I dont think an altimeter would do the job, because it's distance above sea level.
You might be able to do it with IR LED's and Sensors. I don't know how effective they are at a distance of 4 ft. Also, there really isn't a uniform object for it to reflect off of.
An ultrasonic transducer would do the job. It sends out ultrasonic soundwaves, and these waves echo off nearby objects and then you can measure the time between sending the wave and recieving the echo. then multiply that time by the speed of sound and you've got your distance but that would require a microcontroller, which gets fairly complicated if youve never used one before.
Hopefully I didn't confuse you even more.