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@@ -50,29 +50,34 @@ components = [
 # in s3, such that there is only the AST left. The AST is symmetric
 # to the y axis such that there is a straight line drawn, later.
 
-(s, rt) = pyrateoptics.build_simple_optical_system(components, name="s")
+(opticalsystem, raytrace_order) =\
+    pyrateoptics.build_simple_optical_system(components, name="s")
 # Notice: It is always a good idea to provide names for systems, elements
 # and components. There is also a convenience function for rotationally
 # symmetric systems `build_rotationally_symmetric_optical_system`.
 
-tiltx_s2 = s.elements["stdelem"].surfaces["s2"].rootcoordinatesystem.tiltx
-tiltx_s3 = s.elements["stdelem"].surfaces["s3"].rootcoordinatesystem.tiltx
+tiltx_s2 = opticalsystem.elements["stdelem"].surfaces["s2"].\
+    rootcoordinatesystem.tiltx
+tiltx_s3 = opticalsystem.elements["stdelem"].surfaces["s3"].\
+    rootcoordinatesystem.tiltx
 tiltx_s3.to_pickup((FunctionObject("f = lambda x: -x", ["f"]), "f"),
                    (tiltx_s2,))
 
-s.rootcoordinatesystem.update()
+opticalsystem.rootcoordinatesystem.update()
 # Setting tiltx of s3 as -tiltx of s2 via pickup and update coordinate systems
 # afterwards.
 
-osa = OpticalSystemAnalysis(s, rt, name="osa")
-osa.aim(21, {"radius": 5})
+osa = OpticalSystemAnalysis(opticalsystem, raytrace_order, name="osa")
+osa.aim(21, {"radius": 5.})
 rays = osa.trace()
+# traces 21 rays through system in a rectangular grid sampling a round pupil
+# with radius 5 mm.
 
-# pyrateoptics.listOptimizableVariables(s, max_line_width=75)
+pyrateoptics.listOptimizableVariables(opticalsystem, max_line_width=75)
 # Lists optimizable variables (the identifiers are keys to a dict which
 # collects them all).
 
-pyrateoptics.draw(s, rays)
+pyrateoptics.draw(opticalsystem, rays)
 # This function can get a list of raypath argument to draw rays.
 ```