Are you saying the water/water-droplets, or moisture formed on just the target surface. Then it is explainable.
But if lots of water is being found all around the target, and the amount of water is increasing, then it can be due to some water leakage from a pipe. But a good system design will never allow water leaked from the pipe to get into the chamber and that too on the target surface.
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I presume you have a horizontally mounted target, and there is a fine coverage of water droplets on the target surface. If this is so, then the explanation given below would anser your question.
Now coming back to the question if just water droplets are being formed on the target surface which can be wiped away by a tissue paper or cloth.
It means it is due to condensation from atmosphere.
The target is being cooled by a water chiller. In your room there is a lot of moisture, despite the running of your air conditioner. As soon as you opened the chamber door, the moisture in the room entered into your chamber, and condensed onto the target surface as fine water droplets, because your target is at a much lower temperature, as it is being cooled by a water chiller. Just like you find water droplets on the outside of a Coca cola bottle. This kind of condensation is often seen in rainy season when the humidity level are very high, and the air conditioner is not effective.