How to convert the SRTM DEM orthometric to ellipsoidal heights using ArcGIS or others GIS?

Recently I got the SRTM DEM from Cgiar,which based on WGS84/EGM96.

and I merged the tiles to one tiff file. I want to get the WGS84 ellipsoidal heights.

According the steps from the Arcgis Help 10.2 "Converting from orthometric to ellipsoidal heights",I do the whole steps,but I found the tif file was not changed,the height was the orthometric height based on EGM96 geoid. I Want one tif format DEM with ellipsoidal heights based on WGS84 ellipsoid.

I don't know where the problem is?

The steps I followed :

Create a file geodatabase

Steps:

1. Click the Catalog button on the Standard toolbar. This opens the Catalog window. In the Location text box, type C:\arcgis\ArcTutor\Raster and press ENTER.


2. Right-click the Raster folder and click New > Folder. Name the folder Exercises.


3. Right-click the Exercises folder and click New > File Geodatabase. Rename the new file geodatabase ImageGDB.

Set the default geodatabase

Right-click the ImageGDB geodatabase in the Catalog window and click Make Default Geodatabase.

Create a new mosaic dataset

Steps:

1. Right-click ImageGDB in the Catalog window and click New > Mosaic Dataset. Type HMA in the Mosaic Dataset Name text box.



2. Click the Coordinate System browse button . Expand Projected Coordinate Systems >, choose wgs84 world mercator.prj, then click OK. Click OK on the Create Mosaic Dataset tool dialog box.

Add rasters to the mosaic dataset

Steps:

1. Right-click the SRTM mosaic dataset in the Catalog window and click Add Rasters. This opens the Add Rasters To Mosaic Dataset tool.In the Raster Type list, choose Raster Dataset.


2. Click the drop-down arrow and click Workspace.


3. Click the Input browse button. Navigate to C:\arcgis\ArcTutor\Raster\Data\SRTM_tif and click Add.


4. Check Update Overviews.


5. Click OK to run the tool.

Add the Arithmetic function

Steps:

1. Open the Catalog Window and navigate to the mosaic dataset. Right-click the mosaic dataset and click Properties.Click the Functions tab.


2. Right-click the Mosaic Function and click Insert > Arithmetic Function.

Input Raster 1 is identified as the current contents of the mosaic dataset and will not be changed. Click the Input Raster 2 browse button and navigate to the \pedata\geoid folder in the ArcGIS install location.Choose the WGS84.img and click Add.

3. Click the Operation drop-down arrow and click Plus.



4. Click OK to close the Raster Functions Properties dialog box.


5. Click OK to close the Mosaic Dataset Properties dialog box.