How can I create a flat projection at the micro scale?

[SuzannaMichener]

For my PhD research I am using ArcGIS to map the shape and size of microscopic structures in a human tissue sample. The microscope images I am using have been mounted onto microscopy slides and are therefore flat.

In order to determine the area of the structures, I need to project my image of the structures on a map of a known scale. However, the map projections available in ArcMap are at the kilometer-level, where the scale of microns is irrelevant. When I project my images onto a map of a known scale, the problem of distortion arises, since all the provided projections are spheroid.

Is it possible to create a flat projection at the micro (mm or µm) scale?

[DanPatterson_Retired]

Are you simply looking for a way to translate, rotate and scale your data to something else? 

If the data frame (arcmap) or the map frame (PRO) has no projection set (ie unknown) there are no spherical/elliptical transformations set.  You simply need to know the real world distance that is represented by a distance a linear unit represents.  For images, the cell size (cell width) in real world units is all that needs to be known. 

If you have a representative scenario I can provide assistance since I have done so with ice thin section and stills from ct and mri scans and other sources of data in raster and vector forms for other planar objects

[SuzannaMichener]

I am trying to find a way to measure the area of microscopic features.

These features are measured in microns, which ArcGIS does not recognize. I

have an image with a known scale derived from the microscopy software, but

when I input into ArcMap, it is in unknown units so the area calculations

are meaningless. I can project it using any metric projection, but even

then the distance measures in ArcMap do not coincide with the known

distance provided by the scale bar.

I have included a sample image with a known scale. Is there any way to

create a projection using that information?

Thank you.

[DanPatterson_Retired]

drop the micro... your scalebar can be considered as meters, everything just scales by 1 micrometer = 1 e-06 m2

So your 1000 micrometers is 0.001 m, and area is simply the squared version 

1 micrometers^2 1 e-36 m^2 etc

What ArcMap doesn't know won't hurt it