Difference between revisions of "Equations"

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**a ≈ 2b  
 
**a ≈ 2b  
 
**T = λ/(n-1) ± 10%  
 
**T = λ/(n-1) ± 10%  
**Surface shadows reduce D.E. by <math>\lambda^2 / n d^2</math>&nbsp;[[Image:Equ1.gif]] 
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**Surface shadows reduce D.E. by <math>\textstyle \frac{\lambda^2}{n d^2}</math>
**Wavelength changes reduce D.E. by <math>(\pi\Delta\lambda / b\lambda)^2/</math>&nbsp;[[Image:Equ2.gif]]    
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**Wavelength changes reduce D.E. by <math>\textstyle \left(\frac{\pi\Delta\lambda}{b\lambda}\right)^2</math>   
 
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*Φ = wedge angle of glass  
 
*Φ = wedge angle of glass  
 
*Special case of linear scan and near wobble invariance a ~ b ~ 45° max straight scan angle ~ 36°   
 
*Special case of linear scan and near wobble invariance a ~ b ~ 45° max straight scan angle ~ 36°   
*Dynamic wobble <math>\simeq \Delta\Omega/128</math>  
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*Dynamic wobble <math>\scriptstyle \simeq \Delta\Omega/128</math>  
 
*Wedge wobble = (n-1)Φ  
 
*Wedge wobble = (n-1)Φ  
 
*Scan angle multiplier = 1.4 @ 90° cross scan angle  
 
*Scan angle multiplier = 1.4 @ 90° cross scan angle  

Latest revision as of 15:05, 12 May 2013

Common DOE surfaces

Sinusoidal, triangle

Sine.gif

  • 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

Square.gif
  • 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

Blazed.gif
  • 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
    • Wavelength changes reduce D.E. by

Holographic Deflectors (hologons)

Scan.gif

  • 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
  • Wedge wobble = (n-1)Φ
  • Scan angle multiplier = 1.4 @ 90° cross scan angle

Last modified on 9/29/97