Surface can reflect beam from lidar.

factors that influence reflectivity

Surface Properties

  1. Material Reflectivity (Albedo)
  2. Color
  3. Surface Roughness (Texture)
  4. Surface Orientation (Incident Angle)

LiDAR Sensor Characteristics

  1. Wavelength: The reflectivity of surfaces varies with wavelength.

reflectance models

Reflectance Type example Effect When direction of light and viewpoint are the same
Lambertian unpolished chalk No change — still view-independent
Phong polished plastic or wood with a shiny coating Specular highlight is maximized
Blinn-Phong   Specular term maximized (via halfway vector)
Cook-Torrance brushed metal, skin, or real-world materials under realistic lighting Strong specular peak (especially at oblique angles)

Reflectance Models.

Here is a picture for reflectance models. A python script to generate this image is provided below.

import numpy as np
import matplotlib.pyplot as plt

# Define angles from 0 to 90 degrees (converted to radians)
theta_deg = np.linspace(0, 90, 500)
theta_rad = np.radians(theta_deg)

# Lambertian: Intensity ~ cos(theta)
lambertian = np.cos(theta_rad)

# Phong: Specular ~ cos(theta)^n, assume n = 20 for shiny surface
n_phong = 20
phong_specular = np.cos(theta_rad) ** n_phong

# Blinn-Phong: also uses cos(theta)^n; here we approximate similar behavior
# This assumes halfway vector H close to the normal; use same exponent for comparison
blinn_phong_specular = np.cos(theta_rad) ** n_phong

# Cook-Torrance (simplified model): peak at grazing angles
# We'll model a simplified specular peak near 0 degrees (oblique incidence)
cook_torrance = np.exp(-((theta_rad - 0) / 0.2)**2)  # Gaussian centered at 0 rad

# Plot all
plt.figure(figsize=(10, 6))
plt.plot(theta_deg, lambertian, label='Lambertian (Diffuse)', linewidth=2)
plt.plot(theta_deg, phong_specular, label='Phong (n=20)', linestyle='--', linewidth=2)
plt.plot(theta_deg, blinn_phong_specular, label='Blinn-Phong (n=20)', linestyle='-.', linewidth=2)
plt.plot(theta_deg, cook_torrance, label='Cook-Torrance (simplified)', linestyle=':', linewidth=2)

plt.xlabel('Angle between Light/View Direction and Surface Normal (degrees)')
plt.ylabel('Relative Reflected Intensity')
plt.title('Reflectance Models: Lambertian vs. Non-Lambertian')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

Here is a picture to describe curve between cosine and reflectivity for reflectance models and python script is provide, too.

Reflectance Models.

import numpy as np
import matplotlib.pyplot as plt

# Define angles from 0 to 90 degrees (converted to radians)
theta_deg = np.linspace(0, 90, 500)
theta_rad = np.radians(theta_deg)

# Compute cos(theta) for x-axis
cos_theta = np.cos(theta_rad)

# Lambertian: Intensity ~ cos(theta)
lambertian = cos_theta

# Phong: Specular ~ cos(theta)^n, assume n = 20 for shiny surface
n_phong = 20
phong_specular = cos_theta ** n_phong

# Blinn-Phong: similar form, using same exponent
blinn_phong_specular = cos_theta ** n_phong

# Cook-Torrance (simplified): peak at grazing angles (theta = 0 -> cos(theta) = 1)
cook_torrance = np.exp(-((theta_rad - 0) / 0.2)**2)  # Gaussian centered at 0 rad

# Plot all
plt.figure(figsize=(10, 6))
plt.plot(cos_theta, lambertian, label='Lambertian (Diffuse)', linewidth=2)
plt.plot(cos_theta, phong_specular, label='Phong (n=20)', linestyle='--', linewidth=2)
plt.plot(cos_theta, blinn_phong_specular, label='Blinn-Phong (n=20)', linestyle='-.', linewidth=2)
plt.plot(cos_theta, cook_torrance, label='Cook-Torrance (simplified)', linestyle=':', linewidth=2)

plt.xlabel(r'$\cos(\theta)$')
plt.ylabel('Relative Reflected Intensity')
plt.title('Reflectance Models: Lambertian vs. Non-Lambertian')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

While intensity values can match, they do not mean the surfaces are the same. This is why raw LiDAR intensity is not reliable alone for material or surface classification.

Surface Type 0° (Normal) ~45° ~80° Characteristic Pattern
Lambertian High Medium Low Cosine decay
Specular Low Low High only if sensor = specular Sharp peak at specular angle
Diffuse + Specular Mix High Medium Bump Cosine + spike
Retroreflective High High High Flat or inverted V
Subsurface Scatter High Medium Medium Gentle decline

Some materials may look similar to the human eye (in visible light) but have very different reflectivity in the infrared, vice versa.