Imaging properties of rotating nulling interferometers

Oliver P. Lay

doi:10.1364/AO.44.005859

Imaging properties of rotating nulling interferometers

Oliver P. Lay

Applied Optics
Vol. 44,
Issue 28,
pp. 5859-5871
(2005)
•doi: 10.1364/AO.44.005859

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Oliver P. Lay, "Imaging properties of rotating nulling interferometers," Appl. Opt. 44, 5859-5871 (2005)

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Abstract

Nulling interferometers combine on-axis suppression with high angular resolution, making them ideal instruments for the direct detection of faint planets close to their parent star. The synthesized point-spread function for a rotating nulling interferometer utilizing phase chopping is shown to consist of a main peak, satellite peaks, and their associated sidelobes, and simple analytic expressions are derived for the modulation efficiency and angular resolution. Sufficient angular resolution is vital for the detection and characterization of multiple-planet systems and requires that some configurations be substantially larger than previously thought. The corresponding increase in stellar leakage has a major effect on performance and can be a deciding factor in the choice of array configuration.

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Collector j	X_j (m)	Y_j (m)	a_j (m²)	η_opt,_j	η_opt,_j	A_j (m)	ϕ_j (rad)
1	−40	20	10	0.1	0.25	0.5	0
2	−40	−20	10	0.1	0.25	0.5	π
3	40	20	10	0.1	0.25	0.5	π/2
4	40	−20	10	0.1	0.25	0.5	3π/2

Distinct Baselines	Contributions (jk)	Baseline Length (m)	sin ϕ_jk	Baseline Type	C_i
1	13, 31, 24, 42	80	±1	Imaging	4A²
2	12, 21, 34, 43	40	0	Nulling	0
3	23, 32	89	±1	Imaging	2A²
4	14, 42	89	±1	Imaging	2A²

		Collector Position								Array Size

Configuration	j	X_j (L)	Yj (L)	Amplitude A_j (m)	Phase ϕ_j (rad)	Modulation Efficiency η_mod∞	IWA θ_IWA (λ/L)	FWHM θ_FWHM (λ/L)	Number of Peaks in PSF	L_IWA (m)	L_res (m)	Stellar Leak (m⁴)
X-Array 2:1	1	−0.45	0.22	0.5	0
	2	−0.45	−0.22	0.5	π	0.22	0.9	0.51	14	62	71	506
	3	0.45	0.22	0.5	π/2
	4	0.45	−0.22	0.5	3π/2
X-Array 3:1	1	−0.47	0.16	0.5	0
	2	−0.47	−0.16	0.5	π	0.22	1.3	0.50	14	86	68	378
	3	0.47	0.16	0.5	π/2
	4	0.47	−0.16	0.5	3π/2
Linear DCB A	1	−0.50	0	0.5	0
	2	−0.17	0	0.5	π	0.22	1.1	0.72	14	76	99	543
	3	0.17	0	0.5	π/2
	4	0.50	0	0.5	3π/2
Linear DCB B	1	−0.50	0	0.5	0
	2	−0.17	0	0.5	π/2	0.28	0.6	1.20	6	41	165	6067
	3	0.17	0	0.5	π
	4	0.50	0	0.5	3π/2
Diamond DCB	1	−0.29	0	0.5	0
	2	0	0.50	0.5	π	0.22	0.7	0.74	14	48	102	1735
	3	0	−0.50	0.5	π/2
	4	0.29	0	0.5	3π/2
Z-Array	1	−0.23	0.45	0.5	0
	2	0.075	0.45	0.5	π	0.22	1.3	0.53	14	89	72	355
	3	−0.075	−0.45	0.5	π/2
	4	0.23	−0.45	0.5	3π/2
Linear-3	1	−0.50	0	0.56	0
	2	0	0	0.56	2π/3	0.29	0.6	0.80	6	41	110	2816
	3	0.50	0	0.56	4π/3
Triangle	1	−0.5	0	0.56	0
	2	0	0.87	0.56	2π/3	0.22	0.5	0.48	14	34	66	2028
	3	0.5	0	0.56	4π/3

Collector j	X_j (m)	Y_j (m)	a_j (m²)	η_opt,_j	η_opt,_j	A_j (m)	ϕ_j (rad)
1	−40	20	10	0.1	0.25	0.5	0
2	−40	−20	10	0.1	0.25	0.5	π
3	40	20	10	0.1	0.25	0.5	π/2
4	40	−20	10	0.1	0.25	0.5	3π/2

Distinct Baselines	Contributions (jk)	Baseline Length (m)	sin ϕ_jk	Baseline Type	C_i
1	13, 31, 24, 42	80	±1	Imaging	4A²
2	12, 21, 34, 43	40	0	Nulling	0
3	23, 32	89	±1	Imaging	2A²
4	14, 42	89	±1	Imaging	2A²

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