FAST Radio Telescope 2D: Collecting Area & Signal Detection

Dish

Diameter D 25 m

Observation

Integration time t 60 s

Source flux density S 80 mJy

Detection readout

Ambiguous

Collecting area A

–

SNR

–

SEFD

–

Min. detectable ΔS

–

Time to SNR = 7 (confident)

–

The radiometer equation

Collecting area grows with the dish's radius squared, so a bigger mirror gathers proportionally more signal power for the same faint source:

A = π(D/2)²          (geometric area)
Aeff = η·A            (η ≈ 0.7 illumination efficiency)
SEFD = 2kB·Tsys / Aeff   (system equiv. flux density)
ΔSmin = SEFD / √(2·B·t)  (radiometer equation)
SNR = S / ΔSmin ∝ A·√t / √Tsys

kB is Boltzmann's constant, Tsys the receiver's system temperature (fixed here at 20 K, a cooled-receiver value close to FAST's own), B the search bandwidth (400 MHz) and t the integration time. Doubling the diameter quadruples A and quadruples SNR; doubling t only buys √2 more SNR — area wins far faster than patience. FAST's real 500 m dish has 400× the area of a 25 m dish, which is why it can pull sources roughly 400× fainter out of the noise in the same integration time.

SNR below ~3: indistinguishable from noise
SNR 3–7: marginal, needs more integration time to confirm
SNR above ~7: confident detection

This model illuminates the full dial-in diameter for clarity; the real FAST reflector actively reshapes only ~300 m of its 500 m surface into a paraboloid at any one pointing, which is why its published SEFD (~24 Jy) is higher than the idealized full-aperture number here.

Current dish FAST 500 m reference Detection threshold (SNR 7)