Surface-roughness measurement based on scalar field correlation with active millimeter-wave imaging system

Ziye Wang; Yang Yu; Lingbo Qiao; Yingxin Wang; Ziran Zhao

doi:10.1364/AO.58.009186

Applied Optics
Vol. 58,
Issue 33,
pp. 9186-9194
(2019)
•https://doi.org/10.1364/AO.58.009186

Surface-roughness measurement based on scalar field correlation with active millimeter-wave imaging system

Ziye Wang, Yang Yu, Lingbo Qiao, Yingxin Wang, and Ziran Zhao

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Ziye Wang, Yang Yu, Lingbo Qiao, Yingxin Wang, and Ziran Zhao, "Surface-roughness measurement based on scalar field correlation with active millimeter-wave imaging system," Appl. Opt. 58, 9186-9194 (2019)

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Abstract

Active millimeter-wave (MMW) imaging is of interest because it has played an important role in the area of personnel surveillance over the past decades. Through reconstructing reflectivity, potential threats can be recognized based on shape. Besides reflectivity, diverse physical characteristics should be explored so that supplementary information can be used to assist recognition. This paper presents a surface-roughness measurement method using holographic data that has already been acquired during security checks. Based on scalar diffraction theory and speckle metrology, a simple mathematical relation between the correlation of holographic fields and surface roughness has been derived. Consequently, another kind of information, that is, the surface-roughness estimate, can be used to help differentiate similarly shaped articles. Results of simulations and laboratory experiments have shown its validation and potential in application to MMW imaging systems.

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Actual Roughness (µm)	Calculated Results (µm)
Actual Roughness (µm)	Frequency Used (GHz)
	$f_{1} = 29$ , $f_{2} = 31$	$f_{1} = 28$ , $f_{2} = 32$	$f_{1} = 27$ , $f_{2} = 33$	$f_{1} = 26$ , $f_{2} = 34$	$f_{1} = 25$ , $f_{2} = 35$	$f_{1} = 24$ , $f_{2} = 36$
115.6	120.71	120.88	121.16	121.56	122.08	122.72
218.3	234.39	234.18	233.82	233.30	232.59	231.64
333.7	352.42	352.65	353.04	353.60	354.34	355.29
417.6	431.86	431.47	430.81	429.89	428.69	427.20
532.3	520.00	520.47	521.26	522.39	523.85	525.69

Actual Roughness (µm)	Calculated Results (µm)
Actual Roughness (µm)	Frequency Used (GHz)
	$f_{1} = 280$ $f_{2} = 320$	$f_{1} = 282$ $f_{2} = 318$	$f_{1} = 284$ $f_{2} = 316$	$f_{1} = 286$ $f_{2} = 314$	$f_{1} = 288$ $f_{2}$	$= 312$ $f_{1} = 290$
23.8	21.95	24.67	26.22	26.89	26.91	26.41
32.8	37.07	35.69	34.34	33.07	31.93	30.99
41.9	39.12	42.01	43.77	44.71	45.08	45.05
50.6	56.98	55.66	54.01	52.26	50.18	47.84

Actual Roughness (µm)	Calculated Results (µm)
Actual Roughness (µm)	Frequency Used (GHz)
	$(k_{1}^{'} + k_{2}^{'}) σ$ $f_{1} = 296$	$f_{2} = 304$ $f_{1}$	$= 292$ $f_{2} = 308$	$f_{1} = 288$ $f_{2} = 312$	$f_{1} = 284$ $f_{2} = 316$	$f_{1} = 280$ $f_{2} = 320$
70.4	165.8	160.2	151.5	140.3	127.6	113.9
84.8	161.0	156.56	149.3	139.7	128.5	116.8
105.0	64.2	65.6	67.6	69.9	72.5	74.9

Actual Roughness (µm)	Calculated Results (µm)
Actual Roughness (µm)	Frequency Used (GHz)
	$D = 2 Z \tan (θ / 2) \approx 5.3 c m$ $r_{L}$	$f_{1} = 21$ $f_{2} = 39$	$f_{1} = 23$ $f_{2} = 37$	$f_{1} = 25$ $f_{2} = 35$	$f_{1} = 27$ $f_{2} = 33$	Average
149.8	130.8	136.0	139.8	150.9	157.6	143.0
200.4	184.3	172.8	163.7	174.9	183.4	175.8
249.7	218.1	244.2	238.0	225.2	216.4	228.3
306.7	347.8	332.3	319.6	300.3	288.4	317.7
394.4	355.0	378.6	385.8	405.8	433.8	391.8

		Calculated Results (µm)
Grit Designation	Actual Roughness (µm)	First Time	Second Time	Third Time
P80	58	67.65	66.24	67.48
P150	34	39.73	37.49	38.89
P180	25	30.91	25.33	31.88

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Equations (14)

Applied Optics