Apparatus and method for quantitive phase tomography through linear scanning with coherent and non-coherent detection

Abstract

The disclosed invention describes a new apparatus performing a new data acquisition for quantitative refractive index tomography. It is based on a linear scanning of the specimen, opposed to the classical approaches based on rotations of either the sample or the illumination beam, which are based on the illumination with plane waves, which orientation is successively modified in order to acquire angular information. On the contrary, the inventive apparatus and method rely on a specially shaped illumination, which provides straightforwardly an angular distribution in the illumination of the specimen. The specimen can thus be linearly scanned in the object plane in order to acquire the data set enabling tomographic reconstruction, where the different positions directly possess the information on various angles for the incoming wave vectors.

1 . An apparatus for performing quantitative phase tomography on a specimen, comprising:
 an illumination source for providing an illuminating beam;   an optical device arranged to transform the illuminating beam into a shaped illuminating beam directed according to an optical axis direction to irradiate the specimen;   a microscope objective arranged to collect a beam scattered by the specimen;   a wave front analyser for wave field amplitude and phase determination and further comprising   an array sensor for measuring the intensity of beam scattered by the specimen and collected by the microscope objective, and outputting a measurement signal;   displacement means to slide the specimen in a plane normal to the optical axis direction;   computing means to process the measurement signal output at the array sensor and delivering quantitative phase tomography images representing the object in 3D and providing quantitative values of the refractive index distribution.   
     
     
         2 . The apparatus of  claim 1 , further comprising
 means for analysing the scattered wave front and based on either of the techniques used to analyse the wave front in term of amplitude and phase for a given wavelength,   such as Hartmann-Shack analyser, or   techniques based on transport of intensity equations (TIE)   common path interferometry, wherein the means for producing the reference beam comprises an optically filter, in most situation a grating, that is arranged to filter the beam scattered to derive the reference beam from the light scattered by the specimen. Examples are: Quadriwave interferometry, SLIM and others,   digital holography (DHM) where the beam is derived from the illumination beam before crossing the object   shearing interferometry and many other techniques used to analyse wavefronts.   
     
     
         3 . The apparatus of  claim 1 , further comprising
 means for producing a reference beam that is coherent relative to the illuminating beam;   means for directing the reference beam and combining it with the beam scattered by the specimen such that measurement signal output by the array sensor corresponds to a coherent detection of the beam scattered or light scattered by the specimen itself.   
     
     
         4 . The apparatus of  claim 3  wherein the means for producing the reference beam comprises a beam splitter that is arranged to derive the reference beam from the illuminating beam. 
     
     
         5 . The apparatus according to  claim 1 , wherein the optical device is a condenser lens arranged to transform the illuminating beam into a convergent illuminating beam. 
     
     
         6 . The apparatus of  claim 2 , where the condenser lens is confounded with the collecting Microscope Objective, and means are arranged for illuminating the object from the same side as the collected beam, thus providing a mean to achieve tomographic images from the beam back-scattered by the object. 
     
     
         7 . The apparatus of  claim 1 , where the scattered light is collected by two Microscope Objectives symmetrically positioned on each side of the object and permitting to collect simultaneously transmitted and backscattered light with a convergent illuminating beam provided by one or the other MO, on a single side or on both side in alternance (4π geometry). 
     
     
         8 . The apparatus according to  claim 1 , wherein the illumination source is for providing the illuminating beam with a linear polarisation. 
     
     
         9 . The apparatus according to  claim 1 , wherein the illumination source is for providing the illuminating beam with a radial polarisation. 
     
     
         10 . The apparatus according to  claim 9  comprising:
 A MO with optional tube lens and 
 one or two beamsplitters permitting to superimpose on the object beam, one or two linearly polarised reference beams, permitting to irradiate the detector array with alternate or simultaneous orthogonally linearly polarized beams which can be derived from the radially polarised beam by a combination of linear polarizers and mirrors. Optionally polarization maintaining fibers can be used for handling the beams to the beam splitters, 
 and where the polarisation state of the scattered field is analysed along two orthogonal directions by using simultaneously two reference beams polarised linearly along two orthogonal directions. 
 
     
     
         11 . The apparatus of  claim 1  where
 the wave front analyser is composed of one or several cameras arranged at one or several distances from the focal point to provide intensities measurements and providing means to reconstruct the wave front of the scattered field complex wavefront according to any of the technique of intensity based restoration of complex wavefront: techniques from intensity measurements: either derived from Gershberg-Saxton iterative method when a single intensity measurement is available, or based on the multiple distance intensity measurements required for Transport of Intensity Equations (TIE) based methods. A mechanical slider can optionally be used to move the camera in the optical axis direction. 
 
     
     
         12 . The apparatus of  claim 1  where
 the wave front analyser is composed of optical elements arranged according to the requirements of the wavefront analyser used to reconstruct the complex wavefront: i.e. an array of microlenses, gratings, and other optional lenses 
 The reconstruction of the scattered field complex wavefront is performed by using any of the technique of intensity based restoration of complex wavefront: techniques derived from Hartmann Shack wavefront measuring techniques and derived methods like Talbot techniques or quad-riwave lateral shearing interferometry. 
 
     
     
         13 . The apparatus of  claim 1  comprising the optical elements to derive the reference beam from the illumination source before object illumination, for instance with a beamsplitter or a diffracting grating, and then superimposing this reference beam to the object beam impinging on the detector array, collecting therefore an hologram which permits the complex wavefront reconstruction teached by the so-called Digital holographic Microscopy (DHM), or more generally Quantitative Phase Microscopy (QPS). 
     
     
         14 . The apparatus of  claim 1  comprising the optical elements composing a wavefront analyser delivering the data stacks needed for tomographic data processing, in the case of objects significantly larger than the wavelength, the locus of the wave vectors corresponding to one incidence can be assimilated to a straight line passing through zero and perpendicular to the illumination direction, the wave vector space therefore being able to be populated in the following sequence:
 acquiring the stack of phase projection plane according to the fan beam emitted by the structured illumination beam and collected on the camera 
 reconstructing the complex wave front 
 translating the data in each acquired projection plane to a position corresponding to the fixed object 
 rearranging the data in the stack to collect in each plane the data corresponding to a defined incidence angle 
 applying the Fourier Slice theorem: FST, i.e computing the Fourier transform of the phase distribution in each plane perpendicular to the illumination direction 
 grouping in 3D the obtained data in the wavevector space 
 finally computing the inverse Fourier transform of the 3D data to obtain the scattering potential which is one minus the square of the refractive index. 
 
     
     
         15 . The apparatus of  claim 1  comprising the same optical elements. In the case of objects having approximately the same size as the wavelength, the locus of the wave vectors corresponding to one incidence must be assimilated to a sphere (Ewald sphere) passing through zero and having his center on the line passing through zero and pointing in the illumination direction. The wavevector space can therefore be populated in the following sequence:
 acquiring the stack of phase projection plane according to the fan beam emitted by the structured illumination beam and collected on the camera 
 reconstructing the complex wave front 
 translating the data in each acquired projection plane to a position corresponding to the fixed object 
 rearranging the data in the stack to collect in each plane the data corresponding to a defined incidence angle 
 applying the Fourier Diffraction Theorem: FDT, i.e computing the Fourier transform of the phase distribution in each plane perpendicular to the illumination direction 
 mapping the results on the Ewald sphere corresponding to each illumination direction 
 grouping the obtained data in 3D in the wavevector space: they take place in a sphere extending to the cutoff spatial frequency, the radius of which is the diameter of the Ewald sphere. 
 finally computing the inverse Fourier transform of the 3D data to obtain the scattering potential which is one minus the square of the refractive index. 
 
     
     
         16 . The apparatus of  claim 1 , where the tomography of the RI is performed with adaptive methods to refine knowledge about measuring conditions and improve the 3D reconstruction. 
     
     
         17 . A method for performing quantitative phase tomography on a specimen, comprising the steps of
 providing an illuminating beam;   transforming the illuminating beam into a shaped illuminating beam;   directing the shaped illuminating beam along an optical axis direction to irradiate the specimen;   collecting a beam scattered by the specimen;   measuring the intensity of the beam scattered by the specimen and collected in the step of collecting;   displacing the specimen in a plane normal to the optical axis direction;   processing measurement data collected at the step of measuring the intensity to reconstruct the complex wavefront of the light scattered by the specimen,   building-up a stack of complex wavefronts data obtained by the step of displacing the specimen in the shaped illuminating beam according to a scanning strategy,   computing the dielectric properties of the specimen in the form of the Refractive Index (RI) distribution in 3D, and   representing the specimen in a 3D graphical representation.