Aplanatic path factor; transparent stack has zero absorbance; Köhler = coherent

← Verification · Thin films · Focused beam

Reference: aplanatic path factor; transparent stack has zero absorbance; Köhler = coherent
Kind: analytic: a closed form, limit or conservation law: independent of any code
Calculated: apparent absorbance
Agreement: 1e-12

A weak absorber (α = 10 cm⁻¹, 1 µm) in n = 1.5 under an aplanatic NA 0.23–0.5 cone: the path factor A focused beam crosses a film obliquely, so a weak absorber looks thicker by the cone's mean path factor ⟨1 / cos θ⟩, 1.0357 for an aplanatic NA 0.23–0.5 pupil in n = 1.5, the ruling the test pins. The test also checks that an empty stack, or a sample that is its own reference, has zero absorbance and that Köhler illumination equals coherent for a film.

ln10 A / (α d), PyStratify ⟨1 / cos θ⟩ of the aplanatic cone, 1.0357

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largest |difference| (1.0357 is printed to 5 digits): 4.16×10⁻⁵
PyStratify the lines, the reference the circles

A film (1.2 µm, n = 1.55 + 0.03i) in air under NA 0.5/0.23: Köhler illumination against a coherent focus A laterally uniform film cannot tell how the pupil's plane waves are phased: coherent and Köhler illumination see the same cone and must give the same detected power.

coherent focus, PyStratify Köhler (field stop 40 µm)

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largest |difference|: 0
PyStratify the lines, the reference the circles

Run it yourself: focused_checks.py · test_focused.py · figures.py · FOCUSED_CHECKS.md on GitHub, PyStratify 97e52a9