Real-time detection and elimination of nonorthogonality error in interference fringe processing

Haijiang Hu; Fengdeng Zhang

doi:10.1364/AO.50.002140

Applied Optics
Vol. 50,
Issue 15,
pp. 2140-2144
(2011)
•https://doi.org/10.1364/AO.50.002140

Real-time detection and elimination of nonorthogonality error in interference fringe processing

Haijiang Hu and Fengdeng Zhang

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Haijiang Hu and Fengdeng Zhang, "Real-time detection and elimination of nonorthogonality error in interference fringe processing," Appl. Opt. 50, 2140-2144 (2011)

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Abstract

In the measurement system of interference fringe, the nonorthogonality error is a main error source that influences the precision and accuracy of the measurement system. The detection and elimination of the error has been an important target. A novel method that only uses the cross-zero detection and the counting is proposed to detect and eliminate the nonorthogonality error in real time. This method can be simply realized by means of the digital logic device, because it does not invoke trigonometric functions and inverse trigonometric functions. And it can be widely used in the bidirectional subdivision systems of a Moiré fringe and other optical instruments.

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Detected Signal	Cross-Zero Detection	Sign of Current Signals		Counting Value
Detected Signal	Cross-Zero Detection	$u_{1}$	$u_{2}$	Counting Value
$u_{1}$	$+ \to -$	n/a^a	−	$+ 1$
$u_{1}$	$+ \to -$	n/a	+	$- 1$
$u_{1}$	$- \to +$	n/a	+	$+ 1$
$u_{1}$	$- \to +$	n/a	−	$- 1$
$u_{2}$	$+ \to -$	+	n/a	$+ 1$
$u_{2}$	$+ \to -$	−	n/a	$- 1$
$u_{2}$	$- \to +$	−	n/a	$+ 1$
$u_{2}$	$- \to +$	+	n/a	$- 1$
$r_{11}$	$+ \to -$	+	−	$+ 1$
$r_{11}$	$+ \to -$	−	+	$- 1$
$r_{11}$	$- \to +$	−	+	$+ 1$
$r_{11}$	$- \to +$	+	−	$- 1$
$r_{12}$	$+ \to -$	−	−	$+ 1$
$r_{12}$	$+ \to -$	+	+	$- 1$
$r_{12}$	$- \to +$	+	+	$+ 1$
$r_{12}$	$- \to +$	−	−	$- 1$

Number of Subinterval	Range of θ in $[0, 2 π)$	Interval Length
I	$[0, \frac{π}{4} - \frac{Δ φ}{2})$	$\frac{π}{4} - \frac{Δ φ}{2}$
II	$[\frac{π}{4} - \frac{Δ φ}{2}, \frac{π}{2} - Δ φ)$	$\frac{π}{4} - \frac{Δ φ}{2}$
III	$[\frac{π}{2} - Δ φ, \frac{3 π}{4} - \frac{Δ φ}{2})$	$\frac{π}{4} + \frac{Δ φ}{2}$
IV	$[\frac{3 π}{4} - \frac{Δ φ}{2}, π)$	$\frac{π}{4} + \frac{Δ φ}{2}$
V	$[π, \frac{5 π}{4} - \frac{Δ φ}{2})$	$\frac{π}{4} - \frac{Δ φ}{2}$
VI	$[\frac{5 π}{4} - \frac{Δ φ}{2}, \frac{3 π}{2} - Δ φ)$	$\frac{π}{4} - \frac{Δ φ}{2}$
VII	$[\frac{3 π}{2} - Δ φ, \frac{7 π}{4} - \frac{Δ φ}{2})$	$\frac{π}{4} + \frac{Δ φ}{2}$
VIII	$[\frac{7 π}{4} - \frac{Δ φ}{2}, 2 π)$	$\frac{π}{4} + \frac{Δ φ}{2}$

Presetting Nonorthogonality Error	Sampling Frequency	Nonorthogonality Error in Measurement
0	$1 MHz$	0
	$10 MHz$	0
	$100 MHz$	0
$0.166667 π$	$1 MHz$	$0.166000 π$
$(\frac{1}{6} π)$	$10 MHz$	$0.166600 π$
$(\frac{1}{6} π)$	$100 MHz$	$0.166660 π$
$- 0.166667 π$	$1 MHz$	$- 0.168000 π$
$(- \frac{1}{6} π)$	$10 MHz$	$- 0.166800 π$
$(- \frac{1}{6} π)$	$100 MHz$	$- 0.166680 π$
$0.011111 π$	$1 MHz$	$0.010000 π$
$(\frac{1}{90} π)$	$10 MHz$	$0.011000 π$
$(\frac{1}{90} π)$	$100 MHz$	$0.011100 π$
$0.0027778 π$	$1 MHz$	$0.002000 π$
$(\frac{1}{360} π)$	$10 MHz$	$0.002600 π$
$(\frac{1}{360} π)$	$100 MHz$	$0.002760 π$

Presetting Nonorthogonality Error	Sampling Frequency	Movement Distance
0	$1 MHz$	$113.0000 μm$
	$10 MHz$	$113.0000 μm$
	$100 MHz$	$113.0000 μm$
$0.166667 π$	$1 MHz$	$112.9900 μm$
$(\frac{1}{6} π)$	$10 MHz$	$112.9990 μm$
$(\frac{1}{6} π)$	$100 MHz$	$112.9999 μm$
$- 0.166667 π$	$1 MHz$	$113.0000 μm$
$(- \frac{1}{6} π)$	$10 MHz$	$113.0000 μm$
$(- \frac{1}{6} π)$	$100 MHz$	$113.0000 μm$
$0.011111 π$	$1 MHz$	$112.9900 μm$
$(\frac{1}{90} π)$	$10 MHz$	$112.9990 μm$
$(\frac{1}{90} π)$	$100 MHz$	$112.9999 μm$
$0.0027778 π$	$1 MHz$	$112.9900 μm$
$(\frac{1}{360} π)$	$10 MHz$	$112.9990 μm$
$(\frac{1}{360} π)$	$100 MHz$	$113.0000 μm$

Presetting Nonorthogonality Error	Sampling Frequency	Movement Distance
0	$1 MHz$	$- 113.0000 μm$
	$10 MHz$	$- 113.0000 μm$
	$100 MHz$	$- 113.0000 μm$
$0.166667 π$	$1 MHz$	$- 113.0000 μm$
$(\frac{1}{6} π)$	$10 MHz$	$- 113.0000 μm$
$(\frac{1}{6} π)$	$100 MHz$	$- 113.0000 μm$
$- 0.166667 π$	$1 MHz$	$- 113.0000 μm$
$(- \frac{1}{6} π)$	$10 MHz$	$- 113.0000 μm$
$(- \frac{1}{6} π)$	$100 MHz$	$- 113.0000 μm$
$0.011111 π$	$1 MHz$	$- 113.0100 μm$
$(\frac{1}{90} π)$	$10 MHz$	$- 113.0010 μm$
$(\frac{1}{90} π)$	$100 MHz$	$- 113.0001 μm$
$0.0027778 π$	$1 MHz$	$- 113.0100 μm$
$(\frac{1}{360} π)$	$10 MHz$	$- 113.0010 μm$
$(\frac{1}{360} π)$	$100 MHz$	$- 113.0000 μm$

Abstract

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Applied Optics