Uncertainty evaluation of a fiber-based interferometer for the measurement of absolute dimensions

ABSTRACT
The evaluation of the measurement uncertainty of a robust all-fiber-based low-coherence interferometer for the
measurement of absolute thickness of transparent artifacts is described. The performance of the instrument is evaluated
by measuring the length of air-gaps in specially constructed artifacts and the observed measurement errors are discussed
in the context of the uncertainty associated with them. A description of the construction of the artifacts is presented,
accompanied by an uncertainty analysis to estimate the uncertainty associated with the artifacts. This analysis takes into
account the dimensional uncertainty of the artifacts (including wringing effects), thermal effects, and effects of the
environment on refractive index. The ‘out-of-the-box’ performance of the instrument is first evaluated. A maximum
error of 350 nm for an air-gap of 10.1 mm is observed. A linear trend between the measured length and the error is also
observed. The relative magnitude of the errors and the uncertainty associated with the error suggests that this trend is
real and that a performance enhancement can be expected by mapping the error. Measurements of the artifacts are used
to develop an error map of the instrument. The uncertainty associated with the predicted error is determined based on
the uncertainty associated with the error. This analysis suggests that the uncertainty in the predicted error at the 2σ level
may be conservatively estimated to be (2.9L+37.5) nm, where L is in units of mm.
Keywords: Low-coherence, interferometer, high-accuracy, uncertainty estimate, laser, absolute dimensions

1. INTRODUCTION
The ability to perform non-contact, absolute distance measurements with high precision is essential in a number of
applications in science and industry. As these types of measurements move out of the laboratory and into a
manufacturing environment, the need arises for the instruments to perform these measurements in a real-time mode. The
most accurate methods of performing absolute distance measurements are based on optical interferometry. Some
interferometric methods for absolute distance measurement are based on high-coherence laser measurements such as
two-wavelength super-heterodyne detection1 while other techniques use low-coherence interferometry. Low-coherence
interferometry (LCI) is a measurement technique based on white light interferometry that led to the development of
optical coherence domain reflectometry (OCDR). This one-dimensional optical ranging technique uses a low-coherence
light source to obtain highly accurate distance measurements. OCDR was originally developed for locating faults in
fiber optic cables and network components. The use of OCDR has since spread from fiber-optic reflectometry,3 to
Bragg grating measurements,4 to optical coherence tomography in biological imaging applications.5
The demand for a robust, accurate, user-friendly, and precise instrument for use in an industrial setting led to the
development of the instrument described in this paper. Early work on a robust low-coherence interferometer was done
by Marcus et al. 6-9 of Eastman Kodak for a variety of industrial applications, including liquid layer thickness
monitoring on coating hoppers, film base thickness uniformity, digital camera focus assessment, optical cell path length
assessment, and CCD imager and wafer surface profile mapping. The first generation instrument was a Michelson
interferometer in an autocorrelator configuration. A mechanical assembly driven by a brushless DC motor produced the
path length change by moving retro-reflectors in the arms of the interferometer in a reciprocating motion. A highaccuracy determination of the sample dimensions requires a determination of the change in path length with a
commensurate degree level of accuracy. This was accomplished by using a second interferometer based on a laser
source that occupied the same air path as the low-coherence interferometer. A frequency stabilized helium-neon laser
was used to produce a stable fringe signal serving as a reference “clock” for the data acquisition. This “clock” produced
trigger signals at constant intervals along the path length change.10
The next generation interferometer replaced the motor-driven bulk optics and the helium-neon laser with piezoelectric
(PZT) fiber stretchers and a 1550 nm distributed-feedback (DFB) semiconductor diode laser respectively.11 In this
embodiment, the interferometer has no moving parts and utilizes telecom-grade components with long lifetimes and
high reliability. The latest instrument, evaluated in this paper, incorporates additional features such as real-time data
acquisition and computation to allow for rapid measurements of optical thickness in an industrial environment.
2. DESCRIPTION OF INSTRUMENT
This section briefly outlines the theory behind low-coherence interferometry and describes the principle of operation of
the instrument and the instrument layout.
2.1. Theory of operation
The differences between low-coherence and high-coherence interferometry are illustrated in Fig. 1. The interference
signal from a typical Michelson interferometer is represented by