Influence of a converging incident beam and variations in the surface complex index of refraction on optical profilometric measurements

Jacob Politch; Dan Pantzer

doi:10.1364/AO.27.003185

Applied Optics
Vol. 27,
Issue 15,
pp. 3185-3189
(1988)
•https://doi.org/10.1364/AO.27.003185

Influence of a converging incident beam and variations in the surface complex index of refraction on optical profilometric measurements

Jacob Politch and Dan Pantzer

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Jacob Politch and Dan Pantzer, "Influence of a converging incident beam and variations in the surface complex index of refraction on optical profilometric measurements," Appl. Opt. 27, 3185-3189 (1988)

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Abstract

When a focused beam with a Gaussian profile impinges a surface, the reflected beam is sensitive to a macroscopic wavelength Λ = Λ (Δz,ω₀,n), where Δz is the out-of-focus distance, ω₀ is the diameter of the beam in the focal region, and n is the index of refraction of the media. However for n = const, we have found that Λ = const, certifying such optical surface height measurements. The phase variations of the reflected beam were calculated for changes in the complex index of refraction for several metals and dielectric materials, demonstrating the possibility of distinguishing between various metals when their surface profiles are below the measuring limit of the instrument.

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MATERIAL	CHANGE IN n(Δn)	CHANGE IN K(ΔK)	TOTAL PHASE ϕ_i(n,K) (rad)	CHANGED TOTAL PHASE (ϕ_i+Δϕ_i)(n+Δn,K−ΔK) (rad)	PHASE CHANGE ϕ_i = (ϕ_i+Δϕ_i)−ϕ_i (rad)

Al	0.000	0.002	1.138	1.137	−0.598
Al	0.000	0.020	1.138	1.132	−5.901
Al	0.002	0.000	1.138	1.137	−0.692
Al	0.002	0.002	1.138	1.137	−1.290
Al	0.002	0.020	1.138	1.131	−6.382
Al	0.020	0.020	1.138	1.131	−6.865
Al	0.020	0.002	1.138	1.131	−7.392
Al	0.020	0.020	1.138	1.125	−12.594

Cu	0.000	0.002	1.495	1.493	−1.190
Cu	0.000	0.020	1.495	1.493	−11.733
Cu	0.002	0.000	1.495	1.493	−1.314
Cu	0.002	0.002	1.495	1.492	−2.504
Cu	0.002	0.020	1.495	1.492	−13.030
Cu	0.020	0.000	1.495	1.482	−12.953
Cu	0.020	0.002	1.495	1.481	−14.124
Cu	0.020	0.020	1.495	1.470	−24.497

Au	0.000	0.002	1.450	1.448	−1.178
Au	0.000	0.020	1.450	1.438	−11.604
Au	0.002	0.000	1.450	1.448	−1.237
Au	0.002	0.002	1.450	1.447	−2.413
Au	0.002	0.020	1.450	1.437	−12.823
Au	0.020	0.000	1.450	1.437	−12.174
Au	0.020	0.002	1.450	1.436	−13.333
Au	0.020	0.020	1.450	1.426	−23.592

Ag	0.000	0.002	1.350	1.348	−1.061
Ag	0.000	0.020	1.350	1.339	−10.441
Ag	0.002	0.000	1.350	1.348	−1.068
Ag	0.002	0.002	1.350	1.347	−2.127
Ag	0.002	0.020	1.350	1.338	−11.491
Ag	0.020	0.000	1.350	1.337	−10.505
Ag	0.020	0.002	1.350	1.338	−11.548
Ag	0.020	0.020	1.350	1.329	−20.771

MATERIAL	CHANGE IN n(Δn)	CHANGE IN K(ΔK)	TOTAL PHASE ϕ_i(n,K) (rad)	CHANGED TOTAL PHASE (ϕ_i+Δϕ_i)(n+Δn,K−ΔK) (rad)	PHASE CHANGE ϕ_i = (ϕ_i+Δϕ_i)−ϕ_i (rad)

Al	0.000	0.002	1.132	1.132	−0.574
Al	0.000	0.020	1.132	1.127	−5.664
Al	0.002	0.000	1.132	1.132	−0.680
Al	0.002	0.002	10132	1.131	−1.253
Al	0.002	0.020	1.132	1.126	−6.334
Al	0.020	0.000	1.132	1.126	−6.685
Al	0.020	0.002	1.132	1.125	−7.249
Al	0.020	0.020	1.132	1.120	−12.243

Cu	0.000	0.002	1.484	1.483	−1.141
Cu	0.000	0.020	1.484	1.473	−11.259
Cu	0.002	0.000	1.484	1.483	−1.291
Cu	0.002	0.002	1.484	1.481	−2.430
Cu	0.002	0.020	1.484	1.471	−12.532
Cu	0.020	0.000	1.484	1.471	−12.707
Cu	0.020	0.002	1.484	1.470	−13.830
Cu	0.020	0.020	1.484	1.460	−23.788

Au	0.000	0.002	1.443	1.442	−1.147
Au	0.000	0.020	1.443	1.432	−11.302
Au	0.002	0.000	1.443	1.442	−1.222
Au	0.002	0.002	1.443	1.441	−2.367
Au	0.002	0.020	1.443	1.431	−12.506
Au	0.020	0.000	1.443	1.431	−12.027
Au	0.020	0.002	1.443	1.430	−13.156
Au	0.020	0.020	1.443	1.420	−23.150

Ag	0.000	0.002	1.349	1.348	−1.054
Ag	0.000	0.020	1.349	1.339	−10.373
Ag	0.002	0.000	1.349	1.348	−1.066
Ag	0.002	0.002	1.349	1.347	−2.118
Ag	0.002	0.020	1.349	1.338	−11.421
Ag	0.020	0.000	1.349	1.339	−10.484
Ag	0.020	0.002	1.349	1.338	−11.521
Ag	0.020	0.020	1.349	1.328	−20.685

MATERIAL	CHANGE IN n(Δn)	CHANGE IN K(ΔK)	TOTAL PHASE ϕ_i(n,K) (rad.)	CHANGED TOTAL PHASE (ϕ_i+Δϕ_i)(n+Δn,K−ΔK) (rad.)	PHASE CHANGE ϕ_i = (ϕ_i+Δϕ_i)−ϕ_i (mrad.)

FK-5	0.000	0.0002	0.785	0.786	0.493
FX-5	0.000	0,002	0.785	0.790	4.925

BK-7	0.000	0.0002	0.785	0.786	0.468
BK-7	0.000	0.002	0.785	0.790	4.684

K-5	0.000	0.0002	0.785	0.786	0.464
K-5	0.000	0.002	0.785	0.790	4.641

SF-10	0.000	0.0002	0.785	0.786	0.351
SF-10	0.000	0.002	0.785	0.789	3.510

MATERIAL	CHANGE IN n(Δn)	CHANGE IN K(ΔK)	TOTAL PHASE ϕ_i(n,K) (rad.)	CHANGED TOTAL PHASE (ϕ_i+Δϕ_i)(n+Δn,K−ΔK) (rad.)	PHASE CHANGE ϕ_i = (ϕ_i+Δϕ_i)−ϕ_i (mrad.)

FK-5	0.000	0.0002	0.693	0.694	0.489
FK-5	0.000	0.002	0.693	0.698	4.887

BK-7	0.000	0.0002	0.695	0.696	0.465
BK-7	0.000	0.002	0.695	0.700	4.647

K-5	0.000	0.0002	0.695	0.696	0.460
K-5	0.000	0.002	0.695	0.700	4.604

SF-10	0.000	0.0002	0.707	0.707	0.348
SF-10	0.000	0.002	0.707	0.710	3.482

MATERIAL 1	MATERIAL 2	ϕ₁	ϕ₂	Δϕ

		(rad)	(rad)	(mrad)

Cu	Al	1.495	1.138	357
Au	Al	1.450	1.138	317
Ag	Al	1.350	1.138	217
Cu	Au	1.495	1.450	45
Cu	Ag	1.495	1.350	145
Au	Ag	1.450	1.350	100

Abstract

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Tables (5)

Equations (21)

Applied Optics