The data must be placed in a document of the correct size for printers to be able to make any sense of it, i.e. your document dimensions must be set to the exact 15.92 inches at 300 dpi and the artwork scaled to fit correctly. Also you need to add bleed for cutting, if necessary.
You say Based on a scanned version… is this document you've created still raster based or have you used a scan as an FPO to create vector art?
I am very new to illustrator, first project, so I may ask dumb questions. Are you saying I need to put htis image into another product as a png or tiff or pdf or are you saying I can do this all in Illustrator?
Second question - I was originally attempting to restore the image in PS CS4 but soon realized that I can do all the work in Illustrator. It did a magnificent job. I am using the original scan as a layer in Illustrator to correctly position the new information and copy some of the old information. A a next step I also would like to use my new map as an overlay onto either a photo image of the area or an image from another source such as the USGS which leaves me with a very large image as the bottom layer.
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Your description of what you have done and your requirements are not clear. All the responses thus far involve some degree of guessing.
I have reproduced a very detailed map that I now want to print.
What do you mean by "reproduced"? Traced it as vector paths in Illustrator? Reworked it in Photoshop?...?...?
The original was based on a scanned version that measures in PS 36 X 45 inches or 10440 X 13920 px.
Okay. You have a 10440 x 13920 pixel raster image.
Those proportions do not scale to 36 x 45 inches.
They scale to 33.75 x 45 or 36 x 48.
I want one copy to be at the larger size and it does not need to be exact.
What "larger size"?
What do you mean by "a copy"? How is this going to be printed? Offset lithography? One-off large format inkjet printer?...?
Assuming we're talking about offset, sheetfed, CMYK printing the raster image combined with some native Illusrator artwork, do this:
1. Open the image in Photoshop. Perform whatever raster retouching you want. Perform whatever color correction you want. When all rework of the image itself is done, be sure you end up in CMYK mode. Save the file in Photoshop format as "Original".
2. ReSIZE it to the desired print scale. Crop it to the area you want to print, plus at least .125" extra on any side that bleeds. ReSAMPLE it to 1-to-2 times the halftone screen ruling that will be used when it is printed. Flatten layers. Remove any extra channels. Sharpen it appropriately. Save in TIFF format, as "LargeMap".
3. Set up a new Illustrator document an appropriate size. "Appropriate size" depends upon the printing setup and whether there are bleeds. You can set the Artboard size to the size of the press sheet (assuming sheetfed printing), or to the trim size plus any bleed, plus room for any trim or fold marks you want to include.
4. Import the raster image. Position it correctly relative to the trim marks or guides. Put it on its own layer and lock the layter.
5. Draw the native Illustrator stuff on Layer(s) above it.
6. Save as Press Ready PDF.
I want a second print to exactly match the original at 15.92 inches wide.
For best results, open the cleaned up, full-res image you saved and named as "Original" in step 1. Then repeat steps 2 (saving it as "SmallMap") through 6.
I don't see how to get this exact size print in AI
You can scale a raster image that you have placed in Illustrator, just as you would scale any other object. For example, assuming the image you place is the original 10440 x 13920 scan. You could simply turn on the proportional link in the Transform palette, and set the width to, say 15.92 inches. But that would scale the image to a grossly oversampled 656 ppi.The excess data would simply get averaged away in the imaging process, resulting in a slight blurring and "muddying" of the image. (In other words, it would effectively undo your careful sharpening.)
and since I will be taking this to an outside printer I thought it would be nice if I knew how to get this exact size print.
Raster images should be sampled so as to achieve a ppi that is appropriate to the specific printing method, when scaled to the printed size. Too many people just offhandedly say to "make everything 300 ppi". That is just a corruption of the general rule-of-thumb mentioned above in step 2: Sample your images so that their effective ppi is 1-to-2 times the halftone ruling.
Assuming the common 150 lpi halftone, 225 ppi would be considered dead center of that range, not 300 ppi. 150 ppi is the "low side" of the range; 300 is the "high side". When a range is given, you don't just automatically set everything at the "high side"; otherwise, there would be no reason for providing a range. (If your tires say the maximum inflation is 45 psi, is that the pressure you always use?).
The "high side" is not necessarily for "best results"; it's to allow some fudge room convenience if you decide to scale the image larger on page. Neither is the "low side" necessarily "worst results" or "borderline results": It depends on the image. For example, there is no reason to set a soft-edged drop shadow at higher than the halftone ruling. There is no sharp detail to worry about preserving; the only concern is to avoid visible pixelation, which will not occur if sampled to the halftone ruling. (One round halftone dot cannot render the square shape of a single pixel.)