Abstract

We theoretically and experimentally examined the effects of the different positions between receiving lens (RL) and detector, namely, defocus, off-axis, and tilt, on the time-domain pulsed echo laser profile (TDPELP). Results show that distortions including saturation and broadening of TDPELP are obtained, regardless of the position between RL and detector. Thus, we adjust the focal length of RL to successfully obtain an optimal TDPELP using tunable lens under extreme situations, such as too strong or too weak intensity of the TDPELP.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (4)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

J. Cao, Q. Hao, Y. Cheng, Y. Peng, K. Zhang, J. Mu, and P. Wang, “Differential time domain method improves performance of pulsed laser ranging and three-dimensional imaging,” Appl. Opt. 55(2), 360–367 (2016).
[Crossref] [PubMed]

Q. Hao, Y. Cheng, J. Cao, F. Zhang, X. Zhang, and H. Yu, “Analytical and numerical approaches to study echo laser pulse profile affected by target and atmospheric turbulence,” Opt. Express 24(22), 25026–25042 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (3)

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Q. Hao, J. Cao, Y. Hu, Y. Yang, K. Li, and T. Li, “Differential optical-path approach to improve signal-to-noise ratio of pulsed-laser range finding,” Opt. Express 22(1), 563–575 (2014).
[Crossref] [PubMed]

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

2012 (2)

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
[Crossref]

W. Armbruster and M. Hammer, “Segmentation, classification, and pose estimation of maritime targets inflash-ladar imagery,” Proc. SPIE 8542, 11079–11090 (2012).

2011 (1)

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

2010 (3)

Y. Li and Z. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18(16), 16788–16796 (2010).
[Crossref] [PubMed]

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

B. Schwarz, “LIDAR: Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

2009 (1)

S. E. Johnson, “Effect of target surface orientation on the range precision of laser detection and ranging systems,” J. Appl. Remote Sens. 3(1), 033564 (2009).
[Crossref]

2005 (1)

2001 (1)

T. Ruotsalainen, P. Palojarvi, and J. Kostamovaara, “A wide dynamic range receiver channel for a pulsed time-of-flight laser radar,” IEEE J. Solid-State Circuits 36(8), 1228–1238 (2001).
[Crossref]

2000 (1)

Eberly, “Intersection of ellipses,” Geom. Tools 200, 1998–2008 (2000).

1996 (1)

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

1993 (1)

Amiranoff, F.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Antonetti, A.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Arbat, A.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Armbruster, W.

W. Armbruster and M. Hammer, “Segmentation, classification, and pose estimation of maritime targets inflash-ladar imagery,” Proc. SPIE 8542, 11079–11090 (2012).

Audebert, P.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Cao, J.

Chen, H.

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Chen, M.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Cheng, Y.

Cheng, Z.

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

Choi, H.

Chryssolouris, G.

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

Chu, Y.

Comerma, A.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Deen, M. J.

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

Dieguez, A.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Eberly,

Eberly, “Intersection of ellipses,” Geom. Tools 200, 1998–2008 (2000).

Faccio, D.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Fysikopoulos, A.

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

Gan, Z.

Gariepy, G.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Garrido, L.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Gascon, D.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Gauthier, J. C.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Geindre, J. P.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Gong, W.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Grillon, G.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Hammer, M.

W. Armbruster and M. Hammer, “Segmentation, classification, and pose estimation of maritime targets inflash-ladar imagery,” Proc. SPIE 8542, 11079–11090 (2012).

Han, S.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Han, Y.

Hao, Q.

Henderson, R.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Hu, Y.

Johnson, S. E.

S. E. Johnson, “Effect of target surface orientation on the range precision of laser detection and ranging systems,” J. Appl. Remote Sens. 3(1), 033564 (2009).
[Crossref]

Kavehrad, M.

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Kim, S.

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kim, S. W.

Kim, Y.

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kostamovaara, J.

T. Ruotsalainen, P. Palojarvi, and J. Kostamovaara, “A wide dynamic range receiver channel for a pulsed time-of-flight laser radar,” IEEE J. Solid-State Circuits 36(8), 1228–1238 (2001).
[Crossref]

K. Määttä, J. Kostamovaara, and R. Myllylä, “Profiling of hot surfaces by pulsed time-of-flight laser range finder techniques,” Appl. Opt. 32(27), 5334–5347 (1993).
[Crossref] [PubMed]

Kwon, O.

Leach, J.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Lee, J.

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, K.

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, S.

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Li, K.

Li, T.

Li, Y.

Liang, X.

Lou, Y.

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Määttä, K.

Marquès, J. R.

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

McManamon, P. F.

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
[Crossref]

Mu, J.

Myllylä, R.

Oh, J. S.

Palojarvi, P.

T. Ruotsalainen, P. Palojarvi, and J. Kostamovaara, “A wide dynamic range receiver channel for a pulsed time-of-flight laser radar,” IEEE J. Solid-State Circuits 36(8), 1228–1238 (2001).
[Crossref]

Pastras, G.

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

Peng, H.

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

Peng, Y.

Ruotsalainen, T.

T. Ruotsalainen, P. Palojarvi, and J. Kostamovaara, “A wide dynamic range receiver channel for a pulsed time-of-flight laser radar,” IEEE J. Solid-State Circuits 36(8), 1228–1238 (2001).
[Crossref]

Schwarz, B.

B. Schwarz, “LIDAR: Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

Shim, Y. B.

Stavropoulos, P.

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

Tonolini, F.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Trenado, J.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Vilà, J.

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Wang, P.

Wu, Z.

Xu, L.

Xu, W.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Yang, H.

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Yang, Y.

Yu, H.

Yu, L.

Zhang, F.

Zhang, K.

Zhang, X.

Zhao, C.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Zheng, X.

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

Appl. Opt. (3)

Geom. Tools (1)

Eberly, “Intersection of ellipses,” Geom. Tools 200, 1998–2008 (2000).

IEEE J. Solid-State Circuits (1)

T. Ruotsalainen, P. Palojarvi, and J. Kostamovaara, “A wide dynamic range receiver channel for a pulsed time-of-flight laser radar,” IEEE J. Solid-State Circuits 36(8), 1228–1238 (2001).
[Crossref]

IEEE Trans. Electron Dev. (1)

Z. Cheng, X. Zheng, M. J. Deen, and H. Peng, “Recent developments and design challenges of high-performance ring oscillator CMOS time-to-digital converters,” IEEE Trans. Electron Dev. 63(1), 235–251 (2016).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

G. Pastras, A. Fysikopoulos, P. Stavropoulos, and G. Chryssolouris, “An approach to modelling evaporation pulsed laser drilling and its energy efficiency,” Int. J. Adv. Manuf. Technol. 72(9–12), 1227–1241 (2014).
[Crossref]

J. Appl. Remote Sens. (1)

S. E. Johnson, “Effect of target surface orientation on the range precision of laser detection and ranging systems,” J. Appl. Remote Sens. 3(1), 033564 (2009).
[Crossref]

J. Opt. Soc. Korea (1)

Nat. Photonics (3)

J. Lee, Y. Kim, K. Lee, S. Lee, and S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

B. Schwarz, “LIDAR: Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Opt. Eng. (1)

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

H. Chen, H. Yang, M. Kavehrad, and Y. Lou, “Time-dependent scintillations of pulsed Gaussian-beam waves propagating in generalized atmospheric turbulence,” Opt. Laser Technol. 61, 8–14 (2014).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. R. Marquès, J. P. Geindre, F. Amiranoff, P. Audebert, J. C. Gauthier, A. Antonetti, and G. Grillon, “Temporal and spatial measurements of the electron density perturbation produced in the wake of an ultrashort laser pulse,” Phys. Rev. Lett. 76(19), 3566–3569 (1996).
[Crossref] [PubMed]

Proc. SPIE (1)

W. Armbruster and M. Hammer, “Segmentation, classification, and pose estimation of maritime targets inflash-ladar imagery,” Proc. SPIE 8542, 11079–11090 (2012).

Sci. Rep. (1)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref] [PubMed]

Sen. Act. A (1)

J. Vilà, J. Trenado, A. Arbat, A. Comerma, D. Gascon, L. Garrido, and A. Dieguez, “Characterization and simulation of Avalanche PhotoDiodes for next-generation colliders,” Sen. Act. A 172(1), 181–188 (2011).
[Crossref]

Other (1)

R. D. Richmond and S. C. Cain, Direct-detection LADAR Systems (SPIE, 2010).

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Figures (12)

Fig. 1
Fig. 1 Principle of forming the time-domain pulsed echo laser profile (TDPELP).
Fig. 2
Fig. 2 Positions between receiving lens (RL) and avalanche photodiode (APD) under focused and defocused conditions. (a) Several typical positions between the RL and APD. (b) Corresponding cross-sections of APD and TDPELP.
Fig. 3
Fig. 3 Effects of different off-axis conditions on the TDPELP. (a)△d < (D/2)– r0. (b) Overlap between the active area of APD, i.e. (D/2)–r0<△d<(D/2) + r0. (c) TDPELP and the active area of APD are tangent, i.e., △d = (D/2) + r0. (d) The spot leaving from the active area of APD, i.e., △d>(D/2) + r0. (e) Details on the overlap of (b).
Fig. 4
Fig. 4 Relative positions between RL and APD under tilted APD or RL (a) Tilt angle between RL and APD. (b) △b≤(D/2)–a. (c) (D/2)–a <△b<(D/2) + a. (d) and (e) are situations when △b≥(D/2) + a. (f) Details on the overlap of (c).
Fig. 5
Fig. 5 Experimental setup and components. FWG-function wave generator, PL-pulsed laser, TL-transmitting lens, DR-diffused reflector, RL-receiving lens, and APD-avalanche photo diode.
Fig. 6
Fig. 6 Comparison of simulation and experimental results of the TDPELP under diverse cases. (a) Experimental results under different △l values. (b) and (f) are the cases when △l is ± 20 mm. (c) and (e) are cases when △l is ± 10 mm. (d) is the case for the focal position.
Fig. 7
Fig. 7 Comparison of simulations and experimental results under off-axis case. (a) △d increases from 0.1 mm to 1.6 mm. (b) Δd = 1.6 mm.
Fig. 8
Fig. 8 Comparison of simulations and experimental results with tilt angle between the RL and APD. (a) when α is increased from 0.5° to 1.75°. (d) when α is 0.75°.
Fig. 9
Fig. 9 TDPELPs under combined defocus and off-axis cases. (a) Experimental diagram. (b) TDPELs under different △d values when the distance between RL and APD is 144 mm, i.e., defocused case.
Fig. 10
Fig. 10 Experiments under the combined effects of defocus, off-axis, and tilt angles between the RL and APD. (a) Experimental diagram. (b) Experimental results under combined effects with different △d values when the distance between the RL and APD is 144 mm, and tilt angle is 0.5°.
Fig. 11
Fig. 11 Adjusting the TDPELP under strong and weak situations.
Fig. 12
Fig. 12 Two features of TDPELP are affected by the relative positions between the tunable RL and APD. (a) Amplitude of TDPELP versus displacement. (b) Width of TDPELP versus displacement. Comparison of the simulation and experimental results at attenuation rate of [(c) and (d)] 0.4 and [(e) and (f)] 0.7.

Equations (20)

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P t ( t ) = E t τ 2 π exp ( t 2 2 τ 2 ) ,
P i l l u ( t ) = T o t T a E t τ 2 π exp [ 1 2 τ 2 ( t R c ) 2 ] ,
P s ( t ) = ( ρ r / π ) P i l l u ( t R / c ) A t ,
P r ( t ) = P s ( t R / c ) S r e c S i l l u R 2 T o t T o r T a η D ,
P r ( t ) = E t τ r 2 π exp [ 1 2 τ r 2 ( t 2 R c ) 2 ] ρ r D 2 S i l l u S r e c π R 2 T o T a 2 η D ,
{ P r ( t ) = E t T a 2 T o ρ r D 2 S r e c η D π R 2 2 π τ r S i l l u exp [ 1 2 τ r 2 ( t 2 R c ) 2 ] τ r 2 = [ τ 2 + tan 2 ( θ ) w 2 ( z ) c 2 ] + k τ 2 w ( z ) = w 0 [ 1 + ( λ z π w 0 2 ) 2 ] 1 / 2 ,
P r d ' ( t ) = P r ( t ) 1 + ( λ ( f Δ l ) / π r 0 2 ) 2 = E t τ 2 π exp [ 1 2 τ r 2 ( t 2 R c ) 2 ] ρ r D 2 S i l l u S r e c π R 2 T o T a 2 η D 1 1 + ( λ ( f Δ l ) / π r 0 2 ) 2 ,
{ S O 1 A B = D 2 θ 1 / 8 S Δ O 1 A C = D 2 sin ( θ 1 ) cos ( θ 1 ) / 8 S A B C = D 2 [ θ 1 sin ( θ 1 ) cos ( θ 1 ) ] / 8 .
{ S O 2 A D = r 0 2 θ 2 / 8 S Δ O 2 A C = r 0 2 sin ( θ 2 ) cos ( θ 2 ) / 8 S A D C = r 0 2 [ θ 2 sin ( θ 2 ) cos ( θ 2 ) ] / 8 .
{ θ 1 = arc cos [ ( D 2 / 4 + Δ d 2 r 0 2 ) / D Δ d ] θ 2 = arc cos [ ( r 0 2 + Δ d 2 D 2 / 4 ) / 2 r 0 Δ d ] .
2 S A D B = r 0 2 [ arc cos ( r 0 2 + Δ d 2 D 2 / 4 2 r 0 Δ d ) ] r 0 2 + Δ d 2 D 2 / 4 2 r 0 Δ d 1 ( r 0 2 + Δ d 2 D 2 / 4 2 r 0 Δ d ) 2 + D 2 4 [ arc cos ( D 2 / 4 + Δ d 2 r 0 2 D Δ d ) D 2 / 4 + Δ d 2 r 0 2 D Δ d 1 ( D 2 / 4 + Δ d 2 r 0 2 D Δ d ) 2 ] .
{ P r o ' ( t ) = P r ( t ) , Δ d D / 2 r 0 P r o ' ( t ) = ( 2 S A D B π r 0 2 ) 2 P r ( t ) , D / 2 r 0 < Δ d < D / 2 + r 0 P r o ' ( t ) = 0 , Δ d D / 2 + r 0 .
{ x 2 a 2 + y 2 b 2 = 1 ( x + Δ b ) 2 + y 2 = ( D / 2 ) 2 .
{ x = a ( a 2 b 2 ) ( D / 2 ) 2 + b 4 a 2 b 2 + b 2 Δ b 2 Δ b a 2 a 2 b 2 y = ± ( D / 2 ) 2 ( Δ b + x ) 2 .
Δ b + x = a ( a 2 b 2 ) ( D / 2 ) 2 + b 4 a 2 b 2 + b 2 Δ b 2 Δ b b 2 a 2 b 2 .
{ Δ b = [ d cos ( α ) + cot ( β ) d sin ( α ) ] [ f d f d cos ( α ) ] + [ 2 f sin ( α ) 2 cot ( β ) f cos ( α ) ] 2 f 2 sin ( α ) [ d cos ( α ) + cot ( β ) d sin ( α ) ] 2 [ 2 f sin ( α ) 2 cot ( β ) f cos ( α ) ] 2 a = 1 sin ( β ) 2 [ d cos ( α ) + cot ( β ) d sin ( α ) ] 2 f sin 2 ( α ) + 2 [ 2 f 2 sin ( α ) cot ( β ) 2 f cos ( α ) ] [ f d f d cos ( α ) ] [ d cos ( α ) + cot ( β ) d sin ( α ) ] 2 [ 2 f sin ( α ) 2 cot ( β ) f cos ( α ) ] 2 b = d 2 f [ Δ b cot ( β ) + f f cos ( α ) ] .
{ γ 1 = arc sin ( 2 | y | / D ) γ 2 = arc tan ( | y | / | x | ) .
{ S H E G = 0 γ 2 [ ( a b ) 2 / 2 ] a 2 cos 2 ( θ ) + b 2 sin 2 ( θ ) d θ 1 2 ( | x y | ) S E F G = 1 2 [ ( D / 2 ) 2 γ 1 ( Δ b | x | ) | y | ] .
S l a p = 2 ( S H E G + S E F G ) .
{ P r t ' ( t ) = P r ( t ) , Δ b D / 2 a P r t ' ( t ) = ( S l a p π a b ) 2 P r ( t ) , D / 2 a < Δ b < D / 2 + a P r t ' ( t ) = 0 , Δ b D / 2 + a .

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