Abstract

A novel method is proposed for simulating free-space diffraction propagation. This method is an improvement of the angular spectrum (AS) method and the band-limited angular spectrum (BLAS) method. Due to the sampling problem about the transfer function, AS is not suited for the long-distance propagation. For BLAS, the calculation accuracy would decrease when the propagation distance is relatively large. Using a wide calculation window can largely reduce the numerical error of AS and BLAS. However, a wide calculation window generally causes a huge calculation burden in the simulation. For the proposed method, the calculation window size is chosen to make sure all the sampling points in the frequency domain are effective in the sense of Nyquist theorem. The calculation complexity is independent of the calculation window size because of the use of the linear convolution. The linear convolution can be evaluated effectively by fast Fourier transform. This method can produce simulation results with high accuracy for far and near field propagation.

© 2012 Optical Society of America

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References

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2010

2009

2006

2005

2003

1999

1997

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

1989

1975

Endo, M.

Fujioka, T.

Haykin, S.

S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).

Kawakami, M.

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

Matsushima, K.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

Nanri, K.

Roggemann, M. C.

Rusch, J. J.

Schimmel, H.

Shen, F.

Shimobaba, T.

Siegman, A. E.

Stamnes, J. J.

Sziklas, E. A.

Takeda, S.

Urbach, H. P.

Van Veen, B.

S. Haykin and B. Van Veen, Signals and Systems (Wiley, 2005).

Veerman, J. A. C.

Voelz, D. G.

Wang, A.

Wyrowski, F.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Geometry of the model and definition of the coordinate system.

Fig. 2.
Fig. 2.

(a) Calculation accuracy of IR, AS, and BLAS and (b)  the effective sampling number Ne for BLAS as a function of propagation distance (W=1024λ).

Fig. 3.
Fig. 3.

Calculated irradiance distribution on the centerline of the square observation aperture when z=2000W.

Fig. 4.
Fig. 4.

(a) SNR as a function of propagation distance for IR, AS, BLAS, and WWAS and (b) the calculation window size for WWAS (W=1024λ).

Equations (9)

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SNR=I(x,y)dxdy|I(x,y)αIrig(x,y)|dxdy,
α=I(x,y)dxdyIrig(x,y)dxdy.
Ne=2ulim/Δu.
ulim=1λ[(2z/S)2+1]1/2.
Δu=1/S=2ulim/M,
S=22zMλM2λ2+M4λ4+64z2M2λ2.
A1(um,vn,0)=h=16Nw16Nw1g=16Nw16Nw1U(x1g,y1h,0)exp[i2π(umx1g+vny1h)]·Δx1·Δy1,
A1(um,vn,0)=h=Nw/2Nw/21g=Nw/2Nw/21U(x1g,y1h,0)exp[i2π(umx1g+vny1h)]·Δx1·Δy1,
A1(um,vn,0)=h=Nw/2Nw/21g=Nw/2Nw/21U(x1g,y1h,0)exp[i2πα(αumx1g+αvny1h)]·Δx1·Δy1=h=Nw/2Nw/21g=Nw/2Nw/21U(x1g,y1h,0)Δx1Δy1exp{iπα[(umαx1g)2+(vnαy1h)2um2vn2(αx1g)2(αy1h)2]}=exp[iπα(um2+vn2)]Δx1Δy1h=Nw/2Nw/21g=Nw/2Nw/21U(x1g,y1h,0)exp{iπα[(αx1g)2+(αy1h)2]}exp{iπα[(umαx1g)2+(vnαy1h)2]}=exp[iπα(um2+vn2)]Δx1Δy1·[f1(x1,y1)*f2(x1,y1)]

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