This isn't a question, but I'm just so pleased with figuring something out that I will post it here in the hopes that it will help someone else (searching on ENVI conversions didn't bring up anything here, which there needs to be).
I've got several Landsat ETM scenes which are georeferenced in ENVI3.5.
My problem was:
I used various ENVI image export routines to get to something ArcGIS could use, e.g. BIL or TIFF.
The images are from Madagascar and are in an obscure Madagascar-specific georefencing system:
HOM (Hotine Oblique Mercator) aka LaBorde
Datum: Tannanarive 1925, etc.
Problem was, once these were imported into ArcCatalog, and the projection matched to my coverage files (also in the above projection), the Landsat images were out in the middle of the Indian Ocean, rather than Madagascar!
After much plinking and futile web searching, here was the solution:
My coverages were in Oblique Mercator (Hotine) "Natural Origin", but my images needed Oblique Mercator (Hotine) "Azimuth Center". Made this change and re-entered the referencing parameters (annoyingly cleared when you switch between types of HOM projections) and everything lined up perfectly.
I know, I know, this is a ridiculously specific problem/solution, but perhaps it will help someone...
(BTW, it is also useful to know that ENVI has put up an add-in that outputs image projections to a text file:
ENVI User Function that outputs an ASCII text georeferencing report file