Dynamic noncontact surface profilometry using a fast eigenspace method in diffraction phase microscopy

Sreeprasad Ajithaprasad; Jagadesh Ramaiah; Rajshekhar Gannavarpu; Rajshekhar Gannavarpu

doi:10.1364/AO.393845

Applied Optics
Vol. 59,
Issue 19,
pp. 5796-5802
(2020)
•https://doi.org/10.1364/AO.393845

Dynamic noncontact surface profilometry using a fast eigenspace method in diffraction phase microscopy

Sreeprasad Ajithaprasad, Jagadesh Ramaiah, and Rajshekhar Gannavarpu

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Sreeprasad Ajithaprasad, Jagadesh Ramaiah, and Rajshekhar Gannavarpu, "Dynamic noncontact surface profilometry using a fast eigenspace method in diffraction phase microscopy," Appl. Opt. 59, 5796-5802 (2020)

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Table of Contents Category
- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: March 30, 2020
- Revised Manuscript: May 31, 2020
- Manuscript Accepted: June 1, 2020
- Published: June 30, 2020

Abstract

Dynamic measurement of surface profile is an important requirement in nondestructive testing, especially for the inspection of large samples with consecutive area scans or test objects under translation. In this paper, we propose the application of an eigenspace signal analysis method in diffraction phase microscopy for reliable and noncontact dynamic surface metrology. We also propose the inclusion of a graphics processing unit (GPU) computing framework in our method to enable fast interferogram processing for dynamics-based investigations. The practical viability of the proposed method is demonstrated for noninvasive nanoscale topography of a test target.

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1:	function gpu_thread (int $N_{x}$ , int $N_{y}$ , $M$ )
2:	$(m, n)$ ← Calculate indices of the pixel
3:	if ( $m < N_{x}$ and $n < N_{y}$ )
4:	$Γ \leftarrow (M \times M)$ symmetric window around $(m, n)$
5:	$U,S,V \leftarrow SVD$ ( $Γ$ )
6:	Initialize $S_{x}$ and $S_{y}$ as zero vectors
7:	for $i \in [2, M]$
8:	$u_{i}$ ← Column $i$ from $U$
9:	$v_{i}$ ← Row $i$ from $V$
10:	$S_{y} = S_{y} + \| FT (u_{i}) \|$
11:	$S_{x} = S_{x} + \| FT (v_{i}^{T}) \|$
12:	end for
13:	${\hat{ω}}_{y} \leftarrow \underset{ω_{y}}{a r g m i n} (S_{y})$
14:	${\hat{ω}}_{x} \leftarrow \underset{ω_{x}}{a r g m i n} (S_{x})$
15:	Compute $ϕ$ using Eqs. (13), (14)
16:	end if
17:	end function

	Execution Time (sec)
Image Size (in pixels)	CPU (Sequential)	GPU (Parallel)
$256 \times 256$	42.1	0.9
$512 \times 512$	169.3	3.4
$1024 \times 1024$	669.4	13.7
$2048 \times 2048$	2656.2	54.8

1:	function gpu_thread (int $N_{x}$ , int $N_{y}$ , $M$ )
2:	$(m, n)$ ← Calculate indices of the pixel
3:	if ( $m < N_{x}$ and $n < N_{y}$ )
4:	$Γ \leftarrow (M \times M)$ symmetric window around $(m, n)$
5:	$U,S,V \leftarrow SVD$ ( $Γ$ )
6:	Initialize $S_{x}$ and $S_{y}$ as zero vectors
7:	for $i \in [2, M]$
8:	$u_{i}$ ← Column $i$ from $U$
9:	$v_{i}$ ← Row $i$ from $V$
10:	$S_{y} = S_{y} + \| FT (u_{i}) \|$
11:	$S_{x} = S_{x} + \| FT (v_{i}^{T}) \|$
12:	end for
13:	${\hat{ω}}_{y} \leftarrow \underset{ω_{y}}{a r g m i n} (S_{y})$
14:	${\hat{ω}}_{x} \leftarrow \underset{ω_{x}}{a r g m i n} (S_{x})$
15:	Compute $ϕ$ using Eqs. (13), (14)
16:	end if
17:	end function

	Execution Time (sec)
Image Size (in pixels)	CPU (Sequential)	GPU (Parallel)
$256 \times 256$	42.1	0.9
$512 \times 512$	169.3	3.4
$1024 \times 1024$	669.4	13.7
$2048 \times 2048$	2656.2	54.8

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Tables (2)

Equations (14)

Applied Optics