Optical Geometry Engine

Focal Lens & F-Theta Calculator

Calculate focused spot waist diameter, Rayleigh depth of focus (DOF), beam divergence angle, and F-Theta Galvo scan field dimensions. Select the optimal lens focal length for your cutting depth or marking field.

Lens & Beam Parameters

Laser Optical Wavelength

Focal Length (f)160 mm (6.30")

Entrance Beam Dia D (mm)Beam diameter at lens aperture

Beam Quality Factor (M²)Ideal Gaussian is 1.0; single-mode fiber is 1.1-1.3

Optical Configuration

Focal Spot & Optics Metrics

Focused Beam Spot Diameter (2w₀)

37µm (0.037 mm)

Diffraction-limited optical spot waist at focal plane

Depth of Focus (2z_R)

1.7 mm

±0.85 mm

Divergence Angle

21.9 mrad

1.25° half-angle

Galvo Scan Field Dimensions

Working Marking Field:112 × 112 mm

Diagonal Coverage:158 mm

Working Distance (WD):~147 mm

Optical Principles

The Trade-off Between Spot Size and Depth of Focus

1. Spot Size vs. Focal Length Trade-off

In optical physics, spot diameter scales linearly with focal length $f$, but Rayleigh length (depth of focus) scales with the square of spot diameter:

w₀ ∝ f / D
z_R ∝ w₀² / λ ∝ (f / D)²

Halving focal length cuts spot diameter in half (yielding 4x higher power density!), but shrinks your usable depth of focus by a factor of 4.

2. Selecting the Right Optics

Short Lenses (38.1 - 50.8 mm): Ideal for micro-machining, raster engraving high-resolution photo portraits, and cutting sheet material under 3 mm.
Long Lenses (101.6 mm / 4.0"): Wide beam waist creates parallel rays through thick materials (up to 20 mm), preventing sloped hourglass bevels on cut edges.
F-Theta Lenses: Designed specifically for dual-axis galvanometer mirrors so that scan position $y = f \cdot \theta$ remains flat across the entire field.