I wondered what digital camera resolution I required to archive documents of
various sizes.
This is simply stating the numerically fairly obvious in a way which may be
useful to others.
(Many could derive this themselves in 2 shakes of a lambs tail (if NZers
:-) ) - this saves the shaking.)

SUMMARY

This assumes the camera image is in approximately "A" format (long side is
1.414 x short side)

1.    Megapixels required to store an image of width W and "A" format aspect
ratio (A4, A5 etc)

        MP = 1.4 x W^2R^2/1000000        ... [1]

        W = width in units of your choice
        R = resolution in pixels per unit of width
        MP = megapixels

Rearranging

2.    Resolution required in pixels per unit width for an A format document
of width W

        R = sqrt [ (MP x 1000000) / (1.4 x W^2) ] ... [2]


or        A4 sheet, 1 MP ==> 105 dpi
            A4 sheet, 3 MP ==> 300 dpi

Conclude that 3 MP is fairly desirable if a camera is to be used for this
purpose.

___________________________________


Discussion:

An A4 sheet (or any sheet in the A series) has a height which is sqrt(2) =
1.414 greater than its width.
If short side has length L then area is L x L x 1.4

For a resolution of R dots per unit length (lets start with dots per inch =
dpi as it's commonly used) then total dots =

    (L x R) x (L x R) x 1.414 = 1.414 x L^2R^2 = number of pixels

If this page is digitised this becomes the number of pixels resolution
needed for a given L and R or, as more commonly expressed, if we divide by 1
million, the megapixel rating required.

Megapixels = MP = 1.4 x L^2R^2/1000000        ... [1]

Rearranging        R = sqrt [ (MP x 1000000) / (1.4 x L^2) ] ... [2]

        (1,000,000/1,414 = 707,000 near enough

Equations 1 & 2 are useful for determining either how good a "camera" we
need to archive a given document or how good a job a given "camera" will do.

A standard A4 sheet is 8" wide.
How many DPI will I get in a 1 MP image?

R = sqrt (707000/64) = 105 dpi

This is about poor fax quality

What about with a 3 MP camera
A 3 appears inside the sqrt so the figure increases by root(3) = 1.732 to
give about 300 dpi
This is early laser quality but without the edge rounding and line smoothing
used in all modern laser printers (added first by HP AFAIK.)
ie a 3 megapixel camera will provide a reasonable copy of an A4 document but
the quality will still be less than ideal.

A 3 MP image saved at 1 byte per pixel (8 bit grey scale) requires 3 MByte
storage per image with no compression. JPEG will reduce this to 100k-300k
for a typical document with not too much quality loss.

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