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Improved Accuracy in Phase Computation with Continuous Dithering

IP.com Disclosure Number: IPCOM000237640D
Publication Date: 2014-Jun-30
Document File: 5 page(s) / 409K

Publishing Venue

The IP.com Prior Art Database

Abstract

In this paper we describe a method to accurately correct for offset/gain/tilt in quadrature terms (I and Q) for accurate calculation of phase in a 3x3 demodulated interferometric sensing system.

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Improved Accuracy in Phase Computation with Continuous Dithering

Abstract

In this paper we describe a method to accurately correct for offset/gain/tilt in quadrature terms (I and Q) for accurate calculation of phase in a 3x3 demodulated interferometric sensing system.

Introduction

There are several ways to derive phase information from interferometric sensing. Examples are heterodyne mixing1 using frequency shifting with AOM or EOM, modulation/demodulation method using some type of quadrature modulation such as PGC (Phase Generated Carrier)2 and homodyne detection using 3X3 demodulation. The specific implementation of 3X3 demodulation has been well illustrated in many previous publications3-6 as well as the challenge in accurately deriving phase in the presence of temperature and polarization movement. The base of the 3X3 demodulation algorithm assumes that the 3 signals out of the 3X3 coupler are equally split in amplitude, and the phases are exactly 120° apart. In practice, those assumptions are very difficult, if not impossible, to hold true, and the resulting variation in amplitude and phase separation out of the 3 signals tend to result in error in phase calculation.7 In this paper we describe a method to continuously provide the means to correct for accurate phase calculation.

Description

Homodyne detection using 3X3 demodulation method has been widely reported and used in many interferometric sensing applications. The method is simple to implement in that it does not require front-end modulation mechanism or any extensive optical/electronic hardware to demodulate the signal. The signal processing part to derive phase is also quite straightforward. Below is an example block diagram of the compensator design for 3X3 demodulation method.

Figure 1. Typical 3X3 compensating interferometer

The light from the sensing element passes through the compensator to generate three mixed signals with 120° phase difference. Those 3 signals are used to generate the phase quadrature terms (I and Q) via simple mathematical formula as

I = A+B-2C, and Q = sqrt(3)*(A-B),


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where A, B, and C are the 3 output signals from the 3X3 coupler.

These I and Q signals in turn are used to compute for the linearized response of the sensor perturbation in phase (ɵ) with arc tan calculation as
ɵ = tan-1(Q/I).

Ideally, those three output signals out of the compensator are assumed to be identical in their amplitude, and their phase separations are assumed to be exactly 120 degrees. However, in reality, none of those assumptions are true. Furthermore, as the optical signals are converted to electrical signal through some type of O to E conversion, there will be further discrepancy introduced. Therefore, some degree of correction is necessary to help ensure accurate determination of the end product. Such corrections can be done directly on the three output signals after O to E conversion, but it is easier to perform the correction after the quadrat...