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Printing of images in newspapers use halftones to create the various shades of grey in the photos. The resolution of halftones is given in lines per inch (LPI). For standard newsprint, which is rather porous, the maximum LPI is 85 -- any higher than that, the dots bleed and run together.
This photograph linked to was published in Current Events, the "national school newspaper". It is possible that this paper used higher quality paper than newsprint. This would allow a much higher LPI, thus providing for higher-quality images. LIFE Magazine, a photojournalism magazine of that era, used 150 LPI. A very high quality magazine, like National Geographic, uses 300 LPI (essentially, a "retina" display on paper).
I remember reading something like this called "My Weekly Reader" while in grade school in the early 1950's. I don't think it was printed on newsprint, as the pages were more like regular typing paper (but not glossy magazine paper) as I recall.
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Apart from the half-tone process, the other component was the process that allowed the photographer to scan their photo on location, and then send it back to the home office by way of telegraph or telephone.
The first of these technologies was the Telediagraph that demanded special telegraph connections. By WWII, the process was refined enough to use ordinary telephone connections, even over intercontinental lines, and inexpensive enough where even remote branch offices of major news services and large daily papers had one on-site. Some offices had equipment could scan and send photos by short-wave radio.