ArcGIS Tutorial: Merging and clipping of ArcGIS raster data

　　1. Merger: Arctoolbox->datamanagement->raster->mosaic.

　　2. Cut: in ArcMap, call the spatial analysis extension to set the Shapefile polygon layer of your area of interest as a mask (the drop-down menu of the spatial Analyst toolbar is set in >option), then recalculate your image in the raster calculator, It will be cut along the mask.

　　

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ArcGIS Tutorial: Merging and clipping of ArcGIS raster data