Here is a dropbox link to a spreadsheet tool I made a while back that does that conversion for you: The formulas are
I converted the densities from your post to Lab L* and pasted them below. If you graph them you'll see that the ideal one from the ideal density PDF is a straight line, and yours is a curved line (that would print too light compared to the QTR Linear Standard).
Step
My
ID
0
100
100
5
98.05771213
95.80416674
10
96.06190196
91.5948099
15
94.01654174
87.38510882
20
91.84284155
83.18773869
25
89.6309833
79.01481401
30
87.30578826
74.808114
35
84.8768059
70.58805598
40
82.27838004
66.37422138
45
79.60002134
62.1852188
50
76.70958903
57.9817595
55
73.63094787
53.78969857
60
70.32262847
49.58300658
65
66.81798427
45.34671649
70
62.90865773
41.16426922
75
58.55177521
36.98154954
80
53.68264961
32.76684459
85
47.99184854
28.54421631
90
41.03279505
24.34514889
95
31.76663589
20.15136133
100
15.94905296
15.94905296