# Difference between revisions of "Equations"

## 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/(n-1) ± 10% Surface shadows reduce D.E. by $\textstyle {\frac {\lambda ^{2}}{nd^{2}}}$ Wavelength changes reduce D.E. by $\textstyle \left({\frac {\pi \Delta \lambda }{b\lambda }}\right)^{2}$ ## 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 = (n-1)Φ Scan angle multiplier = 1.4 @ 90° cross scan angle