AngularSpectrumMethod

ASM!(u, λ, Δx, Δy, z; expand=true)

Same as ASM, but operates in-place on u, which must be an array of complex floating-point numbers.

ASM(u, λ, Δx, Δy, z; expand=true)

return diffracted field by the angular spectrum method (ASM). Evanescent waves are not eliminated but attenuated as $\exp(-2{\pi}wz)$. Without attenuation, the total energy $\iint|u|\mathrm{d}x\mathrm{d}y$ is conserved.

Arguments

• u: input field.
• λ: wavelength.
• Δx: sampling interval the in x-axis.
• Δy: sampling interval the in y-axis.
• z: diffraction distance.
• expand=true: if true (default), perform 4× expansion and zero padding for aliasing suppression.

BandLimitedASM!(u, λ, Δx, Δy, z; expand=true)

Same as BandLimitedASM, but operates in-place on u, which must be an array of complex floating-point numbers.

BandLimitedASM(u, λ, Δx, Δy, z; expand=true)

return diffracted field by the band-limited ASM (see Ref. 1).

1. Kyoji Matsushima and Tomoyoshi Shimobaba, "Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields," Opt. Express 17, 19662-19673 (2009)

ScalableASM!(u, λ, Δx, Δy, z; expand=true)

Same as ScalableASM, but operates in-place on u, which must be an array of complex floating-point numbers.

ScalableASM(u, λ, Δx, Δy, z; expand=true)

return automatically scaled diffraction field by the scalable ASM (see Ref. 1). The sampling pitch in the destination plane $\Delta_{d}$ is $\Delta_{d}=\dfrac{\lambda z}{pN\Delta_{s}}$, where $\Delta_{s}$ is the sampling pitch in the source plane, $N$ is the number of pixels in the source or destination plane, and $p=2$ is the padding factor.

1. Rainer Heintzmann, Lars Loetgering, and Felix Wechsler, "Scalable angular spectrum propagation," Optica 10, 1407-1416 (2023)

ScaledASM!(u, λ, Δx, Δy, z, R; expand=true)

Same as ScaledASM, but operates in-place on u, which must be an array of complex floating-point numbers.

ScaledASM(u, λ, Δx, Δy, z, R; expand=true)

return scaled diffraction field according to the scale factor $R$ by the scaled ASM (see Ref. 1).

1. Tomoyoshi Shimobaba, Kyoji Matsushima, Takashi Kakue, Nobuyuki Masuda, and Tomoyoshi Ito, "Scaled angular spectrum method," Opt. Lett. 37, 4128-4130 (2012)

ShiftedASM!(u, λ, Δx, Δy, z, x₀, y₀; expand=true)

Same as ShiftedASM, but operates in-place on u, which must be an array of complex floating-point numbers.

ShiftedASM(u, λ, Δx, Δy, z, x₀, y₀; expand=true)

return shifted diffraction field with the shift distance $x_{0}$ and $y_{0}$ by the shifted ASM (see Ref. 1).

1. Kyoji Matsushima, "Shifted angular spectrum method for off-axis numerical propagation," Opt. Express 18, 18453-18463 (2010)

TiltedASM!(u, λ, Δx, Δy, T; expand=true, weight=false)

Same as TiltedASM, but operates in-place on u, which must be an array of complex floating-point numbers.

TiltedASM(u, λ, Δx, Δy, T; expand=true, weight=false)

return tilted diffraction field for a rotation matrix $T$ by the tilted ASM (see Ref. 1, 2). If weight=true, a diagonal weighting matrix is used as the Jacobian determinant (default false). In this case, the energy conservation improves, but the computational cost is high (see Ref. 3).

1. Kyoji Matsushima, Hagen Schimmel, and Frank Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves," J. Opt. Soc. Am. A 20, 1755-1762 (2003)
2. Kyoji Matsushima, "Formulation of the rotational transformation of wave fields and their application to digital holography," Appl. Opt. 47, D110-D116 (2008)
3. James G. Pipe and Padmanabhan Menon, "Sampling density compensation in MRI: Rationale and an iterative numerical solution," Magn. Reson. Med. 41, 179-186 (1999)