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Resolution and Size

1. Optical Resolution
The pixel density of a film or flatbed scanner, or in other words the number of pixels in the CCD allotted to scanning one horizontal inch of the original (i.e., one inch in the main scan direction of the CCD), is expressed in dots per inch (dpi) or pixels per inch (ppi).
In catalogues and other literature, this figure is referred to as the scanner's basic, or optical, resolution.
2. Understanding Resolution and Size in Terms of Scanner Operations
Many scanner drivers allow you to specify not only resolution (output resolution) but also scale and size.
"Output resolution" is the resolution of the image when displayed on an output device such as a monitor (72 dpi) or printer.
In the case of images destined for output on a color inkjet printer, enter a value for resolution equivalent to the printer's effective resolution (typically around 240 dpi).
Scale is set according to the degree to which the image is to be enlarged or reduced (i.e., at what size the image is to be output on the selected output device) as compared to the physical dimensions of the original.
An image scanned at 100% will be output at the same dimensions as the original, whereas an image scanned at 50% will be output at half its original width and height.
Once scale and resolution have been set, the resulting number of pixels is determined according to the following formula:
resolution (dpi) x size (inches) = number of pixels (dots)
It therefore follows that to display a Japanese "service size" photograph (12.5 cm x 9 cm) at its original dimensions (100%) on a
(A) monitor (72 dpi)
(B) inkjet printer (150 dpi)
(C) dye-sublimation printer (300 dpi)
the number of pixels required in each case would be respectively:

72dpi 72 dpi x (12.5/2.54) = 354 pixels
72 dpi x (9/2.54) = 255 pixels
150dpi 150 dpi x (12.5/2.54) = 738 pixels
150 dpi x (9/2.54) = 531 pixels
300dpi 300 dpi x (12.5/2.54) = 1476 pixels
300 dpi x (9/2.54) = 1063 pixels

(1 inch = 2.54 cm, results rounded to the nearest pixel).
Images scanned at these three different settings will be output at the same size when printed.
Note : On the other hand, it is evident that images can have the same number of pixels while differing in resolution and size.
For example, the number of pixels in (and consequently the file size of) an image scanned at 300 dpi and a scale of 100% is the same as in the case of an image scanned at 150 dpi and a scale of 200%.
These images will however print at different sizes.
This can easily be confirmed in the driver:
(1) First, enter the output resolution and size
(2) The number of pixels in the image can now be obtained by changing the units for size from centimeters (cm) to pixels.

Below is an example that uses a Nikon LS-2000 film scanner with the Nikon Scan 2.5 driver.

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Scan settings adjusted to scan a selected portion of frame of 35 mm film at a resolution of 150 dpi and a size of 12 cm (W) x 9 cm (H).
This image will print at a size of 12 cm (W) x 9 cm (H).

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Confirming the number of pixels in an image scanned at settings of 150 dpi, width 12 cm, height 9 cm.
3. Checking the Resolution of an Image
If you do not know the resolution of an image, you can check it using imaging software such as Adobe Photoshop.
For example, you can display the image resolution in Photoshop 5.5 as shown below by selecting Image Resolution from the Image menu.

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