Grupo de Óptica

Universidad de CantabriaSantander

Optical Differentiation in High Resolution Wavefront Sensing

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

High Resolution Wavefront Sensing

D/r0>>13/5

0866.02 )(2944.0 rDj

2( ) ( ) iuxf x F u e du

The FT differentiation property

2( )2 ( ) iuxdf xiu F u e du

dx

( , ) ( , )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

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

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

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)

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

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

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

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

mask mask

+

1I 2I

x direction y direction

3I 4I

Mask analysis

- + -

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

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<<

Performance analysis

max

1R

2 b

2SNR nb

The maximum resolution is

The SNR is :

Position

Seco

nd d

eri

vati

ve (

a.u

.)

Position

Seco

nd d

eri

vati

ve (

a.u

.)Performance analysis

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)

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

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