Artemisia absinthium (wormwood, grand wormwood absinthe wormwood)
green anise, Pimpinella species, (not star anise) same as ouzo and raki
Florence fennel, (Foeniculum vulgare Azoricum Group; syn. F. vulgare var. azoricum) a.k.a. 
finocchio.  can be mis-labeled in american superparkets as anise
Hyssop : Hyssopus officinalis
Melissa : in mint family.

other common herbs:
petite wormwood (Artemisia pontica or Roman wormwood), hyssop, melissa, star anise, angelica, peppermint, coriander, and veronica
main trinity:
  1. grande wormwood
  2. green anise
  3. florence fennel
Some consider proper absinthe to be a re-distilled tincture from macerated herbs. (I guess proper gin is made this way) Most modern products are just filtered tinctures (cold mix process).

Higher quality ones start with grape alchahol.

Thujone may be a psychedelic... from wormwood. Menthol odor.

green color makes me think that fennel, anise, and wormwood plants may have been processed, not just seeds.

my best guess would be that traditional methods started with a fermented base, or perhaps a single distilled base, made a macerated tincture with plants (green), then (re)distilled to 70% ish strength. recipe excerpts: 

    larger absinthe, dried and ground (greater wormwood?) 2.5kg
    green anise 5kg
    fennel 5kg
    alchahol at 85   95l

    12 hours in water bath (85C?).  add 45l water when ready to distill.

    green coloring:
    1kg small absinthe, dried and picked
    1kg hyssop tops and flowers
    500g lemon balm, dried and picked

    brew like tea in perfumed spirit.
Montpellier 
    2.5kg large absinthe dried (greater wormwood?)
    6kg green anise
    4kg flourentine fennel
    1 kg corriander
    500f angelica seed
    95l alchahol at 85c

    distill

    then color:
    750g dried hyssop herb and flowers
    750g dried balm of moldavia
    1kg small absinthe
more recipes in this text
Had a conversation with a modern absinthe maker.

He does a 2-3 month tincture using fairly high strength alchahol. As high as he can get efficiently from a single distallation... around 80% (160 proof). For his first distallation he does not worry too much about quality, and keeps most of the "tails" to get a high proof.
I think that we will be fine with a commercial alchahol at this stage. Everclear, Bacardi 151 or similar very high strength ethanol.

Dilute down to a more typical 70-80 proof (40%) for second distillation. Be careful on this distillation to remove the tails. There will be bad stuff in there, including from the herbs that should be removed.

You should get a fairly high proof from this distillation... around 70-80% (150ish proof). Tincture the flavor/color herbs in this alchahol for about 2 days. strain, filter, and bottle.

Note that you CANNOT dilute this distillate. Water will make it cloud like ouzo or raki. It is traditional to dilute into the glass, and let it cloud at that stage.