Measurement and Modeling of Bidirectional Reflection Distribution Function of Deep Hole Inner Surfaces

Qiang Sheng; Jianming Zheng; Lijun Yang; Haitao Li; Junyan Sun

doi:10.3788/LOP232691

Laser & Optoelectronics Progress, Volume. 61, Issue 15, 1512004(2024)

Measurement and Modeling of Bidirectional Reflection Distribution Function of Deep Hole Inner Surfaces

Qiang Sheng^1,2、*, Jianming Zheng^2、**, Lijun Yang¹, Haitao Li¹, and Junyan Sun¹

¹College of Mechanical and Electrical Engineering, Shaanxi University of Science and technology, Xi'an 710021, Shaanxi, China

²School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi'an 710048, Shaanxi, China

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Figures & Tables(10)

Fig. 1. Imaging principle of endoscope

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Fig. 2. Measurement scheme and equipment. (a) Measurement experimental platform and equipment; (b) M20, M14, and M8 stainless steel internal threads; (c) M20, M14, and M8 galvanized surface internal threads; (d) self made endoscope probe sleeve

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Fig. 3. Image processing process and results. (a) (c) Original endoscopic images; (b) (d) pre-processing results; (e) (f) corrected images

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Fig. 4. Images after correction of internal threaded hole. (a) M20 stainless steel threaded hole; (b) M14 stainless steel; (c) M8 stainless steel; (d) M20 galvanized; (e) M14 galvanized; (f) M8 galvanized

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Fig. 5. (a) Thread size and (b) point cloud image

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Fig. 6. Relationship between BRDF and normal deflection angle of inner surface. (a) Stainless steel hole; (b) galvanized surface hole

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Fig. 7. Comparison between calculation and measurement results. (a) Stainless steel hole; (b) galvanized surface hole

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Table 1. Fitting results of inBRDF model parameters

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Table 1. Fitting results of inBRDF model parameters

Model	Surface material	k_d	k_s	a	b
$f_{P h o n g}^{*}$	Stainless steel	0.21	0.48	2.71	4.70
$f_{P h o n g}^{*}$	Galvanized	0.28	0.55	4.70	4.56
$f_{C - T}^{*}$	Stainless steel	0.06	20.03	19.87	1.09
$f_{C - T}^{*}$	Galvanized	0.06	12.63	12.31	0.93
$f_{W a r d}^{*}$	Stainless steel	0.13	6.17	-18.08	8.05
$f_{W a r d}^{*}$	Galvanized	0.15	9.76	-16.98	9.42

Table 2. Model error statistics

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Table 2. Model error statistics

Model	Surface material	inBRDF model	Total deviation	Average error /%	Model error /%
$f_{P h o n g}^{*}$	Stainless steel	$f_{P h o n g}^{*} = 0.21 c o s θ + 0.49 c o s^{2.71} (4.7 θ)$	86.34	25.58	26.10
$f_{P h o n g}^{*}$	Galvanized	$f_{P h o n g}^{*} = 0.28 c o s θ + 0.55 c o s^{4.7} (4.56 θ)$	89.57	28.62	26.10
$f_{C - T}^{*}$	Stainless steel	$f_{C - T}^{*} = 0.07 c o s θ + 13.17 \frac{e x p (- 25.7 θ^{1.33})}{π \cdot c o s θ}$	17.22	5.50	6.22
$f_{C - T}^{*}$	Galvanized	$f_{C - T}^{*} = 0.03 c o s θ + 24.99 \frac{e x p (- 7.66 θ^{0.53})}{π \cdot c o s θ}$	21.72	6.94	6.22
$f_{W a r d}^{*}$	Stainless steel	$f_{W a r d}^{*} = 0.13 c o s θ + 6.17 \frac{e x p [- t a n^{- 18.08} (θ^{8.05})]}{π \sqrt[]{c o s θ}}$	31.52	10.07	9.52
$f_{W a r d}^{*}$	Galvanized	$f_{W a r d}^{*} = 0.15 c o s θ + 9.76 \frac{e x p [- t a n^{- 16.98} (θ^{9.42})]}{π \sqrt[]{c o s θ}}$	28.05	8.96	9.52

Table 3. Parameter error analysis of inBRDF model
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Table 3. Parameter error analysis of inBRDF model
Surface material M20 M14 M8 All samples
Stainless steel 2.26 4.11 12.69 5.50
Galvanized 2.88 5.22 15.94 6.94

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Qiang Sheng, Jianming Zheng, Lijun Yang, Haitao Li, Junyan Sun. Measurement and Modeling of Bidirectional Reflection Distribution Function of Deep Hole Inner Surfaces[J]. Laser & Optoelectronics Progress, 2024, 61(15): 1512004

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