Shutter characteristics The ALIS cameras are equipped with iris shutters that open and close radially. The open-close characteristics of the cameras are not known, but the time required to open and close the shutter fully is of the order of magnitude of 10 ms (Brändström private communication). Thus the time of exposure for pixels varies with the position on the image plane. A first order model of the exposure time as a function of image coordinate is given by: $$t(u,v) = t_0 + dt - 4\,dt\,\sqrt{\frac{(u-u_0)^2}{u_s^2}+\frac{(v-v_0)^2}{v_s^2}}$$ (5.17) where $t_0$ is the nominal exposure time, $dt$ is the open and close time of the shutter, $u$ and $v$ are the horizontal and vertical image coordinates, respectively, $u_0$ and $v_0$ are the horizontal and vertical image coordinates of the centre of the shutter, and $u_s$ and $v_s$ are the horizontal and vertical image sizes, respectively. Figure 5.6: Exposure times for different radial positions in images for the simple shutter characteristic model. Here $R = \sqrt {\frac {(u-u_0)^2}{u_s^2}+\frac {(v-v_0)^2}{v_s^2}}$ With exposure times between 1.0 and 10 s, the relative error in pixel exposures varies from 1 to 0.1 % and the accuracy of the exposure time is good enough even without corrections but for exposure times shorter than 1.0 s the shutter characteristics start to become important.