Validity of diffraction tomography based on the first Born and the first Rytov approximations

Chen, Bingquan; Stamnes, Jakob J.

doi:10.1364/ao.37.002996

Cited by 144 publications

(96 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…V C). Both have already shown to deliver usable results in different situations (e.g., [23], [24]). For weakly scattering objects the potential itself can be treated as a perturbation and the solution can be expanded into powers of the potential giving the Rytov series [25,26].…”

Section: The Riccati Methodsmentioning

confidence: 99%

Rytov approximation in electron scattering

Krehl

Lubk

2017

Phys. Rev. B

View full text Add to dashboard Cite

In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the Phase Grating Approximation, have reached their limits in current and forseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.

show abstract

Section: The Riccati Methodsmentioning

confidence: 99%

Rytov approximation in electron scattering

Krehl

Lubk

2017

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Whether involving holographic or non-holographic methods [10][11][12][13][14][15][16] , QPI presents new opportunities for studying cells and tissues non-invasively, quantitatively and without the need for staining or tagging [17][18][19][20][21][22][23] . Projection tomography using laser QPI has made use of ideas from X-ray imaging and enabled three-dimensional imaging of transparent structures [24][25][26] . More recently, this method has been applied to live cells [27][28][29][30] .…”

mentioning

confidence: 99%

White-light diffraction tomography of unlabelled live cells

et al. 2014

View full text Add to dashboard Cite

We present a technique called white-light diffraction tomography (WDT) for imaging microscopic transparent objects such as live unlabelled cells. The approach extends diffraction tomography to white-light illumination and imaging rather than scattering plane measurements. Our experiments were performed using a conventional phase contrast microscope upgraded with a module to measure quantitative phase images. The axial dimension of the object was reconstructed by scanning the focus through the object and acquiring a stack of phase-resolved images. We reconstructed the threedimensional structures of live, unlabelled, red blood cells and compared the results with confocal and scanning electron microscopy images. The 350 nm transverse and 900 nm axial resolution achieved reveals subcellular structures at high resolution in Escherichia coli cells. The results establish WDT as a means for measuring three-dimensional subcellular structures in a non-invasive and label-free manner.A transparent object illuminated by an electromagnetic field generates a scattering pattern that carries specific information about its internal structure. Inferring this information from measurements of the scattered field, that is, solving the inverse scattering problem, is the fundamental principle that has allowed X-ray diffraction measurements to reveal the molecular-scale organization of crystals 1 and more recently, image cells with nanoscale resolution 2,3 . The scattered field is related to the spatially varying dielectric susceptibility of the scattering object by a transformation that simplifies considerably and, more importantly, becomes invertible, when the incident field is only weakly perturbed by the presence of the object. In this regime, the first-order Born approximation 4 and the Rytov approximation 5 have been used to unambiguously retrieve the three-dimensional spatial distribution of the dielectric constant. Implementation of inverse scattering requires knowledge of both the amplitude and phase of the scattered field. This obstacle, known as the phase problem, has been associated with X-ray diffraction measurement throughout its century-old history (for a review, see ref. 6).In 1969, Wolf proposed diffraction tomography as a reconstruction method combining the X-ray diffraction principle with optical holography 7 . Unlike X-rays, light at lower frequencies can be used in phase imaging measurements, as demonstrated by Gabor 8 . In recent years, as a result of new advances in light sources, detector arrays and computing power, quantitative phase imaging (QPI), in which optical path-length delays are measured at each point in the field of view, has become a very active field of study 9 . Whether involving holographic or non-holographic methods 10-16 , QPI presents new opportunities for studying cells and tissues non-invasively, quantitatively and without the need for staining or tagging [17][18][19][20][21][22][23] . Projection tomography using laser QPI has made use of ideas from X-ray imaging and enabled three-dimensional ...

show abstract

“…This principle is valid under the first-order Born or Rytov approximation. The latter is known to be less strict in terms of the weak-scattering requirement [26]. For this reason, this work focuses solely on the Rytov solution.…”

Section: Tomographic Reconstruction With the Direct Inversion Methodsmentioning

confidence: 99%

Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy

Kostencka¹,

Kozacki²,

Kuś³

et al. 2016

Biomed. Opt. Express

View full text Add to dashboard Cite

Abstract:The paper presents two novel, space-domain reconstruction algorithms for holographic tomography utilizing scanning of illumination and a fixed detector that is highly suitable for imaging of living biomedical specimens. The first proposed algorithm is an adaptation of the filtered backpropagation to the scanning illumination tomography. Its spacedomain implementation enables avoiding the error-prone interpolation in the Fourier domain, which is a significant problem of the state-of-the-art tomographic algorithm. The second proposed algorithm is a modified version of the former, which ensures the spatially invariant reconstruction accuracy. The utility of the proposed algorithms is demonstrated with numerical simulations and experimental measurement of a cancer cell.

show abstract

Validity of diffraction tomography based on the first Born and the first Rytov approximations

Cited by 144 publications

References 15 publications

Rytov approximation in electron scattering

Rytov approximation in electron scattering

White-light diffraction tomography of unlabelled live cells

Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy

Contact Info

Product

Resources

About