Where are you measuring this? Try and measure right at the regulators output terminal not at the load, that way you can eliminate resistance between the output and the load as a cause. ... What is the timebase set at on that scope mS or seconds?
Answer to these questions, please.
I'm using an LM317 to regulate a 12VDC input down to the ~3.9V required to emulate the camera's original battery.
Can you confirm precisely which LM317 variant you're using? Manufacturer and P/N? If I trust your single-shots, the 2nd plot suggests you're using a I
Omax=500mA variant, whereas your application requires more current. This is my initial suspicion and I wouldn't bother pressing forward until this has been validated.
I just tested 2 x 2200uF caps in parallel on the output to try and deal with any sudden current spikes - it doesn't seem to have made much difference, unfortunately.
If part of the problem is in fact a consequence of insufficient decoupling, then it's not so much the size of the cap that matters, but it's equivalent series resistance spec. Unfortunately, aluminum electrolytics (like the one used in your pic) are good for cheap low frequency bulk decoupling, but are ineffective for fast transients (apologies for the handwavy explanation). Tantalum (for large values) and ceramic (for smaller values) are best suited for this.
Is it normal to expect the voltage to drop from the compensated* target output voltage when ANY load is applied?
* I mean compensated for the drop caused by the current sink resistor + LED that I added to ensure I'm meeting the minimum regulation current requirement.
Yes, it's normal, which is why the device datasheet's load regulation spec is very important to engineers. Unfortunately, your application is camera which we really know nothing about. Furthermore, the LM317 is a linear regulator, which may not have sufficient load regulation for your application (assuming it can source enough current).
Other than that, mikerj's comment on breadboard contact resistance and high current, and mariush's on linear regulators and heat dissipation are important and need to be kept in mind.
P.S.
With R
1=120R, R
2=270R, and without LED, you're pretty much at threshold for min. load current to maintain stability. If you want to remove the LED to allow for more current to the real load, try R
1=100R and R
2=220R. That should give you 12.5mA load @ 4V output.
Are those carbon composition resistors?
They look like standard carbon film.