A quasi-optimal stacking method for up-the-ramp readout images

The non-destructive readout mode of a detector allows its pixels to be read multiple times during integration, generating a series of "up-the-ramp" images that keep accumulating photons between successive frames. Since the noise is correlated across these images, an optimal stacking generally requires weighting them unequally to achieve the best signal-to-noise ratio (SNR) for the target. Objects in the sky show wildly different brightness, and the counts in the pixels of the same object also span a wide range. Therefore, a single set of weights cannot be optimal for all cases. To keep the stacked image more easily calibratable, however, we choose to apply the same weight to all the pixels in the same frame. In practice, we find that the results of high-SNR cases degrade only slightly by adopting weights derived for low-SNR cases, whereas the low-SNR cases are more sensitive to the weights applied. We therefore propose a quasi-optimal stacking method that maximizes the stacked SNR for the case of SNR=1 per pixel in the last frame and demonstrate with simulated data that it always enhances the SNR more than the equal-weight stacking method and the ramp fitting method. Furthermore, we give an estimate of the improvement of limiting magnitudes for the China Space Station Telescope (CSST) based on this method. Compared with the conventional readout mode, which is equivalent to taking the last frame of the non-destructive readout, stacking 30 up-the-ramp images can improve the limiting magnitude by about 0.5 mag for CSST near-infrared observations, effectively reducing the readout noise by about 62%.