**Digital Demodulation of Interferometric Signals**

Tristan J. Tayag and R. Collins Watson *Texas Christian University USA* 

#### **1. Introduction**

316 Modern Metrology Concerns

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The marriage of optical sensing techniques with sophisticated digital signal processing has resulted in a myriad of practical metrology systems. Optical metrology systems offer many attractive measurement features. These systems are inherently non-contacting, nondestructive, and immune from electromagnetic interference. In addition, since light is used as the sensing probe, the measurement system is capable of high sensitivity, fine resolution (both spatial and temporal), and absolute calibration.

The leap from the vibration stabilized table of the laboratory to the harsh milieu of the factory floor has been a major challenge for optical metrology systems. However, on-going advances in digital processor speed and algorithmic complexity have in large part made this leap possible. Full-field optical inspection methods include holographic interferometry, speckle metrology, and interferometric computed tomography (Tayag & Bachim, 2010). These techniques have been applied to a wide range of applications in biological tissue characterization, the automotive industry, dentistry, the semiconductor industry (Pitt et al., 2003; Tayag et al., 2003; Tayag et al., 2010; Weber et al., 2004), and fiber optic and bulk optic characterization (Osten et al., 2010). Here, we focus our attention on digital demodulation applied to "point measurements" as opposed to full-field measurements.

In this chapter of *Modern Metrology Concerns*, we present recent digital signal processing techniques used in interferometry. Application areas range from biotechnology to industrial to military. Specific examples will be cited throughout the literature as well as from our own research. Our research in digital demodulation techniques include applications in myofibroblast cell contraction (Kern et al., 2003), ballistic shock characterization (Kumar et al., 2009), and down-hole oil well drilling. In addition, we present a new (unpublished) digital demodulation algorithm. The novelty of our technique lies in the frequency domain manipulation of the well-known phase-generated carrier modulation approach.

Section 2 contains background information on interferometry and practical modulation techniques. The Michelson, Mach-Zehnder, Sagnac, and Fizeau optical configurations will be described. Once the basic optical geometries are established, we describe the modulation and demodulation techniques which are needed in practice. These techniques convert the measured phase change into the desired displacement, velocity, or index change.

Our novel digital demodulation algorithm will be presented in Section 3. The application of this research is in sensing down-hole drill bit parameters for oil well drilling systems. We present a new demodulation algorithm for phase-generated carrier based interferometers. The theoretical background is presented along with simulation results.

Section 4 will follow with a summary and directions for future research.
