Measurement of differential magnification
  In gravitational lensing, the magnification effect changes the luminosity and
size of a background galaxy. If the image sizes are not small compared to the
scale over which the magnification and shear vary, higher-order distortions
occur which are termed differential magnification. We give an approximation of
the magnification gradient for several halo models. Assuming a symmetric
distribution of source brightness, estimates for the differential magnification
are obtained and then tested with simulations. One of the main uncertainties of
our estimators comes from the finite resolution of the image. We study the
strength of our method with the resolution of current and future telescopes. We
point out that out method is a potential approach to estimate the first
flexion, and can be used to study galaxy and cluster mass profiles.
