In this paper we study photon emission in the interaction of the laser beam with an under-dense target and the attached reflecting plasma mirror. Photons are emitted due to the inverse Compton scattering when accelerated electrons interact with a reflected part of the laser pulse. The enhancement of photon generation in this configuration lies in using the laser pulse with a steep rising edge. Such a laser pulse can be obtained by the preceding interaction of the incoming laser pulse with a thin solid-density foil. Using numerical simulations we study how such a laser pulse affects photon emission. As a result of employing a laser pulse with a steep rising edge, accelerated electrons can interact directly with the most intense part of the laser pulse that enhances photon emission. This approach increases the number of created photons and improves photon beam divergence.