Nondestructive, fast, and cost-effective image processing method for roughness measurement of randomly rough metallic surfaces

Sajjad Ghodrati; Saeideh Gorji Kandi; Mohsen Mohseni

doi:10.1364/JOSAA.35.000998

Journal of the Optical Society of America A
Vol. 35,
Issue 6,
pp. 998-1013
(2018)
•https://doi.org/10.1364/JOSAA.35.000998

Nondestructive, fast, and cost-effective image processing method for roughness measurement of randomly rough metallic surfaces

Sajjad Ghodrati, Saeideh Gorji Kandi, and Mohsen Mohseni

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Sajjad Ghodrati, Saeideh Gorji Kandi, and Mohsen Mohseni, "Nondestructive, fast, and cost-effective image processing method for roughness measurement of randomly rough metallic surfaces," J. Opt. Soc. Am. A 35, 998-1013 (2018)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: January 31, 2018
- Revised Manuscript: April 17, 2018
- Manuscript Accepted: April 29, 2018
- Published: May 22, 2018

Abstract

In recent years, various surface roughness measurement methods have been proposed as alternatives to the commonly used stylus profilometry, which is a low-speed, destructive, expensive but precise method. In this study, a novel method, called “image profilometry,” has been introduced for nondestructive, fast, and low-cost surface roughness measurement of randomly rough metallic samples based on image processing and machine vision. The impacts of influential parameters such as image resolution and filtering approach for elimination of the long wavelength surface undulations on the accuracy of the image profilometry results have been comprehensively investigated. Ten surface roughness parameters were measured for the samples using both the stylus and image profilometry. Based on the results, the best image resolution was 800 dpi, and the most practical filtering method was Gaussian $convolution + cutoff$ . In these conditions, the best and worst correlation coefficients ( $R^{2}$ ) between the stylus and image profilometry results were 0.9892 and 0.9313, respectively. Our results indicated that the image profilometry predicted the stylus profilometry results with high accuracy. Consequently, it could be a viable alternative to the stylus profilometry, particularly in online applications.

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Element	Wt. %	Element	Wt. %	Element	Wt. %
Fe	98.01	P	0.05	Mn	0.28
C	0.16	Al	0.04	S	0.04
Si	0.30	O	1.12

Sample	Blasting Pressure (MPa)	Abrasive Type	Nozzle Diameter (mm)	Nozzle Distance (cm)	Nozzle Angle (Relative to Substrate)	Average Particle Diameter (μm)
1	Raw surface, without abrasive blasting surface treatment
2	0.7	Sand	6	30	60°	200
3	0.7	Sand	6	30	60°	350
4	0.7	Sand	6	30	60°	480
5	0.7	Steel grit	8	50	90°	600
6	0.7	Steel grit	8	50	90°	800
7	0.7	Steel shot	8	50	90°	900
8	0.7	Steel grit	8	50	90°	1200

Sampling length	2.5 mm
Evaluation length	12.5 mm
Stylus radius	2 μm
Stylus cone angle	90°
Stylus load	0.7 mN
Stylus scanning speed	0.5 mm/s

Parameter	Equation
$R_{a}$	$R_{stylus} = 93.7468 \times R_{image} - 2.0241$
$R_{q}$	$R_{stylus} = 93.4609 \times R_{image} - 1.8956$
$R_{p}$	$R_{stylus} = 118.7374 \times R_{image} - 12.7631$
$R_{v}$	$R_{stylus} = 108.5161 \times R_{image} - 10.1516$
$R_{z}$	$R_{stylus} = 119.8179 \times R_{image} - 25.5574$
$R_{t}$	$R_{stylus} = 152.3519 \times R_{image} - 51.6884$
$R_{s k}$	$R_{stylus} = 1.0038 \times R_{image} - 0.1123$
$R_{k u}$	$R_{stylus} = 0.6758 \times R_{image} + 1.2620$
$R_{S m}$	$R_{stylus} = 31.4235 \times R_{image} + 34.0790$
$R_{Δ q}$	$R_{stylus} = 18.7558 \times R_{image} - 0.5010$

Roughness Parameter	Description	Mathematical Definition^a
Amplitude parameters
Arithmetic average height or central line average ( $R_{a}$ )	This parameter shows the average of absolute profile points’ distances from the reference line in a sampling length	$R_{a} = \frac{1}{5} \sum_{j = 1}^{5} R_{a_{j}}$ , $R_{a_{j}} = \frac{1}{n} \sum_{i = 1}^{n} \| Z_{i} \|$
Root mean square roughness ( $R_{q}$ )	This parameter shows the standard deviation of profile points’ distances from the reference line in a sampling length	$R_{q} = \frac{1}{5} \sum_{j = 1}^{5} R_{q_{j}}$ , $R_{q_{j}} = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} Z_{i}^{2}}$
The maximum peak height ( $R_{p}$ )	This parameter shows distance of the highest peak from the reference line in a sampling length	$R_{p} = \frac{1}{5} \sum_{j = 1}^{5} R_{p_{j}}$ , $R_{p_{j}} = \binom{\max (Z_{p_{i}})}{i = 1, 2, \dots, n}$
The maximum valley depth ( $R_{v}$ )	This parameter shows distance of the deepest valley from the reference line in a sampling length	$R_{v} = \frac{1}{5} \sum_{j = 1}^{5} R_{v_{j}}$ , $R_{v_{j}} = \binom{\max (Z_{v_{i}})}{i = 1,2, \dots, n}$
The maximum peak to valley height ( $R_{z}$ )	This parameter shows vertical distance between the highest peak and the deepest valley in a sampling length	$R_{z} = \frac{1}{5} \sum_{j = 1}^{5} R_{z_{j}}$ $R_{z_{j}} = \binom{\begin{matrix} \max (Z_{p_{i}}) \end{matrix}}{i = 1,2, \dots, n} + \binom{\max (Z_{v_{i}})}{i = 1,2, \dots, n}$
The absolute profile height ( $R_{t}$ )	This parameter shows vertical distance between the highest peak and the deepest valley in the evaluation length	$R_{t} = \binom{\max (Z_{p_{i}})}{i = 1,2, \dots, N} + \binom{\max (Z_{v_{i}})}{i = 1,2, \dots, N}$
Skewness ( $R_{s k}$ )	This parameter shows symmetry of probability density distribution of the profile points’ distances from the reference line in the evaluation length. If the distribution is symmetric, $R_{s k}$ will be zero. Otherwise, depends on direction of asymmetry, $R_{s k}$ can be a positive or negative value.	$R_{s k} = \frac{1}{N \times R_{q}^{3}} \sum_{i = 1}^{N} Z_{i}^{3}$
Kurtosis ( $R_{k u}$ )	This parameter shows sharpness of probability density distribution of the profile points’ distance from the reference line in the evaluation length. If the distribution is normal, $R_{k u}$ will be equal to 3. If the distribution is sharper/broader than the normal distribution, $R_{k u}$ will be bigger/smaller than 3.	$R_{k u} = \frac{1}{N \times R_{q}^{4}} \sum_{i = 1}^{N} Z_{i}^{4}$
Frequency (spacing) parameters
Arithmetic average width of profile elements or mean spacing ( $R_{S m}$ )	This parameter shows the average of profile elements’ horizontal lengths in a sampling length	$R_{S m} = \frac{1}{5} \sum_{j = 1}^{5} R_{S m_{j}}$ , $R_{S m_{j}} = \frac{1}{m} \sum_{i = 1}^{m} X_{s_{i}}$
Hybrid parameters
Root mean square slopes of profile ( $R_{Δ q}$ )	This parameter shows root mean square slopes of the profile points in the evaluation length.	$R_{Δ q} = \sqrt{\frac{1}{N} \sum_{i = 1}^{n} {(θ_{i} - \bar{θ})}^{2}}$ $\bar{θ} = \frac{1}{N} \sum_{i = 1}^{N} θ_{i}$ , $θ_{i} = \frac{Z_{i} - Z_{i - 1}}{Δ x}$

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Journal of the Optical Society of America A