Sharpness Evaluation Function for Line Patterns in Focal Length Measurement

Fig. 6. Normalized evaluation function curves (top left is partial magnification near peak). (a) 0° line pattern; (b) 30° line pattern; (c) 45° line pattern; (d) 60° line pattern; (e) 90° line pattern

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Fig. 7. Ideal normalized clarity evaluation function

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Table 1. Direction of gradient operator of grayscale evaluation function
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Table 1. Direction of gradient operator of grayscale evaluation function
Evaluation function Gradient direction
Brenner 0°（horizontal direction）
Roberts 45°，135°
Laplace 0°，90°
Tenengrad Sobel operator direction
EOG 0°，90°

Table 2. Detection results of Hough transform on 5 sets of line sequences
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Table 2. Detection results of Hough transform on 5 sets of line sequences
Angle Average value Standard deviation Maximum deviation
0 0.034 0.104 0.5
30 29.672 0.355 1.4
45 44.870 0.673 1.8
60 59.714 0.356 1.1
90 89.984 0.148 0.4

Table 3. Quantitative evaluation results of evaluation function (0° line)

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Table 3. Quantitative evaluation results of evaluation function (0° line)

Type of evaluation function	Percentage of steep areas $P_{S}$ /%	Focusing position deviation	Mean of smoothing area $M_{S}$	Standard deviation of smoothing area $σ$	Average time $\bar{T}$ /ms
Roberts	58.02	0.079	0.103	0.051	14.771
Laplace	65.50	1.650	0.118	0.059	21.057
Tenengrad	52.30	0.048	0.043	0.029	47.200
EOG	65.68	1.587	0.118	0.061	15.114
Proposed function	48.59	0.047	0.049	0.031	14.257

Table 4. Quantitative evaluation results of evaluation function (30° line)

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Table 4. Quantitative evaluation results of evaluation function (30° line)

Type of evaluation function	Percentage of steep areas $P_{S}$ /%	Focusing position deviation	Mean of smoothing area $M_{S}$	Standard deviation of smoothing area $σ$	Average time $\bar{T}$ /ms
Brenner	51.61	0.063	0.097	0.069	14.486
Roberts	44.95	0.016	0.160	0.072	14.771
Laplace	33.63	2.357	0.255	0.105	21.057
Tenengrad	44.19	0.053	0.058	0.037	47.200
EOG	33.94	2.232	0.259	0.104	15.114
Proposed function	43.81	0.063	0.059	0.039	14.257

Table 5. Quantitative evaluation results of evaluation function (45° line)

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Table 5. Quantitative evaluation results of evaluation function (45° line)

Type of evaluation function	Percentage of steep areas $P_{S}$ /%	Focusing position deviation	Mean of smoothing area $M_{S}$	Standard deviation of smoothing area $σ$	Average time $\bar{T}$ /ms
Brenner	42.87	0.153	0.086	0.066	14.200
Roberts	45.70	0.165	0.131	0.074	14.400
Laplace	42.56	0.157	0.165	0.080	20.886
Tenengrad	41.68	0.051	0.051	0.042	46.886
EOG	42.95	0.157	0.160	0.080	14.286
Proposed function	43.81	0.052	0.051	0.042	14.229

Table 6. Quantitative evaluation results of evaluation function (60° line)

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Table 6. Quantitative evaluation results of evaluation function (60° line)

Type of evaluation function	Percentage of steep areas $P_{S}$ /%	Focusing position deviation	Mean of smoothing area $M_{S}$	Standard deviation of smoothing area $σ$	Average time $\bar{T}$ /ms
Brenner	51.25	0.176	0.084	0.045	14.545
Roberts	54.05	0.160	0.134	0.073	15.152
Laplace	54.36	1.876	0.167	0.082	21.485
Tenengrad	51.99	0.084	0.051	0.042	48.455
EOG	54.11	1.876	0.166	0.083	15.424
Proposed function	51.99	0.096	0.053	0.043	14.364

Table 7. Quantitative evaluation results of evaluation function (90° line)

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Table 7. Quantitative evaluation results of evaluation function (90° line)

Type of evaluation function	Percentage of steep areas $P_{S}$ /%	Focusing position deviation	Mean of smoothing area $M_{S}$	Standard deviation of smoothing area $σ$	Average time $\bar{T}$ /ms
Brenner	49.91	0.080	0.041	0.029	14.182
Roberts	45.94	0.470	0.152	0.080	14.485
Laplace	46.14	2.092	0.195	0.120	21.727
Tenengrad	50.31	0.082	0.039	0.031	47.455
EOG	46.14	2.092	0.192	0.123	14.545
Proposed function	49.91	0.080	0.041	0.029	14.242

Table 8. Measurement results of focal length of lens

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Table 8. Measurement results of focal length of lens

Function	Lens focal length f /mm					Error /%
Function	0°	30°	45°	60°	90°	Error /%
Roberts	39.9905	39.9731	39.9697	39.9532	39.9677	0.117
Laplace	39.8554	39.8912	39.9727	39.8780	39.8468	0.383
Tenengrad	39.9934	39.9800	39.9690	39.9639	39.9647	0.090
EOG	39.8431	39.9062	39.9797	39.8737	39.8526	0.392
Proposed function	39.9922	39.9795	39.9726	39.9629	39.9637	0.093

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Jihao Liu, Rongsheng Lu, Zilong Zhang, Ailin Zhang. Sharpness Evaluation Function for Line Patterns in Focal Length Measurement[J]. Acta Optica Sinica, 2023, 43(9): 0912001

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