## Abstract

We demonstrate for the first time the use of digital range-gating in OFDR to allow for orders of magnitude reduction in the required sampling rates. This allows for sensing over long lengths of fiber with fast sweeps of the optical source frequency, without requiring impractical sampling rates. The range-gating is achieved using digitally enhanced interferometry (DI), which isolates individual sections of OFDR signal bandwidth. The reductions in sampling rates permitted by the bandwidth-division are demonstrated both numerically and experimentally.

© 2013 OSA

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### Equations (12)

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(1)
$${\tilde{E}}_{P}={E}_{R1}{e}^{-i\left(\omega (t+{\eta}_{1})t+{\varphi}_{R1}\right)}c(t-{\tau}_{1})+{E}_{R2}{e}^{-i\left(\omega (t+{\eta}_{2})t+{\varphi}_{R2}\right)}c(t-{\tau}_{2})+{E}_{R3}{e}^{-i\left(\omega (t+{\eta}_{3})t+{\varphi}_{R3}\right)}c(t-{\tau}_{3}).$$
(2)
$${\tilde{E}}_{LO}={E}_{L}{e}^{-i(\omega (t+{\eta}_{LO})t+{\varphi}_{LO})}.$$
(3)
$$P(t)={\tilde{E}}_{S}{\tilde{E}}_{S}{}^{*}\stackrel{}{},\stackrel{}{}\stackrel{}{}{\tilde{E}}_{S}={\tilde{E}}_{LO}+{\tilde{E}}_{P}.$$
(4)
$$P(t)\approx 2{E}_{L}{\displaystyle \sum _{j=1}^{N=3}{E}_{Rj}\mathrm{cos}(\omega (t+{\eta}_{j})t-\omega (t+{\eta}_{LO})t+{\varphi}_{Rj}-{\varphi}_{LO})c(t-{\tau}_{j})}.$$
(5)
$$\therefore {P}_{R1}(t)\approx 2{E}_{L}{E}_{R1}\mathrm{cos}(\omega (t+{\eta}_{1})t-\omega (t+{\eta}_{LO})t+{\varphi}_{R1}-{\varphi}_{LO})+{\epsilon}_{R2}+{\epsilon}_{R3}.$$
(6)
$${\epsilon}_{Rj}=2{E}_{L}{E}_{Rj}\mathrm{cos}(\omega (t+{\eta}_{j})t-\omega (t+{\eta}_{LO})t+{\varphi}_{Rj}-{\varphi}_{LO})c(t-{\tau}_{j})c(t-{\tau}_{1}).$$
(7)
$$FFT\left\{\frac{{\epsilon}_{Rj}}{2{E}_{L}{E}_{Rj}}\right\}=FFT\left\{\mathrm{cos}(\omega (t+{\eta}_{j})t-\omega (t+{\eta}_{LO})t+{\varphi}_{Rj}-{\varphi}_{LO})\right\}\otimes FFT\left\{c(t-{\tau}_{j})c(t-{\tau}_{1})\right\}.$$
(8)
$$\overline{FFT}\left\{c(t-{\tau}_{j})c(t-{\tau}_{1})\right\}\cong 2/\sqrt{{t}_{s}{f}_{PRN}},\begin{array}{cc}& \end{array}{t}_{s}\le ({2}^{n}-1)/{f}_{PRN}.$$
(9)
$$\overline{FFT}\left\{c(t-{\tau}_{j})c(t-{\tau}_{1})\right\}\cong 2/\sqrt{{2}^{n}-1}.$$
(10)
$$FFT\left({P}_{R1}(t)\right)=2{E}_{L}{E}_{R1}FFT\left\{\mathrm{cos}({\left[\omega (t+{\eta}_{1})-\omega (t+{\eta}_{LO})\right]}^{}t)\right\}.$$
(11)
$$M=\mathrm{min}\left(\frac{2}{{v}_{g}}L{f}_{PRN},\frac{{f}_{b\mathrm{max}}}{{f}_{s}}\right);\begin{array}{cc}& \end{array}{f}_{s}\ge {f}_{PRN}.$$
(12)
$$N=\frac{2L{\gamma}^{1/2}}{{v}_{g}}\begin{array}{c}\end{array}\begin{array}{c}\text{when}\end{array},\begin{array}{c}\end{array}{f}_{PRN}={f}_{s}={\gamma}^{1/2}.$$