Effects of coherence length on optical interference filter

[shiweiliu]

I have an optical interference filter that is used to block (reflect) solar light heat between 800nm and 1100nm. That filter is made by using 200 layers of quarter wave high and low index coatings on plastic film. The total thickness of the coating is 25 micrometers or even 50 micrometers.

I was told that interference effect can only happen when the thickness of coating is less than coherence length of light. How can my filter work when the total thickness of interference coating is much larger than the coherence length of solar light that is only about one micrometer?

I can understand locally the adjacent coating layers can still have interference effect but how can the light beam reflected by the top coating layer interfere with light beam reflected by bottom coating layer since the optical path difference between these two beams is far larger than coherence length of solar light?

 

[renormalize]

I was told that interference effect can only happen when the thickness of coating is less than coherence length of light. How can my filter work when the total thickness of interference coating is much larger than the coherence length of solar light that is only about one micrometer?

The coherence length of sunlight is significantly larger than $1 \mu\text{m}$.
From this reference: Spatial coherence of sunlight... I quote an excerpt (from pg. 98):

So for a solar wavelength of $0.5 \mu\text{m}$ the coherence length $L_\bot$ amounts to $40 \mu\text{m}$.

 

[shiweiliu]

The coherence length of sunlight is significantly larger than $1 \mu\text{m}$.
From this reference: Spatial coherence of sunlight... I quote an excerpt (from pg. 98):
View attachment 355358
So for a solar wavelength of $0.5 \mu\text{m}$ the coherence length $L_\bot$ amounts to $40 \mu\text{m}$.

Oh. I estimated it according to formula: wavelength^2/Delta wavelength. Wavelength is about 500nm and Delta wavelength is about 300nm. It is about one micrometer. Something is wrong in my method?