Spatial resolution enhancement of fiber-opticscanning white-light interferometer by use of aVernier principle

Changsen Sun, Yang Zhao, Adam Tennant, and Farhad Ansari

A Vernier principle is employed to improve the spatial resolution of a fiber-optic white-light interferom-eter to the accuracy of 0.2 �m. The Vernier principle is implemented by combination of interferencefringes itself and a virtual fringe that is generated by means of software tracing the scanning mirror.Two rulers are read with respect to each other. This design is insensitive to intensity fluctuation of theinterference fringe. The applications, submicrometer estimation for the quadrature-locking selectionand the tolerance of the relative measurement, demonstrate its effectiveness. © 2003 Optical Society ofAmerica

OCIS codes: 030.0030, 060.2370.

1. Introduction

Distance measurement can reach the micrometerscale at unambiguous resolution by the scanningwhite-light interferometer �SWLI�.1,2 These sys-tems have proved to be convenient devices, providingthe combination of distance measurements with alarge dynamic range and high accuracy. The spatialresolution is generally limited by how to read thepeak fringe based on an interferogram. An electri-cally scanned SWLI3 has the advantage with the ab-sence of moving parts and its two-step design thatcan locate the peak fringe within half a fringe period.This method needs a fine calibration in its linearphotodiode array on which the interference fringesare projected. This calibration is necessary for ab-solute measurement. An optical scanning techniquewas introduced, and a spatial resolution of a few tensof nanometers was achieved by the return-zero meth-od.4 However, its complex optical adjustment andthe limited measurement range made it difficult toimplement a practical measurement. A novelsignal-processing method,5 which modified the

The authors are with Smart Sensor and Nondestructive TestingLaboratory, Civil and Material Engineering, University of Illinoisat Chicago, Chicago, Illinois 60607. C. Sun �suncs@dlut.edu.cn� isalso with the Physics Department, Dalian University of Technol-ogy, Dalian 116023, China.

Received 16 March 2003.0003-6935�03�224431-03$15.00�0© 2003 Optical Society of America

forward–backward least-mean-square algorithm,was used to read the interference fringe. A thresh-old equal to 0.37 of the maximum power was used toswitch the algorithms on and off. This threshold isintensity dependent and makes the system unstable.

A single-mode optical fiber can make the fiber-opticSWLI working with the geometric versatile in itsoptical fiber sensing arm.6 This method is preferredfor practical application. Here, we present a simpleand in situ method to read the interferometer for therelative measurement based on the interferencefringe itself instead of reading the position of thescanning mirror. One implements a Vernier princi-ple by combining the interference fringe itself �i.e.,measurand fringe� and the virtual fringe generatedby means of software tracing the position of the scan-ning mirror. When two rulers are read with respectto each other, the virtual fringes provide a 1.0-�mspatial resolution, and one can calculate the submi-crometer sensitivity by combining the interferencefringes in a Vernier scalar way.

2. Vernier Principle

The principle of the proposed interferometer, shownin Fig. 1, was designed as a scanning mirror Michel-son arrangement. The light source, an LED with1310-nm central wavelength and 60-nm spectralwidth, was coupled into a single-mode optical fiber2 � 2 coupler �3 dB�. One of the outgoing beams wasconnected to a sensing single-mode optical fiber, l, 8cm in length. The other beam was collimated to ascanning mirror through an appropriate single-mode

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optical fiber, l�, with a range that matches the mea-surand optical path difference. The scanning mirrorwas glued on to a stepping-motor moving stage �New-port Corporation, Irvine, California�, and the mirrorwas collimated by a He–Ne laser. The equationused to describe the system is

I � x� � �B����1 � cos�2�

�x��d� , (1)

where I�x� is the intensity of the beam at the detectorthat corresponds to the sum of all the cosine waves;x l l� is the mirror displacement; � is the wave-length of the light source; and B��� represents theintensity of the source as a function of the wave-length.

This signal will be essentially constant over mostof the positions of the movable mirror. When thetwo arms of the interferometer are of equal length,all the cosine waves are in phase and the interfero-gram shows a center burst. A high-speed data-acquisition board, with a 1-MHz sampling rate, wasused for acquisition of the intensity of the interfer-ence fringes signal. The scanning mirror is con-trolled by voltage pulses from the controlling boxthat connected with the computer. The positivevoltage from the computer can move the mirrorforward through the controlling box, and the nega-tive voltage function moves the mirror in the oppo-site direction. To form the virtual fringe as aspatial resolution in the Vernier reading principle,we use the software to generate a control signal andto mark the mirror position on the computer. Be-cause one step of the scanning mirror is 1 �m thevirtual fringe interval is also 1 �m in space. Thatis to say, along with the same mirror scanning pro-cess, we can get two fringes at the same time; one isfrom the interference fringes itself, and the other isfrom the software-traced scanning mirror. Wenamed these two fringes as fringes ruler �FR� andvirtual ruler �VR�. The mirror scanning makes theinterference fringes appear, and VR can always pro-vide us 1-�m resolution in space. But we oftendesire to read accurately at submicrometer levelswithout changing the configuration of the system.Suppose that FR acts as a separate scale and that itis added to the VR. We can read the interferome-ter based on the Vernier space formed by the dif-ference between FR and VR. The VR has seven

markings on it that take up the same distance asthe six markings on the FR scale. This Vernierprinciple formed from the result is shown in Fig. 2and the Vernier makes accurate readings to 0.167 �0.2 �m �7�6 1 1.167 1 0.167 �m � 0.2 �m�possible.

3. Vernier Reading and Its Application

We choose the peak fringe as the reading fringe. InFig. 2 we demonstrate the structure of the Vernierprinciple. Figure 3 is the start point of a practicalmeasurement. On the basis of these overlappedpoints, A, B, C, and D, formed by overlapping inter-ference fringes and the virtual one, we can divide theinterference waveform into three parts, AB, BC, andCD. The reading of the position of the scanning mir-ror at the point P0 in Fig. 3 is P0 38456 �m. On

Fig. 1. Configuration of fiber-optic scanning white-light inter-ferometer.

Fig. 2. Vernier principle based on the fringes.

Fig. 3. Start point of the measurement.

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the basis of this point we can calculate the position ofthe other points on a micrometer scale:

P � P0 � �C � P0���f

�v� 1� . (2)

In this micrometer scale, P0 is the step next to thestep of the scanning mirror that makes the peakfringe occur; P is the position of the peak fringe thatwe want to locate by Vernier principle; C is the over-lapped point following the peak fringe P; and �f and�v are the sensitivity of the FR and the VR, respec-tively.

In Fig. 3 the sensitivities of the VR and the FR is�f 1.0 �m and �v 7�6 1.167 �m. With C 38458 �m and P0 38456 �m �from Fig. 3� we canobtain P by means of Eq. �2�: P 38455.67 �m.Thus we can calculate the submicrometer part of P0by P.

The same procedure is applied to Fig. 4. We dis-cover that there are eight intervals and that sevenintervals occurred in the same segment BC corre-sponding to the virtual fringes and the interferencefringes. Although the three segments AB, BC, andCD, have demonstrated the nonequal distributedfringes at this measurement, we still can calculatethe intensity of the interference fringes of this mea-surement on the basis of the segment in which thepeak point occurred. Thus the sensitivities of the

VR and the FR is �f 1.0 �m and �v 8�7 1.14 �0.2 �m. With C 38489 �m and P0 38487 �m�Fig. 4� we can calculate P by Eq. �2�, that is, P 38486.72 �m.

The reading of the method used is

P0 � P0 � 38487 � 38456 � 31 �m.

The reading based on the Vernier method is

P � P � 38486.72 � 38455.67 � 31.05 �m,

where P values are from Figs 4 and 3.This result means the SWLI is most appreciated in

relative displacement measurement from the point ofview of accuracy.

4. Conclusions

The Vernier principle can be used to carry out theprecision measurement with submicrometer accu-racy at 0.2 �m. The distance measurement canreach the submicrometer accuracy in a several-centimeters range. This principle can also be usedfor the other low-coherence interferometer; however,the reading speed needs further improvement.

References1. K. T. V. Grattan and B. T. Meggitt, Optical Fiber Sensor Tech-

nology �Chapman & Hall, London, 1995�.2. J. Tapia-Mercado, A. V. Khomenko, and A. Garcia-Weidner,

“Precision and sensitivity optimization for white-light interfero-metric fiber-optic sensors,” J. Lightwave Technol. 19, 70–74�2001�.

3. R. Dandliker, E. Zimmermann, and G. Frosio, “Electronicallyscanned white-light inteferometry: a novel noise-resistant sig-nal processing,” Opt. Lett. 17, 679–681 �1992�.

4. D. N. Wang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, and K.Weir, “An optical scanning technique in a white light interfero-metric system,” IEEE Photon. Technol. Lett. 6, 855–857 �1994�.

5. D. Romare, M. Sabry Rizk, K. T. V. Grattan, and A. W. Palmer,“Superior LMS-based technique for a white-light interferomet-ric system,” IEEE Photon. Technol. Lett. 8, 104–106 �1996�.

6. U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute dis-tance measurement with synchronously sampled white-lightchannelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 �1995�.

Fig. 4. Termination of the measurement.

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