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Grupo de Óptica
Universidad de CantabriaSantander
Optical Differentiation in High Resolution Wavefront Sensing
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Optical differentiation
Mask analysisSensor optimization
Performance analysis
Multi-object sensing
Estimate of the second derivative
Estimate of the first derivative
Mask analysisArrangementsPerformance analysis
Conclusions
OUTLINE
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High Resolution Wavefront Sensing
D/r0>>13/5
0866.02 )(2944.0 rDj
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2( ) ( ) iuxf x F u e du
The FT differentiation property
2( )2 ( ) iuxdf xiu F u e du
dx
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( , ) ( , )FT E x y E u v
( , )( , ) i x yE x y A e 1 ( , )( , )2
E x yFT E u v ui
x
( , ) 2E u v ui
( , )( , ) ( , ) x yE x y i x yA ex x
Optical differentiation
CCD
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2 uib
Oti J.E., Canales V.F. & Cagigal M.P., Optics Express (2003)
Amplitude transmittance
1
0 u
a
1
2b
W0.5a
w
2 ub a
22 2 ( , ) ( , )
( , ) 2x y x y
I x y a b abx x
,( , )
I(x y)ax y A
x b
Optical differentiation
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We perform 4 different intensity measurements, 2 with the mask slope along the x direction and 2 with the mask slope along the y direction
1 3
1 3
( , )
2
I Ix y a
x I I b
1I 2I
x direction
x
y
Mask analysis
y direction
2 4
2 4
( , )
2
I Ix y a
y I I b
3I 4I
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A semi reflecting mask allows to use the transmitted and reflected energy
I1(x,y)
I3(x,y)
Sensor optimization
Oti J.E., Canales V.F. y Cagigal M.P. Mon. Not. R Astron. Soc (2005)
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The resolution is controlled by the size of the differentiation mask
Resolution
max
1R
4 b
4 positions 2SNR nb
Signal-to-noise ratio
2SNR nb Transmitted and reflected
compromise between signal-to-noise ratio and resolution
Performance analysis
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The optimum size of the mask is related to the atmospheric conditions
Mask size (Airy rings)
Resi
dual vari
ance
(r
ad2 )
Performance analysis
D/r0=25
D/r0=20
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Multi-object operation: could be used in MCAO systems
Multi-object sensing
Simultaneously use the light from different reference stars to estimate its wavefront phase derivative independently
CCD
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21
22
(2 )
(2 )
M u b ia
M u b ia
Estimate of the second derivativeThe optical differentiation can be extended to higher order derivatives by modifying the focal plane mask
22 2
2
( )(2 ) ( ) i uxd f xiu F u e du
dx
To retain information about the sign is necessary to use a differentiation mask
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mask mask
+
1I 2I
x direction y direction
3I 4I
Mask analysis
- + -
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23 1 3 1
21 3 1 3
( , )
2 2 r
I I I Ix y a a
x I I b I I b f
Arrangement #1
b<<
M-Z
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Arrangement #2
23 1 3 1
21 3 1 3
( , )
2 2 r
I I I Ix y a a
x I I b I I b f
b<<
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Performance analysis
max
1R
2 b
2SNR nb
The maximum resolution is
The SNR is :
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Position
Seco
nd d
eri
vati
ve (
a.u
.)
Position
Seco
nd d
eri
vati
ve (
a.u
.)Performance analysis
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Conclusions
- The optical differentiation sensor is a high resolution sensor - It is able to estimate the first or the second derivative- It provides measurements not affected by scintillation- Multi-object sensor
Publications •“Analysis of the signal-to-noise ratio in the optical differentiation wavefront sensor”, Oti J.E., Canales V.F. & Cagigal M.P.,
Optics Express 11, 2783-2790 (2003)
•“Improvements on the optical differentiation wavefront sensor”, Oti J. E., Canales V.F. & Cagigal M.P.
Non. Not. R. Astron. Soc. 360, 1448-1454 (2005)
•“The optical differentiation coronagraph”, Oti J.E., Canales V.F. & Cagigal M.P.
The Astrophysical Journal, 630, 631-636 (2005)
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http://www.optica.unican.es/Linea1/
publicaciones.html
Dpto. de Física Aplicada Universidad de Cantabria
Santander (SPAIN)www.optica.unican.es
Future work
- Balance between resolution and SNR- Experimental checking to check some aspects of the first and second derivative for wavefront sensing- Systematic comparison between arrangements
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Comparison ODS - Pyramid Sensor
- Same expressions- Same resolution
Pyramid Sensor
ODS
- No moving, only rotating, parts- Multi-object
- Light absorbed by filter - Light reflected by the pyramid
- Energy efficiency