Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space

Vertu, Stanislas; Delaunay, Jean‐Jacques; Yamada, Isao; Haeberlé, Olivier

doi:10.2478/s11534-008-0154-6

Cited by 32 publications

(33 citation statements)

References 20 publications

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“…This approach permits a quasi-isotropic resolution, with only a small, missing Fourier domain along the specimen rotation axis [42]. The main difficulty of this technique is to perform a precise rotation of the sample at the microscopic scale that is compatible with interferometric measurements.…”

Section: Tomography With Specimen Rotationmentioning

confidence: 99%

See 1 more Smart Citation

Tomographic diffractive microscopy: basics, techniques and perspectives

Haeberlé

Belkebir

Giovaninni

et al. 2010

Journal of Modern Optics

160

143

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Section: Tomography With Specimen Rotationmentioning

confidence: 99%

“…Figure 8 describes the object frequency support in the case of transmission TDM with a complete specimen rotation about the x-axis and a plane wave illumination along the z-axis [40][41][42].…”

Section: Tomography With Specimen Rotationmentioning

confidence: 99%

Tomographic diffractive microscopy: basics, techniques and perspectives

Haeberlé

Belkebir

Giovaninni

et al. 2010

Journal of Modern Optics

160

143

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“…3 shows how for rotation of the illumination, the Ewald sphere translates (a), but for rotation of the object, the Ewald sphere rotates (b). Rotation of the sample gives a CTF with a diablo shape, with a region of missing spatial frequencies of toroidal shape [17].…”

Section: Holographic Tomographymentioning

confidence: 99%

3D Imaging with Holographic Tomography

Sheppard¹,

Kou²,

Rastogi³

et al. 2010

AIP Conference Proceedings

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There are two main types of tomography that enable the 3D internal structures of objects to be reconstructed from scattered data. The commonly known computerized tomography (CT) give good results in the x-ray wavelength range where the filtered back-projection theorem and Radon transform can be used. These techniques rely on the Fourier projection-slice theorem where rays are considered to propagate straight through the object. Another type of tomography called 'diffraction tomography' applies in applications in optics and acoustics where diffraction and scattering effects must be taken into account. The latter proves to be a more difficult problem, as light no longer travels straight through the sample. Holographic tomography is a popular way of performing diffraction tomography and there has been active experimental research on reconstructing complex refractive index data using this approach recently. However, there are two distinct ways of doing tomography: either by rotation of the object or by rotation of the illumination while fixing the detector. The difference between these two setups is intuitive but needs to be quantified. From Fourier optics and information transformation point of view, we use 3D transfer function analysis to quantitatively describe how spatial frequencies of the object are mapped to the Fourier domain. We first employ a paraxial treatment by calculating the Fourier transform of the defocused OTF. The shape of the calculated 3D CTF for tomography, by scanning the illumination in one direction only, takes on a form that we might call a 'peanut', compared to the case of object rotation, where a diablo is formed, the peanut exhibiting significant differences and non-isotropy. In particular, there is a line singularity along one transverse direction. Under high numerical aperture conditions, the paraxial treatment is not accurate, and so we make use of 3D analytical geometry to calculate the behaviour in the non-paraxial case. This time, we obtain a similar peanut, but without the line singularity. IMAGING IN HOLOGRAPHYPeople often regard holography as giving a three-dimensional (3D) image, but actually it has been known for many years that the 3D information in a holographic image is far from complete [1]. This is understandable because a holographic image contains only 2N 2 pixels, where N is the lateral width of the image and the 2 accounts for the modulus and phase information. It is difficult to see how complete 3D information could be recorded or stored on the 2D surface of a photographic film (for a thin hologram) or CCD detector. This information is sufficient to record the surface height of a bulk 3D object, but not the detail inside the 3D object. In consequence, a hologram is often described as providing a 2 1 / 2 D image. It is not desirable to refer to the precision of surface height measurement as "resolution" as resolution refers to resolving the image of two objects, and holography cannot measure the separation of two surfaces. Precision or sensitivity are acceptable descri...

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“…The resulting optical transfer function is depicted on Fig. 3, and takes the shape of a "ball", but because of the curvature of the successive caps of sphere, a small subset of uncaptured frequencies does remain along the rotation axis (here the -axis), which takes a characteristic shape of an apple-core [18,19]. The resolution is therefore almost isotropic, but is lower than in the previous configuration for two reasons.…”

Section: Tdm With Sample Rotationmentioning

confidence: 99%

“…However, for transmission or reflection tomographic set-ups with fixed specimen, it is always anisotropic. With a rotating specimen, the resolution is almost isotropic [18,19], but is lower than what is achievable with tomographic diffractive microscopy with illumination rotation.…”

Section: Introductionmentioning

confidence: 97%

Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation

et al. 2011

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Abstract:Tomographic Diffractive Microscopy is a technique, which permits to image transparent living specimens in three dimensions without staining. It is commonly implemented in two configurations, by either rotating the sample illumination keeping the specimen fixed, or by rotating the sample using a fixed illumination. Under the first-order Born approximation, the volume of the frequency domain that can be mapped with the rotating illumination method has the shape of a "doughnut", which exhibits a so-called "missing cone" of non-captured frequencies, responsible for the strong resolution anisotropy characteristic of transmission microscopes. When rotating the sample, the resolution is almost isotropic, but the set of captured frequencies still exhibits a missing part, the shape of which resembles that of an apple core. Furthermore, its maximal extension is reduced compared to tomography with rotating illumination. We propose various configurations for tomographic diffractive microscopy, which combine both approaches, and aim at obtaining a high and isotropic resolution. We illustrate with simulations the expected imaging performances of these configurations. 42.30.-d, 42.40.-i, 42.90.+m PACS (2008):

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Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space

Cited by 32 publications

References 20 publications

Tomographic diffractive microscopy: basics, techniques and perspectives

Tomographic diffractive microscopy: basics, techniques and perspectives

3D Imaging with Holographic Tomography

Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation

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