Grupo de Óptica Universidad de Cantabria Santander

1. Optical Differentiation in High Resolution Wavefront Sensing Grupo de Óptica Universidad de Cantabria Santander

2. OUTLINE Optical differentiation Estimate of the first derivative Mask analysis Sensor optimization Performance analysis Multi-object sensing Estimate of the second derivative Mask analysis Arrangements Performance analysis Conclusions

3. D/r0>>1 High Resolution Wavefront Sensing

4. The FT differentiation property

5. Optical differentiation CCD

6. Amplitude transmittance 1 a u 0 Optical differentiation w Oti J.E., Canales V.F. & Cagigal M.P., Optics Express (2003)

7. y x Mask analysis 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 y direction x direction

8. Sensor optimization A semi reflecting mask allows to use the transmitted and reflected energy I1(x,y) I3(x,y) Oti J.E., Canales V.F. y Cagigal M.P. Mon. Not. R Astron. Soc (2005)

9. Performance analysis Resolution The resolution is controlled by the size of the differentiation mask Signal-to-noise ratio Transmitted and reflected 4 positions compromise between signal-to-noise ratio and resolution

10. Residual variance(rad2) Mask size (Airy rings) Performance analysis The optimum size of the mask is related to the atmospheric conditions D/r0=25 D/r0=20

11. Multi-object sensing Multi-object operation: could be used in MCAO systems Simultaneously use the light from different reference stars to estimate its wavefront phase derivative independently CCD

12. Estimate of the second derivative The optical differentiation can be extended to higher order derivatives by modifying the focal plane mask To retain information about the sign is necessary to use a differentiation mask

13. + + - - Mask analysis x direction y direction

14. Arrangement #1 M-Z b<<

15. Arrangement #2 b<<

16. 1 = R max p 2 b Performance analysis The maximum resolution is The SNR is :

17. Second derivative (a.u.) Second derivative (a.u.) Position Position Performance analysis

18. 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)

19. 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 Dpto. de Física Aplicada Universidad de Cantabria Santander (SPAIN) www.optica.unican.es http://www.optica.unican.es/Linea1/publicaciones.html

20. Comparison ODS - Pyramid Sensor ODS Pyramid Sensor • Same expressions • Same resolution • No moving, only rotating, parts • Multi-object • Energy efficiency - Light reflected by the pyramid - Light absorbed by filter