Apparently there is at least one method of doing this, by chemically breaking down or replacing wood lignin with acrylic.
However this method may only be practical in laboratory-type settings, or at least its not like there is an obvious readily-available product to do it. But it could be with some more digging that a practical process could be described. So I thought it was at least worth posting an answer.
Source: Transparent wood can store and release heat
...scientists report a new kind of transparent wood that ... transmits
Three years ago, lead investigator Lars Berglund, Ph.D., and
colleagues at KTH Royal Institute of Technology in Stockholm, Sweden,
reported an optically transparent wood in the ACS journal
Biomacromolecules. The researchers made the material by
removing a light-absorbing component called lignin from the cell walls
of balsa wood. To reduce light scattering, they incorporated acrylic
into the porous wood scaffold. The team could see through the
There is a video link in the source. Here is an example of one of the steps in altering the balsa wood:
And the results of a later stage:
Interestingly this research seems oriented towards the use of wood as a construction material, but nonetheless might have some knock-on uses in other areas, maybe even fine woodworking.