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The sounding rocket experiment FOXSI-4, successfully launched in April 2024, conducted the world's first focusing imaging spectroscopic observation of a solar flare in x-rays. It aims to investigate the magnetic energy release and the magnetic to other forms of energy conversion mechanism caused by magnetic reconnection in solar flares. For soft x-ray observations, a non-dispersive type imaging-spectroscopy, that is, photon counting, was performed using back-illuminated CMOS sensors. The sensor has a sensitive layer of fully depleted silicon which is 25μm-thick and can achieve a high-speed continuous exposure at a rate of ~250fps. To evaluate the sensor's performance, we irradiated the sensor with monochromatic x-rays from 0.8 to 10keV at synchrotron facilities. Based on this data set, we evaluated the relationship between incident x-ray photon energy and the output signals from the sensor, known as a response matrix for use in analyzing flight data. We confirmed that the sensor outputs signals mainly proportional to the incident photon energy with little charge loss. We also analyzed charge sharing, which refers to the spread of electrons produced by a single photon across multiple pixels. The energy resolution is better than 400eV FWHM for the energy range of up to 10keV, which is sufficient to diagnose the spectrum of a solar flare.
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