Computer-Generated Holography

Replay field λz/Δx, diffraction angle, replay spot and first-order efficiency of a phase-quantised hologram on a pixelated SLM.

Model: Textbook approximation

Wavelength λ (nm)SLM pixel pitch Δx (µm)SLM width N_x (px)SLM height N_y (px)Replay distance or Fourier-lens focal length z (mm)Pixel fill factor (area)

Modulation

Phase bit depth

Results

Largest diffraction angle arcsin(λ/2Δx)2.267°

Replay field λz/Δx39.56 mm

Replay spot λz/(NΔx), x × y20.61 × 36.63 µm

Resolvable spots N_x × N_y1920 × 1080

Angular resolution λ/(N_xΔx)0.04121 mrad

First-order efficiency99.99 %

Pixel envelope at the field edge0.447

SLM aperture N_xΔx × N_yΔx15.36 × 8.640 mm

Hologram frame size2.074 MB

First-order efficiency against bit depth

Pixel envelope across the replay field (x)

Model

θ_max = arcsin(λ/(2Δx)), replay field λz/Δx, spot λz/(NΔx)

η = sinc²(π/L) for L phase levels (4/π² = 40.5 % binary), 1/π² = 10.1 % binary amplitude

Envelope sinc²(π√F Δx f), f = x/(λz); at the field edge sinc²(π√F/2)

Scalar paraxial replay of a pixelated SLM, either in the Fresnel region at distance z or in the focal plane of a lens of focal length z. The replayed pattern repeats every λz/Δx; beyond it lie the higher orders. The efficiency is the first-order efficiency of an L-level phase staircase (Swanson 1989) and assumes ideal phase levels; fringing fields between pixels, phase flicker, the zero order from the dead space and the iterative algorithm's own error are not included. The frame size counts the bits per pixel only.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Scalar paraxial replay of a pixelated SLM at distance z, or in the focal plane of a lens of focal length z. The efficiency is the first-order efficiency of an L-level phase staircase with ideal levels; fringing fields, phase flicker, the dead-space zero order and algorithm error are not included.

Swanson G. J. (1989). Binary optics technology: the theory and design of multi-level diffractive optical elements. MIT Lincoln Laboratory Technical Report 854. First-order efficiency sinc²(π/L) of an L-level phase profile. apps.dtic.mil
Schnars U., Jüptner W. P. O. (2002). Digital recording and numerical reconstruction of holograms. Meas. Sci. Technol. 13, R85–R101. Fresnel pixel λz/(NΔx) and the pitch-limited diffraction angle. doi:10.1088/0957-0233/13/9/201

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