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R

raster
raster graphics
ray-tracing
receptor
Region
Region Manager
regular expression
regularization method
regularization parameter
rendering
residual delay
residual fringe rate
restoring beam
RFI
RGB
right ascension
RLE
rotation measure

raster

In a video display unit, the pattern of horizontal scan lines that is swept by the electron beam from the top to bottom of the display while refreshing the emission from the phosphors at individual pixels.

raster graphics

Computer graphics in which images composed of an array of pixels arranged in rows and columns are generated on a display space. The data to be displayed on the raster are computed as a bitmap and stored in a frame buffer. Operations that can be performed efficiently on portions of the raster assist the handling of blocks of pixel data in the frame buffer. For instance, bit BLTs (bit block transfers) move blocks of bits from one portion of the buffer to another. Contrast with vector graphics.

ray-tracing

A technique used in computer graphics to create images by calculating the paths taken by rays of light entering the observer's eye at different angles and using these to compute the intensities and colors of individual pixels in the image. Objects in the scene are modeled as collections of abutting surfaces which may be rectangles, triangles, or more complicated shapes such as 3D splines. The color, reflectance, transmittance, refraction, texture, etc. of these surfaces affect how they contribute to the color and brightness of the ray, and the location, spectrum and brightness of light sources are accounted for.

receptor

Combination of a radiation-receiving conductor and a signal pick-off device. Example: a dipole. In general, a receptor can have considerable internal structure. For instance, when an interferometer array is used as a phased (tied) array, it behaves as if connected to a single pair of receptors. Also, a receptor in an array such as the Ooty radio telescope may consist of a group of dipoles which can be phased independently for steering the beam, but which are connected to a single signal pick-off device. See also: feed and antenna.

region

A region specifies a region of an Image in either world or pixel coordinates. It is a generalization of the BLC, TRC coordinates used in other packages. Construction, destruction, and interaction with regions is via the regionmanager.

region manager

The regionmanager allows construction, destruction, and interaction with regions.

regular expression

(RE): one of the wildcard patterns used by Unix utilities and editors such as EMACS.

An ordinary character (not one of the special characters discussed below) matches that character.
A backslash (\) followed by any special character matches the special character itself.
The special characters are:
- "." matches any character except NEWLINE
- "RE*" matches zero or more occurrences of RE. If there is any choice, the longest leftmost matching string is chosen.
- "^" at the beginning of an RE matches the start of a line and "$" at the end of an RE matches the end of a line.
- [string] matches any one character in that string. If the first character of the string is a "^" it matches any character except NEWLINE and the remaining characters in the string. "-" may be used to indicate a range of consecutive ASCII characters.
- $ RE $ matches whatever RE matches and \n, where n is a digit, matches whatever was matched by the RE between the n'th $ and its corresponding $ earlier in the same RE.
- The concatenation of REs is a RE that matches the concatenation of the strings matched by each RE.
- \< matches the beginning of a word
- \> matches the end of a word.
RE\m\ matches m occurrences of RE.
RE\m,\ matches m or more occurrences of RE.
RE\m,n\ matches between m and n occurrences.

regularization method

In the numerical solution of ill-posed problems, given noisy data, a method in which the original problem is converted into a well-posed problem by requiring of the solution to the modified problem (which now is an approximate solution to the original problem) that it satisfy some smoothness constraint. The prototypical ill-posed problem has the form Kf = g + where K is a known linear integral operator (e.g., a convolution operator), where g + , which is given, represents some noisy measurement, and where f is unknown. In the context of radio interferometry, one may take g + to be the dirty image and K to be the operator which convolves the ``true'' radio source brightness distribution f with the dirty beam. Now, our approximate solution, , to the ill-posed problem is found by minimizing the expression

for some given choice of the regularization parameter , in the range [0,1]. is the mean squared residual (occasionally some other measurement of the error is used), and S() is a measure of the roughness of the computed solution---say, some power of a norm or seminorm of , or a similar quantity, such as the negative of the (Shannon) entropy of .

Proper choice of must be based on statistical considerations which depend on the distribution of measurement errors; often, one chooses in order achieve an a priori reasonable value of the mean squared residual. The Maximum Entropy Method, Tikhonov regularization, and the Prussian helmet CLEAN algorithm are special cases of the regularization method. Appropriate choice of S is discussed by J. Cullum [The effective choice of the smoothing norm in regularization, Math. Comp., 33 (1979) 149-170], and the choice of S and , by a statistical method known as cross validation, is described by G. Wahba [Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal., 14 (1977) 651-677]. Often, some Sobolev norm is chosen for S.

Usually, in addition to the smoothness constraint, f is assumed to be of known, compact support. Other constraints, such as non-negativity, may also be included. In the case in which the data are exact---i.e., when =0, so that g = Kf ---one may obtain the regularized solution corresponding to =0 as the limit of regularized solutions as -->0. See variational method; also see D. M. Titterington [General structure of regularization procedures in image reconstruction, Astron. Astrophys., 144 (1985) 381-387].

regularization parameter

In the regularization method for the solution of ill-posed problems, a smoothing parameter in the range [0,1], which controls the trade-off between an error term, measuring agreement of the computed solution with the given data, and a term S(), which measures the roughness of . I.e., controls the amount of "regularization". See super-resolution.

rendering

Construction of an image from a mathematical model of a three-dimensional object or scene, e.g., by ray-tracing.

residual delay

Expressing the antenna/i.f. phase, , for antenna k of a VLBI array as a function of frequency as well as of time, the residual delay on the i-j baseline at (t,) is given by

where denotes the visibility phase on the i-j baseline. (The corresponding partial with respect to t is called the residual fringe rate.) Usually, the major contributor to residual delay is the difference in the station clock errors. The residual delay is a group delay, rather than a phase delay. It is termed "residual" because it is assumed that geometric effects have already been compensated for.

The "antenna components" of , namely

are called the antenna residual delays and the corresponding partials w.r.t. t are called the antenna residual fringe rates. They are among the solution parameters of the global fringe fitting algorithm for VLBI.

residual fringe rate

See residual delay.

restoring beam

In radio astronomical imaging, an elliptical Gaussian function h with which the final iterate of a deconvolution algorithm such as the Högbom CLEAN, Clark CLEAN, or the Maximum Entropy Method is convolved, in order to diminish any spurious high spatial frequency features. h is specified by its major axis (usually the FWHM), its minor axis, and the position angle on the sky of its major axis. Usually these parameters are set by fitting to the central lobe of the dirty beam. When applied to the final iterate of a CLEAN deconvolution, also called the CLEAN beam.

RFI

Radio Frequency Interference.

RGB

Red, Green, Blue: The three primary colors of light which can be mixed to produce any other color. Colored images are often stored as a sequence of RGB triplets or as separate red, green and blue overlays though this is not the only possible representation (see CMYK and HSV). These colors correspond to the three "guns" in a color cathode-ray tube and to the color receptors in the human eye. The term RGB is often used as a synonym for color, as in "RGB monitor" as opposed to monochrome (black and white) monitor.