S.4 Dual-nuller configuration

Figure S2 shows a configuration that results when additional nullers are added to the individual apertures. In this configuration, each aperture is divided in the pupil plane and its light fed into nulling combiners. The effective baseline for these interferometers is approximately D' = 5 m. The output of these aperture nullers is then fed into the interferometer nuller already described. A second interferometer nuller is added to use the second nulled output of each aperture nuller. Four delay lines are shown in the system, one preceding each input of the aperture nullers. The nullers themselves maintain fixed internal pathlengths for background stability. By adjusting the optical delay lines, all combinations of aperture nulling "on" or "off" and interferometer nulling "on" or "off" can be achieved.

Figure S2:

Block diagram for achromatic dual-nulling (once at each aperture plus once for the 2-telescope interferometer as a whole).

As discussed above, the interferometer nuller cancels most of the starlight, leaving residuals _L (finite stellar diameter) and dL (into which are lumped the leakage terms attributable to path jitter and scintillation). Part of the dust emission also gets nulled, leaving residual Z where ~ 0.5. With their much smaller baseline, the aperture nullers will cancel all the star light [strictly, a factor of (D/D')2 more than provided by the interferometer nuller] as well as some of the exozodiacal emission, leaving residual Z. Signals provided by the various nulling combinations are listed in Table S4.

Table S4: Signals for Various Nulling Combinations

mode	nuller	nuller	signal
(a)	off	on	2S + Z + B
(b)	off	on	S + L S + Z+ B
(c)	on	off	L S + Z + B
(d)	on	on	L S + Z + B

Switching among these combinations requires only changes in pathlength delay, not pointing. It is accomplished by motion of a PZT transducer by 5 µm and can occur quickly. If only OPD modulation external to the nulling interferometers is used the background does not change; thus, this approach can be used as a source chopper in order to calibrate the background. This procedure is essential to allow detection of faint exozodiacal signals.

The same approach can also be used to calibrate the random star leakage. For changes in the instrument background and star leakage slower than the chop rate, the difference between modes (b) - (d) is a "white noise" process which should average out with integration time as 1/t. In addition, since S >> Z, mode (a) can be used to calibrate S, which, along with knowledge of the star's diameter, can be used to calibrate the exozodiacal excess. This dual-nuller approach therefore should allow the detection of a weak exozodiacal signal embedded in a strong background.