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**1 - 3**of**3**### THE FOURIER DIFFRACTION THEOREM

"... Fundamental to diffraction tomography is the Fourier Diflraction Projectiola Theorem, which relates the Fourier transform of the measured forward scattered data with the Fourier transform of the object. The theorem is valid when the inhomogeneities in the object are only weakly scattering and ..."

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Fundamental to diffraction tomography is the Fourier Diflraction Projectiola Theorem, which relates the Fourier transform of the measured forward scattered data with the Fourier transform of the object. The theorem is valid when the inhomogeneities in the object are only weakly scattering and

### CHAPTER 1

"... The word tomography comes from the Greek words tomo, meaning sectional, and graphy, meaning representation. Thus a tomographic image is a cross sectional image of an object. As the term is used today tomography refers to a procedure to collect data about the internal structure of an object ..."

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The word tomography comes from the Greek words tomo, meaning sectional, and graphy, meaning representation. Thus a tomographic image is a cross sectional image of an object. As the term is used today tomography refers to a procedure to collect data about the internal structure of an object

### 4 Measurement of Projection Data-

"... The mathematical algorithms for tomographic reconstructions described in Chapter 3 are based on projection data. These projections can represent, for example, the attenuation of x-rays through an object as in conventional x-ray tomography, the decay of radioactive nucleoids in the body as in emissio ..."

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The mathematical algorithms for tomographic reconstructions described in Chapter 3 are based on projection data. These projections can represent, for example, the attenuation of x-rays through an object as in conventional x-ray tomography, the decay of radioactive nucleoids in the body as in emission tomography, or the refractive index variations as in ultrasonic tomography. This chapter will discuss the measurement of projection data with energy that travels in straight lines through objects. This is always the case when a human body is illuminated with x-rays and is a close approximation to what happens when ultrasonic tomography is used for the imaging of soft biological tissues (e.g., the female breast). Projection data, by their very nature, are a result of interaction between the radiation used for imaging and the substance of which the object is composed. To a first approximation, such interactions can be modeled as measuring integrals of some characteristic of the object. A simple example of this is the attenuation a beam of x-rays undergoes as it travels through an object. A line