Abstract

The aperture field integration method (AFIM) is proposed and utilized to efficiently compute the field distributions of infrared/microwave (IR/MW) micro-mirror array beam combiners, including the MW near-field distribution and the IR far-field distribution. The MW near-field distributions of single-dielectric-layer beam combiners with 1, 11, and 101 micromirrors are analyzed by AFIM. Compared to the commonly used multilevel fast multipole method (MLFMM) in the computation of MW near-field distribution, the memory requirement and CPU time consumption are reduced drastically from 16.92 GB and 3.26 h to 0.66 MB and 0.55 s, respectively. The calculation accuracy is better than 96%, when the MW near-field distribution is computed. The IR far-field computational capability is validated by comparing the results obtained through AFIM and experiment. The MW near field and IR far field of a circular and a square shape of three-layer micro-mirror array beam combiners are also analyzed. Four indicators Epv, Erms, φpv, and φrms representing the amplitude and phase variations are proposed to evaluate the MW near-field uniformity. The simulation results show that the increase of beam combiner size can improve the uniformity of the MW near field, and that the square shape has less influence on the uniformity of the MW near field than the circular one. The zeroth-order diffraction primary maximum intensity of the IR far field is decreased by 1/cos2α0 times compared to that of the equivalent mirror, where α0 is the oblique angle of each micromirror. When the periodic length of the micro-mirror array is less than 0.1 mm, the position of the secondary maximum will exceed the size of the focal plane array. Simultaneously, the half-width of the zeroth-order diffraction primary maximum is less than the size of a single pixel. Thus, IR images with high quality will be obtained. The simulation results show that the AFIM as a unified method can be applied to design, analyze, evaluate, and optimize IR/MW micro-mirror array beam combiners.

© 2014 Optical Society of America

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    [CrossRef]
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2013 (3)

2012 (1)

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

2011 (2)

Y. Liu, J. Tan, and J. Ma, “Use of conducting inductive meshes with periodic rectangle units as an infrared/microwave dual-mode detecting beamsplitter,” J. Opt. 13, 035407 (2011).
[CrossRef]

G. C. Holst, “Imaging system fundamentals,” Opt. Eng. 50, 052601 (2011).
[CrossRef]

2010 (1)

S. Quan, “Time domain analysis of the near-field radiation of shaped electrically large apertures,” IEEE Trans. Antennas Propag. 58, 300–306 (2010).
[CrossRef]

2007 (2)

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

V. Lomakin and E. Michielssen, “Beam transmission through periodic subwavelength hole structures,” IEEE Trans. Antennas Propag. 55, 1564–1581 (2007).
[CrossRef]

2005 (1)

S. Clarke and J. Ulrich, “Dielectric material modeling in the MoM-based code FEKO,” IEEE Antennas Propag. Mag. 47, 140–147 (2005).
[CrossRef]

2003 (1)

C. C. Lu, “A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes,” IEEE Trans. Antennas Propag. 51, 606–612 (2003).
[CrossRef]

2000 (1)

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

1998 (2)

S. Mobley and J. Cole, “Dichroic beam combiner to support hardware-in-the-loop testing of dual-mode common aperture seekers,” Proc. SPIE 3368, 32–41 (1998).
[CrossRef]

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).

1996 (1)

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
[CrossRef]

1995 (2)

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).

1994 (1)

S. Mobley, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).

1993 (3)

1992 (1)

1991 (1)

J. P. McKay and R. S. Yahya, “Compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate,” IEEE Trans. Antennas Propag. 39, 746–753 (1991).
[CrossRef]

1986 (1)

1984 (1)

D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984).
[CrossRef]

1983 (1)

1982 (1)

S. M. Rao, D. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Baird, W. E.

Ballard, G. H.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Bunfield, D.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Clarke, S.

S. Clarke and J. Ulrich, “Dielectric material modeling in the MoM-based code FEKO,” IEEE Antennas Propag. Mag. 47, 140–147 (2005).
[CrossRef]

Cole, J.

S. Mobley and J. Cole, “Dichroic beam combiner to support hardware-in-the-loop testing of dual-mode common aperture seekers,” Proc. SPIE 3368, 32–41 (1998).
[CrossRef]

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
[CrossRef]

Cooper, J.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
[CrossRef]

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).

Feng, X. C.

Gareri, J.

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

Gareri, J. P.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Gaylord, T. K.

Gearhart, S. A.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Glisson, A. W.

D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984).
[CrossRef]

S. M. Rao, D. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Glytsis, E. N.

Haggans, C. W.

Harris, T. J.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Holst, G. C.

G. C. Holst, “Imaging system fundamentals,” Opt. Eng. 50, 052601 (2011).
[CrossRef]

Jarem, J.

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
[CrossRef]

Jiang, L. W.

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

Y. Tian, L. J. Lv, L. W. Jiang, X. Wang, Y. H. Li, H. M. Yu, X. C. Feng, Q. Li, L. Zhang, and Z. Li, “Infrared/microwave (IR/MW) micromirror array beam combiner design and analysis,” Appl. Opt. 52, 5411–5419 (2013).
[CrossRef]

Jin, P.

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Kardian, C. J.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Kostuk, R. K.

Li, L.

Li, Q.

Li, Y. H.

Li, Z.

Liu, J.

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Liu, Y.

Y. Liu, J. Tan, and J. Ma, “Use of conducting inductive meshes with periodic rectangle units as an infrared/microwave dual-mode detecting beamsplitter,” J. Opt. 13, 035407 (2011).
[CrossRef]

Lomakin, V.

V. Lomakin and E. Michielssen, “Beam transmission through periodic subwavelength hole structures,” IEEE Trans. Antennas Propag. 55, 1564–1581 (2007).
[CrossRef]

Lu, C. C.

C. C. Lu, “A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes,” IEEE Trans. Antennas Propag. 51, 606–612 (2003).
[CrossRef]

Lu, Z.

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Lv, L. J.

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

Y. Tian, L. J. Lv, L. W. Jiang, X. Wang, Y. H. Li, H. M. Yu, X. C. Feng, Q. Li, L. Zhang, and Z. Li, “Infrared/microwave (IR/MW) micromirror array beam combiner design and analysis,” Appl. Opt. 52, 5411–5419 (2013).
[CrossRef]

Ma, J.

Y. Liu, J. Tan, and J. Ma, “Use of conducting inductive meshes with periodic rectangle units as an infrared/microwave dual-mode detecting beamsplitter,” J. Opt. 13, 035407 (2011).
[CrossRef]

Manasson, A.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).

Manasson, V.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).

McKay, J. P.

J. P. McKay and R. S. Yahya, “Compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate,” IEEE Trans. Antennas Propag. 39, 746–753 (1991).
[CrossRef]

Michielssen, E.

V. Lomakin and E. Michielssen, “Beam transmission through periodic subwavelength hole structures,” IEEE Trans. Antennas Propag. 55, 1564–1581 (2007).
[CrossRef]

Mobley, S.

S. Mobley and J. Cole, “Dichroic beam combiner to support hardware-in-the-loop testing of dual-mode common aperture seekers,” Proc. SPIE 3368, 32–41 (1998).
[CrossRef]

S. Mobley, J. Cole, J. Cooper, and J. Jarem, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2741, 316–331 (1996).
[CrossRef]

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).

S. Mobley, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2223, 100–111 (1994).

Mobley, S. B.

S. B. Mobley and J. Gareri, “Hardware-in-the-loop simulation (HWIL) facility for development, test, and evaluation of multi-spectral missile systems—update,” Proc. SPIE 4027, 11–21 (2000).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Morris, J. W.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Prendergast, D. T.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Quan, S.

S. Quan, “Time domain analysis of the near-field radiation of shaped electrically large apertures,” IEEE Trans. Antennas Propag. 58, 300–306 (2010).
[CrossRef]

Raguin, D.

Rao, S. M.

S. M. Rao, D. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Sadovnik, L.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).

Saylor, D.

J. P. Gareri, G. H. Ballard, J. W. Morris, D. Bunfield, and D. Saylor, “Application of scene projection technologies at the AMRDEC SSDD HWIL facilities,” Proc. SPIE 8356, 83560L (2012).
[CrossRef]

Schaubert, D. H.

D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984).
[CrossRef]

Sheng, X. Q.

X. Q. Sheng and W. Song, Essentials of Computational Electromagnetics (Wiley, 2012).

Shi, R.

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

Y. Tian, R. Xu, R. Shi, X. Wang, Q. Li, L. Zhang, and Z. Li, “IR/MW multilayered dielectric plate beam combiner design, optimization and evaluation,” Appl. Opt. 52, 288–297 (2013).
[CrossRef]

Song, W.

X. Q. Sheng and W. Song, Essentials of Computational Electromagnetics (Wiley, 2012).

Tan, J.

Y. Liu, J. Tan, and J. Ma, “Use of conducting inductive meshes with periodic rectangle units as an infrared/microwave dual-mode detecting beamsplitter,” J. Opt. 13, 035407 (2011).
[CrossRef]

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Thomas, B.

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).

Tian, Y.

Ulrich, J.

S. Clarke and J. Ulrich, “Dielectric material modeling in the MoM-based code FEKO,” IEEE Antennas Propag. Mag. 47, 140–147 (2005).
[CrossRef]

Vanderford, V.

S. Mobley, V. Vanderford, J. Cooper, and B. Thomas, “U.S. Army Missile Command dual-mode millimeter wave/infrared simulator development,” Proc. SPIE 2469, 15–19 (1995).

Wang, X.

Wang, X. L.

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

Wang, Y.

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Wilton, D.

S. M. Rao, D. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

Wilton, D. R.

D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984).
[CrossRef]

Winters, D. T.

S. A. Gearhart, T. J. Harris, C. J. Kardian, D. T. Prendergast, and D. T. Winters, “A hardware-in-the-loop test facility for dual-mode infrared and radar guidance systems,” Proc. SPIE 2469, 170–180 (1995).
[CrossRef]

Xu, R.

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

Y. Tian, R. Xu, R. Shi, X. Wang, Q. Li, L. Zhang, and Z. Li, “IR/MW multilayered dielectric plate beam combiner design, optimization and evaluation,” Appl. Opt. 52, 288–297 (2013).
[CrossRef]

Yahya, R. S.

J. P. McKay and R. S. Yahya, “Compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate,” IEEE Trans. Antennas Propag. 39, 746–753 (1991).
[CrossRef]

Yepishin, V.

L. Sadovnik, A. Manasson, V. Manasson, and V. Yepishin, “Infrared/millimeter wave beam combiner utilizing holographic optical element,” Proc. SPIE 3464, 155–163 (1998).

Yu, H. M.

Zhang, L.

Appl. Opt. (6)

IEEE Antennas Propag. Mag. (1)

S. Clarke and J. Ulrich, “Dielectric material modeling in the MoM-based code FEKO,” IEEE Antennas Propag. Mag. 47, 140–147 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

C. C. Lu, “A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes,” IEEE Trans. Antennas Propag. 51, 606–612 (2003).
[CrossRef]

S. M. Rao, D. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[CrossRef]

D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984).
[CrossRef]

J. P. McKay and R. S. Yahya, “Compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate,” IEEE Trans. Antennas Propag. 39, 746–753 (1991).
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[CrossRef]

J. Opt. (1)

Y. Liu, J. Tan, and J. Ma, “Use of conducting inductive meshes with periodic rectangle units as an infrared/microwave dual-mode detecting beamsplitter,” J. Opt. 13, 035407 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

J. Tan, Z. Lu, J. Liu, P. Jin, and Y. Wang, “Analysis of Fraunhofer diffractive characteristics of a tilted metallic mesh for its effect on optical measurement,” Meas. Sci. Technol. 18, 1703–1709 (2007).
[CrossRef]

Opt. Eng. (2)

L. J. Lv, Y. Tian, R. Shi, R. Xu, L. W. Jiang, X. L. Wang, X. Wang, and Z. Li, “Infrared/microwave micro-mirror array beam combiner test and analysis,” Opt. Eng. 52, 114103 (2013).
[CrossRef]

G. C. Holst, “Imaging system fundamentals,” Opt. Eng. 50, 052601 (2011).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Dual-mode common-aperture MW/IR HWIL system overview.

Fig. 2.
Fig. 2.

Principle of IR far-field computation by AFIM.

Fig. 3.
Fig. 3.

MW field distribution along the x axis with (a) N=1, (b) N=11, and (c) N=101 computed by AFIM (solid) and MLFMM (dashed).

Fig. 4.
Fig. 4.

Photograph of optical far-field experimental configuration.

Fig. 5.
Fig. 5.

Far-field distribution caused by a single micromirror for (a) experimental results and (b) simulation results.

Fig. 6.
Fig. 6.

Far-field distribution caused by 20 micromirrors for (a) experimental results and (b) simulation results.

Fig. 7.
Fig. 7.

MW near-field distribution along the x axis of (a) a circular and (b) a square-shaped aperture computed by AFIM, with D=1m.

Fig. 8.
Fig. 8.

Amplitude and phase of Epv, Erms, φpv, and φrms distributions along the x axis versus D.

Fig. 9.
Fig. 9.

IR far-field distribution along the x axis with g=10, 1, 0.1, and 0.01 mm.

Fig. 10.
Fig. 10.

IR far-field distribution along the x axis with g=0.1mm.

Tables (1)

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Table 1. Comparison of Computational Efficiency

Equations (25)

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Jm=×EA.
Am=ε4πΩJmejk0RRdx1dy0.
E(x,y)=1ε×Am=14πΩ[R×(×EA)]·(1+jk0R)ejk0RR3dx1dy0,
R=(xx0)2+(yy0)2+(z0x0)2,
R=(xx0)2+(yy0)2+(fx0tanα0)2.
E(x,y)jk04πΣEA·ejk0RRdx0dy0,
EA(x1,y0)=Eiexp[j(k0x0tanα0)],
R=R0[1++12(1+tan2θ)x02+y022(xx0+yy0+fx0tanθ)R02],
R0=x2+y2+f2.
R=R0xx0+yy0+x1tanθR02x2y2R0.
E(x,y)=Cn=0N1nghcosα0/2ng+hcosα0/2w/2w/2expjk0R0(β1x0+β2y0)dy0dx0,
C=EA4πjk0ejk0R0R0,
β1=x+tanα0R02x2y2R0tanα0,
h=g(cosα0sinα0tanα0).
E(x,y)=Chwcosα0sinc(β1hλR0)sinc(ywλR0)×n=0Nexpjk0β1ngR0,
β1=β1cosα0.
EN(x,y)=CNgwcosα0sinc(β1hλR0)sinc(ywλR0)×sinc(Nβ1gλR0)/sinc(β1gλR0).
EN(x,y)=CNgwcos2α0sinc(β1Ngcosα0λR0)sinc(ywλR0).
I(x,y)=1cos2α0sinc2(β1hλR0)sinc2(ywλR0)×sinc2(Nβ1gλR0)/sinc2(β1gλR0),
β1hλR0=m,m=±1,2,3.
xcosα0hλf=m,m=±1,2,3.
Nβ1gλR0=q,q=±1,2,3.
xNgλf=q,q=±1,2,3.
β1gλR0=p,p=±1,2,3.
xgλf=p,p=±1,2,3.

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