I believe our fundamental disagreement stems from the distinction between
narrowband vs.
wideband optical filters. The Fabry-Perot etalon talked about by
@Gleb1964 is an optical cavity whose spatial extent (mms to cms) and reflectivity is carefully engineered to employ interference to pass what is (almost) a single specific wavelength, and so requires coherence-lengths on the order of at least mms to cms to function. In other words, an etalon is an
ultra-narrowband filter. When illuminated by the incoherent spectrum of sunlight, it selects-out from that spectrum only those particular wave-trains of sufficient length and precise frequency and blocks the rest. As such, the coherence-length of the transmitted radiation says
precisely nothing about the source (sunlight), rather it is simply a characteristic of the etalon itself. This is obvious since if we replace the source by a highly-coherent laser of the appropriate wavelength and intensity, the transmitted light is unchanged. Thus, an observer with access only to the output from the etalon cannot distinguish whether its input is the broadband sun or the narrowband laser. Thus, the light emerging from an etalon
bears no relation to the average coherence-length of the broad solar spectrum.
In contrast, the OP's question is aimed at the design of
wideband thin-film filters intended to pass sunlight over a broad part of its spectrum. Particular examples are antireflection (AR) coatings that act as UV-IR cutoff filters, passing only visible light for photography, eyeglasses and the like, and AR coatings for solar cells to match the transmitted solar radiation to the power-band of those cells, while reflecting undesirable radiation outside that band. Here is a reference describing such a coating for cadmium-telluride cells:
Multilayer Broadband Antireflective Coatings.... In section II the authors state:
I now examine how the highlighted restriction impacts the design of the coating:
From the wavelength range, I can use the relation ##l_{coh}\approx\frac{\lambda^2}{2 \,\Delta\lambda }## given by
@Charles Link to estimate the coherence-length to be ##l_{coh}\approx 625^2/2/\left(850-400\right)=434\text{nm}##. Note that ##l_{coh}## falls into the solar longitudinal-coherence range ##170-900\text{nm}## that I quoted in post #17. This coherence length is to be compared with the ##\text{Optical Thickness}\equiv\text{(Refractive Index)}\times\text{(Physical Thickness)}## of each layer, as well as to the entire 4-layer stack:
\begin{matrix}
\text{Material} & \text{Index} & \text{Thick.(nm)} & \text{Opt. Thick.(nm)} & \text{< 434nm?}\\
\hline \text{SiO}_2 & \text{1.45} & \text{94.12} & \text{136.47} & \text{Yes}& \\
\hline \text{ZrO}_2 & \text{2.13} & \text{133.99} & \text{285.20} & \text{Yes}& \\
\hline \text{SiO}_2 & \text{1.45} & \text{30.40} & \text{44.08} & \text{Yes}& \\
\hline \text{ZrO}_2 & \text{2.13} & \text{18.81} & \text{40.07} & \text{Yes}& \\
\hline & & \text{Total OT:} & \text{505.83} & \text{No}
\end{matrix}
Clearly, even though the optical stack-height exceeds the coherence-length ##l_{coh}\,##, this filter functions because the optical thickness of
each individual layer is less than ##l_{coh}\,##, completely consistent with the highlighted statement above. Thus, I claim that the declaration:
Gleb1964 said:
That short coherence length ##1 \mu\text{m}## of unfiltered solar light, that have been intensively disputed here, has about nothing [to do] with the performance of the interference filters.
is simply wrong.
@Gleb1964 is focused on "apples" (ultra-narrowband interference filters) when he should be examining "oranges" (wideband interference filters).
