First, we open a world image that has a WGS84 coordinate system.
Click the Transform button in the Geographic Imager main panel. It will open the Transform dialog box.
Click the Specify button. We are going to create a custom coordinate system based on the Robinson projection by modifying the existing Robinson projection. Find the existing Robinson projection from the list.
On the left side, navigate to Coordinate system > Projected > World. Highlight the folder "World". You will see the list of the predefined coordinate systems available on the right side of the window. Find the "Robinson" and highlight it.
Once the predefined Robinson projection is highlighted, click the Copy button at the bottom. It will duplicate the existing coordinate system and will open the "Projected Coordinate System Editor" dialog box for the duplicated coordinate system.
In the Projected Coordinate System Editor dialog box, there are two tabs: Identification and Definition. In the Identification tab, enter a new name for this customer coordinate system. This name will be used when you are searching the object.
Click the Definition tab. Change the value of central_meridian from 0 (default) to 160. Click OK to apply this new setting. You have just made a custom coordinate system based on the existing Robinson projection.
Once you select the custom coordinate system in the "Specify Coordinate System" dialog box, it will be indicated in the Transformation dialog box (in the example below, a custom coordinate system "Robinson cm @ 160 degree East" is selected as a destination coordinate system).
As soon as you click the Transform button, the transformation process will start. Once the transformation process is completed, the Geographic Imager main panel will indicate the new custom coordinate system name.