Now lets take a look at AGSMap class mentioned earlier. Given below is the complete code for this class. Since I have added comments in between the code describing each part of the code, this should be self explanatory.

package com.esri.arcgis.sample;

import com.esri.arcgis.server.IServerConnection;
import com.esri.arcgis.server.ServerConnection;
import com.esri.arcgis.server.IServerObjectManager;
import com.esri.arcgis.server.IServerContext;

import com.esri.arcgis.carto.IMapServer;
import com.esri.arcgis.carto.IMapServerProxy;
import com.esri.arcgis.carto.IMapDescription;
import com.esri.arcgis.carto.IMapServerObjects;
import com.esri.arcgis.carto.IMapServerObjectsProxy;
import com.esri.arcgis.carto.IMap;
import com.esri.arcgis.carto.IMapProxy;
import com.esri.arcgis.carto.IMapDescriptionProxy;
import com.esri.arcgis.carto.MapDescription;
import com.esri.arcgis.carto.IImageDescription;
import com.esri.arcgis.carto.IImageDescriptionProxy;
import com.esri.arcgis.carto.ImageDescription;
import com.esri.arcgis.carto.IImageType;
import com.esri.arcgis.carto.IImageTypeProxy;
import com.esri.arcgis.carto.ImageType;
import com.esri.arcgis.carto.IImageDisplay;
import com.esri.arcgis.carto.IImageDisplayProxy;
import com.esri.arcgis.carto.ImageDisplay;
import com.esri.arcgis.carto.IMapImage;
import com.esri.arcgis.carto.IMapImageProxy;
import com.esri.arcgis.carto.MapImage;
import com.esri.arcgis.carto.IMapExtent;
import com.esri.arcgis.carto.IMapExtentProxy;
import com.esri.arcgis.carto.MapExtent;
import com.esri.arcgis.carto.IMapArea;
import com.esri.arcgis.carto.IMapAreaProxy;
import com.esri.arcgis.carto.esriImageFormat;
import com.esri.arcgis.carto.esriImageReturnType;
import com.esri.arcgis.carto.IImageResult;

import com.esri.arcgis.system.LongArray;
import com.esri.arcgis.system.ILongArray;
import com.esri.arcgis.system.ILongArrayProxy;

import com.esri.arcgis.geometry.IPoint;
import com.esri.arcgis.geometry.IPointCollection;
import com.esri.arcgis.geometry.IEnvelope;
import com.esri.arcgis.geometry.Envelope;
import com.esri.arcgis.geometry.IEnvelopeProxy;

import com.esri.arcgis.webcontrols.ags.data.*;

public class AgsMap {

  public synchronized static String
    getImageUrl(AGSWebContext context, int x, int y){
   try{
     //get IMapServer from AGSWebContext
     IMapServer m_mapServer = context.getServer();
     //QI to IMapServerObjects
     IMapServerObjects m_mapServerObj =
        new IMapServerObjectsProxy(m_mapServer);
     // get IServerContext from AGSWebContext
     IServerContext m_context = context.getServerContext();

     IMap m_map = null;
     //if there is a default map, get IMap
     if (m_mapServer.getDefaultMapName() != null) {
       m_map = new IMapProxy(m_mapServerObj.getMap(
                m_mapServer.getDefaultMapName()));
     } else return null;

     //get Default MapDescription from AGSWebContext
     IMapDescription m_mapDesc = context.getMapDescription(
                m_mapServer.getDefaultMapName());
     /*
       create a new ImageType and set the properties
       we are getting the image url, so make sure to
       specify output directory in ArcCatalog
       for the server object config being used in
       this application
     */ 
     IImageType m_imageType = new IImageTypeProxy(
                m_context.createObject(ImageType.getClsid()));
      m_imageType.setFormat(esriImageFormat.esriImagePNG);
      m_imageType.setReturnType(
               esriImageReturnType.esriImageReturnURL);

      //create a new IImageDisplay
      //set width and height same as that of the Map Control
      //because we will be using it to convert pixel
      //point to Map point
      IImageDisplay m_imageDisplay = new IImageDisplayProxy(
            m_context.createObject(ImageDisplay.getClsid()));
      m_imageDisplay.setDeviceResolution(96D);
      m_imageDisplay.setWidth(context.getWebMap().getWidth());
      m_imageDisplay.setHeight(context.getWebMap().getHeight());

      //set the above IImageDisplay and IImageType
      //  to IImageDescription
      IImageDescription m_imageDesc = new IImageDescriptionProxy(
             m_context.createObject(ImageDescription.getClsid()));
      m_imageDesc.setDisplay(m_imageDisplay);
      m_imageDesc.setType(m_imageType);

      //convert pixel point into map point
      //notice that we are using the above map
      //description and image description
      // in mapserver.toMapPoints method
      ILongArray longArrayX = new ILongArrayProxy(
             m_context.createObject(LongArray.getClsid()));
      longArrayX.insert(0, x-10);
      ILongArray longArrayY = new ILongArrayProxy(
             m_context.createObject(LongArray.getClsid()));
      longArrayY.insert(0, y+10);
      longArrayX.insert(1,x+10);
      longArrayY.insert(1,y-10);
      IPointCollection pointColl = m_mapServer.toMapPoints(
                         m_mapDesc,
                         m_imageDesc.getDisplay(),
                        longArrayX,
                        longArrayY);
      IPoint point1 = null;
      IPoint point2 = null;
      if (pointColl.getPointCount() > 0) {
       point1 = pointColl.getPoint(0);
       point2 = pointColl.getPoint(1);
      }

      //generate a small envelope based on map points
      IEnvelope env = new IEnvelopeProxy(
            m_context.createObject(Envelope.getClsid()));
      env.setXMin(point1.getX());
      env.setYMin(point1.getY());
      env.setXMax(point2.getX());
      env.setYMax(point2.getY());

      //reset the Image size to 200X200
      //this is the size of the magnified image
      m_imageDesc.getDisplay().setWidth(200);
      m_imageDesc.getDisplay().setHeight(200);

      //set the new MapExtent based on the above envelope
      IMapExtent mapExtent = new IMapExtentProxy(
          m_context.createObject(MapExtent.getClsid()));
      mapExtent.setExtent(env);

      //create a new map description and set above
      //extent and default LayerDescriptions to it
      IMapDescription m_mapDesc1 = new IMapDescriptionProxy(
         m_context.createObject(MapDescription.getClsid()));
      IMapArea mapArea = new IMapAreaProxy(mapExtent);
      m_mapDesc1.setMapArea(mapArea);
      m_mapDesc1.setLayerDescriptions(
                 m_mapDesc.getLayerDescriptions());
      m_mapDesc1.setName(m_mapServer.getDefaultMapName());

      //export the map image and get its URL
      IMapImage mapImage = m_mapServer.exportMapImage(
              m_mapDesc1, m_imageDesc);
      String url = mapImage.getURL();
      //finally release the context
      m_context.removeAll();
      m_context.releaseContext();
      return url;
     }catch (Exception ex){
        ex.printStackTrace();
        return null;
     }
  }
}