1. Optical Diffraction Tomography A.J. Devaney Department of Electrical Engineering Northeastern University Boston, MA 02115 USA E-mail: tonydev2@aol.com • Review problems with classical optical microscopy • Review experimental setup and goal of optical diffraction tomography (ODT) • Describe two approaches to ODT • Phase retrieval • Holographic • Review results to date • Outline future goals Holography, Acoustical, Encyclopedia of Applied Physics, Vol.7 , 511-530, 1992 Optical Diffraction Tomography

2. Image Semi-transparent Object Condenser Objective Lens What’s Wrong With Optical Microscopy? • Illuminating light spatially coherent over small scale: • Poor image quality for 3D objects • Need to thin slice • Cannot image phase only objects: • Need to stain • Need to use special phase contrast methods • Require high quality optics Optical Diffraction Tomography

3. Diffraction Plane Test tube with sample collimator d HE-NE Laser incident plane wave transmitted wave Magnifying Lens Magnified diffraction pattern Experimental Setup Digital Camera Digital Camera Images Intensity Distribution Over Diffraction Plane Image is Gabor hologram of diffraction plane field distribution Optical Diffraction Tomography

4. Inverse Problem Diffraction Plane d Measure transmitted intensity over diffraction plane transmitted wave Inverse Problem: Given intensity of transmitted wave estimate the complex index of refraction distribution of the object. • Difficulties: • Phase Problem • Phase retrieval • Holography • Quantitative Inversion • Diffraction tomography • Born Model • Rytov Model • Limited Data • Multiple experiments Optical Diffraction Tomography

5. s 0 Scattering Models Born Model Rytov Model Diffraction tomography solves inverse problem within either Born or Rytov approximation.Requires phase of field. Optical Diffraction Tomography

6. s 0 Why Tomography? Measurement Plane Integral along straightline ray path: Inversion via CT Diffraction tomography (DT) is generalization of CT to diffracting wavefields • Inversion methods include: • Filtered backpropagation • Generalized ART and SIRT • Various non-linear and limited view algorithms Optical Diffraction Tomography

7. Diffraction Tomography Scattered Field Filtering Filtered Scattered Field Backpropagation Induced Source Filtered Backpropagation Algorithm Sum over Views Optical Diffraction Tomography

8. Quality of Inversion Point Spread Function approaches delta function as number of views and wavenumber k approach infinity Optical Diffraction Tomography

9. Camera # 2 Diffraction Plane # 1 Magnifying Lens Test tube with sample Beam Splitter collimator HE-NE Laser incident plane wave Diffraction Plane # 2 Camera # 1 Phase Retrieval • Phase Retrieval • Gerchberg Saxton iterative procedure • Approximate algebraic method Diffraction tomography (DT) generates quantitative image of real and imaginary parts of object’s index of refraction distribution from complex (amplitude and phase) distribution of field Optical Diffraction Tomography

10. Diffraction Plane d transmitted wave conjugate image ( s ) y Holography Filter and backpropagate A.J. Devaney, Phys. Rev. Letts.62 (1989) Q Optical Diffraction Tomography

11. Born Inversion Procedures • Phase retrieval Measured intensity distribution(s) Diffraction Tomographic Reconstruction Algorithm Complex index of refraction distribution of object d backpropagated filtered data Diffraction Plane Can employ single view theory to deal with thin phase only objects Optical Diffraction Tomography

12. Quest for a Better Microscope Coherent Tomographic Microscope • Use coherent light and one or more Gabor holograms of diffraction plane field • Employ phase retrieval and DT reconstruction algorithm to reconstruct object • Employ direct holographic based DT reconstruction algorithm • Can operate in thin object or thick object mode Comparison with scanning confocal microscope • Theoretical better image quality • No need to stain or use floresence • Much less expensive Optical Diffraction Tomography