Abstract

In this paper, an indirect holographic image reconstruction algorithm was studied for terahertz imaging with a quasi-optics receiver. Based on the combination of the reciprocity principle and modified quasi-optics theory, analytical expressions of the received spatial power distribution and its spectrum are obtained for the interference pattern of target wave and reference wave. These results clearly give the quantitative relationship between imaging quality and the parameters of a Gaussian beam, which provides a good criterion for terahertz quasi-optics transceivers design in terahertz off-axis holographic imagers. To validate the effectiveness of the proposed analysis method, some imaging results with a 0.3 THz prototype system are shown based on electromagnetic simulation.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.
  2. A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
    [CrossRef]
  3. R. Appleby and H. Bruce Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 Thz region,” IEEE Trans. Antennas Propag. 55, 2944–2956 (2007).
    [CrossRef]
  4. D. R. Vizard and R. Doyle, “Advances in millimeter wave imaging and radar systems for civil applications,” in 2006 International Microwave Symposium Digest (IEEE, 2006), pp. 94–97.
  5. X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
    [CrossRef]
  6. D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.
  7. A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging at 310 GHz,” in Proceedings of European Radar Conference (IEEE, 2008), pp. 168–171.
  8. M. S. Heimbeck, M. K. Kim, D. A. Gregory, and H. O. Everitt, “Terahertz digital holography using angular spectrum and dual wavelength reconstruction methods,” Opt. Express 19, 9192–9200 (2011).
    [CrossRef]
  9. A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).
  10. A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.
  11. U. Schnars and W. Jueptner, Digital Holography (Springer-Verlag, 2005), Chap. 3, pp. 41–69.
  12. P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 6–28.
  13. G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), pp. 257–275.

2012 (1)

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

2011 (1)

2010 (1)

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).

2007 (1)

R. Appleby and H. Bruce Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 Thz region,” IEEE Trans. Antennas Propag. 55, 2944–2956 (2007).
[CrossRef]

2005 (1)

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
[CrossRef]

Ala-Laurinaho, J.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging at 310 GHz,” in Proceedings of European Radar Conference (IEEE, 2008), pp. 168–171.

Appleby, R.

R. Appleby and H. Bruce Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 Thz region,” IEEE Trans. Antennas Propag. 55, 2944–2956 (2007).
[CrossRef]

Bruce Wallace, H.

R. Appleby and H. Bruce Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 Thz region,” IEEE Trans. Antennas Propag. 55, 2944–2956 (2007).
[CrossRef]

Carrier, G. F.

G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), pp. 257–275.

Cole, B. E.

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
[CrossRef]

Doyle, R.

D. R. Vizard and R. Doyle, “Advances in millimeter wave imaging and radar systems for civil applications,” in 2006 International Microwave Symposium Digest (IEEE, 2006), pp. 94–97.

Enayati, A.

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

Everitt, H. O.

Fang, G.

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

Fitzgerald, A. J.

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
[CrossRef]

Gao, X.

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 6–28.

Gregory, D. A.

Gu, S.

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

Hall, T. E.

D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.

Heimbeck, M. S.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer-Verlag, 2005), Chap. 3, pp. 41–69.

Kim, M. K.

Krook, M.

G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), pp. 257–275.

Li, C.

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

Lu, M.-H.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

McMakin, D. L.

D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.

Mu, K.-J.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

Pearson, C. E.

G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), pp. 257–275.

Raedt, W. De

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

Raisanen, A. V.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging at 310 GHz,” in Proceedings of European Radar Conference (IEEE, 2008), pp. 168–171.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer-Verlag, 2005), Chap. 3, pp. 41–69.

Severtsen, R. H.

D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.

Sheen, D. M.

D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.

Taday, P. F.

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
[CrossRef]

Tamminen, A.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging at 310 GHz,” in Proceedings of European Radar Conference (IEEE, 2008), pp. 168–171.

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

Vandenbosch, G. A. E.

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

Vizard, D. R.

D. R. Vizard and R. Doyle, “Advances in millimeter wave imaging and radar systems for civil applications,” in 2006 International Microwave Symposium Digest (IEEE, 2006), pp. 94–97.

Zhang, C.-L.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

Zhang, Z.-W.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

Zhou, Y.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

IEEE Antennas Wirel. Propag. Lett. (1)

X. Gao, C. Li, S. Gu, and G. Fang, “Study of a new millimeter-wave imaging scheme suitable for fast personal screening,” IEEE Antennas Wirel. Propag. Lett. 11, 787–790 (2012).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. Appleby and H. Bruce Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 Thz region,” IEEE Trans. Antennas Propag. 55, 2944–2956 (2007).
[CrossRef]

J. Pharm. Sci. (1)

A. J. Fitzgerald, B. E. Cole, and P. F. Taday, “Non destructive analysis of tablet coating thicknesses using terahertz pulsed imaging,” J. Pharm. Sci. 94, 177–183 (2005).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging: evaluation of image equality at 310 GHz,” Proc. SPIE 7670, A1–A11 (2010).

Other (8)

A. Enayati, A. Tamminen, J. Ala-Laurinaho, A. V. Raisanen, G. A. E. Vandenbosch, and W. De Raedt, “THz holographic imaging: a spatial-domain technique for phase retrieval and image reconstruction,” in International Microwave Symposium Digest (IEEE, 2012), pp. 1–3.

U. Schnars and W. Jueptner, Digital Holography (Springer-Verlag, 2005), Chap. 3, pp. 41–69.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 6–28.

G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable (McGraw-Hill, 1966), pp. 257–275.

Y. Zhou, K.-J. Mu, M.-H. Lu, Z.-W. Zhang, and C.-L. Zhang, “Characteristics and application of terahertz imaging non-destructive detection,” in Proceedings of the International Conference of the International Society of Infrared, Millimeter, and Terahertz Waves (IEEE, 2006), p. 156.

D. R. Vizard and R. Doyle, “Advances in millimeter wave imaging and radar systems for civil applications,” in 2006 International Microwave Symposium Digest (IEEE, 2006), pp. 94–97.

D. M. Sheen, D. L. McMakin, T. E. Hall, and R. H. Severtsen, “Active millimeter-wave standoff and portal imaging techniques for personnel screening,” in IEEE Conference on Technologies for Homeland Security (IEEE, 2009), pp. 440–447.

A. Tamminen, J. Ala-Laurinaho, and A. V. Raisanen, “Indirect holographic imaging at 310 GHz,” in Proceedings of European Radar Conference (IEEE, 2008), pp. 168–171.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic of a terahertz indirect off-axis holographic imaging system.

Fig. 2.
Fig. 2.

Amplitude spectrum distribution of p(x,y).

Fig. 3.
Fig. 3.

Simulation results of a point target.

Fig. 4.
Fig. 4.

Imaging results of a five-metal-strip target arranged in the x direction.

Fig. 5.
Fig. 5.

Imaging results of a five-metal-strip target arranged in the y direction.

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

2ψx2+2ψy22jkψz=0,
ψ=(2πw(z)2)0.5exp(x2+y2w(z)2jπ(x2+y2)λR(z)+jφ0(z)jkz),
w(z)=w0[1+(λzπw02)2]0.5,
R(z)=z+1z(πw02λ)2,
φ0(z)=arctan(λzπw02),
E=jωψy^+2ωyk(1w(z)2+jπλR(z))ψz^,
H=jkψμx^2xμ(1w(z)2+jπλR(z))ψz^.
Er=y^E0exp(j2πfrxxj2πfrzz),
Hr=(x^frz+z^frx)2πE0ωμexp(j2πfrxxj2πfrzz),
Jr=2z^×Hr=y^4πE0frzωμexp(j2πfrxxj2πfrzd).
Jt=Jo+Jr=y^δ(xxo,yyo)+y^4πE0frzωμexp(j2πfrxxj2πfrzd).
Et=Et0[y^jωz^2ω(yy)kw02](2πw02)0.5exp[(xx)2+(yy)2w02],
Ht=Et0[x^jkμ+z^2(xx)μw02](2πw02)0.5exp[(xx)2+(yy)2w02],
z=dEaJtds=z=0EtJaHtMads,
Ea=y^jωψ(xx,yy,d)+z^2(yy)ωk(1w(d)2+jπλR(d))ψ(xx,yy,d),
Ja=y^jkμ(2πw02)0.5exp[(xx)2+(yy)2w02],
Ma=x^jω(2πw02)0.5exp[(xx)2+(yy)2w02].
Et0=jμ2kψ(xox,yoy,d)+μ2ωkC(frx,d)exp(j2πfrxx),
C(frx,d)=4πλR(d)E0frzμ(2πw(d)2)0.5exp(λ2R(d)2frx2w(d)2)exp[j2πfrzd+jϕ0(d)jkd+jπλR(d)frx2].
p(x,y)=12z=0Et×Ht*ds=ωkEt0Et0*2μ=μ8ωk|C(frx,d)|2+ωμ8k|ψ(xox,yoy,d)|2+jμ8kC(frx,d)ψ*(xox,yoy,d)exp(j2πfrxx)jμ8kC*(frx,d)ψ(xox,yoy,d)exp(j2πfrxx).
P(fx,fy)=μ8ωk|C(frx,d)|2δ(fx,fy)+ωμ8kexp[π2w(d)2fx22π2w(d)2fy22j2πfxxoj2πfyyo]+jμ8kC(frx,d)Ψ*(fxfrx,fy)jμ8kC*(frx,d)Ψ(fxfrx,fy),
Ψ(fx,fy)=sψ(xox,yoy,d)exp(j2πfxxj2πfyy)dxdy=j(2λ2R(d)2πw(d)2)0.5exp(jϕ0(d)jkd)exp[λ2R(d)2w(d)2(fx2+fy2)]exp[jπλR(d)fx2+jπλR(d)fy2j2πfxxoj2πfyyo].
frx=sin(θ)λ0.5(B2x+B4x)=0.5(B2x+B3x),
B2x0.48Lπw(d),
B3x=B4x0.68w(d)LλR(d).
θarcsin[0.5λ(B2x+B4x)].
dx12(frx+0.5B4x)1B2x+2B4x,
dy1max(B2y,B4y),
Pnew(fx,fy)=jμ8kC*(frx,d)Ψ(fx,fy),
Es(x,y)=ifft[Pnew(fx,fy)]=jμ8kC*(frx,d)ψ(xox,yoy,d).
Erc(x,y)=jexp(jkd)λ(d)sEs(x,y)exp{jπλd[(xx)2+(yy)2]}dxdyD(frx,d)exp[(xxo)2+(yyo)2w02]exp[jπ(xxo)2+(yyo)2λd],
D(frx,d)=πE0*frzkexp(π2w02frx2)exp(j2πfrzd+jkdjπλdfrx2).
ρx=ρy=2w0ln(12)1.18w0.

Metrics