Thank you Grant, for fast response.
Using a filter is a good idea for an appropriate signal. But in this case using a moving average or something like this wouldn't help because the signal doesn't look like there is a useful average. What I mean is that voltage output values doesn't differ so much in a sensing range between 100 to 150 cm. They are somewhere between 800 and 600 mV. I see on the scope that voltage fluctuates between 800 and 500 mV when pointing sensor to an object that is in a distance between 100 to 150 cm.
To avoid other influences my set up is very simple: 5V supply, short cables and a scope to see output voltage of sensor. In addition I put a 100uF capacitor between Vcc and Ground but this made no difference.
At the moment I am at one's wits' end
This evening I will be back in laboratory and I am going to examine output signals of our other Sharp IR sensors (e.g. older GP2Y0A02YK0F with range 20 - 150 cm). I am looking forward to see the difference to the new sensor. During the last years we used older GP2Y0A02YK0F a lot with good results. But the new sensor could be great because it is smaller and has a faster sensing rate.