Peak-to-peak tracking method for measurement of optical path difference: Revisited
Introduction
The field of interferometry concerns mainly on the recovery of phase information which is directly related to the optical path difference. There are myriad of methods available for such purpose as exhibited in [1] which includes Fourier transform, Hilbert transform, Wavelet transform, and other conventional methods such as phase shifting and simultaneous phase measurement, each with its own pros and cons depending on the design of the experiment layout and data processing capabilities. The peak-to-peak tracking method is applicable when the interference spectrum is obtained in the wavelength domain. Although the accuracy of this method is greatly limited by the spectral resolution and electronic noise of the detector [2], [3], the interference spectrum do not require much pre-processing in order to obtain the phase information unlike in Fourier transform method whereby the filtering are involved which may jeopardise the information contained in the signal. Besides, data presented by a spectrum analyser with unequal wavelength interval as the horizontal axis may not be suitable for Fourier transform to be applied [4] although not impossible as an alternative method of windowed Fourier transform has been suggested by Hlubina et al. [5]. In this paper, we present an improvisation to the peak-to-peak tracking method in retrieving the optical path difference from an interference spectrum.
Section snippets
Theory
Peak-to-peak tracking method is derived from a fairly basic principle of interference, which is the condition for the formation of bright fringes is that the phase difference of interfering waves equal to an integer of 2π. In an interference spectrum obtained from a spectrum analyser, these fringes will manifest as the peak in the intensity. Hence by taking two neighbouring intensity peak wavelength, the phase change Δφ is equal to 2π which relates to the optical path difference D [2], [3], [4]
Numerical simulation
The use of two fibre couplers with 50:50 splitting ratio at 532 nm central wavelength should be taken into account where the wavelength transmission response of the fibre output port are measured experimentally. This modifies Eq. (2) into:where C1 and C2 are the intensity transmission response as a function of wavelength for the fibre couplers obtained experimentally in our previous study [6]. The response functions C1 and C2 describes the light that propagates in the same fibre
Results and discussion
Interference spectrum and the wrapped phase plot obtained are illustrated in Fig. 2, Fig. 3, respectively, whereas Fig. 4 shows the phase versus wavenumber plot for measurement of the gradient according to Eq. (5). Results of the optical path difference computed from the wavelength values obtained from intensity peaks and phase minima are summarised in Table 1.
The results presented in Table 1 are the optical path difference values averaged from the set of wavelength values obtained in the
Conclusion
The peak-to-peak tracking method for measuring optical path difference is improvised in this paper. Interference output signal can be processed without much treatment that may result in loss of information. Simultaneous frames are not required to process the spectral interference which simplifies the data acquisition setup. Measurement made with the wavelength values obtained via phase method offers higher accuracy with lower uncertainty as compared to the conventional intensity and slope
Acknowledgements
This research is supported by Research University Grant (Vote no. 02J40) from Malaysian Ministry of Education.
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