Point-spread function associated with underwater imaging through a wavy air–water interface: theory and laboratory tank experiment

William C. Brown; Arun K. Majumdar

doi:10.1364/AO.31.007650

Applied Optics
Vol. 31,
Issue 36,
pp. 7650-7659
(1992)
•https://doi.org/10.1364/AO.31.007650

Point-spread function associated with underwater imaging through a wavy air–water interface: theory and laboratory tank experiment

William C. Brown and Arun K. Majumdar

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William C. Brown and Arun K. Majumdar, "Point-spread function associated with underwater imaging through a wavy air–water interface: theory and laboratory tank experiment," Appl. Opt. 31, 7650-7659 (1992)

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Abstract

The point-spread function needed for imaging underwater objects is theoretically derived and compared with experimental results. The theoretical development is based on the emergent-ray model, in which the Gram–Charlier series for the non-Gaussian probability-density function for emergent angles through a wavy water surface was assumed. To arrive at the point-spread model, we used a finite-element methodology with emergent-ray angular probability distributions as fundamental building functions. The model is in good agreement with the experiment for downwind conditions. A slight deviation between theory and experiment was observed for the crosswind case; this deviation may be caused by the possible interaction of standing waves with the original air-ruffled capillary waves that were not taken into account in the model.

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Run	Direction	Wind Speed (m/s)	Incidence Angle (deg)	Emergent

				Means (deg)	SD (deg)	Skew
1	Downwind	4.9	31	40.62	2.68	0.0885
2	Downwind	2.5	31	44.47	1.57	−4.83
3	Downwind	2.5	21.3	28.92	1.007	2.006
4	Downwind	4.9	21.3	26.43	3.52	8.313
5	Downwind	4.9	8.0	9.18	4.058	−34.55
6	Downwind	2.4	8.0	11.20	0.881	0.323
7	Downwind	2.4	4.0	−7.56	0.943	3.38
8	Downwind	5.0	4.0	−6.32	1.43	3.36
9	Downwind	5.0	−4.0	−6.83	4.24	−63.26
10	Downwind	2.4	−4.0	−5.12	0.626	−0.055
11	Downwind	2.4	−8.0	−10.96	1.93	−8.59
12	Downwind	5.0	−8.0	−12.93	4.046	−25.20
13	Downwind	5.0	−20.0	−27.45	3.83	−32.24
14	Downwind	2.5	−20.0	−26.43	1.50	−3.52
15	Downwind	5.0	−26.0	−36.42	4.02	−5.47
16	Downwind	2.4	−26.0	−35.79	1.984	−2.39
17	Downwind	2.7	0	0.075	0.728	0.155
18	Downwind	3.7	0	−2.19	3.65	−56.88
19	Crosswind	1.0	0	−0.310	0.642	−0.60
20	Crosswind	2.0	0	−0.721	0.805	−1.52
21	Crosswind	2.6	0	0.880	0.768	−0.116
22	Crosswind	3.5	0	−0.973	2.380	−41.25
23	Crosswind	3.7	0	−3.241	4.584	−96.91
24	Crosswind	3.9	0	0.00465	1.990	−14.51
25	Crosswind	4.1	0	−4.439	4.973	−66.91
26	Crosswind	4.7	0	−5.211	4.190	−27.42
27	Crosswind	5.4	0	−4.236	4.988	−72.82
28	Crosswind	5.03	0	−2.571	4.515	−59.84
29	Crosswind	3.16	0	−1.754	4.415	−83.64
30	Crosswind	3.16	4.12	1.533	3.814	−69.92
31	Crosswind	5.09	4.12	0.482	4.305	−57.89
32	Crosswind	5.09	−4.12	−6.278	3.763	−63.94
33	Crosswind	3.00	−4.12	−3.822	1.537	−15.74
34	Crosswind	3.00	11.75	12.20	0.544	−0.899
35	Crosswind	5.19	11.75	7.402	4.168	−39.209
36	Crosswind	5.19	−9.05	−11.59	3.33	−34.35
37	Crosswind	2.78	−9.05	−8.944	1.916	−20.28
38	Downwind	1.0	0	−0.324	0.795	0.484
39	Downwind	2.0	0	−0.0068	0.775	0.374
40	Downwind	2.6	0	−1.213	0.771	−0.0854
41	Downwind	2.7	0	0.0751	0.728	0.155
42	Downwind	3.5	0	−1.113	2.228	−23.01
43	Downwind	3.7	0	−2.187	3.648	−56.885
44	Downwind	3.9	0	−1.671	3.861	−64.42
45	Downwind	4.1	0	−1.501	1.837	−40.73
46	Downwind	5.4	0	−2.132	2.702	−45.264

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Applied Optics