Inter-dependencies

Tables of dependencies for the terms described in this document. Only direct inter-dependencies are listed in Tables 6 and 7, while Tables 8 and 9 include all interdependencies. The tables are include one row per item in the error calculations. For Tables 6 and 8 the right-hand column give the other error terms that the term in this row is dependent on. For Tables 7 and 9 the right-hand column give the other error terms which depend on the term in this row.

At present these dependencies are only available in tabular form, but it is hoped that a graphical description of the dependencies will be produced at a later date.

表 6: Table including only direct dependencies of each error term.
Term Section of this document Other terms this is dependent on (and the appropriate section numbers)

Wavefront amplitude and phase fluctuations above M1 4 Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Position and separation of stars (L), Observing parameters (N).

Wavefront corrugations before and after the StS 5 Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C). Performance of STRAP (G),

Wavefront corrugations before VCM 6 Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C).

Wavefront corrugations before FSU spatial filter 7 Wavefront corrugations before VCM (6), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C).

Internal vibration in the VLTI 8 Seismic Activity (H).

Atmospheric scintillation and thermal background fluctuations 9 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Drift in image plane VCMs (13), Thermal loading in the VLTI (B), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F).

Effect of detector noise and photon shot noise 10 Observing parameters (N).

Refractive index of air and colour of correlated flux 12 Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Model for the refractive index of air (I), Observing parameters (N).

Drift in image plane VCMs 13 Large scale structure in the atmosphere above Paranal (E).

Variation in VLTI fundamental length calibration 14 Large scale structure in the atmosphere above Paranal (E).

VLTI baseline geometry 15 Wavefront amplitude and phase fluctuations above M1 (4), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Large scale structure in the atmosphere above Paranal (E), Earth rotation model (K).

Systematic differences in baseline length for primary and secondary star 16 Wavefront amplitude and phase fluctuations above M1 (4), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Large scale structure in the atmosphere above Paranal (E).

Galactic effects 17 Position and separation of stars (L).

Solar System effects 18 Position and separation of stars (L), Date and time of the observations (M).

Systematic effects from the atmosphere 19 Large scale structure in the atmosphere above Paranal (E).

Effect of aberrations in image plane optical components 20 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Position error between beam footprints in Star Separator calibration mode (22), Position and separation of stars (L).

Image plane optics in the star separator 21 Wavefront corrugations before and after the StS (5).

Position error between beam footprints in Star Separator calibration mode 22 Large scale structure in the atmosphere above Paranal (E).

Effect of aberrations in pupil plane optical components 23 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Drift in image plane VCMs (13), Position error between beam footprints in Star Separator calibration mode (22), Position and separation of stars (L).

Effect of beam walk on optics before the Star Separator 24 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5).

Systematic errors in the FSU phase 25 Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11).

Total spectral response of PRIMA system 27 Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Spectral Response of PRIMA Hardware (J).

Fringe jumps and group tracking errors 28 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12).

Limiting magnitudes for PRIMA 29 Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Fringe jumps and group tracking errors (28).

Total astrometric error 30 Wavefront corrugations before FSU spatial filter (7), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28).

Temporal and spatial properties of seeing at Paranal A Large scale structure in the atmosphere above Paranal (E).

Internal seeing within the VLTI C Thermal loading in the VLTI (B), Air flow through the VLTI (F).

Isoplanatism at Paranal D Large scale structure in the atmosphere above Paranal (E).

Air flow through the VLTI F Large scale structure in the atmosphere above Paranal (E).

Performance of STRAP G Observing parameters (N).

Earth rotation model K Date and time of the observations (M).

**表 6:** Table including only direct dependencies of each error term.
Term	Section of this document	Other terms this is dependent on (and the appropriate section numbers)
Wavefront amplitude and phase fluctuations above M1	4	Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Position and separation of stars (L), Observing parameters (N).
Wavefront corrugations before and after the StS	5	Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C). Performance of STRAP (G),
Wavefront corrugations before VCM	6	Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C).
Wavefront corrugations before FSU spatial filter	7	Wavefront corrugations before VCM (6), Internal vibration in the VLTI (8), Internal seeing within the VLTI (C).
Internal vibration in the VLTI	8	Seismic Activity (H).
Atmospheric scintillation and thermal background fluctuations	9	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Drift in image plane VCMs (13), Thermal loading in the VLTI (B), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F).
Effect of detector noise and photon shot noise	10	Observing parameters (N).
Refractive index of air and colour of correlated flux	12	Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Model for the refractive index of air (I), Observing parameters (N).
Drift in image plane VCMs	13	Large scale structure in the atmosphere above Paranal (E).
Variation in VLTI fundamental length calibration	14	Large scale structure in the atmosphere above Paranal (E).
VLTI baseline geometry	15	Wavefront amplitude and phase fluctuations above M1 (4), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Large scale structure in the atmosphere above Paranal (E), Earth rotation model (K).
Systematic differences in baseline length for primary and secondary star	16	Wavefront amplitude and phase fluctuations above M1 (4), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Large scale structure in the atmosphere above Paranal (E).
Galactic effects	17	Position and separation of stars (L).
Solar System effects	18	Position and separation of stars (L), Date and time of the observations (M).
Systematic effects from the atmosphere	19	Large scale structure in the atmosphere above Paranal (E).
Effect of aberrations in image plane optical components	20	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Position error between beam footprints in Star Separator calibration mode (22), Position and separation of stars (L).
Image plane optics in the star separator	21	Wavefront corrugations before and after the StS (5).
Position error between beam footprints in Star Separator calibration mode	22	Large scale structure in the atmosphere above Paranal (E).
Effect of aberrations in pupil plane optical components	23	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Drift in image plane VCMs (13), Position error between beam footprints in Star Separator calibration mode (22), Position and separation of stars (L).
Effect of beam walk on optics before the Star Separator	24	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5).
Systematic errors in the FSU phase	25	Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11).
Total spectral response of PRIMA system	27	Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Spectral Response of PRIMA Hardware (J).
Fringe jumps and group tracking errors	28	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12).
Limiting magnitudes for PRIMA	29	Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Fringe jumps and group tracking errors (28).
Total astrometric error	30	Wavefront corrugations before FSU spatial filter (7), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28).
Temporal and spatial properties of seeing at Paranal	A	Large scale structure in the atmosphere above Paranal (E).
Internal seeing within the VLTI	C	Thermal loading in the VLTI (B), Air flow through the VLTI (F).
Isoplanatism at Paranal	D	Large scale structure in the atmosphere above Paranal (E).
Air flow through the VLTI	F	Large scale structure in the atmosphere above Paranal (E).
Performance of STRAP	G	Observing parameters (N).
Earth rotation model	K	Date and time of the observations (M).

表 7: Table including only direct dependencies of each error term.
Term Section of this document Other terms directly dependent on this (and the appropriate section numbers)

Wavefront amplitude and phase fluctuations above M1 4 Wavefront corrugations before and after the StS (5), Atmospheric scintillation and thermal background fluctuations (9), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).

Wavefront corrugations before and after the StS 5 Wavefront corrugations before VCM (6), Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28).

Wavefront corrugations before VCM 6 Wavefront corrugations before FSU spatial filter (7), Effect of aberrations in image plane optical components (20).

Wavefront corrugations before FSU spatial filter 7 Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Total astrometric error (30).

Internal vibration in the VLTI 8 Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).

Atmospheric scintillation and thermal background fluctuations 9 Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).

Effect of detector noise and photon shot noise 10 Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).

Polarisation effects 11 Systematic errors in the FSU phase (25).

Refractive index of air and colour of correlated flux 12 Fringe jumps and group tracking errors (28), Total astrometric error (30).

Drift in image plane VCMs 13 Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in pupil plane optical components (23), Total astrometric error (30).

VLTI baseline geometry 15 Total astrometric error (30).

Systematic differences in baseline length for primary and secondary star 16 Total astrometric error (30).

Galactic effects 17 Total astrometric error (30).

Solar System effects 18 Total astrometric error (30).

Systematic effects from the atmosphere 19 Total astrometric error (30).

Effect of aberrations in image plane optical components 20 Total astrometric error (30).

Image plane optics in the star separator 21 Total astrometric error (30).

Position error between beam footprints in Star Separator calibration mode 22 Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23).

Effect of aberrations in pupil plane optical components 23 Total astrometric error (30).

Effect of beam walk on optics before the Star Separator 24 Total astrometric error (30).

Systematic errors in the FSU phase 25 Total astrometric error (30).

Knowledge of stellar spectra 26 Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16).

Total spectral response of PRIMA system 27 Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16).

Fringe jumps and group tracking errors 28 Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Temporal and spatial properties of seeing at Paranal A Wavefront amplitude and phase fluctuations above M1 (4).

Thermal loading in the VLTI B Atmospheric scintillation and thermal background fluctuations (9), Internal seeing within the VLTI (C).

Internal seeing within the VLTI C Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7).

Isoplanatism at Paranal D Wavefront amplitude and phase fluctuations above M1 (4).

Large scale structure in the atmosphere above Paranal E Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Variation in VLTI fundamental length calibration (14), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic effects from the atmosphere (19), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Air flow through the VLTI (F).

Air flow through the VLTI F Atmospheric scintillation and thermal background fluctuations (9), Internal seeing within the VLTI (C).

Performance of STRAP G Wavefront corrugations before and after the StS (5).

Seismic Activity H Internal vibration in the VLTI (8).

Model for the refractive index of air I Refractive index of air and colour of correlated flux (12).

Spectral Response of PRIMA Hardware J Total spectral response of PRIMA system (27).

Earth rotation model K VLTI baseline geometry (15).

Position and separation of stars L Wavefront amplitude and phase fluctuations above M1 (4), Galactic effects (17), Solar System effects (18), Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23).

Date and time of the observations M Solar System effects (18), Earth rotation model (K).

Observing parameters N Wavefront amplitude and phase fluctuations above M1 (4), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Performance of STRAP (G).

**表 7:** Table including only direct dependencies of each error term.
Term	Section of this document	Other terms directly dependent on this (and the appropriate section numbers)
Wavefront amplitude and phase fluctuations above M1	4	Wavefront corrugations before and after the StS (5), Atmospheric scintillation and thermal background fluctuations (9), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).
Wavefront corrugations before and after the StS	5	Wavefront corrugations before VCM (6), Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28).
Wavefront corrugations before VCM	6	Wavefront corrugations before FSU spatial filter (7), Effect of aberrations in image plane optical components (20).
Wavefront corrugations before FSU spatial filter	7	Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Total astrometric error (30).
Internal vibration in the VLTI	8	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).
Atmospheric scintillation and thermal background fluctuations	9	Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).
Effect of detector noise and photon shot noise	10	Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29).
Polarisation effects	11	Systematic errors in the FSU phase (25).
Refractive index of air and colour of correlated flux	12	Fringe jumps and group tracking errors (28), Total astrometric error (30).
Drift in image plane VCMs	13	Atmospheric scintillation and thermal background fluctuations (9), Effect of aberrations in pupil plane optical components (23), Total astrometric error (30).
VLTI baseline geometry	15	Total astrometric error (30).
Systematic differences in baseline length for primary and secondary star	16	Total astrometric error (30).
Galactic effects	17	Total astrometric error (30).
Solar System effects	18	Total astrometric error (30).
Systematic effects from the atmosphere	19	Total astrometric error (30).
Effect of aberrations in image plane optical components	20	Total astrometric error (30).
Image plane optics in the star separator	21	Total astrometric error (30).
Position error between beam footprints in Star Separator calibration mode	22	Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23).
Effect of aberrations in pupil plane optical components	23	Total astrometric error (30).
Effect of beam walk on optics before the Star Separator	24	Total astrometric error (30).
Systematic errors in the FSU phase	25	Total astrometric error (30).
Knowledge of stellar spectra	26	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16).
Total spectral response of PRIMA system	27	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16).
Fringe jumps and group tracking errors	28	Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Temporal and spatial properties of seeing at Paranal	A	Wavefront amplitude and phase fluctuations above M1 (4).
Thermal loading in the VLTI	B	Atmospheric scintillation and thermal background fluctuations (9), Internal seeing within the VLTI (C).
Internal seeing within the VLTI	C	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7).
Isoplanatism at Paranal	D	Wavefront amplitude and phase fluctuations above M1 (4).
Large scale structure in the atmosphere above Paranal	E	Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Variation in VLTI fundamental length calibration (14), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic effects from the atmosphere (19), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Air flow through the VLTI (F).
Air flow through the VLTI	F	Atmospheric scintillation and thermal background fluctuations (9), Internal seeing within the VLTI (C).
Performance of STRAP	G	Wavefront corrugations before and after the StS (5).
Seismic Activity	H	Internal vibration in the VLTI (8).
Model for the refractive index of air	I	Refractive index of air and colour of correlated flux (12).
Spectral Response of PRIMA Hardware	J	Total spectral response of PRIMA system (27).
Earth rotation model	K	VLTI baseline geometry (15).
Position and separation of stars	L	Wavefront amplitude and phase fluctuations above M1 (4), Galactic effects (17), Solar System effects (18), Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23).
Date and time of the observations	M	Solar System effects (18), Earth rotation model (K).
Observing parameters	N	Wavefront amplitude and phase fluctuations above M1 (4), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Performance of STRAP (G).

表 8: Table of direct and indirect dependencies.
Term Section of this document Terms this is directly or indirectly dependent on (and the appropriate section numbers)

Wavefront amplitude and phase fluctuations above M1 4 Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Position and separation of stars (L), Observing parameters (N).

Wavefront corrugations before and after the StS 5 Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Wavefront corrugations before and after the StS (5).

Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Wavefront corrugations before VCM 6 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Wavefront corrugations before FSU spatial filter 7 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Internal vibration in the VLTI 8 Seismic Activity (H).

Atmospheric scintillation and thermal background fluctuations 9 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Effect of detector noise and photon shot noise 10 Observing parameters (N).

Refractive index of air and colour of correlated flux 12 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).

Drift in image plane VCMs 13 Large scale structure in the atmosphere above Paranal (E).

Variation in VLTI fundamental length calibration 14 Large scale structure in the atmosphere above Paranal (E).

VLTI baseline geometry 15 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Earth rotation model (K), Position and separation of stars (L), Date and time of the observations (M), Observing parameters (N).

Systematic differences in baseline length for primary and secondary star 16 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).

Galactic effects 17 Position and separation of stars (L).

Solar System effects 18 Position and separation of stars (L), Date and time of the observations (M).

Systematic effects from the atmosphere 19 Large scale structure in the atmosphere above Paranal (E).

Effect of aberrations in image plane optical components 20 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Image plane optics in the star separator 21 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Position error between beam footprints in Star Separator calibration mode 22 Large scale structure in the atmosphere above Paranal (E).

Effect of aberrations in pupil plane optical components 23 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Drift in image plane VCMs (13), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Effect of beam walk on optics before the Star Separator 24 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Systematic errors in the FSU phase 25 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).

Total spectral response of PRIMA system 27 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).

Fringe jumps and group tracking errors 28 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).

Limiting magnitudes for PRIMA 29 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).

Total astrometric error 30 Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Position error between beam footprints in Star Separator calibration mode (22), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Earth rotation model (K), Position and separation of stars (L), Date and time of the observations (M), Observing parameters (N).

Temporal and spatial properties of seeing at Paranal A Large scale structure in the atmosphere above Paranal (E).

Internal seeing within the VLTI C Thermal loading in the VLTI (B), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F).

Isoplanatism at Paranal D Large scale structure in the atmosphere above Paranal (E).

Air flow through the VLTI F Large scale structure in the atmosphere above Paranal (E).

Performance of STRAP G Observing parameters (N).

Earth rotation model K Date and time of the observations (M).

**表 8:** Table of direct and indirect dependencies.
Term	Section of this document	Terms this is directly or indirectly dependent on (and the appropriate section numbers)
Wavefront amplitude and phase fluctuations above M1	4	Temporal and spatial properties of seeing at Paranal (A), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Position and separation of stars (L), Observing parameters (N).
Wavefront corrugations before and after the StS	5	Wavefront amplitude and phase fluctuations above M1 (4), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Wavefront corrugations before and after the StS (5).
Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Wavefront corrugations before VCM	6	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Wavefront corrugations before FSU spatial filter	7	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Internal vibration in the VLTI	8	Seismic Activity (H).
Atmospheric scintillation and thermal background fluctuations	9	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Effect of detector noise and photon shot noise	10	Observing parameters (N).
Refractive index of air and colour of correlated flux	12	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).
Drift in image plane VCMs	13	Large scale structure in the atmosphere above Paranal (E).
Variation in VLTI fundamental length calibration	14	Large scale structure in the atmosphere above Paranal (E).
VLTI baseline geometry	15	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Earth rotation model (K), Position and separation of stars (L), Date and time of the observations (M), Observing parameters (N).
Systematic differences in baseline length for primary and secondary star	16	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).
Galactic effects	17	Position and separation of stars (L).
Solar System effects	18	Position and separation of stars (L), Date and time of the observations (M).
Systematic effects from the atmosphere	19	Large scale structure in the atmosphere above Paranal (E).
Effect of aberrations in image plane optical components	20	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Image plane optics in the star separator	21	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Position error between beam footprints in Star Separator calibration mode	22	Large scale structure in the atmosphere above Paranal (E).
Effect of aberrations in pupil plane optical components	23	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Drift in image plane VCMs (13), Position error between beam footprints in Star Separator calibration mode (22), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Effect of beam walk on optics before the Star Separator	24	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Internal vibration in the VLTI (8), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Systematic errors in the FSU phase	25	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Position and separation of stars (L), Observing parameters (N).
Total spectral response of PRIMA system	27	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Drift in image plane VCMs (13), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).
Fringe jumps and group tracking errors	28	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).
Limiting magnitudes for PRIMA	29	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Position and separation of stars (L), Observing parameters (N).
Total astrometric error	30	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Polarisation effects (11), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Position error between beam footprints in Star Separator calibration mode (22), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Knowledge of stellar spectra (26), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Temporal and spatial properties of seeing at Paranal (A), Thermal loading in the VLTI (B), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F), Performance of STRAP (G), Seismic Activity (H), Model for the refractive index of air (I), Spectral Response of PRIMA Hardware (J), Earth rotation model (K), Position and separation of stars (L), Date and time of the observations (M), Observing parameters (N).
Temporal and spatial properties of seeing at Paranal	A	Large scale structure in the atmosphere above Paranal (E).
Internal seeing within the VLTI	C	Thermal loading in the VLTI (B), Large scale structure in the atmosphere above Paranal (E), Air flow through the VLTI (F).
Isoplanatism at Paranal	D	Large scale structure in the atmosphere above Paranal (E).
Air flow through the VLTI	F	Large scale structure in the atmosphere above Paranal (E).
Performance of STRAP	G	Observing parameters (N).
Earth rotation model	K	Date and time of the observations (M).

表 9: Table of direct and indirect dependencies.
Term Section of this document Other terms directly and indirectly dependent on this (and the appropriate section numbers)

Wavefront amplitude and phase fluctuations above M1 4 Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Wavefront corrugations before and after the StS 5 Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Wavefront corrugations before VCM 6 Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Wavefront corrugations before FSU spatial filter 7 Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Internal vibration in the VLTI 8 Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Atmospheric scintillation and thermal background fluctuations 9 Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Effect of detector noise and photon shot noise 10 Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Polarisation effects 11 Systematic errors in the FSU phase (25), Total astrometric error (30).

Refractive index of air and colour of correlated flux 12 Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Drift in image plane VCMs 13 Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in pupil plane optical components (23), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

VLTI baseline geometry 15 Total astrometric error (30).

Systematic differences in baseline length for primary and secondary star 16 Total astrometric error (30).

Galactic effects 17 Total astrometric error (30).

Solar System effects 18 Total astrometric error (30).

Systematic effects from the atmosphere 19 Total astrometric error (30).

Effect of aberrations in image plane optical components 20 Total astrometric error (30).

Image plane optics in the star separator 21 Total astrometric error (30).

Position error between beam footprints in Star Separator calibration mode 22 Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23), Total astrometric error (30).

Effect of aberrations in pupil plane optical components 23 Total astrometric error (30).

Effect of beam walk on optics before the Star Separator 24 Total astrometric error (30).

Systematic errors in the FSU phase 25 Total astrometric error (30).

Knowledge of stellar spectra 26 Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Total spectral response of PRIMA system 27 Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Fringe jumps and group tracking errors 28 Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Temporal and spatial properties of seeing at Paranal A Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Thermal loading in the VLTI B Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Internal seeing within the VLTI (C).

Internal seeing within the VLTI C Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Isoplanatism at Paranal D Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Large scale structure in the atmosphere above Paranal E Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Variation in VLTI fundamental length calibration (14), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Position error between beam footprints in Star Separator calibration mode (22), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Temporal and spatial properties of seeing at Paranal (A), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Air flow through the VLTI (F).

Air flow through the VLTI F Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Internal seeing within the VLTI (C).

Performance of STRAP G Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Seismic Activity H Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Model for the refractive index of air I Refractive index of air and colour of correlated flux (12), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Spectral Response of PRIMA Hardware J Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Earth rotation model K VLTI baseline geometry (15), Total astrometric error (30).

Position and separation of stars L Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).

Date and time of the observations M VLTI baseline geometry (15), Solar System effects (18), Total astrometric error (30), Earth rotation model (K).

Observing parameters N Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Performance of STRAP (G).

**表 9:** Table of direct and indirect dependencies.
Term	Section of this document	Other terms directly and indirectly dependent on this (and the appropriate section numbers)
Wavefront amplitude and phase fluctuations above M1	4	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Wavefront corrugations before and after the StS	5	Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Wavefront corrugations before VCM	6	Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Wavefront corrugations before FSU spatial filter	7	Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Internal vibration in the VLTI	8	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Atmospheric scintillation and thermal background fluctuations	9	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Effect of detector noise and photon shot noise	10	Systematic errors in the FSU phase (25), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Polarisation effects	11	Systematic errors in the FSU phase (25), Total astrometric error (30).
Refractive index of air and colour of correlated flux	12	Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Drift in image plane VCMs	13	Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in pupil plane optical components (23), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
VLTI baseline geometry	15	Total astrometric error (30).
Systematic differences in baseline length for primary and secondary star	16	Total astrometric error (30).
Galactic effects	17	Total astrometric error (30).
Solar System effects	18	Total astrometric error (30).
Systematic effects from the atmosphere	19	Total astrometric error (30).
Effect of aberrations in image plane optical components	20	Total astrometric error (30).
Image plane optics in the star separator	21	Total astrometric error (30).
Position error between beam footprints in Star Separator calibration mode	22	Effect of aberrations in image plane optical components (20), Effect of aberrations in pupil plane optical components (23), Total astrometric error (30).
Effect of aberrations in pupil plane optical components	23	Total astrometric error (30).
Effect of beam walk on optics before the Star Separator	24	Total astrometric error (30).
Systematic errors in the FSU phase	25	Total astrometric error (30).
Knowledge of stellar spectra	26	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Total spectral response of PRIMA system	27	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Fringe jumps and group tracking errors	28	Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Temporal and spatial properties of seeing at Paranal	A	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Thermal loading in the VLTI	B	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Internal seeing within the VLTI (C).
Internal seeing within the VLTI	C	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Isoplanatism at Paranal	D	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Large scale structure in the atmosphere above Paranal	E	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), Drift in image plane VCMs (13), Variation in VLTI fundamental length calibration (14), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Systematic effects from the atmosphere (19), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Position error between beam footprints in Star Separator calibration mode (22), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Temporal and spatial properties of seeing at Paranal (A), Internal seeing within the VLTI (C), Isoplanatism at Paranal (D), Air flow through the VLTI (F).
Air flow through the VLTI	F	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Internal seeing within the VLTI (C).
Performance of STRAP	G	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Seismic Activity	H	Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Internal vibration in the VLTI (8), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Model for the refractive index of air	I	Refractive index of air and colour of correlated flux (12), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Spectral Response of PRIMA Hardware	J	Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Earth rotation model	K	VLTI baseline geometry (15), Total astrometric error (30).
Position and separation of stars	L	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Galactic effects (17), Solar System effects (18), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30).
Date and time of the observations	M	VLTI baseline geometry (15), Solar System effects (18), Total astrometric error (30), Earth rotation model (K).
Observing parameters	N	Wavefront amplitude and phase fluctuations above M1 (4), Wavefront corrugations before and after the StS (5), Wavefront corrugations before VCM (6), Wavefront corrugations before FSU spatial filter (7), Atmospheric scintillation and thermal background fluctuations (9), Effect of detector noise and photon shot noise (10), Refractive index of air and colour of correlated flux (12), VLTI baseline geometry (15), Systematic differences in baseline length for primary and secondary star (16), Effect of aberrations in image plane optical components (20), Image plane optics in the star separator (21), Effect of aberrations in pupil plane optical components (23), Effect of beam walk on optics before the Star Separator (24), Systematic errors in the FSU phase (25), Total spectral response of PRIMA system (27), Fringe jumps and group tracking errors (28), Limiting magnitudes for PRIMA (29), Total astrometric error (30), Performance of STRAP (G).

___oOo___

Robert Tubbs 平成16年11月18日