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‘Gedankenspektrum’ Methods in Optical Coatings
$ `9 S3 ~0 J2 q4 I- k" _( pFred T. Goldstein*7 ^" k6 B: p3 `* f% V
FTG Software Associates, P.O. Box 579, Princeton, NJ USA 08542
c/ C- B' @5 j! L% ^/ i5 MCopyright 2008 Society of Photo-Optical Instrumentation Engineers (SPIE)
. U4 @4 i' B: h3 W1 V+ M @" P8 fABSTRACT% u1 A: s$ h* C) Z9 C, E5 O/ _6 x9 t
Optical coatings are subject to random and systematic errors. Assuming unvarying dispersion, least-squares fitting of
9 c$ m. e: g2 e2 G: R" }measured spectra provides means to solve for non-gross thickness errors. Unlike coating design, in which many
: s/ K* Q& F6 B+ Qacceptable and nearly equivalent solutions are possible, inverse-synthesis requires the unique and correct solution.! w1 A+ z) v6 ~/ i* x- i4 z
We introduce a ‘Gedankenspektrum’ (thought spectrum) method for determining the range and types of spectra required
8 r% [: k$ ?! g8 Z2 h2 Tfor a correct solution. Starting with an ideal design, we simulate production errors and then calculate the spectrum.) e( a% \4 n" W) {1 t: T
Returning to the original design, we solve for the layers corresponding to the modified spectrum. Finally, if each layer is, v2 a* }+ L% ~; |( A3 J
close to its known value, inverse-synthesis is successful; otherwise it fails. The process is repeated until the statistics
. |9 ?) {4 p* H1 o9 i$ c, y2 Nbecome clear. Reliability depends on the type of design, number of layers, and measurement specifics. Most importantly,/ a. b( Z: K; d0 m
reliability increases markedly when measurements at non-normal incidence are included. This indicates the insufficiency' N. U/ c7 Q+ L( o2 J5 M# K* }
in the (usual?) practice of measuring optical coatings solely according to pass/fail criteria.( a' x) d# W$ D8 z! I4 C
A second ‘Gedankenspektrum’ method helps decide which spectral measurements and film thicknesses are required for0 h7 S6 D: [' k, D) l$ c
determining n&k in single films, particularly metals. Starting with given dispersion values, random noise is added to: s( G1 r3 q. {$ k
calculated spectra, thereby simulating measurement conditions. We then solve for n&k and compare to given values. |
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