Correction: Wang et al. Optical Frequency Transfer on the Order of 10⁻¹⁹ Fractional Frequency Instability over a 64 m Free-Space Link. Photonics 2024, 11, 587

Text Corrections

In the original publication [1], there were some text errors.

(1) Replacing “3.07 × 10⁻¹⁹” with “1.94 × 10⁻¹⁹”. This error appears three times in the article. This modification makes the data consistent with Figure 2. We believe that this revision, necessary due to our clerical error, is very important to the article.

1. A correction has been made to the “Abstract”:

The fractional frequency transfer instability during free running is 9.50 × 10⁻¹⁶ at 1 s, and 4.44 × 10⁻¹⁶ at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10⁻¹⁷ at 1 s, 1.94 × 10⁻¹⁹ at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison.

2. A correction has been made to “3. Results and Discussion”, “3.1. Frequency Instability Performance Evaluation”, Paragraph 3:

In the 2000 s, the MDEV drops to 1.94 × 10⁻¹⁹.

3. A correction has been made to “4. Conclusions”, Paragraph 2:

The experiment shows that compared with free running, after adopting active phase noise compensation at the sender, the MDEV is 7.10 × 10⁻¹⁷ when the integration time is 1 s, and MDEV decreases to 1.94 × 10⁻¹⁹ when the integration time is 2000 s.

(2) Replacing “7.11 × 10⁻¹⁷ at 1 s, and 8.06 × 10⁻¹⁹ at 2000 s” with “7.10 × 10⁻¹⁷ at 1 s, and 1.94 × 10⁻¹⁹ at 2000 s”. This modification has been carried out because the description of the fractional frequency instability in the previous and subsequent articles is the value of the MDEV, in order to unify the data types in the whole paper. We think this change is very important to ensure the reader’s understanding. A correction has been made to “1. Introduction”, Paragraph 4:

The fractional frequency instability of the free-space optical frequency transfer link through 64 m can reach 7.10 × 10⁻¹⁷ at 1 s, and 1.94 × 10⁻¹⁹ at 2000 s, which can support the frequency transfer and the comparison of optical clocks.

(3) Replacing $V_4=\cos (2{\omega }_{1}t)$ with $V_5=\cos (2{\omega }_{1}t)$. A correction has been made to “2. Experimental Methods”, “2.1. Experimental Principle”, Paragraph 7:

After mixing the signals $V_4$ with $V_5=\cos (2{\omega }_{1}t)$ from the microwave source and filtering, an error signal V is generated to control the VCO:

(4) Replacing “National Timing Service Center (NTSC)” with “National Time Service Center (NTSC)”. A correction has been made to “1. Introduction”, Paragraph 3:

In addition, the principle prototype of strontium atomic optical clocks for space stations developed by the National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS) has realized a closed-loop operation.

(5) Deleting the extra parentheses in Equation (7). The corrected Equation (7) appears below:

$$V_2=\cos ({\omega }_{0}t+{\omega }_{1}t+\phi +{\phi }_p+{\phi }_1)=\cos [({\omega }_0+{\omega }_1)t+\phi +D]$$

(7)

(6) Replacing “Modified Allan Variance (MDEV)” with “Modified Allan Deviation (MDEV)“. A correction has been made to “3. Results and Discussion”, “3.1. Frequency Instability Performance Evaluation”, Paragraph 2:

We used the Modified Allan Deviation (MDEV) to characterize the additional fractional frequency instability of the link.

(7) Replacing “2.8 MHz” with “2.8 mHz”. A correction has been made to “3. Results and Discussion”, “3.2. Analysis of Optical Frequency Transfer Accuracy”, Paragraph 1:

The arithmetic mean of the total 144 data points is 35.8 μHz (1.85 × 10⁻¹⁹) and the standard deviation is 2.8 mHz (1.45 × 10⁻¹⁷).

Error in Figure

In the original publication [1], there was an error in Figure 2. Replacing MADEV with MDEV, the corrected Figure 2 appears below:

Figure 2. Additional fractional frequency instability diagram of 64 m indoor space laser frequency transfer experiment link.

Figure 2. Additional fractional frequency instability diagram of 64 m indoor space laser frequency transfer experiment link.

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.