10/17/97Optical Diffraction Tomography1 A.J. Devaney Department of Electrical Engineering Northeastern University Boston, MA USA 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, , 1992

10/17/97Optical Diffraction Tomography2 What’s Wrong With Optical Microscopy? Objective Lens Condenser Semi-transparent Object Image 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

10/17/97Optical Diffraction Tomography3 Experimental Setup Digital Camera Images Intensity Distribution Over Diffraction Plane Digital Camera collimator HE-NE Laser Test tube with sample incident plane wavetransmitted wave Diffraction Plane d Magnifying Lens Magnified diffraction pattern Image is Gabor hologram of diffraction plane field distribution

10/17/97Optical Diffraction Tomography4 Inverse Problem transmitted wave Diffraction Plane d Inverse Problem : Given intensity of transmitted wave estimate the complex index of refraction distribution of the object. Measure transmitted intensity over diffraction plane Difficulties: Phase Problem Phase retrieval Holography Quantitative Inversion Diffraction tomography Born Model Rytov Model Limited Data Multiple experiments

10/17/97Optical Diffraction Tomography5 Scattering Models s 0 Born Model Rytov Model Diffraction tomography solves inverse problem within either Born or Rytov approximation. Requires phase of field.

10/17/97Optical Diffraction Tomography6 Why Tomography? s 0 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

10/17/97Optical Diffraction Tomography7 Diffraction Tomography Filtering Backpropagation Induced Source Scattered Field Filtered Scattered Field Sum over Views Filtered Backpropagation Algorithm

10/17/97Optical Diffraction Tomography8 Quality of Inversion Point Spread Function approaches delta function as number of views and wavenumber k approach infinity

10/17/97Optical Diffraction Tomography9 Phase Retrieval Camera # 2 collimator HE-NE Laser Test tube with sample incident plane wave Magnifying Lens Camera # 1 Diffraction Plane # 1 Diffraction Plane # 2 Beam Splitter 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

10/17/97Optical Diffraction Tomography10 Holography transmitted wave Diffraction Plane d Filter and backpropagate  s)(  conjugate image A.J. Devaney, Phys. Rev. Letts. 62 (1989)

10/17/97Optical Diffraction Tomography11 Born Inversion Procedures backpropagated filtered data Diffraction Plane d Measured intensity distribution(s) Phase retrieval Diffraction Tomographic Reconstruction Algorithm Complex index of refraction distribution of object Can employ single view theory to deal with thin phase only objects

10/17/97Optical Diffraction Tomography12 Quest for a Better 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 Theoretical better image quality No need to stain or use floresence Much less expensive Coherent Tomographic Microscope Comparison with scanning confocal microscope