Image plane

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. 

The projection model (equations 1, 2) describes the mapping of 3D points = m,yw,2wY to 2D image points Pi = (ii,j/i) in a virtual, undistorted image plane. The... 

T- and mapped to the image plane considering scaling (Si,Sy) of the coordinate axes and a shift Ci,Cy) of the center of the coordinate system. The distance between X-ray source and image intensifier tube is called /. 

There is of course no requirement to confine the slice selection to the z-gradient. The gradients may be used in any combination and an image plane selected in any orientation without recourse to rotating the sample. 

Collectively, the post-specimen lenses serve one of two purposes they magnify either the diffraction pattern from the sample produced at the back focal plane of the objective lens or they magnify the image produced at the image plane of the objective lens. These optical planes are illustrated in the elearon ray diagram in... 

In image mode, the post-specimen lenses are set to examine the information in the transmitted signal at the image plane of the objective lens. Here, the scattered electron waves finally recombine, forming an image with recognizable details related to the sample microstructure (or atomic structure). 

Now let us consider imaging by a lens. The disturbance at a point (, r]) in the image plane is given by a superposition of the disturbances from points x, y) across the pupil A, with appropriate propagation delay,... 

If we apply Maxwell s equations to this boundary value problem we can derive a complete solution to the amplitude and phase of this field af every point in space. In general, however we can simplify the problem to describing the field at the entrance (or exit) aperture of a system and at the image plane (which is what we are really interested in the end). 

At distances that are very large compared to either the source dimensions, or the aperture of our optical system the complex amplitude is just the Fourier transform of the object complex amphtude. Furthermore, it can be shown that the complex amplitude in the image plane of an optical system is just the Fourier transform of the complex amplitude at the aperture plane, (for a complete derivation of this see Goodman, 1996). 

Thus, only the tail of the electron density (outside the jellium) contributes. The last term above may further be related11 to the position of the image plane zim so, at the point of zero charge,... 

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