If you want to reduce input lag of Sony VPL-XW6000 Projector, you can follow this menu flow: Menu Operation: Expert Setting > Input Lag Reduction. What is input lag reduction for? This function is aimed at reducing the display delay of the image.
Input lag, or latency, for projectors refers to the time between when the audio/video signal from the input source (the gaming console) is received by the projector
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Sony VPL-XW6000 Projector Zoom Picture Guide