We calculate the root mean square (rms) value of the spectral noise caused by optical path phase measurement errors in a spatial heterodyne spectrometer (SHS) featuring a complex Fourier transformation. In our calculation the deviated phases of each Mach–Zehnder interferometer in the in-phase and quadrature states are treated as statistically independent random variables. We show that the rms value is proportional to the rms error of the phase measurement and that the proportionality coefficient is given analytically. The relationship enables us to estimate the potential performance of the SHS such as the sidelobe suppression ratio for a given measurement error.
© 2013 Optical Society of America
Original Manuscript: January 16, 2013
Revised Manuscript: February 21, 2013
Manuscript Accepted: March 1, 2013
Published: April 12, 2013
Kazumasa Takada, Mitsuyoshi Seino, Akito Chiba, and Katsunari Okamoto, "Detailed calculation of spectral noise caused by measurement errors of Mach–Zehnder interferometer optical path phases in a spatial heterodyne spectrometer with a phase shift scheme," Appl. Opt. 52, 2555-2563 (2013)