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There are many sky surveys that have been conducted by telescopes in different wavelengths of the electromagnetic spectrum like DSS (Digitized Sky Survey), SDSS (Sloan Digital Sky Survey), WISE (wide-field Infrared Survey Explorer,), Fermi, VLA North, etc.

I am currently working on a project in the field of radio astronomy and would like access to the recent and latest images of any radio sky surveys/telescopes (preferably post-year 2000). VLAF and NVSS have great resolution and sensitivity respectively. Also, RACS and LoTSS have superb resolution and sensitivity.

However, I am unaware of any new radio sky surveys that have been happening or new data releases of any of the radio telescopes. Also, if they are publicly accessible?

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"RACS and LoTSS have superb resolution and sensitivity."

Those are both post-2000; RACS was completed in 2020 and LoTSS is still taking data. So I'm not entirely sure why you seem to exclude these when you say, "I am unaware of any new radio sky surveys that have been happening or new data releases of any of the radio telescopes."

But in any case, and restricting ourselves to post-2000 surveys (and ignoring re-analyses of previous surveys, like the VLA Low-frequency Sky Survey Redux (VLSSr)), there appear to be quite a few:

There may be others I have missed (I'm not a radio astronomer).

From what I can glean from the various websites, data is definitely available for FIRST, VLASS, GLEAM, and the various LOFAR-based surveys.

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The Giant Metrewave Radio Telescope (GMRT) operated by the National Centre for Radio Astrophysics provides complete data of all of its observations from 5th November 2001 to 1st March 2023 (the day of writing this answer), a total of 89371 individual observations. GMRT is the largest and most sensitive radio telescope array in the world at low frequencies.

Though not an all sky survey, such an enormous dataset over a long period of observations ensures that almost all of the sky visible from Pune (India) has been covered, with some portions being observed many times.

The dataset can be searched using a variety of parameters including RA/DEC and nearby object names. The search and download tool is available at the GMRT Online Archive.

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