Difference between revisions of "Equations"

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|[[Image:Sine.gif|left]]<br>
 
|[[Image:Sine.gif|left]]<br>
 
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*Max D.E. ~ 30% +/-1 order  
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*Max D.E. ~ 30% ± 1 order  
 
*Power distribution follows Bessel function in the scaler region.  
 
*Power distribution follows Bessel function in the scaler region.  
*T [[Image:Simeq.gif]]&nbsp;[[Image:Lambda.gif]]&nbsp;for transmission.  
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*T ≈ λ for transmission.  
*T [[Image:Simeq.gif]]&nbsp;[[Image:Lambda.gif]]&nbsp;/ 4 for reflection.  
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*T ≈ λ/4 for reflection.  
 
*Easily replicated or deep etch can yield higher efficiency.  
 
*Easily replicated or deep etch can yield higher efficiency.  
 
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|[[Image:Square.gif|left]]
 
|[[Image:Square.gif|left]]
 
|
 
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*Max D.E. ~ 40% +/-1 order.  
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*Max D.E. ~ 40% ± 1 order.  
 
*Power distributions favors odd orders.  
 
*Power distributions favors odd orders.  
 
*Pi phase shift typical.  
 
*Pi phase shift typical.  
 
*Classic binary grating.  
 
*Classic binary grating.  
*T [[Image:Simeq.gif]]&nbsp;[[Image:Lambda.gif]]&nbsp;for transmission.  
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*T ≈ λ for transmission.  
*T [[Image:Simeq.gif]]&nbsp;[[Image:Lambda.gif]]&nbsp;/ 4 for reflection.  
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*T ≈ λ/4 for reflection.  
 
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*Max D.E ~ 98%  
 
*Max D.E ~ 98%  
 
*Reflection Case:  
 
*Reflection Case:  
**[[Image:Lambda.gif]]&nbsp;= 2 d sin a  
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**λ = 2 d sin a  
**T = [[Image:Lambda.gif]]&nbsp;/ 2 +/- 10%   
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**T = λ/2 ± 10%   
 
*Transmission Case:  
 
*Transmission Case:  
**[[Image:Lambda.gif]]&nbsp;= d sin b  
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**λ = d sin b  
**a [[Image:Simeq.gif]]&nbsp;2b  
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**a 2b  
**T = [[Image:Lambda.gif]]&nbsp;/ (n-1) +/- 10%  
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**T = λ/(n-1) ± 10%  
**Surface shadows reduce D.E. by&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&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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|[[Image:Scan.gif|left]]<br>
 
|[[Image:Scan.gif|left]]<br>
 
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*N = [[Image:Theta.gif]]&nbsp;D / ( 1.4 [[Image:Lambda.gif]])  
+
*N = θD/(1.)  
 
*N = number of resolvable spots
 
*N = number of resolvable spots
*[[Image:Theta.gif]] = full scan angle in radians  
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*θ = full scan angle in radians  
 
*D = beam diameter in microns  
 
*D = beam diameter in microns  
*[[Image:Lambda.gif]]&nbsp;= wavelength   
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*λ = wavelength   
*[[Image:Phi.gif]]&nbsp;= wedge angle of glass  
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*Φ = wedge angle of glass  
*Special case of linear scan and near wobble invariance&nbsp;[[Image:Invariance1.gif]] max straight scan angle ~ 36 deg</span>  
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*Special case of linear scan and near wobble invariance a ~ b ~ 45° max straight scan angle ~ 36°  
*Dynamic wobble&nbsp;[[Image:Dynwob1.gif]] 
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*Dynamic wobble <math>\scriptstyle \simeq \Delta\Omega/128</math>
*Wedge wobble = (n-1) [[Image:Phi.gif]]
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*Wedge wobble = (n-1)Φ
*Scan angle multiplier = 1.4 @ 90degrees cross scan angle  
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*Scan angle multiplier = 1.4 @ 90° cross scan angle  
 
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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