams.update(synchrotron_style)

fig = plt.figure(figsize=(18,9.6))

for k, mu in enumerate([2,5,10,50]):

for i,j in enumerate(n):

P[i] = poisson.pmf(j, mu)

markerline, stemline, baseline = plt.stem(n, P, linefmt=linecol[k], basefmt =linecol[k], markerfmt=mk[k], label="$\mu = $"+str(mu))

plt.setp(markerline, markersize = 10)

plt.xticks(fontsize = 28)

plt.yticks(fontsize = 28)

plt.legend(fontsize=30, frameon=True, framealpha=1)

plt.show()

Poisson statistics

The different panels of Fig. 12.7 can be produced with the code below, by changing the value of N.

N = 5
func = 0.1+N*noiseless.reshape(-1,1).flatten()

func1 = np.zeros_like(func)
for i,j in enumerate(func):
    func1[i] = poisson.rvs(j, size=1)[0]

noisy = func1.reshape(101,101)    

fig = plt.figure(figsize=(10,10))
plt.imshow(noisy, cmap = 'gray')
plt.axis('equal')
plt.axis('off')
plt.show()

N = 5

func = 0.1+N*noiseless.reshape(-1,1).flatten()

func1 = np.zeros_like(func)

for i,j in enumerate(func):

func1[i] = poisson.rvs(j, size=1)[0]

noisy = func1.reshape(101,101)

fig = plt.figure(figsize=(10,10))

plt.imshow(noisy, cmap = 'gray')

plt.axis('equal')

plt.axis('off')

plt.show()

Time boxes

See Fig. 12.8.

boxes = [0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0]
time = np.arange(0, len(boxes),1)

with plt.style.context(('seaborn-v0_8-whitegrid')):
    plt.rcParams.update(synchrotron_style)
    fig = plt.figure(figsize=(14,7))
    
    plt.plot(time, boxes, 'o-', lw=4)

boxes = [0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0]

time = np.arange(0, len(boxes),1)

with plt.style.context(('seaborn-v0_8-whitegrid')):

plt.rcParams.update(synchrotron_style)

fig = plt.figure(figsize=(14,7))

plt.plot(time, boxes, 'o-', lw=4)