Chapter Summary

Chapter Summary

Key Points

• 1.

  Neural Radiance Fields represent 3D scenes as continuous volumetric functions $F_\theta: (\mathbf{x}, \mathbf{d}) \mapsto (\sigma, \mathbf{c})$ parameterised by an MLP. Differentiable volume rendering integrates density and colour along camera rays, enabling end-to-end training from posed images. Instant-NGP and Mip-NeRF address the original NeRF's speed and aliasing limitations.

• 2.

  Five key differences separate optical from RF rendering: (1) centimetre wavelengths where diffraction dominates, (2) specular rather than diffuse scattering, (3) no focusing lens (lensless imaging), (4) complex-valued fields requiring coherent summation, and (5) the RF rendering integral sums phasors, not intensities.

• 3.

  NeRF$^2$ was the first neural radiance field for RF, predicting received signal strength from sparse measurements. Its dB-domain loss normalises gradients across the large dynamic range of RF power. The primary limitation is single-ray integration, which ignores multipath.

• 4.

  RF-NeRF variants address specific limitations: WiNeRT adds multi-bounce ray tracing for multipath, DART incorporates Doppler for automotive radar, ISAR-NeRF enables sparse-aperture SAR reconstruction, and material-aware variants learn physically interpretable attenuation maps.

• 5.

  The RF volume rendering equation reduces to the Born forward model $\mathbf{y} = \mathbf{A}\mathbf{c} + \mathbf{w}$ under the assumptions of negligible attenuation, isotropic scattering, and point scatterers. The NeRF framework extends Born by handling shadowing (transmittance) and specular scattering (view dependence) but shares its single-scattering limitation.