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

A detector's nondestructive readout mode allows its pixels to be read multiple times during integration, enabling generation of a series of "up-the-ramp" images that continuously accumulate photons between successive frames. Because noise is correlated across these images, optimal stacking generally requires the images to be weighted unequally to achieve the best possible target signal-to-noise ratio (SNR). Objects in the sky present wildly varied brightness characteristics, and the counts in individual pixels of the same object can also span wide ranges. Therefore, a single set of weights cannot be optimal in all cases. To ensure that the stacked image is easily calibratable, we apply the same weight to all pixels within the same frame. In practice, results for high-SNR cases degraded only slightly when we used weights derived for low-SNR cases, whereas the low-SNR cases remained more sensitive to the weights. Therefore, we propose a quasi-optimal stacking method that maximizes the stacked SNR for the case where the R_SN=1 per pixel in the last frame and use simulated data to demonstrate that this approach enhances the SNR more strongly than the equal-weight stacking and ramp fitting methods. Furthermore, we estimate the improvements in the limiting magnitudes for the China Space Station Telescope using the proposed method. When compared with the conventional readout mode, which is equivalent to selecting the last frame from the nondestructive readout, stacking 30 up-the-ramp images can improve the limiting magnitude by approximately 0.5 mag for the telescope's near-infrared observations, effectively reducing readout noise by approximately 62%.