How do disk imagers like Deepspar and Atola handle bad sectors?

Do they freeze the same way a PC will or do they just quickly skip them?

DDI has an algoritm u can manually change. Basic imaging procedure is pass 1 low tolerance , 200ms time out timer and skip say a 100 sectors after finding bad. This way all good stuff gets imaged 1st and fast. Then 2 pass higher tolerance say 500ms timeot timer. Then 3rd pass with even higher tolerance and no skip and lowered step, then even more indepth with ECC.

So, is Deepspar the only disk imager that can do this?

Not Exactly, DS is just the best one. I use Data Extractor for that too.

About bad sectors, so hardware based "Smart" imagers basically can read with the power control, resetting stuff, soft reset, sectors skip, ECC control, Time out..such functions are not to find in the software based imagers.

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Bitlevel Data Recovery

See also this thread
there-hdd-duplicator-that-doesnt-cost-thousands-t16534.html

and the last post thst contains a link to details of how the Deepspar one works

The beauty of the DDI is in its algorithms and how you can customize a logical if/then/else set of rules for each drive. Since every drive will be somewhat unique in how it images (assuming weak heads and/or random platter damage). It will make up to 4 passes on a drive and while the default options work well, you can watch in real time how the drive is responding and tweak settings such as timeout, sector count, image direction, UDMA/PIO, ECC "long read", etc. From there you can go in and program it how to respond to different circumstances such as when the drive becomes unresponsive, to power it down for x amount of seconds/minutes and then re-power and resume. I had a drive the other day that would only read a million or so sectors at a time and then stop. Programming the DDI to automatically skip a hundred thousand sectors on this event would kick start the drive working again. After running a couple of passes I got 100% of the drive. Took me about 10 minutes of real "work". I was able to repair a few other PC's while the DDI did all the work. I can't see how any data recovery firm can operate without at least one of these.

No, it isn't the only one
There's also Atola Imager, PC-3000/Data Extractor, and Salvation Data tools.

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Dmitry