Detection techniques in low-coherence interferometry and their impact on overall measurement accuracy

Tomáš Pikálek; Tomáš Fořt; Zdeněk Buchta

doi:10.1364/AO.53.008463

Applied Optics
Vol. 53,
Issue 36,
pp. 8463-8470
(2014)
•https://doi.org/10.1364/AO.53.008463

Detection techniques in low-coherence interferometry and their impact on overall measurement accuracy

Tomáš Pikálek, Tomáš Fořt, and Zdeněk Buchta

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Tomáš Pikálek, Tomáš Fořt, and Zdeněk Buchta, "Detection techniques in low-coherence interferometry and their impact on overall measurement accuracy," Appl. Opt. 53, 8463-8470 (2014)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: August 21, 2014
- Revised Manuscript: November 11, 2014
- Manuscript Accepted: November 11, 2014
- Published: December 17, 2014

Abstract

This paper deals with interference fringe center detection techniques used in low-coherence interferometry for contactless 3D inspection of macroscopic objects. It presents a complex analysis of several frequently used detection techniques and shows their impact on the measurement accuracy. The analysis compares those techniques in terms of computational complexity, measurement accuracy, and resistance to optical dispersion caused by wedge-shaped optical components.

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Sampling period [nm]	0.9	2.3	4.8	10.1	20.7	32.1	51.1	64.5
Samples per signal period	144.7	56.8	27.4	13.2	6.4	4.1	2.6	2.1
Method	$R a [nm]$
Weight center	1.1	1.2	1.3	1.5	1.7	29.6	59.2	55.2
Correlation, model 1	0.2	3.9	7.8	0.3	7.1	8.9	12.4	12.7
Correlation, model 2	0.2	0.3	4.7	4.4	5.1	0.5	4.3	25.9
Modified correlation, model 2	0.9	0.8	1.1	1.8	2.6	3.2	4.5	6.0
QPF, top of the envelope	2.0	1.9	2.6	3.8	6.9	11.2	11.5	49.4
QPF, signal maxima	0.1	0.1	0.1	0.1	6.5	9.6	12.2	51.6
FDA	0.9	0.9	1.3	2.0	3.6	4.9	60.7	198.8
FDA, interpolated	0.7	1.1	1.5	2.7	2.9	5.0	7.6	163.8
Detection of top of envelope	35.8	32.4	15.9	13.0	23.1	16.3	21.4	32.5

Measuring mirror	Thorlabs silver	Thorlabs dielectric	Thorlabs dielectric	Thorlabs dielectric	silver	silver	dielectric
Reference mirror	Thorlabs silver	Thorlabs dielectric	aluminum	dielectric	steel	aluminum	dielectric
Method	$R a [nm]$
Weight center	1.4	2.4	5.6	20.4	2.8	1.5	20.1
Correlation, model 2	0.2	0.5	33.0	0.7	0.8	0.9	1.0
Correlation, model 2, abs.	0.2	0.5	4.1	1.2	0.8	2.6	10.3
Correlation, model 2, cropped	0.4	0.5	6.1	0.8	0.8	0.9	1.0
Modified correlation, model 2	0.8	1.0	2.3	1.6	1.8	0.8	1.8
QPF, top of the envelope	7.9	5.5	9.0	24.9	9.4	13.4	34.7
QPF, signal maxima	0.1	0.1	47.1	23.4	0.3	43.3	44.9
FDA	2.3	1.3	3.7	24.5	2.9	2.2	2.2
FDA, cropped	1.5	1.4	6.9	1.9	1.7	1.6	1.7
Detection of top of envelope	10.1	14.5	18.6	20.6	18.3	10.3	21.5

Number of samples	2266		958
Mirror shift	24.62 μm		8.84 μm
Method	$t_{1}$ [s]	$t_{1 p}$ [s]	$t_{2}$ [s]	$t_{2 p}$ [s]
Signal intensity maxima	103	25	134	16
Weight center	1030	184	230	43
Correlation	969	158	542	97
Correlation, cropped	476	85	603	98
Modified correlation	1665	297	1217	219
Modified correlation, cropped	1115	197	1244	217
QPF	157	33	203	27
FDA	1144	197	1101	169
FDA, interpolated	1809	298	1374	219
Detection of top of envelope	522	83	327	52
Detection of top of envelope, filtered data	4627	742	3542	549

Sampling period [nm]	0.9	2.3	4.8	10.1	20.7	32.1	51.1	64.5
Samples per signal period	144.7	56.8	27.4	13.2	6.4	4.1	2.6	2.1
Method	$R a [nm]$
Weight center	1.1	1.2	1.3	1.5	1.7	29.6	59.2	55.2
Correlation, model 1	0.2	3.9	7.8	0.3	7.1	8.9	12.4	12.7
Correlation, model 2	0.2	0.3	4.7	4.4	5.1	0.5	4.3	25.9
Modified correlation, model 2	0.9	0.8	1.1	1.8	2.6	3.2	4.5	6.0
QPF, top of the envelope	2.0	1.9	2.6	3.8	6.9	11.2	11.5	49.4
QPF, signal maxima	0.1	0.1	0.1	0.1	6.5	9.6	12.2	51.6
FDA	0.9	0.9	1.3	2.0	3.6	4.9	60.7	198.8
FDA, interpolated	0.7	1.1	1.5	2.7	2.9	5.0	7.6	163.8
Detection of top of envelope	35.8	32.4	15.9	13.0	23.1	16.3	21.4	32.5

Measuring mirror	Thorlabs silver	Thorlabs dielectric	Thorlabs dielectric	Thorlabs dielectric	silver	silver	dielectric
Reference mirror	Thorlabs silver	Thorlabs dielectric	aluminum	dielectric	steel	aluminum	dielectric
Method	$R a [nm]$
Weight center	1.4	2.4	5.6	20.4	2.8	1.5	20.1
Correlation, model 2	0.2	0.5	33.0	0.7	0.8	0.9	1.0
Correlation, model 2, abs.	0.2	0.5	4.1	1.2	0.8	2.6	10.3
Correlation, model 2, cropped	0.4	0.5	6.1	0.8	0.8	0.9	1.0
Modified correlation, model 2	0.8	1.0	2.3	1.6	1.8	0.8	1.8
QPF, top of the envelope	7.9	5.5	9.0	24.9	9.4	13.4	34.7
QPF, signal maxima	0.1	0.1	47.1	23.4	0.3	43.3	44.9
FDA	2.3	1.3	3.7	24.5	2.9	2.2	2.2
FDA, cropped	1.5	1.4	6.9	1.9	1.7	1.6	1.7
Detection of top of envelope	10.1	14.5	18.6	20.6	18.3	10.3	21.5

Abstract

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Tables (3)

Equations (2)

Applied Optics