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The Focusing Optics X-ray Solar Imager (FOXSI) is a NASA sounding rocket mission which will study particle acceleration and coronal heating on the Sun through high sensitivity observations in the hard X-ray energy band (5-15 keV). Combining high-resolution focusing X-ray optics and fine-pitch imaging sensors, FOXSI will achieve superior sensitivity; two orders of magnitude better than that of the RHESSI satellite. As the focal plane detector, a Double-sided Si Strip Detector (DSSD) with a front-end ASIC (Application Specific Integrated Circuit) will fulfill the scientific requirements of spatial and energy resolution, low energy threshold and time resolution. We have designed and fabricated a DSSD with a thickness of 500 μm and a dimension of 9.6 mm × 9.6 mm, containing 128 strips with a pitch of 75 μm, which corresponds to 8 arcsec at the focal length of 2 m. We also developed a low-noise ASIC specified to FOXSI. The detector was successfully operated in the laboratory at a temperature of -20°C and with an applied bias voltage of 300 V. Extremely good energy resolutions of 430 eV for the p-side and 1.6 keV for the n-side at a 14 keV line were achieved for the detector. We also demonstrated fine-pitch imaging successfully by obtaining a shadow image. Hence the implementation of scientific requirements was confirmed.