‘Gedankenspektrum’ Methods in Optical Coatings

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‘Gedankenspektrum’ Methods in Optical Coatings
4 B/ D  R1 z9 t5 c3 ]Fred T. Goldstein*
FTG Software Associates, P.O. Box 579, Princeton, NJ USA 08542
, G# o! O8 }! ]. y8 }! Y9 jCopyright 2008 Society of Photo-Optical Instrumentation Engineers (SPIE)
  ?6 i1 I3 L0 [5 X5 VABSTRACT
  Y" w6 P+ }1 I3 k! AOptical coatings are subject to random and systematic errors. Assuming unvarying dispersion, least-squares fitting of
* \( F. u% l: s6 e' m$ K( @$ ?) `measured spectra provides means to solve for non-gross thickness errors. Unlike coating design, in which many
acceptable and nearly equivalent solutions are possible, inverse-synthesis requires the unique and correct solution.
. N" e& i9 R) N4 g0 H5 R: s' V9 BWe introduce a ‘Gedankenspektrum’ (thought spectrum) method for determining the range and types of spectra required
for a correct solution. Starting with an ideal design, we simulate production errors and then calculate the spectrum.
Returning to the original design, we solve for the layers corresponding to the modified spectrum. Finally, if each layer is
2 W! g' {& C8 j( ~) f% Vclose to its known value, inverse-synthesis is successful; otherwise it fails. The process is repeated until the statistics
6 i5 V# k0 Z3 L  l+ c% ibecome clear. Reliability depends on the type of design, number of layers, and measurement specifics. Most importantly,
reliability increases markedly when measurements at non-normal incidence are included. This indicates the insufficiency
in the (usual?) practice of measuring optical coatings solely according to pass/fail criteria.
$ b. t# F" h+ R* l+ v3 h! fA second ‘Gedankenspektrum’ method helps decide which spectral measurements and film thicknesses are required for
determining n&k in single films, particularly metals. Starting with given dispersion values, random noise is added to
calculated spectra, thereby simulating measurement conditions. We then solve for n&k and compare to given values.