This our setup:
Our Melles-Griot He-Ne laser tube envelopes a few Torr of He with about one tenth that pressure of Ne inside a quartz plasma discharge tube. You can see the transformer (beside the laser, to the right) which provides an approximately 2000 V potential difference across the tube (suprisingly enough, this will shock you - learned from experience).
You will notice that there is a mirror outside of the tube (the first red dot above the laser is the reflection on the mirror). This mirror acts as the slightly less reflective mirror of the laser cavity which allows the amplified light to pass (about 1% of the intensity of the light incident to it). Having a mirror external to the glass tube allowed us to interfere with the amplified light to observe different modal patterns and determine some of the modes present. Furthermore, having a mirror external from the tube allowed us the pleasure of aligning the cavity so amplification occurs (a smashingly fun exercise).
This apparatus made possible our measurements of the laser's output wavelength.
To study the mode structure of the laser's output, we used a Burleigh Spectrum Analyzer System (SA-200-x) which consists of a scanning Fabry-Perot Interferometer, an electronic controller, an optical mount and a beam splitter. The length of the confocal interferometer cavity was scanned with a piezoelectric crystal. The laser's signal was passed from the interferometer to the oscilloscope. From here, the signal data was available for importation into Mathematica.