Abstract

We present the design and electromagnetic analysis of an all-diffractive millimeter-wave imaging system having a field of view of ±15°. This system consists of two 16-level diffractive lenses, with the stop in contact with the first lens. By considering the Seidel aberrations for a diffractive lens and applying the corresponding stop shift formula, we established the expressions of third-order wave aberrations for this system. By setting all primary Seidel aberrations to zero and solving the corresponding system of equations, we obtained two sets of solutions for this two-element all-diffractive system, which totally compensate for all Seidel aberrations. To assess image system performance, we apply the finite-difference time-domain technique and a vector plane-wave spectrum method, in combination, to validate the performance of the system. To reduce the computational cost and thereby enable the complete electromagnetic analysis of the system, a four-step analysis procedure has been developed and applied as an electromagnetic system model.

© 2004 Optical Society of America

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References

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  1. P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
    [CrossRef]
  2. D. A. Buralli, Diffractive Optics: Design Principles and Applications (University of Rochester, Rochester, N.Y., 1991).
  3. X. Gao, Design, Fabrication and Characterization of Small Diffractive Optical Elements (University of Delaware, Newark, Del., 2000).
  4. C. David, “Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements,” Microelectron. Eng. 53, 677–680 (2000).
    [CrossRef]
  5. D. A. Buralli, G. M. Morris, “Design of diffractive singlets for monochromatic imaging,” Appl. Opt. 30, 2151–2158 (1991).
    [CrossRef] [PubMed]
  6. A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  7. S. Shi, D. W. Prather, “Vector-based plane-wave spectrum method for the propagation of cylindrical electromagnetic fields,” Opt. Lett. 24, 1445–1447 (1999).
    [CrossRef]
  8. A. Ishimaru, “Plane wave spectrum method,” in Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 160–161.
  9. I. V. Minin, O. V. Minin, “Wide angle multicomponent diffraction microwave objective,” J. Commun. Technol. Electron. 31, 16–21 (1986).
  10. S. T. Bobrov, G. I. Greisukh, “Monochromatic aberrations of a two-component diffraction optical system,” Opt. Spectrosc. 49, 809–813 (1980).
  11. G. I. Greisukh, “Correction of third-order chromatic aberrations of a two-lens holographic objective,” Opt. Spectrosc. 49, 1212–1215 (1980).
  12. D. A. Buralli, G. M. Morris, “Design of two- and three-element diffractive Keplerian telescopes,” Appl. Opt. 31, 38–43 (1992).
    [CrossRef] [PubMed]
  13. M. Born, E. Wolf, Principles of Optics, 6th ed. (Wheaton, Exeter, UK, 1986).
  14. D. A. Buralli, G. M. Morris, “Design of a wide field diffractive landscape lens,” Appl. Opt. 28, 3950–3959 (1989).
    [CrossRef] [PubMed]
  15. D. W. Prather, D. Pustai, S. Shi, “Performance of multilevel diffractive lenses as a function of f-number,” Appl. Opt. 40, 207–210 (2001).
    [CrossRef]
  16. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  17. F. L. Teixeira, W. C. Chew, “PML - FDTD in cylindrical and spherical grids,” IEEE Microwave Guid. Wave Lett. 7, 285–287 (1997).
    [CrossRef]
  18. D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
    [CrossRef]
  19. S. D. Gedney, “An anistropic perfectly matched layer-absorbing medium for the truncation of finite-difference time-domain lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
    [CrossRef]
  20. W. Yu, R. Mittra, “A technique for improving the accuracy of the nonuniform (FDTD) algorithm,” IEEE Trans. Microwave Theory Tech. 47, 353–356 (1999).
    [CrossRef]
  21. M. S. Mirotznik, D. W. Prather, J. N. Mait, W. A. Beck, S. Shi, X. Gao, “Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method,” Appl. Opt. 39, 2871–2880 (2000).
    [CrossRef]
  22. A. Navarro, M. J. Nunez, “Finite-difference time-domain method coupled with fast Fourier transform: a generalization to open cylindrical devices,” IEEE J. Microwave Theo. Tech. 42, 870–874 (1994).
    [CrossRef]
  23. G. Mur, “Finite-difference method for the solution of electromagnetic waveguide discontinuity problem,” IEEE Trans. Microwave Theory Tech. MTT-22, 54–57 (1974).
    [CrossRef]
  24. N. Morita, N. Kumagai, J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, Norwood, Mass., 1991).

2001

2000

1999

1997

F. L. Teixeira, W. C. Chew, “PML - FDTD in cylindrical and spherical grids,” IEEE Microwave Guid. Wave Lett. 7, 285–287 (1997).
[CrossRef]

1996

S. D. Gedney, “An anistropic perfectly matched layer-absorbing medium for the truncation of finite-difference time-domain lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

1994

A. Navarro, M. J. Nunez, “Finite-difference time-domain method coupled with fast Fourier transform: a generalization to open cylindrical devices,” IEEE J. Microwave Theo. Tech. 42, 870–874 (1994).
[CrossRef]

1992

1991

1989

1986

I. V. Minin, O. V. Minin, “Wide angle multicomponent diffraction microwave objective,” J. Commun. Technol. Electron. 31, 16–21 (1986).

1980

S. T. Bobrov, G. I. Greisukh, “Monochromatic aberrations of a two-component diffraction optical system,” Opt. Spectrosc. 49, 809–813 (1980).

G. I. Greisukh, “Correction of third-order chromatic aberrations of a two-lens holographic objective,” Opt. Spectrosc. 49, 1212–1215 (1980).

1974

G. Mur, “Finite-difference method for the solution of electromagnetic waveguide discontinuity problem,” IEEE Trans. Microwave Theory Tech. MTT-22, 54–57 (1974).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Agravante, H.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

Beck, W. A.

Bobrov, S. T.

S. T. Bobrov, G. I. Greisukh, “Monochromatic aberrations of a two-component diffraction optical system,” Opt. Spectrosc. 49, 809–813 (1980).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Wheaton, Exeter, UK, 1986).

Buralli, D. A.

Chew, W. C.

F. L. Teixeira, W. C. Chew, “PML - FDTD in cylindrical and spherical grids,” IEEE Microwave Guid. Wave Lett. 7, 285–287 (1997).
[CrossRef]

Chu, R.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

David, C.

C. David, “Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements,” Microelectron. Eng. 53, 677–680 (2000).
[CrossRef]

Fornaca, S.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

Gao, X.

Gedney, S. D.

S. D. Gedney, “An anistropic perfectly matched layer-absorbing medium for the truncation of finite-difference time-domain lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Greisukh, G. I.

S. T. Bobrov, G. I. Greisukh, “Monochromatic aberrations of a two-component diffraction optical system,” Opt. Spectrosc. 49, 809–813 (1980).

G. I. Greisukh, “Correction of third-order chromatic aberrations of a two-lens holographic objective,” Opt. Spectrosc. 49, 1212–1215 (1980).

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Ishimaru, A.

A. Ishimaru, “Plane wave spectrum method,” in Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 160–161.

Jordan, K.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

Kumagai, N.

N. Morita, N. Kumagai, J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, Norwood, Mass., 1991).

Mait, J. N.

Mautz, J. R.

N. Morita, N. Kumagai, J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, Norwood, Mass., 1991).

Minin, I. V.

I. V. Minin, O. V. Minin, “Wide angle multicomponent diffraction microwave objective,” J. Commun. Technol. Electron. 31, 16–21 (1986).

Minin, O. V.

I. V. Minin, O. V. Minin, “Wide angle multicomponent diffraction microwave objective,” J. Commun. Technol. Electron. 31, 16–21 (1986).

Mirotznik, M. S.

Mittra, R.

W. Yu, R. Mittra, “A technique for improving the accuracy of the nonuniform (FDTD) algorithm,” IEEE Trans. Microwave Theory Tech. 47, 353–356 (1999).
[CrossRef]

Moffa, P.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

Morita, N.

N. Morita, N. Kumagai, J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, Norwood, Mass., 1991).

Morris, G. M.

Mur, G.

G. Mur, “Finite-difference method for the solution of electromagnetic waveguide discontinuity problem,” IEEE Trans. Microwave Theory Tech. MTT-22, 54–57 (1974).
[CrossRef]

Navarro, A.

A. Navarro, M. J. Nunez, “Finite-difference time-domain method coupled with fast Fourier transform: a generalization to open cylindrical devices,” IEEE J. Microwave Theo. Tech. 42, 870–874 (1994).
[CrossRef]

Nunez, M. J.

A. Navarro, M. J. Nunez, “Finite-difference time-domain method coupled with fast Fourier transform: a generalization to open cylindrical devices,” IEEE J. Microwave Theo. Tech. 42, 870–874 (1994).
[CrossRef]

Prather, D. W.

Pustai, D.

Shi, S.

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Teixeira, F. L.

F. L. Teixeira, W. C. Chew, “PML - FDTD in cylindrical and spherical grids,” IEEE Microwave Guid. Wave Lett. 7, 285–287 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Wheaton, Exeter, UK, 1986).

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Yu, W.

W. Yu, R. Mittra, “A technique for improving the accuracy of the nonuniform (FDTD) algorithm,” IEEE Trans. Microwave Theory Tech. 47, 353–356 (1999).
[CrossRef]

Yujiri, L.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

Appl. Opt.

IEEE J. Microwave Theo. Tech.

A. Navarro, M. J. Nunez, “Finite-difference time-domain method coupled with fast Fourier transform: a generalization to open cylindrical devices,” IEEE J. Microwave Theo. Tech. 42, 870–874 (1994).
[CrossRef]

IEEE Microwave Guid. Wave Lett.

F. L. Teixeira, W. C. Chew, “PML - FDTD in cylindrical and spherical grids,” IEEE Microwave Guid. Wave Lett. 7, 285–287 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

S. D. Gedney, “An anistropic perfectly matched layer-absorbing medium for the truncation of finite-difference time-domain lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

IEEE Trans. Microwave Theory Tech.

W. Yu, R. Mittra, “A technique for improving the accuracy of the nonuniform (FDTD) algorithm,” IEEE Trans. Microwave Theory Tech. 47, 353–356 (1999).
[CrossRef]

G. Mur, “Finite-difference method for the solution of electromagnetic waveguide discontinuity problem,” IEEE Trans. Microwave Theory Tech. MTT-22, 54–57 (1974).
[CrossRef]

J. Commun. Technol. Electron.

I. V. Minin, O. V. Minin, “Wide angle multicomponent diffraction microwave objective,” J. Commun. Technol. Electron. 31, 16–21 (1986).

J. Opt. Soc. Am. A

Microelectron. Eng.

C. David, “Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements,” Microelectron. Eng. 53, 677–680 (2000).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

S. T. Bobrov, G. I. Greisukh, “Monochromatic aberrations of a two-component diffraction optical system,” Opt. Spectrosc. 49, 809–813 (1980).

G. I. Greisukh, “Correction of third-order chromatic aberrations of a two-lens holographic objective,” Opt. Spectrosc. 49, 1212–1215 (1980).

Other

A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Wheaton, Exeter, UK, 1986).

A. Ishimaru, “Plane wave spectrum method,” in Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 160–161.

P. Moffa, L. Yujiri, K. Jordan, R. Chu, H. Agravante, S. Fornaca, “Passive millimeter wave camera flight tests,” in Passive Millimeter-wave Imaging Technology IV, R. M. Smith, R. Appleby, eds., Proc. SPIE4032, 9–17 (2000).
[CrossRef]

D. A. Buralli, Diffractive Optics: Design Principles and Applications (University of Rochester, Rochester, N.Y., 1991).

X. Gao, Design, Fabrication and Characterization of Small Diffractive Optical Elements (University of Delaware, Newark, Del., 2000).

N. Morita, N. Kumagai, J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, Norwood, Mass., 1991).

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Figures (8)

Fig. 1
Fig. 1

Scheme of the two-diffractive-lens MMW imaging system.

Fig. 2
Fig. 2

EM analysis model of the two-diffractive-lens MMW imaging system.

Fig. 3
Fig. 3

Performance of the two-cylindrical-diffractive-lens MMW imaging system for normal incidence: (a) propagation plot of the field intensity, (b) line scan of the field intensity on the focal plane.

Fig. 4
Fig. 4

Performance of the two-cylindrical-diffractive-lens MMW imaging system for a 5° incident angle: (a) propagation plot of the field intensity, (b) line scan of the field intensity on the focal plane.

Fig. 5
Fig. 5

Performance of the two-cylindrical-diffractive-lens MMW imaging system for a 10° incident angle: (a) propagation plot of the field intensity, (b) line scan of the field intensity on the focal plane.

Fig. 6
Fig. 6

Performance of the two-cylindrical-diffractive-lens MMW imaging system for a 15° incident angle: (a) propagation plot of the field intensity, (b) line scan of the field intensity on the focal plane.

Fig. 7
Fig. 7

Performance of the two-axially-symmetric-diffractive-lens MMW imaging system for normal incidence: (a) image of the field intensity on the focal plane, (b) line scans of the field intensity on the focal plane.

Fig. 8
Fig. 8

Line scans of the fields for the two-cylindrical-diffractive-lens MMW imaging system for 15° incident angle: (a) line scan of the fields on plane 2, (b) line scan of the fields on plane 3, as indicated in Fig. 2.

Equations (20)

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

h2=h1-dϕ1,
u1=hϕ1,
u2=hϕ,
bfl=h2/u2=1-dϕ1F,
h¯=ūd,
ϕ=ϕ1+ϕ2-dϕ1ϕ2F=1/ϕ.
S1=h4ϕ341+B2+4BC+3C2-8Gh4S2=-h2ϕ2H2B+2CS3=H2ϕS4=S5=0,
B=2CsϕC=u+uu-u,
B1=B2=0C1=-1C2=2ϕ1+1-dϕ1ϕ2dϕ1-1ϕ2H=-ūh,
S11=h4ϕ13-8G1h4S12=-h3ϕ12ūS13=ū2h2ϕ1S14=S15=0.
=h¯h2=ūdh1-dϕ1.
S21=h41-dϕ14ϕ2341+3C22-8G2S22=ūh31-dϕ12ϕ22C2+ūh3d1-dϕ13ϕ2341+3C22-8G2S23=ū2h2ϕ2+2ū2h2d1-dϕ1ϕ22C2+d2ū2h21-dϕ12ϕ2341+3C22-8G2S24=0S25=ū3h3ϕ2+3d1-dϕ1ϕ22C2+d21-dϕ12ϕ2341+3C22-8G2.
S1=h4ϕ13-8G1+1-dϕ14ϕ2341+3C22-8G2S2=ūh3-ϕ12+1-dϕ12ϕ22C2+d1-dϕ13ϕ2341+3C22-8G2S3=ū2h2ϕ1+ϕ2+2d1-dϕ1ϕ22C2+d21-dϕ12ϕ2341+3C22-8G2S4=0S5=ū3h3ϕ2+3d1-dϕ1ϕ22C2+d21-dϕ12ϕ2341+3C22-8G2.
a=2x-x+1±x+12-41/2x,b=a2-xa+1,G1=1-dϕ1ϕ128d-1-dϕ13ϕ22C28d+ϕ138,G2=ϕ13-8G11-dϕ14-ϕ2341+3C22.
ϕ=ϕ1+ϕ2-dϕ1ϕ2.
x=1.1848 for a=2x-x+1+x+12-41/2x,
x=2.2267 for a=2x-x+1-x+12-41/2x.
d=1.1848F,f1=2.53218F,f2=0.87943F,G1=0.063833/F3,G2=0.078256/F3,bfl=0.5321F,
d=2.2267F,f1=1.3473F,f2=-2.5321F,G1=0.0145/F3,G2=-0.063883/F3,bfl=-0.65271F.
fx=intN lev-1×modAx2+Gx4, λλN lev×λn-1,

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