Table I
Comparison of FS and SA
Dominant noise term | Detector background D ≫ M + BΔω | Background light BΔω ≫ M + D | Narrowband background M ≫ BΔω + D |
---|
Γθf/Γθs |
|
|
|
ρθ,Rf/ρθ,Rs | ∽1 | ∽1 | ∽1 |
ρθ,Mf/ρθ,Ms | ≫1 | ≫1 | ≫1 |
Note: Γ
θ is the Fisher number for
θ. Subscript
f indicates FS; subscript s indicates SA.
ρ is a correlation coefficient. A large Fisher number infers a good estimate, a large
ρ indicates that lack of knowledge about a secondary parameter (
R or
M) has a large (negative) effect on the estimation of
θ. It is assumed that SA is done in parallel, if not Γ
θ,s must be divided by the number
N of spectral values; the ratio Γ
θf/Γ
θs is then enhanced in favor of FS.
Table II
Performance of Different Filters
| Γθ | ρ | Ta |
---|
Optimum rectangular filter (no implementation given) |
| | |
FS derived filter, a two-arm interferometer 1 |
| >0.2 | T |
Gaussian filters |
| >0.2 | T/2 |
FS derived filter, a two-arm interferometer 2 |
| >0.27 | T/2 |
Note: Δ
ω can be considered as a prefilter bandwidth that necessarily is larger than √
θ. In general there is an optimum Δ
ω. It has been assumed here that Δ
ω ≫ √
θ.
Ta is the averaging time and
T the observation, or measuring time. For the three first filters it is assumed that
R ≪ 2
BΔ
ω +
D.