Preheat oven to 350 degrees. Process cookies in a food processor or blender until finely ground crumbs. Pour melted butter into the cookie crumbs & mix well. 

Press cookie crumbs into the bottom of a greased 9 X 13 inch baking pan. Bake until lightly browned, about 10 minutes. Cool completely, about 30 minutes. Reduce oven temperature to 325 degrees.

Combine raspberries, 1 tbsp. water & 1 tbsp. sugar in a saucepan, bring to a boil & cook until thickened, stirring frequently to mash up the berries. You can also do this in the microwave - cook about 30 seconds at a time, stirring between each. 

Place raspberries in a fine wire mesh strainer over a bowl and press until you have about 3 tbsp. of puree. Discard the solids in the strainer. Cool puree completely. 

Now repeat the same procedure with the blueberries.

Beat softened cream cheese, salt, & remaining 3/4 cup sugar until smooth. Add egg whites & egg one at a time, beating well after each addition. Add sour cream, flour, lemon juice, & vanilla. Mix well. Pour over top of cooled cookie crust, smoothing out the top.  

Drop level teaspoons of raspberry & blueberry purees all over top of batter, gently swirl with a knife. 

Bake at 325 degrees until cheesecake is almost set (top will still jiggle when dish is touched), 25 to 28 minutes. Run a knife or offset spatula around the edges of the dish to loosen the sides. Cool on a wire rack at room temperature for 1 hour. Cover & chill in the refrigerator 4 hours or overnight. Cut into bars.