A nulling interferometer combines light from two collectors with a half-wave (180°) phase shift on one arm, so on-axis starlight (angle θ = 0) always interferes destructively. Off-axis light — from an orbiting planet — arrives with a path-length difference and only partially cancels. For a baseline B and wavelength λ, the transmission at angle θ projected onto the baseline is:
T(θ) = sin²(π B θ / λ)
The LIFE mission concept (Large Interferometer For Exoplanets) flies four free-flying collector spacecraft — two long-baseline pairs at 90° — around a central beam-combiner, forming an X-array. Combining the two orthogonal Bracewell baselines gives a 2D transmission map:
T(u,v) = sin²(πBu/λ) · sin²(π(B/2)v/λ)
u(t) = θₚ·cos(γₚ − Ωt), v(t) = θₚ·sin(γₚ − Ωt)
Because the star sits at u = v = 0, it stays nulled at every rotation angle. The planet, at fixed separation θₚ and position angle γₚ ≈ 35° here, sweeps through the fringe pattern as the whole formation rotates at rate Ω — its transmitted flux rises and falls once per rotation. That periodic modulation, synchronous with the known rotation rate, is what lets the instrument pull a faint planet signal out of instrumental and zodiacal-light noise that does not modulate the same way.
- Baseline B — longer baselines narrow the fringe spacing, sharpening resolution but also shrinking the "sweet spot" angle where transmission peaks near 100%.
- Wavelength λ — LIFE observes 4–18.5 μm thermal infrared, covering CO₂ (15 μm), O₃ (9.6 μm) and H₂O bands used to weigh biotic O₂/O₃ against abiotic false positives (photolysis-driven O₂ on a planet with no liquid water, for example).
- Residual leakage — real stars have a finite angular size (θ⋆ here fixed at 0.6 mas), so the null is never perfectly zero; it is estimated as sin²(πBθ⋆/λ).
This is a simplified, single-epoch illustration of the Bracewell rotating-baseline principle — the real LIFE design combines more than one baseline pair and integrates over many rotations to beat down noise, but the destructive-interference formula above is the exact physics each baseline uses.