Sandwich hologram interferometry. 5: Measurement of in-plane displacement and compensation for rigid body motion

Nils Abramson; Hans Bjelkhagen

doi:10.1364/AO.18.002870

Sandwich hologram interferometry. 5: Measurement of in-plane displacement and compensation for rigid body motion

Nils Abramson and Hans Bjelkhagen

Applied Optics
Vol. 18,
Issue 16,
pp. 2870-2880
(1979)
•https://doi.org/10.1364/AO.18.002870

Get Citation
Copy Citation Text
Nils Abramson and Hans Bjelkhagen, "Sandwich hologram interferometry. 5: Measurement of in-plane displacement and compensation for rigid body motion," Appl. Opt. 18, 2870-2880 (1979)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Get PDF (2297 KB)
Set citation alerts
Save article

Related Topics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: February 5, 1979
- Published: August 15, 1979

Not Accessible

Your account may give you access

Abstract

Sandwich holography has been used for measurements of in-plane displacement of an object. The sign of the displacement is found by tilting the sandwich hologram during reconstruction. Fringes caused by in-plane rigid body motion can be compensated for, and local displacements evaluated. It is shown that an in-plane motion of more than 1 mm of the object placed at a distance of about 1 m from the plates can be compensated for and a local tilt of 1.5 × 10⁻³ degrees evaluated. A comparision between conventional evaluation and evaluation of sandwich holograms by measuring the tilt angle of the plates to calculate an object’s displacement is shown with a series of experiments.

Full Article | PDF Article

OSA Recommended Articles

Pulsed sandwich holography. 2: Practical application

N. Abramson and H. Bjelkhagen
Appl. Opt. 17(2) 187-191 (1978)

Sandwich hologram interferometry. 4: Holographic studies of two milling machines

Nils Abramson
Appl. Opt. 16(9) 2521-2531 (1977)

Sandwich Hologram Interferometry: a New Dimension in Holographic Comparison

Nils Abramson
Appl. Opt. 13(9) 2019-2025 (1974)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (22)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (13)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

	Sandwich evaluation						Conventional evaluation		Pure translation

Hologram no.	ϕ Virtual (°)	ϕ Real (°)	ϕ Average (°)	ϕ Corrected (°)	d Thickness (mm)	Δx f(ϕ) (μm)	Δx Fringe object (μm)	Δx Fringe plate (μm)	Δx Instrument (μm)
1 RY-13	4.15	4.11	4.13	4.01	1.32	33.3	35.3	39.2	40
2 RY-10	6.34	6.74	6.54	6.32	1.35	53.7	54.7	58.9	60
3 RY-24	9.86	9.32	9.59	9.20	1.21	70.1	68.9	78.5	80
4 RY-14	8.79	8.59	8.69	8.36	1.39	73.1	72.4	78.5	80
5 RY-28	11.2	10.6	10.9	10.4	1.25	81.8	79.5	78.5	90
6 RY-25	10.5	10.7	10.6	10.1	1.30	82.6	83.0	78.5	90
7 RY-29	11.5	10.8	11.2	10.7	1.25	84.2	83.0	78.5	90
8 RY-15	14.5	14.6	14.6	13.9	1.44	126	122	—	120
9 RY-20	14.9	14.9	14.9	14.1	1.34	119	122	—	120
10 RY-17	15.4	15.0	15.2	14.4	1.39	126	125	—	120

	Sandwich evaluation						Conventional evaluation		Pure translation

Hologram no.	ϕ Virtual (°)	ϕ Real (°)	ϕ Average (°)	ϕ Corrected (°)	d Thickness (mm)	Δx f(ϕ) (μm)	Δx Fringe object (μm)	Δx Fringe plate (μm)	Δx Instrument (μm)
1 RY-49	4.96	4.92	4.94	4.78	1.32	39.7	40.6	39.2	50
2 RY-53	5.65	5.42	5.54	5.36	1.23	41.4	42.4	49.0	50
3 RY-32	5.61	5.46	5.55	5.37	1.34	45.2	44.1	49.0	50
4 RY-44	5.45	5.35	5.40	5.22	1.34	44.0	44.1	49.0	50
5 RY-66	5.65	5.65	5.65	5.47	1.31	45.0	44.4	49.4	51
6 RY-64	5.79	5.89	5.84	5.65	1.26	44.7	45.1	49.4	50
7 RY-51	4.96	4.90	4.93	4.77	1.45	43.5	45.2	49.0	50
8 RY-56	5.77	5.76	5.77	5.58	1.33	46.7	47.0	49.0	48
9 RY-38	5.65	5.91	5.78	5.59	1.31	46.0	47.7	49.0	51
10 RY-61	5.65	5.77	5.72	5.53	1.39	48.3	49.0	49.4	51
11 RY-65	6.16	6.39	6.28	6.07	1.26	48.1	49.0	49.4	49
12 RY-37	6.16	6.06	6.11	5.91	1.34	49.8	49.4	39.2	51
13 RY-59	6.00	6.00	6.00	5.80	1.36	49.6	49.7	49.4	49
14 RY-63	6.48	5.97	6.23	6.02	1.28	48.4	49.7	49.4	50
15 RY-41	6.04	6.25	6.15	5.95	1.34	50.1	50.5	49.0	50
16 RY-31	6.68	6.54	6.61	6.39	1.25	50.2	51.2	49.0	51
17 RY-45	7.00	7.05	7.03	6.78	1.28	54.6	53.7	49.0	50
18 RY-40	6.48	6.66	6.57	6.35	1.34	53.5	54.0	49.0	51
19 RY-57	6.45	6.71	6.58	6.34	1.33	53.0	54.0	49.0	49
20 RY-58	6.57	6.60	6.59	6.35	1.31	52.3	55.4	49.0	49
21 RY-69	7.73	7.55	7.64	7.37	1.25	57.9	61.5	59.2	51
22 RY-55	7.89	7.62	7.78	7.50	1.36	64.2	61.8	49.0	49
23 RY-72	8.49	8.63	8.56	8.23	9.36	485	—	—	500
24 RY-78	17.7	18.4	18.1	17.0	9.20	987	—	—	1052

	Sandwich evaluation						Conventional evaluation

Hologram no.	ϕ Virtual (°)	ϕ Real (°)	ϕ Average (°)	ϕ Corrected (°)	d Thickness (mm)	φ Object (°)	φ Object (°)	n Number of fringes
1 RY-32	1.74	1.98	1.86	1.81	1.34	0.518 × 10⁻³	0.769 × 10⁻³	2.5
2 RY-41	4.37	4.73	4.55	4.41	1.34	1.26 × 10⁻³	1.20 × 10⁻³	3.9
3 RY-31	5.19	5.18	5.19	5.03	1.25	1.34 × 10⁻³	1.22 × 10⁻³	4.0
4 RY-65	5.61	5.46	5.54	5.36	1.26	1.44 × 10⁻³	1.41 × 10⁻³	4.6
5 RY-53	6.13	5.83	5.98	5.78	1.23	1.52 × 10⁻³	1.48 × 10⁻³	4.8
6 RY-51	5.20	5.02	5.11	4.95	1.45	1.53 × 10⁻³	1.51 × 10⁻³	4.9
7 RY-56	6.24	5.76	6.00	5.80	1.33	1.65 × 10⁻³	1.54 × 10⁻³	5.0
8 RY-58	5.61	5.48	5.55	5.37	1.31	1.50 × 10⁻³	1.54 × 10⁻³	5.0
9 RY-37	6.41	6.10	6.26	6.05	1.34	1.73 × 10⁻³	1.57 × 10⁻³	5.1
10 RY-57	6.23	6.28	6.26	6.05	1.33	1.72 × 10⁻³	1.60 × 10⁻³	5.2
11 RY-63	6.48	6.08	6.28	6.07	1.28	1.66 × 10⁻³	1.60 × 10⁻³	5.2
12 RY-69	6.49	6.36	6.43	6.21	1.25	1.66 × 10⁻³	1.60 × 10⁻³	5.2
13 RY-55	6.38	6.07	6.23	6.02	1.36	1.75 × 10⁻³	1.66 × 10⁻³	5.4
14 RY-59	6.24	6.06	6.15	5.95	1.36	1.73 × 10⁻³	1.69 × 10⁻³	5.5
15 RY-61	5.89	5.94	5.92	5.72	1.39	1.70 × 10⁻³	1.69 × 10⁻³	5.5
16 RY-64	6.51	6.48	6.50	6.28	1.26	1.69 × 10⁻³	1.69 × 10⁻³	5.5
17 RY-66	6.18	6.14	6.16	5.96	1.31	1.68 × 10⁻³	1.69 × 10⁻³	5.5
18 RY-45	7.66	7.31	7.49	7.22	1.28	1.98 × 10⁻³	1.88 × 10⁻³	6.1
19 RY-40	7.19	7.31	7.25	6.99	1.34	2.00 × 10⁻³	2.00 × 10⁻³	6.5
20 RY-44	8.19	8.20	8.20	7.89	1.34	2.26 × 10⁻³	2.15 × 10⁻³	7.0
21 RY-49	8.29	8.08	8.19	7.88	1.32	2.22 × 10⁻³	2.18 × 10⁻³	7.1
22 RY-38	8.15	8.24	8.20	7.89	1.31	2.21 × 10⁻³	2.24 × 10⁻³	7.3
23 RY-72	0.92	0.83	0.88	0.86	9.36	1.72 × 10⁻³	1.53 × 10⁻³	5.0
24 RY-78	0.93	—	0.93	0.91	9.20	1.79 × 10⁻³	1.53 × 10⁻³	5.0

	Sandwich evaluation						Conventional evaluation		Pure translation

Hologram no.	ϕ Virtual (°)	ϕ Real (°)	ϕ Average (°)	ϕ Corrected (°)	d Thickness (mm)	Δx f(ϕ) (μm)	Δx Fringe object (μm)	Δx Fringe plate (μm)	Δx Instrument (μm)
1 RY-13	4.15	4.11	4.13	4.01	1.32	33.3	35.3	39.2	40
2 RY-10	6.34	6.74	6.54	6.32	1.35	53.7	54.7	58.9	60
3 RY-24	9.86	9.32	9.59	9.20	1.21	70.1	68.9	78.5	80
4 RY-14	8.79	8.59	8.69	8.36	1.39	73.1	72.4	78.5	80
5 RY-28	11.2	10.6	10.9	10.4	1.25	81.8	79.5	78.5	90
6 RY-25	10.5	10.7	10.6	10.1	1.30	82.6	83.0	78.5	90
7 RY-29	11.5	10.8	11.2	10.7	1.25	84.2	83.0	78.5	90
8 RY-15	14.5	14.6	14.6	13.9	1.44	126	122	—	120
9 RY-20	14.9	14.9	14.9	14.1	1.34	119	122	—	120
10 RY-17	15.4	15.0	15.2	14.4	1.39	126	125	—	120

	Sandwich evaluation						Conventional evaluation		Pure translation

Hologram no.	ϕ Virtual (°)	ϕ Real (°)	ϕ Average (°)	ϕ Corrected (°)	d Thickness (mm)	Δx f(ϕ) (μm)	Δx Fringe object (μm)	Δx Fringe plate (μm)	Δx Instrument (μm)
1 RY-49	4.96	4.92	4.94	4.78	1.32	39.7	40.6	39.2	50
2 RY-53	5.65	5.42	5.54	5.36	1.23	41.4	42.4	49.0	50
3 RY-32	5.61	5.46	5.55	5.37	1.34	45.2	44.1	49.0	50
4 RY-44	5.45	5.35	5.40	5.22	1.34	44.0	44.1	49.0	50
5 RY-66	5.65	5.65	5.65	5.47	1.31	45.0	44.4	49.4	51
6 RY-64	5.79	5.89	5.84	5.65	1.26	44.7	45.1	49.4	50
7 RY-51	4.96	4.90	4.93	4.77	1.45	43.5	45.2	49.0	50
8 RY-56	5.77	5.76	5.77	5.58	1.33	46.7	47.0	49.0	48
9 RY-38	5.65	5.91	5.78	5.59	1.31	46.0	47.7	49.0	51
10 RY-61	5.65	5.77	5.72	5.53	1.39	48.3	49.0	49.4	51
11 RY-65	6.16	6.39	6.28	6.07	1.26	48.1	49.0	49.4	49
12 RY-37	6.16	6.06	6.11	5.91	1.34	49.8	49.4	39.2	51
13 RY-59	6.00	6.00	6.00	5.80	1.36	49.6	49.7	49.4	49
14 RY-63	6.48	5.97	6.23	6.02	1.28	48.4	49.7	49.4	50
15 RY-41	6.04	6.25	6.15	5.95	1.34	50.1	50.5	49.0	50
16 RY-31	6.68	6.54	6.61	6.39	1.25	50.2	51.2	49.0	51
17 RY-45	7.00	7.05	7.03	6.78	1.28	54.6	53.7	49.0	50
18 RY-40	6.48	6.66	6.57	6.35	1.34	53.5	54.0	49.0	51
19 RY-57	6.45	6.71	6.58	6.34	1.33	53.0	54.0	49.0	49
20 RY-58	6.57	6.60	6.59	6.35	1.31	52.3	55.4	49.0	49
21 RY-69	7.73	7.55	7.64	7.37	1.25	57.9	61.5	59.2	51
22 RY-55	7.89	7.62	7.78	7.50	1.36	64.2	61.8	49.0	49
23 RY-72	8.49	8.63	8.56	8.23	9.36	485	—	—	500
24 RY-78	17.7	18.4	18.1	17.0	9.20	987	—	—	1052

Abstract

References

Cited By

Figures (22)

Tables (3)

Equations (13)

Metrics

Login or Create Account