Gaussian Beam Propagation
w(z)=w₀√(1+(z/z_R)²), z_R=πw₀²/λ, divergence θ=M²λ/πw₀. Beam profile drawn to scale.
Thin Lens / Lensmaker
1/f=1/s'−1/s; m=−s'/s; 1/f=(n−1)(1/R₁−1/R₂).
f/# ↔ NA & FOV
f/#=f/D; NA≈1/2(f/#); FOV from sensor.
Diffraction Limit & Airy
Airy Ø=2.44λ(f/#); focused spot 4λf/πD.
FMCW Range/Velocity Resolution
ΔR=c/2B; v-res from chirp & wavelength.
Detector — NETD & D*
D*=√(A·Δf)/NEP; higher D* = more sensitive.
Formula reference
Lens 1/f=1/s'−1/s, m=−s'/s; lensmaker 1/f=(n−1)(1/R₁−1/R₂). f/#=f/D, NA≈1/2(f/#).
Gaussian z_R=πw₀²/λ, w(z)=w₀√(1+(z/z_R)²), θ=M²λ/πw₀. Airy 2.44λ(f/#), focused spot 4λf/πD.
FMCW ΔR=c/2B. Detector D*=√(AΔf)/NEP (cm·√Hz/W).