High resolution tomographic diffraction microscopy

Transcription

1 High resolution tomographic diffraction microscopy J. Girard,Y. Ruan 1, E. Mudry 1, F. Drsek G. Maire 1, P. Chaumet 1, H. Giovannini 1,K. Belkebir 1, A. Talneau 2, A. Sentenac 1 1 Institut Fresnel (Marseille) 2 Laboratoire de Photonique et de Nanostructures (Marcoussis)

2 Basic principles of an active far-field imaging system P(r) = X (r) E objet (r) X objet k with k = 2 / e(k) Monochromatic illumination e(k) proportional to P(k) = TF (X objet E objet ) taken at k q P(q) At best, P(q) is known on a sphere of radius k 0 = 2 /. The resolution for P is /2 (diffraction limit) k q A much better resolution can be obtained for X objet

3 Optical diffraction tomography ( under Born approimation) E inc (r) = E 0 ep(i k inc.r) X objet k k inc e(k,k inc ) P(k,k inc ) X objet (k-k inc ) Born : P(r, k inc X objet (r) E inc (r) q X objet (q) At best X objet (q) is known on a ball of radius 2k 0 = 4 / - k inc q k The resolution is about 0.35.

4 Scanning optical microscopy X objet Focused illumination Measure of the integrated diffracted intensity Wide field optical microscopy Incoherent illumination k X objet Measure of the total intensity in the image plane The image can not be interpreted as a map of X objet (even under Born approimation)! In both cases, the resolution of the 3D image is about 0.6 in the transverse plane and 1.5 along the optical ais

5 Digital holographic microscopy E inc (r) = E 0 ep(i k inc.r) Incident plane wave k E(,k inc ) k inc k Measure of the field E(,kinc) X objet e(k, k inc ) (amplitude and phase) The measure of E (or e) yields (under Born approimation) X objet (q) for q S q - k inc S q X objet can be reconstructed in 3D with 0.6 transverse resolution but very poor aial resolution.

6 Tomographic diffraction microscopy The angle of incidence varies k k inc k X objet e(k, k inc ) Measure of the field E() (amplitude and phase) for each incident angle The measure of E (or e) for various k inc yields (under Born approimation) X objet (q) pour q D q D X objet can be reconstructed in 3D with 0.35 transverse resolution and ~ aial resolution q

7 Eamples of results found in the literature MIT Nature Methods 4, 717 (2007) 10 µm n 3D refractive inde mapping of a HeLa live cell ODT slices at different depths into the cell Brightfield images for objective focus at depths e and f ODT successfully applied to 3D quantitative refractive inde mapping at low inde contrasts

8 How can we improve the aial resolution in Tomographic diffraction microscopy? Reflection configuration Transmission configuration ideal configuration Mirror solution!

9 Isotropic tomographic diffraction microscopy using a mirror-substrate k E(, k inc ) miroir k X objet k inc e(k, k inc ) Measure of the field E(,k inc ) or e(k, k inc ) k ref k inc ref X objet k k inc Under Born E objet (r) E inc (r)=e 0 ep(ik inc.r)+re 0 ep(ik inc ref.r) e(k, k inc ) X objet (k-k inc )+ rx objet (k-k inc ref ) rx objet (k ref -k inc )+ r 2 X objet (k ref -k inc ref ) With a cosine fourier transform and both polariation the four terms can be distinguished X objet (q) is known on a ball of radius 4 /, Isotropic resolution of 0.35!!

10 Mirror tomographic diffraction microscopy (synthetic data) 0,6λ 2λ without mirror With mirror λ/4 Real part of permittivity Imaginary part of permittivity Mudry et al, OL 2010

11 Tomographic diffraction microscopy : the set-up Reflection scheme set-up : Same NA for illuminating the sample and collecting the scattered field Can image samples deposited on opaque substrates Rotative mirror laser Incident and reflected fields beam epander Phase modulator = 633 nm Diffracted field Reference field sample L 1 L 2 D 1 L 3 f 4 = f 3 L 4 CCD camera D 2 Phase-shifting interferometry in the Fourier space f 1 f 2 = f 1 L 1 : objective f 4 = f 2 f 4 Possibility to add a lens after L 4 to image the sample in direct space

12 Tomographic diffraction microscopy : eperimental results First stage : observation of 2D samples Si Si resin ( r = 2.66) Observed in direct space in the set-up (CCD intensity image) y k inc Si resin µm inc k 100 nm

13 Tomographic diffraction microscopy Wide field microscopy, NA= Tomography (same microscope), NA=0.75 2D permittivity mapping 1 µm 500 nm 100 nm 300 nm Maire et al, PRL 2009

14 Resolution under the diffraction limit in TDM using a grating-substrate Grating substrate k E(, k inc ) k k inc e(k, k inc ) Measure of the field E(,k inc ) or e(k, k inc ) Above the grating, Rayleigh series E inc (r)= A K () ep[i ( k inc + K). ] Under Born E objet (r) E inc (r), X objet is obtained with an iterative reconstruction technique e(k,k inc ) A K X objet ( k-k inc -K) Pb : need to distinguish the terms!

15 Resolution under the diffraction limit in TDM using a grating substrate (synthetic data) h= /12 int = /20 et = /10 Sentenac et al, PRL 2006 Chaumet et al, PRA 2007

16 Focusing under the diffraction limit using a grating substrate Time reversal technique : One simulates the field in the k direction, e(k), emitted by a dipole p placed at the wanted focus point. The incident beam is made of plane waves propagating along k with comple amplitude, e*(k). p r 0 r 0 e(k) Attention : For the spot to be invariant whatever the focus point, one needs specially designed grating with ideally one dominant order!

17 Focusing under the diffraction limit using a grating-substrate Sentenac et al, PRL 2008

18 Imaging under the diffraction limit in the multiple scattering regime P(r) = X objet (r) E objet (r) X objet k avec k = 2 / e(k) Monochromatic illumination e(k) proportional to P(k) = TF (P) taken at k e(k) E objet (k-q)x objet (q)dq If E objet ehibits high spatial frequencies, e(k) will depend on the high spatial frequencies of X objet The sample can change E inc into a field E objet with high spatial frequencies thanks to multiple scattering E objet = E inc + G X objet E objet Is it possible to reconstruct X objet with a resolution much better than 0.35?

19 Reconstruction algorithm X : permittivity contrast d : measured diffracted field e(k, k inc ) e(k, k inc ) k inc Equation for E objet E objet = E inc + G X E objet Equation for e e = g X E objet Under Born: Minimisation of F( X ) = d - g X E inc 2 Without Born: Minimisation of F( X t ) = d - g X t E t 2 with E t = E inc + G X t-1 E t

20 Tomographic diffraction microscopy in the multiple scattering regime Maire et al, PRL, (2009) Girard et al PRA (2010) air glass 25 nm Field in the investigation domain, E objet Weak permittivity contrast : X objet = nm E objet Strong permittivity contrast : X objet = 26 E objet 25 nm Glass Germanium µm E objet close to E inc E objet very different from E inc

21 Tomographic diffraction microscopy in the multiple scattering regime air -50 < 10 incidences < 50 glass E inc,1 E inc,10-55 < 683 detections < 55 E inc,5 We use an oil immersion objective The Abbe resolution limit is 300 nm

22 Tomographic diffraction microscopy in the multiple scattering regime -50 < 10 incidences < < 683 detections < 55 air glass 25 nm 500 nm Diffraction limit = 300 nm Verre : X objet = 1.25 Reconstructed permittivity Germanium : X objet = nm µm Synthetic data! Eperimental data!

23 Conclusion Possible paths to improve the resolution of microsccopy devoted to NON fluorescent samples : - Use a tomographic approach with sophisticated inversion algorithms - replace the glass slides by nanostructured or metallic slides - take advantage of the multiple scattering phenomenon!!!!

24 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < nm -55 < 683 detections < nm µm Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

25 Eperimental validation air glass Ge 25 nm µm Back-propagation 500 nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

26 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

27 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

28 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

29 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

30 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

31 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

32 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

33 Eperimental validation air glass Ge 25 nm µm Iteration nm -50 < 10 incidences < < 683 detections < 55 Resolution = 100 nm < /6 Rayleigh criterion : = 300 nm

34 Eperimental validation air nm AFM profile glass Ge 25 nm 103 nm µm Iteration 9 nm 100 nm Permittivity cut 25 nm 100 nm µm µm

35 Inversion of a single rod sample air 42 nm glass Ge 30 nm µm 30 nm 56 nm µm µm Geometry of a single nanorod correctly retrieved