Does the DG5 print the optical track as part of the picture? That is, does it print out the full silent gate with picture and sound all at once? If it does, it's fairly trivial to find the bitdepth of the audio it can produce. Just take the width (in pixels) of the audio portion of the image, then:
bitdepth = Log2(steps)
As for the question of how much bitdepth is possible on an optical soundtrack, that's more tricky. We would need to know the resolving power and SNR of the red/cyan layer of that particular print stock. However, we can ballpark it. The very best consumer color film (Astia) resolves well below 100 lp/mm. The very best fine grained B&W can resolve upwards of 200-300. Let's be extraordinarily generous and assume color release print stock could achieve 200 lp/mm, which is highly doubtful. A mono soundtrack is what, 2.94mm wide? That means 588 line pairs, which given Nyquist, means we can achieve 294 discrete levels.
However, there's noise in the form of film grain. Let's again be generous and say that the grain will give us an average error of only 2 levels (less than 1%), which is a tiny deviation of only 10 microns! 20 * Log10(294 / 2) = 43.3 dB. In other words, just over 7 bits. (This is actually wrong, because the layout of the levels is not linear, but whatever). For stereo, it's half that, so just over 6 bits.
Still the picture is not so simple as that. Even 1 bit can give you amazing results (see: DSD). Sampling rate and error diffusion matter greatly. The sampling rate (18.66mm * 200 lp/mm) gives us 1866 samples vertically for every frame, which translates to 44,784. Basically, CD quality sampling.
Luckily, that 1% noise actually has the effect of increasing the apparent bitdepth, because you can achieve "in-between" levels. (See: dithering in images). However, the result will sound very slightly noisy.
This seems to model the reality of optical sound pretty well. We know 35mm optical tracks sound different than a CD (slightly noisier, less dynamic range), and this helps explain why. Hopefully it can also serve as the starting point for some back-of-the-envelope calculations for people building filmout machines as well. :)
