Sleepless in Chobham

Oscar and Tess sleep in the kitchen which has a double glass door which gives them a view of much of the garden.
Two nights ago I was awoken at 4am by insistent barking, you know the woof that means "there is something out there and I'm very unhappy about it!". (Having seen the BBC2 Horizon documentary on the Secret Life of Dogs I now know that it's not just me that can understand woofs!).
I was going to try to turn over and ignore it, hoping that husband would get up and tackle the invaders if necessary - but the noise woke my son who also speaks dog. "Mummy there's something outside, Oscar is very worried. I'm scared."
So maternal instincts being what they are of course I had to go down stairs to investigate to prove to son that there was no reason to be afraid.
Outside lights switched to high beam so I could see the burglars, doors opened noisely to offset the impression made by the girly-pink satin pjs (Xmas pressie!).
The two dogs were out that kitchen door like Greyhounds at the races. Woofing and running for the far corner of the garden where probably some poor bunny/fox/deer/badger had long since departed thanks to my light show.
They came back exhilarated at that nighttime expedition. And my heart sank.
I had rewarded their woofing.
Last night the woofing started at 2am.
Will this continue? How do we break the cycle?
Ear plugs for all? Hard to ignore these woofs. The dogs are proudly doing their job - it's just I'd prefer to only be alerted to human invaders rather than four legged ones!
Beverley Cuddy, Editor Dogs Today

Stop Press: Brilliant suggestion re the frosted glass! We tried bin bags last night - not quite so attractive - but it did the trick!
In answer to the comment, we're lucky to live on a very sleepy lane with only three other houses. We're near the common and surrounded by a lot of unfenced open space. It is a haven for wildlife and we see deer, rabbits, foxes in the garden. Our boundaries are far from rabbit/fox proof and deer seem to be able to bounce in and out over the back fence whenever they feel like it.
We don't mind them sharing our space, it's just we're less pleased to hear about their visits in the middle of the night!