Calculating Cauchy from list of refractive indices

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lighting_freak
Posts: 93
Joined: Thu Jan 18, 2018 6:02 pm

Calculating Cauchy from list of refractive indices

Post by lighting_freak » Sat Oct 06, 2018 2:40 pm

Hi all,

let's assume a have a list of refractive indices according to wavelength.
Is it possible to calculate from this list to a valid cauchy value?

Example Diamond:
nominal refractive index given 2,4488

lambda [nm] n (lambda)
364,659375 2,473323675
387,450586 2,464986815
413,280625 2,455051934
442,800669 2,441251728
476,862259 2,431478974
516,600781 2,427076431
563,564488 2,420857286
619,920937 2,411429037
688,801041 2,406543164
774,901171 2,406202402
885,601339 2,400035416

Thanks or your suport and ideas.

BR
OS - Windows 7 X64
CPU - Intel CORE i7
GPU1 - Variants of notebook card from nVidia
GPU2 - Variants of notebook onboard card from Intel
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Dade
Developer
Posts: 1335
Joined: Mon Dec 04, 2017 8:36 pm

Re: Calculating Cauchy from list of refractive indices

Post by Dade » Sat Oct 06, 2018 3:14 pm

lighting_freak wrote:
Sat Oct 06, 2018 2:40 pm
let's assume a have a list of refractive indices according to wavelength.
Is it possible to calculate from this list to a valid cauchy value?

Example Diamond:
nominal refractive index given 2,4488

lambda [nm] n (lambda)
364,659375 2,473323675
387,450586 2,464986815
413,280625 2,455051934
442,800669 2,441251728
476,862259 2,431478974
516,600781 2,427076431
563,564488 2,420857286
619,920937 2,411429037
688,801041 2,406543164
774,901171 2,406202402
885,601339 2,400035416

Thanks or your suport and ideas.
Cauchy's equation is well defined curve so it can not approximate an arbitrary set of values however I assume you are using real world data so there should be a value approximating them.

A simple brute force/one-time solution would be to use Excel, Mathematica or a similar tool, to draw your tabulated data and various Cauchy's curves (https://en.wikipedia.org/wiki/Cauchy%27s_equation) and pick the one better matching your values.
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lighting_freak
Posts: 93
Joined: Thu Jan 18, 2018 6:02 pm

Re: Calculating Cauchy from list of refractive indices

Post by lighting_freak » Sat Oct 06, 2018 3:38 pm

Hi,

so you mean doing something like this to find B & D as refractive index and coefficient combination:

B 2,38 D 0,01

lambda [µm] lambda [nm] n lambda) real world n(lambda) from formula
0,36 364,66 2,47 2,47
0,39 387,45 2,46 2,46
0,41 413,28 2,46 2,45
0,44 442,80 2,44 2,44
0,48 476,86 2,43 2,43
0,52 516,60 2,43 2,42
0,56 563,56 2,42 2,42
0,62 619,92 2,41 2,41
0,69 688,80 2,41 2,41
0,77 774,90 2,41 2,40
0,89 885,60 2,40 2,40
Cauchy.jpg
plot
This values B for IOR and D for dispersion cauchy coefficient are right one to enter them into luxcorerender?
Thanks for your help. This seems to work for diamond. Let's see whether it works for PMMA and PC plastics as well.

BR
OS - Windows 7 X64
CPU - Intel CORE i7
GPU1 - Variants of notebook card from nVidia
GPU2 - Variants of notebook onboard card from Intel
Lux - Latest possible relaease

lighting_freak
Posts: 93
Joined: Thu Jan 18, 2018 6:02 pm

Re: Calculating Cauchy from list of refractive indices

Post by lighting_freak » Tue Oct 09, 2018 9:01 am

Those are values on wikipedia:

Code: Select all

Material 			B  (IOR)C (Cauchy)
Fused silica 			1,458	0,00354
Borosilicate glass BK7 		1,5046	0,0042
Hard crown glass K5 		1,522	0,00459
Barium crown glass BaK4 	1,569	0,00531
Barium flint glass BaF10 	1,67	0,00743
Dense flint glass SF10 		1,728	0,01342
I`m still not sure whether the interpretation of those values is right.
The dispersion curves while using this value pairs is very well.
Please let me know what you're thinking about that.

Code: Select all

This values i got from my excel experiments:
Material 			B  (IOR)C (Cauchy)
Diamond				2,385 	0,0117
PMMA				1,4780 	0,0044
PC 				1,5530 	0,012
OS - Windows 7 X64
CPU - Intel CORE i7
GPU1 - Variants of notebook card from nVidia
GPU2 - Variants of notebook onboard card from Intel
Lux - Latest possible relaease

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