Quantitative Theory for Predicting Fringe Pattern Formation in Holographic Interferometry

Norman L. Hecht; John E. Minardi; David Lewis; Richard L. Fusek

doi:10.1364/AO.12.002665

Applied Optics
Vol. 12,
Issue 11,
pp. 2665-2676
(1973)
•https://doi.org/10.1364/AO.12.002665

Quantitative Theory for Predicting Fringe Pattern Formation in Holographic Interferometry

Norman L. Hecht, John E. Minardi, David Lewis, and Richard L. Fusek

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Norman L. Hecht, John E. Minardi, David Lewis, and Richard L. Fusek, "Quantitative Theory for Predicting Fringe Pattern Formation in Holographic Interferometry," Appl. Opt. 12, 2665-2676 (1973)

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Abstract

The effectiveness of holographic interferometry for displacement studies was investigated and profiles of the fringe patterns characteristic of the basic displacement modes were developed. In addition, techniques were established for determining displacement directions and measuring displacement magnitudes. Procedures were also established for extending these studies to evaluate complex displacements. A quantitative theory for predicting fringe pattern formation was developed.

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		Total Number of Fringes vs Observation Angle
Displacement	Magnitude	$\frac{Angle}{θ_{o}}$	$\frac{Number}{Nt}$	Fringe Geometry	Comments
Translation along x	0.00 1 inches	76°	13	uniformly spaced vertical lines	The fringe lines focus off the surface
		83°	13
		90°	13
Translation along z	−0.02 inches	76°	24	circular fringe lines were observed to focus in front of the specimen	The observed centers (c) were at
		83°	10		The observed centers (c) were at
		90°	11		~ −1.9″
					~−0.6″
					~ +0.9″
Rotation around y	0.81 minutes	76°	48	uniformly spaced vertical lines	Fringes focus on the surface of the specimen
Rotation around y	0.81 minutes	90°	48	uniformly spaced vertical lines	Fringes focus on the surface of the specimen
		Position⁺
Rotation around z	1.65 minutes	1. (at 76°)	0	no fringes arc observed	The mirror image of the observed fringe pattern was obtained when the holographic image was projected on to the screen of the camera
		2. (above 76°)	6	almost vertical and uniformly spaced fringes
		3. (at 83°)	6	uniformly spaced horizontal fringes
		4. (above 83°)	8	uniformly spaced inclined fringes
Rotation around z	1.65 minutes	5. (at 90°)	15	uniformly spaced horizontal fringes	The mirror image of the observed fringe pattern was obtained when the holographic image was projected on to the screen of the camera
Rotation around z	1.65 minutes	6. (above 90°)	16	uniformly spaced inclined fringes

Translation along the x axis, D = +0.001″
θ_O	N_t	N_O	Δ_x	Observed N_t

76°	10.43	−0.132278	0.263556	13
83°	10.54	+ 1.1263	0.260763	13
90°	10.65	+2.37781	0.258081	13

Translation along the z axis, D = −0.02
θ_O	O	C	N_t	Observed N_t	Observed C

76°	14.51	−1.94245	23	~ 24	~ −1.9
83°	14.30	−0.449125	9	~ 10	~ −0.6
90°	14.10	+ 1.05832	13	11	~ +0.9

Rotation around the y axis, D = 0.81′
O	θ_O	N_t	Δ_x	Observed N_t

14.51	76°	50	0.0544571	48
14.10	90°	51	0.0536361	48

Rotation around the z axis of 1.65′
Observation Position	Predicted Fringe Patterns	Fringe Order	Observed Fringe Pattern

1. At the specular position	No fringes are predicted	0	No fringes were observed
2. Perpendicular to the specular position	Vertical fringes are predicted	2	Vertical fringes were observed n ≈ 3
3. Parallel to the specular position	Horizontal fringes are predicted	3	Horizontal fringes were observed n ≈ 3
4. At an oblique position	Inclined (32°) fringes are predicted	3	Inclined fringes (40°) were observed n ≈ 4
5. Parallel to the specular position	Horizontal fringes are predicted	6–7	Horizontal fringes were observed n ≈ 8
6. At an oblique position	Inclined (16°) fringes are predicted	7–8	Inclined fringes (20°) were observed n ≈ 8

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Applied Optics