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As it has a new sensor size it is hard to know what to compare the results from the Nikon V1 with. Although it doesn't resolve as much detail as cameras such as the Olympus PEN E-P3, these chart images look clean and sharp – without being oversharpened.
Resolution charts
If you view our crops of the resolution chart's central section at 100% (or Actual Pixels) you will see that, for example, at ISO 100 the Nikon V1 is capable of resolving up to around 18 (line widths per picture height x100) in its highest quality JPEG files.
Examining images of the chart taken at each sensitivity setting reveals the following resolution scores in line widths per picture height x100:
JPEG images
ISO 100, score: 18 (see full image)
ISO 200, score: 18 (see full image)
ISO 400, score: 18 (see full image)
ISO 800, score: 18 (see full image)
ISO 1600, score: 18 (see full image)
ISO 3200, score: 16 (see full image)
ISO 6400, score: 16 (see full image)
RAW images
ISO 100, score: 22 (see full image)
ISO 200, score: 22 (see full image)
ISO 400, score: 20 (see full image)
ISO 800, score: 16 (see full image)
ISO 1600, score: 16 (see full image)
ISO 3200, score: 16 (see full image)
ISO 6400, score: 14 (see full image)