import numpy as np
import matplotlib.pyplot as plt
from bessel import ric_besselh, ric_besselh_derivative  # Custom functions to compute Riccati-Hankel functions
import pandas as pd

# --------------------------------------------------------
# This script computes the monostatic RCS of a PEC sphere 
# using the analytical Mie series solution.
#
# The normalized RCS is also computed by dividing by the 
# physical cross-sectional area of the sphere (πR²).
# --------------------------------------------------------

# Define frequency sweep from 50 MHz to 5 GHz (1000 points)
frequency = np.linspace(0.05e9, 5e9, 1000)

# Compute corresponding wavelengths
wavelength = 3e8 / frequency  # λ = c / f

# Sphere radius in meters
Radius = 0.1  # 10 cm

# Order of expansion (controls accuracy of Mie series)
OrderN = 100

# Cross-sectional area of sphere (used for normalization)
AreaOfCircle = np.pi * Radius**2

# Initialize result arrays
RCS = np.zeros(len(wavelength), dtype=complex)     # Raw monostatic RCS
RCS_NORM = np.zeros(len(wavelength))               # Normalized RCS (RCS / πR²)

# --------------------------------------------------------
# Loop over all frequencies
# --------------------------------------------------------
for index, w in enumerate(wavelength):

    k = 2 * np.pi / w           # Wavenumber
    kr = k * Radius             # Size parameter (non-dimensional)

    sum_ = 0.0 + 0.0j           # Initialize series sum for current frequency

    kr_vec = kr * np.ones(1)    # Required format for bessel function input

    # Generate orders from 0 to OrderN as column vector
    Order = np.transpose(np.linspace(0, OrderN, OrderN + 1))

    # Evaluate Riccati-Hankel function and its derivative at all orders
    H = ric_besselh(Order, kr_vec, 2)       # Hankel function of 2nd kind
    Hp = ric_besselh_derivative(Order, kr_vec, 2)

    # --------------------------------------------------------
    # Evaluate Mie series sum for monostatic RCS
    # --------------------------------------------------------
    for n_ in range(OrderN):

        n = n_ + 1  # Mie series starts from n = 1

        # Series term from Mie theory:
        # RCS component = (-1)^n * (2n + 1) / (Hn * Hn')
        term = (-1.0)**n * (2.0 * n + 1.0) / (H[n] * Hp[n])

        sum_ += term  # Accumulate into total sum

    # Final RCS value for this frequency (in m²)
    RCS[index] = abs(sum_)**2 * w**2 / (4 * np.pi)

    # Normalize RCS by area (unitless quantity)
    RCS_NORM[index] = RCS[index] / AreaOfCircle

# --------------------------------------------------------
# Plot Normalized RCS vs Circumference (2πR / λ)
# --------------------------------------------------------
Normalized_circumference = 2 * np.pi * Radius / wavelength

plt.figure()
plt.plot(Normalized_circumference, RCS_NORM)
plt.grid()
plt.xticks(np.linspace(0, 10, 11))
plt.xlabel("Normalized Circumference (2πR/λ)")
plt.ylabel("Normalized RCS by Area of Circle")
plt.title("Normalized Monostatic RCS of PEC Sphere")
plt.show()

# --------------------------------------------------------
# Plot Monostatic RCS in dB vs Frequency
# --------------------------------------------------------
plt.figure()
plt.plot(frequency / 1e9, 10 * np.log10(RCS))
plt.grid()
plt.xticks(np.linspace(0, 10, 21))
plt.xlim([min(frequency / 1e9), max(frequency / 1e9)])
plt.xlabel("Frequency (GHz)")
plt.ylabel("Monostatic RCS (dBsm)")
plt.title("Monostatic RCS of PEC Sphere")
plt.show()

# --------------------------------------------------------
# Export Results to Excel
# --------------------------------------------------------
output_df = pd.DataFrame({
    'Frequency (GHz)': frequency / 1e9,
    'Monostatic RCS (dBsm)': np.real(10 * np.log10(RCS))
})
output_df.to_csv("RCS_ANALYTIC.xlsx", index=False)

print("✅ Computation complete. RCS results saved to 'RCS_ANALYTIC.xlsx'")