Absolute distance measurement by two-point-diffraction interferometry

Hyug-Gyo Rhee; Seung-Woo Kim

doi:10.1364/AO.41.005921

Applied Optics
Vol. 41,
Issue 28,
pp. 5921-5928
(2002)
•https://doi.org/10.1364/AO.41.005921

Absolute distance measurement by two-point-diffraction interferometry

Hyug-Gyo Rhee and Seung-Woo Kim

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Hyug-Gyo Rhee and Seung-Woo Kim, "Absolute distance measurement by two-point-diffraction interferometry," Appl. Opt. 41, 5921-5928 (2002)

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Abstract

We present a point-diffraction interferometer that has been specially devised to perform absolute distance measurements in three dimensions. It is composed of two main parts: One is a target that moves in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The target is made of point-diffraction sources that emit two spherical wave fronts, whose interference is monitored by the photodetectors. Application of a phase-shifting technique allows the phase values of the photodetectors to be precisely measured, which are then fitted to a geometric model of multilateration so as to determine the xyz location of the target by minimization of least-squares errors. Experimental results show that the proposed diffraction interferometer is capable of measuring the xyz coordinates of the target with a volumetric uncertainty of less than 1.0 µm over a working volume of a 100-mm side.

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Equations (11)

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Classification	Error Sources	Input Condition	Output Uncertainty
Phase errors	Laser intensity stability	≤0.07% of Π	0.0071 rad
	High-frequency vibration	This term can be neglected	This term can be neglected
	Temperature variation in the fiber	≤0.01 K	0.0084 rad
	Low-frequency pressure variation in the fiber	≤8× 10^-4 rad	5× 10^-5 rad
	Nonlinearity of fiber elongation and PZT	≤0.15 rad	0.009 rad
	Electrical noise	≤0.7% of Π	0.005 rad
	Detector nonlinearity	≤0.8% of Π	0.023 rad
Displacement errors	Sphericity of the spherical wave	≤1× 10^-5 rad	4× 10^-3 nm
	Laser frequency stability	≤1 MHz	1.3× 10^-6 nm
	Air refractive-index variation	≤10^-7	6.3× 10^-5 nm
	Detector position error	≤100 nm	8× 10^-2 nm
Uncertainty of x			U _x = 420 nm
Uncertainty of y			U _y = 550 nm
Uncertainty of z			U _z = 9.7 nm

CCD Size	Uncertainty (nm)
640× 480 (s _x = 8.44 µm, s _y = 9.78 µm)	u _x = 420
	u _y = 550
	u _z = 9.7

1024× 1024 (s _x = 10 µm, s _y = 10 µm)	u _x = 79.0
1024× 1024 (s _x = 10 µm, s _y = 10 µm)	u _y = 79.0
	u _z = 9.6
2048× 2048 (s _x = 10 µm, s _y = 10 µm)	u _x = 19
	u _y = 19
	u _z = 9.6

Classification	Error Sources	Input Condition	Output Uncertainty
Phase errors	Laser intensity stability	≤0.07% of Π	0.0071 rad
	High-frequency vibration	This term can be neglected	This term can be neglected
	Temperature variation in the fiber	≤0.01 K	0.0084 rad
	Low-frequency pressure variation in the fiber	≤8× 10^-4 rad	5× 10^-5 rad
	Nonlinearity of fiber elongation and PZT	≤0.15 rad	0.009 rad
	Electrical noise	≤0.7% of Π	0.005 rad
	Detector nonlinearity	≤0.8% of Π	0.023 rad
Displacement errors	Sphericity of the spherical wave	≤1× 10^-5 rad	4× 10^-3 nm
	Laser frequency stability	≤1 MHz	1.3× 10^-6 nm
	Air refractive-index variation	≤10^-7	6.3× 10^-5 nm
	Detector position error	≤100 nm	8× 10^-2 nm
Uncertainty of x			U _x = 420 nm
Uncertainty of y			U _y = 550 nm
Uncertainty of z			U _z = 9.7 nm

CCD Size	Uncertainty (nm)
640× 480 (s _x = 8.44 µm, s _y = 9.78 µm)	u _x = 420
	u _y = 550
	u _z = 9.7

1024× 1024 (s _x = 10 µm, s _y = 10 µm)	u _x = 79.0
1024× 1024 (s _x = 10 µm, s _y = 10 µm)	u _y = 79.0
	u _z = 9.6
2048× 2048 (s _x = 10 µm, s _y = 10 µm)	u _x = 19
	u _y = 19
	u _z = 9.6

Abstract

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Tables (2)

Equations (11)

Applied Optics