What coordinate system should be used for projecting a non-geographical scan?

Question

This is not precisely GIS problem but still spatial.

I would like to measure certain features of a thin wood slice. I have a scan of that slice.

What coordinate system should be used to obtain a view "just as it is" and to be able to measure features (by ruler tool or by calculating geometry in ArcMap) of a object from scan?

Is that even possible in ArcMap?

Example of a scan:

Answer 1

Use a Cartesian coordinate system you can set 0,0 arbitrarily (ie: Center Of Gravity or a corner. The units can be anything and any math you want to apply will require elementry level geometry skills.

You will want to georectify the *.tiff here is an example of how to do it there are many other tutorials if you google georectify tiff this is an esri article Fundamentals of georeferencing a raster dataset .

If you do not have real world coordintates you will need to start from 0,0.

Answer 2

Knowing the resolution helps. If you have access to Python and GDAL, you can do something like (not run):

from osgeo import gdal

# Read the original file
fn = "c:/fullpath/myfile.tif"
ds = gdal.Open(fn)

# Write out a copy, changing the GeoTransform
driver = gdal.GetDriverByName("GTIFF")
ds_out = driver.CreateCopy("c:/fullpath/out.tif", ds, 0)
ds_out.SetGeoTransform([0, ds.RasterXSize / 2400, 0, 0, ds.RasterYSize / 2400])
ds_out = None
ds = None

The key part is the GeoTransform, it is [xorigin, xpixelsize, 0, yorigin, 0, ypixelsize].

Having the proper origin (0,0) in the upper-left, and a physical pixel size (in inches), you will be able to make relatively accurate measurements. You don't need to set a projection when opening it ArcGIS. It will show as unknown units, but you know that they are in inches. Having a ruler or other known measure in the picture would help confirm that everything is as it should be.

The simpler alternative is to do any tracing / analysis in 1x1 unit pixels, as it is in the raw image, then convert distances and areas appropriately using the known resolution (1 pixel = 1/2400 inches, for distances, in your case).

If you need to assign a projection, something like this "+proj=eqc +ellps=sphere +units=int-in" might work:

PROJ.4 : '+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +a=6370997 +b=6370997 +units=m +no_defs '

OGC WKT :
PROJCS["unnamed",
    GEOGCS["Normal Sphere (r=6370997)",
        DATUM["unknown",
            SPHEROID["sphere",6370997,0]],
        PRIMEM["Greenwich",0],
        UNIT["degree",0.0174532925199433]],
    PROJECTION["Equirectangular"],
    PARAMETER["latitude_of_origin",0],
    PARAMETER["central_meridian",0],
    PARAMETER["false_easting",0],
    PARAMETER["false_northing",0],
    UNIT["int-in",1]]

I don't think it really matters what you pick as long as the units and pixel size are correct, because you are dealing with such a small area, geographically speaking.