3D Top-Hat Beam Shaper — CalculatorVersion 2.3

A focusing lens turns your Gaussian beam into a Gaussian spot — bright in the middle, tapering off towards the edge. A 3D Top-Hat replaces that with a round, flat-topped spot: uniform fluence across the plateau, steep edges, and no strong side orders. The spot gets larger than the unshaped focus, and it holds its shape over a defined depth range. Those two numbers are what this calculator gives you.

3D Top-Hat is part of Midel’s 3D-EDOF (Extended Depth of Focus) portfolio, alongside 3D Gaussian and 3D Ring-Core.

Both charts are schematic, drawn to scale — not a physical simulation. They illustrate the calculated numbers and the guaranteed specification; every design is simulated and confirmed individually before quotation.

Spot cross-section — both profiles are drawn to scale in the transverse axis and normalised to the same peak, so the graphic compares width and shape, not absolute intensity. The flat-top edge is drawn exactly as steep as the Gaussian flank: a focused flat-top is diffraction-limited by the same optics, so its edge is not sharper than the unshaped focus. The plateau and the ≤ 5 % side-order level illustrate the guaranteed specification.

Depth of focus — the two ranges are the calculated numbers above, drawn on one common z-axis. A flat-top profile holds its uniformity over a shorter range than a Gaussian holds its diameter. The two criteria are different, so read each bar against its own definition rather than as a ratio.

Wavelength λ — the laser wavelength. Standard products cover 343–355 nm, 515–532 nm and 1030–1064 nm.

Input beam Ø (1/e²) — beam diameter at the shaper plane, 1/e² intensity definition. Standard sizes are 2.5, 5 and 8 mm.

Beam quality M² — how close your beam is to a perfect Gaussian (M² = 1 is perfect). This model is valid for M² 1.00 – 1.30; outside that range we assess your case individually.

Focal length f — effective focal length of the focusing optic (thin-lens approximation).

Spot Ø (1/e²) — the focus you would get from the same lens without a shaper: d₀ = 4·λ·f·M² / (π·D).

Rayleigh length z_R — zR = π·w₀² / (M²·λ) with w₀ = d₀/2. The distance from focus at which the beam diameter has grown by √2 — about 41 %.

DOF (2·z_R) — the classic textbook depth of focus, twice the Rayleigh length.

Top-hat spot Ø (1/e²) — diameter of the round flat-top spot, derived from the Gaussian reference through Midel’s measured design model. It is always larger than the unshaped focus; that is the trade-off you pay for a uniform profile.

Effective depth of focus — the z-range over which the top-hat holds its specified profile, also from the design model. It is not the same criterion as the Gaussian 2·z_R (diameter growth) — a flat top is judged on uniformity, which is the stricter test.

Minimum clear aperture — every aperture in your beam path (scanner mirrors, focusing lens, whatever comes last) should be at least 2 × D. Go smaller and the numbers here stop holding.

Performance values are specified for a TEM₀₀ Gaussian input with diffraction-limited wavefront quality at the DOE plane (λ/10 RMS or better) and sufficient clear aperture.

Standard product availability requires both a standard input beam Ø (2.5 / 5 / 8 mm, ±0.05 mm) and a wavelength inside one of the three standard bands. Anything else is a custom design — still feasible, just not off the shelf.

Every design is individually simulated and confirmed before quotation. Treat the numbers here as a first estimate, not as a specification.