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Merged
merged 5 commits into from
Jul 1, 2025
Merged

Fresnel coefficients #255

merged 5 commits into from
Jul 1, 2025
+71 −1

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@syhaffert
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I added code to calculate the Fresnel transmission and reflection coefficients for isotropic media.

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codecov bot commented Jan 12, 2025 •
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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.14%. Comparing base (6cd4fc2) to head (d73be96).
Report is 6 commits behind head on master.

Additional details and impacted files 
@@            Coverage Diff             @@
##           master     #255      +/-   ##
==========================================
+ Coverage   83.11%   83.14%   +0.03%     
==========================================
  Files         104      104              
  Lines        7765     7779      +14     
==========================================
+ Hits         6454     6468      +14     
  Misses       1311     1311

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ehpor
ehpor reviewed Jan 25, 2025
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@ehpor ehpor force-pushed the fresnel_coefficients branch from 92b9917 to d843923 Compare June 27, 2025 05:34
@ehpor
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ehpor commented Jun 27, 2025

Small test script:

import hcipy
import matplotlib.pyplot as plt
import numpy as np

n1 = 1.5
n2 = 1
angle_deg = np.linspace(0, 90, 1000)
angle = np.radians(angle_deg)

rs, rp = hcipy.fresnel_reflection_coefficients(n1, n2, angle)
ts, tp = hcipy.fresnel_transmission_coefficients(n1, n2, angle)

# Magnitudes and phases
def mag_phase(x):
    return np.abs(x), np.unwrap(np.angle(x))

mag_rs, phase_rs = mag_phase(rs)
mag_rp, phase_rp = mag_phase(rp)
mag_ts, phase_ts = mag_phase(ts)
mag_tp, phase_tp = mag_phase(tp)

# Plotting
fig, axs = plt.subplots(2, 2, figsize=(12, 8), sharex=True)

axs[0, 0].plot(angle_deg, mag_rs, label='|r_s|')
axs[0, 0].plot(angle_deg, mag_rp, label='|r_p|')
axs[0, 0].set_ylabel('Reflection Coefficient Magnitude')
axs[0, 0].legend()
axs[0, 0].grid()

axs[0, 1].plot(angle_deg, np.degrees(phase_rs), label='arg(r_s)')
axs[0, 1].plot(angle_deg, np.degrees(phase_rp), label='arg(r_p)')
axs[0, 1].set_ylabel('Reflection Coefficient Phase (deg)')
axs[0, 1].legend()
axs[0, 1].grid()

axs[1, 0].plot(angle_deg, mag_ts, label='|t_s|')
axs[1, 0].plot(angle_deg, mag_tp, label='|t_p|')
axs[1, 0].set_xlabel('Angle of Incidence (deg)')
axs[1, 0].set_ylabel('Transmission Coefficient Magnitude')
axs[1, 0].legend()
axs[1, 0].grid()

axs[1, 1].plot(angle_deg, np.degrees(phase_ts), label='arg(t_s)')
axs[1, 1].plot(angle_deg, np.degrees(phase_tp), label='arg(t_p)')
axs[1, 1].set_xlabel('Angle of Incidence (deg)')
axs[1, 1].set_ylabel('Transmission Coefficient Phase (deg)')
axs[1, 1].legend()
axs[1, 1].grid()

plt.tight_layout()
plt.show()

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@ehpor
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ehpor commented Jun 27, 2025

@syhaffert Does this look correct?

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syhaffert commented Jul 1, 2025 •
edited
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I checked for power conservation using the following code block in your script. And the power is conserved to machine precision. I also see the correct behavior when we travel from lower density to higher density (n1 =1 and n2=1.5). So, yes I think everything is correct.

import hcipy
import matplotlib.pyplot as plt
import numpy as np

n1 = 1.0
n2 = 1.5
angle_deg = np.linspace(0, 90, 1000)
angle = np.radians(angle_deg)

rs, rp = hcipy.fresnel_reflection_coefficients(n1, n2, angle)
ts, tp = hcipy.fresnel_transmission_coefficients(n1, n2, angle)

# Calculate the refracted angle
sin_t = n1 / n2 * np.sin(angle)
cos_t = np.real(np.sqrt(1 - sin_t**2 + 0j))
Ts = abs(ts)**2 * n2 / n1 * cos_t / np.cos(angle)
Rs = abs(rs)**2

Tp = abs(tp)**2 * n2 / n1 * cos_t / np.cos(angle)
Rp = abs(rp)**2

# Magnitudes and phases
def mag_phase(x):
    return np.abs(x), np.angle(x)

mag_rs, phase_rs = mag_phase(rs)
mag_rp, phase_rp = mag_phase(rp)
mag_ts, phase_ts = mag_phase(ts)
mag_tp, phase_tp = mag_phase(tp)

fig, axs1 = plt.subplots(1, 2, figsize=(12, 4))
axs1[0].plot(angle_deg, Ts, label='Ts')
axs1[0].plot(angle_deg, Rs, label='Rs')
axs1[0].plot(angle_deg, Tp, label='Tp', ls='--', color='C0')
axs1[0].plot(angle_deg, Rp, label='Rp', ls='--', color='C1')
axs1[0].legend()
axs1[0].grid()
axs1[0].set_xlabel('Angle of Incidence (deg)')
axs1[0].set_ylabel('Power transmission')
axs1[0].set_ylim(-0.03, 1.03)

axs1[1].plot(angle_deg, Ts + Rs, label='Ts + Rs')
axs1[1].plot(angle_deg, Tp + Rp, label='Tp + Rp', ls='--')
axs1[1].legend()
axs1[1].grid()
axs1[1].set_xlabel('Angle of Incidence (deg)')
axs1[1].set_ylabel('Power transmission')
axs1[1].set_ylim(-0.03, 1.03)

# Plotting
fig, axs = plt.subplots(2, 2, figsize=(12, 8), sharex=True)

axs[0, 0].plot(angle_deg, mag_rs, label='|r_s|')
axs[0, 0].plot(angle_deg, mag_rp, label='|r_p|')
axs[0, 0].set_ylabel('Reflection Coefficient Magnitude')
axs[0, 0].legend()
axs[0, 0].grid()

axs[0, 1].plot(angle_deg, np.degrees(phase_rs), label='arg(r_s)')
axs[0, 1].plot(angle_deg, np.degrees(phase_rp), label='arg(r_p)')
axs[0, 1].set_ylabel('Reflection Coefficient Phase (deg)')
axs[0, 1].legend()
axs[0, 1].grid()

axs[1, 0].plot(angle_deg, mag_ts, label='|t_s|')
axs[1, 0].plot(angle_deg, mag_tp, label='|t_p|')
axs[1, 0].set_xlabel('Angle of Incidence (deg)')
axs[1, 0].set_ylabel('Transmission Coefficient Magnitude')
axs[1, 0].legend()
axs[1, 0].grid()

axs[1, 1].plot(angle_deg, np.degrees(phase_ts), label='arg(t_s)')
axs[1, 1].plot(angle_deg, np.degrees(phase_tp), label='arg(t_p)')
axs[1, 1].set_xlabel('Angle of Incidence (deg)')
axs[1, 1].set_ylabel('Transmission Coefficient Phase (deg)')
axs[1, 1].legend()
axs[1, 1].grid()

plt.tight_layout()
plt.show()

@ehpor ehpor force-pushed the fresnel_coefficients branch from 0bdf4ba to d73be96 Compare July 1, 2025 08:53
@ehpor ehpor enabled auto-merge July 1, 2025 08:53
@ehpor ehpor merged commit ac31947 into master Jul 1, 2025
16 checks passed
@ehpor ehpor deleted the fresnel_coefficients branch July 7, 2025 21:21
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@syhaffert @ehpor