Abstract

A pinhole time camera is proposed and analyzed. This instrument is the temporal analog of a conventional pinhole camera and is formed by a succession of dispersion, a time gate, and more dispersion. It is capable of magnifying or demagnifying time waveforms while preserving their envelope profile. The system requirements and the performance of the pinhole time camera in terms of magnification, dispersion, aperture size, and impulse response are examined.

© 1997 Optical Society of America

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References

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  1. A. Gernsheim, The History of Photography (McGraw-Hill, New York, 1969), pp. 17–29.
  2. M. J. Bernstein, F. Hai, “An x-ray pinhole camera with nanosecond resolution,” Rev. Sci. Instrum. 41, 1843–1845 (1970).
    [CrossRef]
  3. L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
    [CrossRef]
  4. M. Young, “The pinhole camera, imaging without lenses or mirrors,” The Physics Teacher 27, 648–655 (1989).
    [CrossRef]
  5. K. Sayanagi, “Pinhole imagery,” J. Opt. Soc. Am. 57, 1091–1099 (1967).
    [CrossRef]
  6. R. E. Swing, D. P. Rooney, “General transfer function for the pinhole camera,” J. Opt. Soc. Am. 58, 629–635 (1968).
    [CrossRef]
  7. M. Young, “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).
    [CrossRef] [PubMed]
  8. X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).
  9. P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).
  10. W. J. Caputi, “Stretch: a time transformation technique,” IEEE Trans. Aerosp. Electron. Syst. AES-7, 269–278 (1971).
    [CrossRef]
  11. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  12. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
    [CrossRef]
  13. L. S. Telegin, A. S. Chirkin, “Reversal and reconstruction of the profile of ultra-short light pulses,” Sov. J. Quantum Electron. 15, 101–102 (1985).
    [CrossRef]
  14. B. H. Kolner, M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630–632 (1989).
    [CrossRef] [PubMed]
  15. A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
    [CrossRef]
  16. C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
    [CrossRef]
  17. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [CrossRef]
  18. B. H. Kolner, “Generalization of the concepts of focal length and f-number to space and time,” J. Opt. Soc. Am. A 11, 3229–3234 (1994).
    [CrossRef]
  19. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  20. A. C. Scott, Nonlinear and Active Wave Propagation in Electronics (Wiley-Interscience, New York, 1970).
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  22. K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
    [CrossRef]

1996 (1)

K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

1995 (1)

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

1994 (4)

X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).

C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

B. H. Kolner, “Generalization of the concepts of focal length and f-number to space and time,” J. Opt. Soc. Am. A 11, 3229–3234 (1994).
[CrossRef]

1993 (1)

A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
[CrossRef]

1989 (2)

B. H. Kolner, M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630–632 (1989).
[CrossRef] [PubMed]

M. Young, “The pinhole camera, imaging without lenses or mirrors,” The Physics Teacher 27, 648–655 (1989).
[CrossRef]

1987 (1)

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
[CrossRef]

1985 (1)

L. S. Telegin, A. S. Chirkin, “Reversal and reconstruction of the profile of ultra-short light pulses,” Sov. J. Quantum Electron. 15, 101–102 (1985).
[CrossRef]

1971 (2)

M. Young, “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).
[CrossRef] [PubMed]

W. J. Caputi, “Stretch: a time transformation technique,” IEEE Trans. Aerosp. Electron. Syst. AES-7, 269–278 (1971).
[CrossRef]

1970 (1)

M. J. Bernstein, F. Hai, “An x-ray pinhole camera with nanosecond resolution,” Rev. Sci. Instrum. 41, 1843–1845 (1970).
[CrossRef]

1968 (2)

R. E. Swing, D. P. Rooney, “General transfer function for the pinhole camera,” J. Opt. Soc. Am. 58, 629–635 (1968).
[CrossRef]

P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).

1967 (1)

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
[CrossRef]

Auld, B. A.

A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
[CrossRef]

Bennett, C. V.

C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

Bernstein, M. J.

M. J. Bernstein, F. Hai, “An x-ray pinhole camera with nanosecond resolution,” Rev. Sci. Instrum. 41, 1843–1845 (1970).
[CrossRef]

Bienvenu, G.

P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).

Bloom, D. M.

A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
[CrossRef]

Breeze, S. P.

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

Caputi, W. J.

W. J. Caputi, “Stretch: a time transformation technique,” IEEE Trans. Aerosp. Electron. Syst. AES-7, 269–278 (1971).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
[CrossRef]

L. S. Telegin, A. S. Chirkin, “Reversal and reconstruction of the profile of ultra-short light pulses,” Sov. J. Quantum Electron. 15, 101–102 (1985).
[CrossRef]

DeLong, K. W.

K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

Fittinghoff, D. N.

K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

Gernsheim, A.

A. Gernsheim, The History of Photography (McGraw-Hill, New York, 1969), pp. 17–29.

Godil, A. A.

A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hai, F.

M. J. Bernstein, F. Hai, “An x-ray pinhole camera with nanosecond resolution,” Rev. Sci. Instrum. 41, 1843–1845 (1970).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Jiang, X.

X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).

Kolner, B. H.

C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

B. H. Kolner, “Generalization of the concepts of focal length and f-number to space and time,” J. Opt. Soc. Am. A 11, 3229–3234 (1994).
[CrossRef]

B. H. Kolner, M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630–632 (1989).
[CrossRef] [PubMed]

Lin, Q.

X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).

Nazarathy, M.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Porter, J. L.

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

Rooney, D. P.

Ruggles, L. E.

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

Sayanagi, K.

Scott, A. C.

A. C. Scott, Nonlinear and Active Wave Propagation in Electronics (Wiley-Interscience, New York, 1970).

Scott, R. P.

C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

Spielman, R. B.

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

Swing, R. E.

Telegin, L. S.

L. S. Telegin, A. S. Chirkin, “Reversal and reconstruction of the profile of ultra-short light pulses,” Sov. J. Quantum Electron. 15, 101–102 (1985).
[CrossRef]

Tournois, P.

P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).

Trebino, R.

K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

Vernet, J.-L.

P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
[CrossRef]

Wang, S.

X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).

Young, M.

M. Young, “The pinhole camera, imaging without lenses or mirrors,” The Physics Teacher 27, 648–655 (1989).
[CrossRef]

M. Young, “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. A. Godil, B. A. Auld, D. M. Bloom, “Time-lens producing 1.9 ps optical pulses,” Appl. Phys. Lett. 62, 1047–1049 (1993).
[CrossRef]

C. V. Bennett, R. P. Scott, B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

C. R. Acad. Sci. (Paris) (1)

P. Tournois, J.-L. Vernet, G. Bienvenu, “Sur l’analogie optique de certains montages électroniques: formation d’images temporelles de signaux électriques,” C. R. Acad. Sci. (Paris) 267, 375–378 (1968).

IEEE J. Quantum Electron. (2)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1996).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

W. J. Caputi, “Stretch: a time transformation technique,” IEEE Trans. Aerosp. Electron. Syst. AES-7, 269–278 (1971).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Optik (1)

X. Jiang, Q. Lin, S. Wang, “Optimum image plane of the pinhole camera,” Optik 97, 41–42 (1994).

Rev. Sci. Instrum. (2)

M. J. Bernstein, F. Hai, “An x-ray pinhole camera with nanosecond resolution,” Rev. Sci. Instrum. 41, 1843–1845 (1970).
[CrossRef]

L. E. Ruggles, R. B. Spielman, J. L. Porter, S. P. Breeze, “Characterization of a high-speed X-ray imager,” Rev. Sci. Instrum. 66, 712 (1995).
[CrossRef]

Sov. J. Quantum Electron. (1)

L. S. Telegin, A. S. Chirkin, “Reversal and reconstruction of the profile of ultra-short light pulses,” Sov. J. Quantum Electron. 15, 101–102 (1985).
[CrossRef]

Sov. Phys. Usp. (1)

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Sov. Phys. Usp. 29, 642–677 (1987).
[CrossRef]

The Physics Teacher (1)

M. Young, “The pinhole camera, imaging without lenses or mirrors,” The Physics Teacher 27, 648–655 (1989).
[CrossRef]

Other (5)

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

A. Gernsheim, The History of Photography (McGraw-Hill, New York, 1969), pp. 17–29.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

A. C. Scott, Nonlinear and Active Wave Propagation in Electronics (Wiley-Interscience, New York, 1970).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic diagram of the conventional pinhole camera. Object Io(x, y) placed a distance do from an aperture is projected as an image Ii(x/M, y/M) at a distance di behind the aperture (Mdi/do=magnification). (b) Temporal analog: the pinhole time camera. Arbitrary object waveform Io(τ) propagates through input dispersion ξ1d2β1/dω2. A shutter acts as a temporal aperture and allows a small burst of the dispersed input waveform to pass through the output dispersion ξ2d2β2/dω2, where it forms a temporal image Ii(τ/M) of the object [M(ξ2d2β2/dω2)/(ξ1d2β1/dω2)]. Features such as magnification and inversion (local time reversal) are common to both space and time.

Fig. 2
Fig. 2

(a) Space-time diagram showing dispersion of a propagating pulse envelope in the z,t plane with traveling-wave coordinates ξ, τ. (b) Impulse response in the traveling-wave coordinate system.

Fig. 3
Fig. 3

(a) Impulse response in a conventional pinhole camera. Index of refraction on both sides of the aperture have the same sign, and thus the wave front continues to expand past the aperture. (b) Impulse response in a hypothetical pinhole camera where the index of refraction has opposite sign on either side of the aperture. This results in a refocusing of the impulse and is analogous to a pinhole time camera with dispersions of opposite sign on either side of the shutter. (This is also a form of dispersion compensation).

Fig. 4
Fig. 4

Optimum temporal aperture duration ΔτOPT versus magnification M for a fixed output dispersion (b=1).

Fig. 5
Fig. 5

Impulse response ΔτIMP normalized to optimum aperture time ΔτOPT versus normalized aperture time Δτ/ΔτOPT for various magnification ratios. Note that when Δτ=ΔτOPT, the impulse response is minimized for any magnification, as expected.

Fig. 6
Fig. 6

Propagation of the envelopes of two pulses showing the overlap and interference required so that energy from each pulse passes through the shutter pupil function P(τ).

Fig. 7
Fig. 7

(a) Input Gaussian pulse sequence to demonstrate resolution effects of varying time-bandwidth product BΔτIN. Pulses are on a 2/16=0.125-ps spacing and form a {1011} sequence. The pulsewidths are 20 fs (intensity FWHM) wide. Bandwidths are adjusted by introducing a quadratic phase term to each pulse. (b) Pinhole temporal images of pulses calculated for various time-bandwidth products and magnification M=-3. For each value of BΔτIN, dispersions a and b and shutter duration ΔτOPT were set for optimum resolution as defined in the text.

Fig. 8
Fig. 8

Evolution of a three-pulse sequence in a pinhole time camera. Asymmetrical {1011} pulse sequence is on a 125-fs period, as in Fig. 7. Shutter function P(τ) occurs at the boundary between input and output dispersions (ξ1, ξ2). Magnification M=-3 and time-bandwidth product BΔτIN=18. Amplitude scaling of 4× is applied in the region of output dispersion for clarity.

Tables (1)

Tables Icon

Table 1 Time- and Frequency-Domain Functions Corresponding to Input and Output Dispersion and the Shutter in a Pinhole Time Camera

Equations (31)

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fT=ω0Δτ(d2ϕ/dt2),
E(x, y, z, t)=A(z, t)exp[i(ω0t-β(ω0)z)],
τ=(t-t0)-z-z0vg,
ξ=z-z0,
A(ξ, τ)ξ=i2d2βdω22A(ξ, τ)τ2.
A(ξ, τ)=12π-A(0, ω)×exp-i ξ2d2βdω2ω2exp(iωτ)dω.
A(ξ,τ)=-h(τ;τ0)A(0,τ0)dτ0,
A(ξ1, τ)=G1(ξ1, τ)*δ(τ-τ0)=G1(ξ1, τ-τ0).
A(ξ1+, τ)=G1(ξ1, τ-τ0)P(τ).
h(τ; τ0)=A(ξ2, τ)=G1(ξ1, τ-τ0)P(τ)*G2(ξ2, τ),
h(τ; τ0)=-G1(ξ1, τ-τ0)P(τ)G2(ξ2, τ-τ)dτ=14πiab-P(τ)×expi(τ-τ0)24aexpi(τ-τ)24bdτ=14πiabexpi4τ02a+τ2b-P(τ)×expiτ241a+1bexp-iτ2τ0a+τbdτ.
-P(τ)exp-iτ2a(τ0-τ)dτ=P τ0-τ4πa,
exp-iτ2τ0a+τb=exp-iτ2b(τ-Mτ0).
expi4τ02a+τ2bexpi4τ2aM2+τ2b=expiτ24b1-1M.
h(τ; τ0)=14πiabexpiτ24b1-1M×-P(τ)expiτ24b(1-M)×exp-iτ2b(τ-Mτ0)dτ.
A(ξ, τ)=-h(τ-τ˜0)A(0, τ˜0/M)dτ˜0.
P(τ)=exp-4 ln2 τΔτ2,
h(τ; τ0)=14πiabexpiτ24b1-1M×- exp-4 ln2 τΔτ2×expiτ24b(1-M)×exp-iτ2b(τ-Mτ0)dτ,
h(τ; τ0)=14πiabπ4 ln 2Δτ2-i4b(1-M)1/2×expiτ24b1-1M×exp-(πf)24 ln 2Δτ2-i4b(1-M).
ΔτOPT=4ln2 b1-M1/2.
h(τ)exp-4 ln2 τΔτIMP2,
ΔτIMP216b ln2Δτ2+Δτ2(1-M)2.
ΔτIMPΔτOPT=|1-M|ΔτOPTΔτ2+ΔτΔτOPT2.
ΔτIMP=|1-M|2ΔτOPT.
ΔτOUT2=ΔτIN2+(BD)2
BT|D|=T4π|a|=T4πMb,
|a|T4πBor|b|T4πB|M|.
ΔτIMP=42 ln2 |b(1-M)|.
ΔτIMP22 ln2 T|M(1-M)πB.
exp-τ2ΔτIMP2+ΔτGEO2,
NTΔτIN=π8 ln 2M1-MBΔτIN,

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