Equations
From HoloWiki  A Holography FAQ
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Contents
1
Common DOE surfaces
1.1
Sinusoidal, triangle
1.2
Square, rectangle
1.3
Blazed, sawtooth
2
Holographic Deflectors (hologons)
Common DOE surfaces
Sinusoidal, triangle
Max D.E. ~ 30% ± 1 order
Power distribution follows Bessel function in the scaler region.
T ≈ λ for transmission.
T ≈ λ/4 for reflection.
Easily replicated or deep etch can yield higher efficiency.
Square, rectangle
Max D.E. ~ 40% ± 1 order.
Power distributions favors odd orders.
Pi phase shift typical.
Classic binary grating.
T ≈ λ for transmission.
T ≈ λ/4 for reflection.
Blazed, sawtooth
Max D.E ~ 98%
Reflection Case:
λ = 2 d sin a
T = λ/2 ± 10%
Transmission Case:
λ = d sin b
a ≈ 2b
T = λ/(n1) ± 10%
Surface shadows reduce D.E. by
$\lambda ^{2}/nd^{2}$
File:Equ1.gif
Wavelength changes reduce D.E. by
$(\pi \Delta \lambda /b\lambda )^{2}/$
File:Equ2.gif
Holographic Deflectors (hologons)
N = θD/(1.4λ)
N = number of resolvable spots
θ = full scan angle in radians
D = beam diameter in microns
λ = wavelength
Φ = wedge angle of glass
Special case of linear scan and near wobble invariance a ~ b ~ 45° max straight scan angle ~ 36°
Dynamic wobble
$\simeq \Delta \Omega /128$
Wedge wobble = (n1)Φ
Scan angle multiplier = 1.4 @ 90° cross scan angle
Last modified on 9/29/97
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