Distance between pixels

Just as for coulombic and polarization terms, short distances between pixels of overlapping densities may cause singularities, so a damping function is used, f(R) = exp[-(D/J ij - 1) ] ( for JJy < D), where D is an adjustable empirical... 

The detector is a Hu es - Santa Barbara Research Corporation LiSb photovoltmc array. The array is sensitive from -<1 foa to 5.5/im and is a 256 X 256 square array of 30 foa square pixels. The distance between pixels is also 30 fan, which corresponds to 0.15" on the sky at the f/25 focus. 

The acquisition mode (detector pixel width, number of projections and scan time) was optimized for CSCT acquisition. Assuming a point source, in CT the spatial resolution is mainly given by the size of the detector pixels, whereas in CSCT it is given by the detector pixel size, the length of the collimator lamellae in front of the detector and the distance between the object and the detector. In the experiment presented here, the combined effects of detector and collimation resulted in an average spatial resolution of 8 mm. Therefore, only a low-resolution image can be expected from the reconstruction, and consequently a low number of projections is sufficient. 

The X-ray microtomograph used was a "Skyscan-1074 X-ray scaimer" (Skyscan, Belgium). The X-ray source operates at 40 kV and 1 mA. The detector is a 2D, 768 x 576 pixels, 8-bit X-ray camera with a spatial resolution of 41 pm. The sample, whose maximum size was a few cm, can be either rotated in a horizontal plane or moved vertically in order to get 2D scans at different vertical positions. The minimum vertical distance between two scans is 41 pm. The reconstruction of two-dimensional slices from the object was achieved by a classical back projection method. 

Since in the images used in this study, objects (fibers) are white on a black background, the images first need to be complemented. In the complement of a binary image, zeros become ones and ones become zeros black and white are reversed. Thus in the complement of the image, fibers are black and background is white. Afterwards, the distance between each pixel and its nearest nonzero pixel is found by using Euclidean distance transform. 

The Euclidean distance is the straight line distance between two pixels. The Euclidean distance between (xi,yi) and (x2,y2) is defined by... 

The performance of the coded aperture mask is not limited by diffraction effects so that, in principal, there is not an intrinsic limitation to the angular resolution which may be achieved. From a technical point of view the limit is set by the distance between the mask and detector and hence the size of the spacecraft. The size of the pixels within the detection plane also provide another technical limitation to fine angular resolution. However, both mask distance and pixel size do have an indirect influence on the large-scale... 

The results of measurements show that point clouds obtained have an average resolution of 80 pm. This resolution corresponds to the average of the minimum distances between points. It is based on the resolution of the camera sensor, which in the case of Comet L3D is 1,92.10 pixels (1600 X 1200), being greater than the resolution provided by laser systems. The equipment analyzed provides uniform distances between points allowing obtain good quality meshes. 

For an image of a fractal represented with pixels, these distances are distributed into bins of width Ar representing different distance ranges so that the total number of times that a distance between r — Ar/2 and r + Ar/1 occurs in the image is recorded for different r. The projected area dimension may then be obtained from a plot of log(Ar) versus log(r), according to... 

This allows for decreasing the vibration that inevitably arises with the use of stepping motors for mechanical moving. The distance between the pixels determines the pixel density and hologram size. The optimal distance is considered equal to the pixel diameter. At smaller distances, pixels overlap, whereas at bigger distances, the pixel density decreases. A significant loss of the diffraction efficiency is observed in both cases. 

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