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create_gaussian_kernel

Creates a 2D Gaussian kernel for simulating the dispersion of light pollution. The kernel is defined by: 
K(r) = exp(-r² / (2σ²))
where r is the distance from the center and σ is the standard deviation. 
def create_gaussian_kernel(
    sigma_km: float,
    max_radius_km: float,
    res_km: float
) -> np.ndarray

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Parameters

​
sigma_km
float
required
The standard deviation of the Gaussian in kilometers
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max_radius_km
float
required
The cutoff radius in kilometers (kernel is set to 0 beyond this distance)
​
res_km
float
required
The spatial resolution per pixel in kilometers

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Returns

​
kernel
np.ndarray
A normalized 2D kernel array with shape (2*halo+1, 2*halo+1) where halo = ceil(max_radius_km / res_km)

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Example

from light_pollution.kernels import create_gaussian_kernel

# Create a Gaussian kernel with 50km spread
kernel = create_gaussian_kernel(
    sigma_km=50.0,
    max_radius_km=150.0,
    res_km=1.0
)

print(kernel.shape)  # (301, 301)
print(kernel.sum())  # ~1.0 (normalized)

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create_power_law_kernel

Creates a 2D power-law kernel typical for atmospheric scattering. The kernel combines a power-law decay with exponential attenuation: 
K(r) = (r₀ / (r + r₀))^p × exp(-r / λ)
where:
  • r is the distance from center
  • p is the power exponent
  • r₀ is the regularization radius (prevents singularity at origin)
  • λ is the exponential decay length (extinction length)
def create_power_law_kernel(
    p: float,
    r0_km: float,
    lambda_km: float,
    max_radius_km: float,
    res_km: float
) -> np.ndarray

​
Parameters

​
p
float
required
Power exponent controlling the rate of decay
​
r0_km
float
required
Regularization radius at the origin in kilometers (prevents division by zero)
​
lambda_km
float
required
Exponential decay factor in kilometers (like an extinction length). Set to 0 to disable exponential decay.
​
max_radius_km
float
required
Cutoff radius in kilometers (kernel is set to 0 beyond this distance)
​
res_km
float
required
Spatial resolution per pixel in kilometers

​
Returns

​
kernel
np.ndarray
A normalized 2D kernel array with shape (2*halo+1, 2*halo+1) where halo = ceil(max_radius_km / res_km)

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Example

from light_pollution.kernels import create_power_law_kernel

# Create a power-law kernel for atmospheric scattering
kernel = create_power_law_kernel(
    p=2.0,
    r0_km=5.0,
    lambda_km=100.0,
    max_radius_km=200.0,
    res_km=1.0
)

print(kernel.shape)  # (401, 401)
print(kernel.sum())  # ~1.0 (normalized)

# Power-law without exponential decay
kernel_no_exp = create_power_law_kernel(
    p=1.5,
    r0_km=3.0,
    lambda_km=0.0,  # Disable exponential decay
    max_radius_km=150.0,
    res_km=1.0
)

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