Answer:

For coefficients of Even Asphere surface,  a1, a2, a3… they have different units, and shown as below in case of lens units was mm  :

a1,  units was 1/mm

a2,  units was 1/mm^3
a3,  units was 1/mm^5
……
So the scaling for above parameters was  1/r, 1/r^3, 1/r^5 ….

The TCE value is the thermal coefficient of expansion in 1e-6/K. We know that TCE=8, and δT=40 K. a1=a2=a3=p=100
Radius of surface7 is 100.

For configuration2:

radius= 100+100*8*40*e-6= 100.032
crvt= 1/100.032= 9.996801024E-03 
a1= p/(scale of r) =  p/(100.032/100)= 0.9996810 p
a2=p/scale of (r^3)= p/ (100.032^3/100^3)= 0.99904614 p
a3=p/ scale of (r^5))=p/(100.032^5/100^5)=  0.99840153 p

For configuration3:

radius= 100+100*8*80*e-6= 100.064
crvt= 1/100.064= 9.993604093E-03 
a1= p/(scale of r) =  p/(100.064/100)= 0.9993604093 p
a2=p/scale of (r^3)= p/ (100.064^3/100^3)= 0.998082455 p
a3=p/ scale of (r^5))=p/(100.064^5/100^5)=  0.9968061348 p

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Thermal formula

What’s the equation for surface shape versus temperature in a sequential code? As it turns out, the equation is in the attached pdf with an explination, it is derived from the realization that the part expands and contracts, while the coordinate system does not. Not sure if this was published by anybody, I worked it out myself in 1986.

-Brien Housand, 05/01/2020

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