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. 2019 Oct 17;10(11):5755–5775. doi: 10.1364/BOE.10.005755

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Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Fig. 3. — Relative SNR improvement by signal averaging for strong input signals (without noise bias correction). (a) The ratios SNR_CPX/SNR₁ and SNR_MAG/SNR₁ are shown for $N$ from 1 to 100. SNR_MAG/SNR₁ is plotted as a dash-dotted line, whereas the SNR₁-dependent ratio SNR_CPX/SNR₁ is plotted in rainbow colors for several SNR₁ values between 5 dB and 50 dB. Note that SNR_CPX/SNR₁ converges to an N-fold improvement. (b) The ratio ${SNR}_{C P X} / {SNR}_{M A G} = (N - (N - 1) / {SNR}_{1}) / \sqrt{N}$ is plotted for the spectrum of SNR₁ values used in (a). Note that in particular for strong input signals with high SNR₁, complex averaging outperforms magnitude averaging and converges to a $\sqrt{N}$ -fold better SNR performance. As the SNR profiles converge for large SNRs, the curves in (a) and (b) start to overlap for values greater than 15 dB.