Assessment of a Rubidium ESFADOF Edge-Filter as ... - tuprints

4.4 Data Acquisition and Evaluation 85
Inserting Eqs. 4.11 and 4.12 into Eq. 4.13 results in
√
∣ ∣ ∣
∆T S,P = ∣∆ ˜T S,P 2 ∣∣∣ ∆κ
2
+ T S,P κ ∣ , (4.14)
which allows an estimation of the maximum observed transmission error:
1. P-Polarized spectra: The fact, that T P ≤ 1 and ∆κ
κ
≤ ∆ ˜T P results in the following
upper limit for the error of the absolute P-polarized transmission:
√ ∣∣ ∣
∆T P ≤ ∆ ˜T P 2 ∣ ∣
+ ∆ ˜T P 2
≤ √ 2 max(∆ ˜T P ). (4.15)
2. S-Polarized spectra: As T S ≪ 1, it is more accurate to insert the maximum
achieved transmission, max(T S ), while keeping ∆κ
κ
≤ ∆ ˜T P . Thus, the following
upper limit for the error of the absolute S-polarized transmission results:
∆T S ≤
√ ∣∣
∆ ˜T S
∣ ∣
2 +
∣ ∣max(TS ) max(∆ ˜T P ) ∣ ∣ 2 . (4.16)
Fig. 4.11 shows typical values for ∆ ˜T P and ∆ ˜T S . By inserting
max(∆ ˜T P ) = 1.0 × 10 -3 and max(∆ ˜T S ) = 1.6 × 10 -4 into Eqs. 4.15 and 4.16, the
following upper error estimations result:
∆T P ≤ 1.4 × 10 -3 and (4.17)
∆T S ≤ 2.3 × 10 -4 . (4.18)
Within this thesis, all quoted transmission errors have been obtained by this
procedure.