grupo de Óptica universidad de cantabria santander
DESCRIPTION
Optical Differentiation in High Resolution Wavefront Sensing. Grupo de Óptica Universidad de Cantabria Santander. OUTLINE. Optical differentiation. Estimate of the first derivative. Mask analysis. Sensor optimization. Performance analysis. Multi-object sensing. - PowerPoint PPT PresentationTRANSCRIPT
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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