What's not there isn't there. Your issue really hasn't anything to do with 300 DPI or not, but total absence of sufficient resolution. It will not print nice if it looks already rubbish on your screen. That is the truth you need to come to terms with. Even if you employ elaborate procedures to upsize your images, they simply started out too small in the first place. In this situation that's like downloading emojis or WhatsApp sticker PNGs from the web and scaling them up - the differences between your product photos and those random other images will not be possible to determine at times. It will look lousy one way or the other.
You need to tell your customer that these size images will not print correctly and they need to supply hi-res originals (they should have access to these via the original photographer). If you proceed on the existing basis you may get the blame for the poor quality of the printing!
If you can't reshoot, forget it. There's just not enough pixels.
Note that nothing stops you from sending these images to print. They won't implode or anything - it'll just look horrible. The individual pixels will be clearly visible if you print as-is. If you upsample to 300ppi, you end up with a blurry blob that looks even worse.
"...my question is this: because it's a pdf do I still have to have 300dpi for the photos or does it no longer matter as they're not using the original image?"
Yes. There are 3rd party applications ( Alien Skin's "Blow Up", etc. ) that will enlarge the low res originals. A.S. also has ( or had ) a very effective application called "Image Doctor" that would repair JPG artifacts before the enlargement procedures.
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There's no application that can enlarge an image that's 134 x 308px effectively, whichever format (at 300PPI it would print at a print size of around 1/3" x 1".
Agree with Derek. That's a real thumbnail.
IMO too much faith is put into upsampling, whether by Photoshop or third-party apps. You never gain anything other than more pixels. And since those pixels contain no new information, they're just wasted.
If you have an image with too few pixels to get optimal ppi at the required print size, but you still need to print it at that size - the best thing to do is generally nothing. Just send it to print as it is.
There's a very widespread myth about print. It says you must have 300ppi. That's a misunderstanding. There's nothing special about that number. It's just a theoretical upper limit - if you go higher, there's no chance even in theory that it will improve quality. That number is based on a standard screen frequency of 150 lines per inch. The theory is that at twice that number, there is no possible way to discern individual pixels. But you can go a lot lower before you start seeing an actual loss of sharpness.
What is much more important than ppi is effective sharpening of the image at actual reproduction size. A properly sharpened image at 240 ppi will look better than an unsharpened one at 300.
It should be said that there are special cases where limited upsampling makes sense. That would be if edge sharpness is more important than high-frequency detail. Then you can use the finer-grained pixel structure to emphasize sharp transistions (again by sharpening). I don't consider a standard photograph to fall into this category, but reproduction of illustrations might. But it depends.
I'd love to see a sample of what Derek is working with. I discovered about ten years ago that most printers are using 150 lpi, even on a non coated paper. I think that is where the standard high res number of 300ppi comes from. I couldn't agree more that 300ppi could be too high. Which leads to the argument that the originator should know what type of press/paper will be used and use the appropriate res.
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You only need 85LPI for printing on newprint, but for a colour catalogue you'll probably be printing on a coated stock so a screen of around 150LPI would be used, therefore original images should be between 200 to 300PPI (assuming you're printing at that size.
For example to print an image on coated stock at say 3" x 6" you want your original image in Photoshop to be around 900 x 1800px.