Drizzle vs Focal Length vs SNR

Anderl:
Fellow Astrophotographers, 

until recently I was under the impression  that drizzle other than 1x is only useful for gaining a bit of detail on under sampled data. 
Few months ago russell croman released his free to use mtf-analyzer https://www.rc-astro.com/mtf-analyzer/ and also an article on why drizzle and deconvolution makes a great combo in image processing. 
As I  would love to create pictures with the best possible resolution, while at the same time only owning a midsized refractor, I am now wanting to know what this implies for me as an astrophotographer. 

1. is drizzle a good substitute for focal length and where are the limitations?
2. how much longer would one need to expose to get the same snr? 4x as long for a 2x drizzle? and what if I just resize the picture after stacking to get back to the initial pixel count. Does that give me back snr without loosing me the gained resolution? 
3. when and how are you use or plan to use drizzle in your workflow?

I know there is already a lot of information available but as with a lot of things in astrophotography, everybody tells a slightly different story. 

cs
Andi

1. As others have mentioned, its not a substitute. Its an approximation, but that's all.
2. You can use 2x drizzling to benefit, without the need to expose longer. See below for my approach. 
3. Here is how I've used drizzling for many years (back to around the middle of last decade):

For many years, I've drizzled for the purposes of deconvolution and NR, with the express intent to downsample back to my native camera resolution after those two processes. I guess these days, it would be NoiseXterminator and BlurXterminator (and I do them in that order, specifically), however in the past I used PI's Richardsen-Lucy deconvolution followed by TGV and MMT for linear noise reduction (usually in that order.) An old example:



As others have mentioned, to get good drizzling results, you need two key things:

A. Aggressive dithering to make sure you are properly and effectively randomizing the distribution of details in each frame.
B. Lots of individual frames. The more frames with sufficient exposure, the better. This is a lot easier to achieve these days with CMOS, especially those with an HCG mode.

Assuming the two factors above, then you can achieve a quality drizzle integration of your data. Sub count, really, is the primary key here. If you acquire tons of signal, but in only say 10-20 frames (which was pretty common back in the CCD era), drizzling won't be nearly as effective, and you could run into issues with the results. With CMOS, acquiring 50-100+ frames is rather strait forward now, and having lots of well dithered frames will help with the way drizzling distributes signal information into the higher-resolution output image. 

Once you have your 2x drizzled image...use it only for the two processes mentioned above. You can be a bit less aggressive with NR and deconvoluition here (or NXT then BXT), because downsampling will have an additional impact to both detail size as well as noise profile. If you acquired plenty of frames, you should have a quality drizzle distribution, and a nice gaussian noise distribution. In my experience, drizzling doesn't just reduce your SNR by half. Its not quite that simple, and a lot of exactly how it changes SNR will depend on what else you are doing during drizzling (i.e. drop shrink, a PI setting, has an effect on the resulting noise level and profile...and the more aggressive you are with drop shrink, which is the key factor that determines the size of details in the drizzle, the more you might notice a difference in SNR.)

Even if you did reduce your SNR by a factor of two...your only goals with the full size drizzled image, is to deconvolve and do initial noise reduction. That's all. After that, you are downsampling, which is going to boost your SNR by a factor of two again. It is again not that simple as you've reduced the noise and enhanced details at 2x scale, so the downsampled output should actually look FANTASTIC.