There are several factors to consider. It's not a simple binary question.
1. The optical resolution of the scanner.
2. The quality of interpolation past the optical, and how it fairs against other methods. Not just simple bicubic or biliear (ala Photoshop), but fractal upsizing.
3. The source image media -- usually negative vs. print.
4. The source image quality.
5. The source image size.
6. The destination image size.
Here's an example:
Right now, today, I'm scanning an old 1950s photo at the request of a family member.
It's a B&W 4x4 print, and is glued into a photo album. It's not 100% perfect, but decent. There is some warping of the image due to aged glue on the back, and some minor crud has dented the image. And the usual dust, lint, etc. (Note that these tiny errors were invisible to the eye, and were only seen when magnified in a scan.)
The original print is pretty blah, lacking any real contrast.
He wants a 12" x 12" print. (Not only that, but he wants me to colorized the B&W. Which I can do quite well.)
The source image is probably not even 300dpi in quality. (I worked for newspapers pre-, during phase-in, and post-digital. We'd scan negatives at about 2000dpi, and downsize those to 200dpi for press. This image closely matches 200dpi quality from my old tearsheets.)
I scanned his photo at 300, 600, 1200, 2400, 3200, and 4800.
The quality of the scanner (Epson V600) is somewhat blurrier than the source at 300dpi. I believe it's from the speed of the scanner -- it moves too fast at 300dpi! At 600dpi, all details were retained. At 1200, 2400, 3200 and 4800 it appeared the same.
However, starting at 2400, the image scan quality was not as good as what I could achieve with a 1200dpi scan, and using some quality Photoshop work (or third-party filters like On1 Perfect Resize, the fractal resizer).
Every situation will work out a bit differently. Examples:
- An old Polaroid usually will not look at different above 600dpi.
- Most large 8x10 images are equally blurry, but can look better when scanned at 1200dpi and shrunk to 300/600dpi (also assuming final image will be displayed smaller, either print or web).
- A 35mm fine-grain negative, however, looks best when scanned at 4000dpi.
There's not a single answer.
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