## Abstract

Ghosts in Fourier-transform spectrometry are important for three reasons: they can give rise to spurious coincidences of frequency differences in spectral analysis, distort the phase correction, and set a limit to the attainable signal-to-noise ratio. The various types of ghost, originating from amplitude modulation, phase modulation, and intermodulation, are described and discussed, together with some hardware and software artifacts. Recipes are given for identifying these features and, where possible, avoiding harmful effects from them.

© 1996 Optical Society of America

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### Equations (13)

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(1)
$$f=v\mathrm{\sigma},$$
(2)
$$\frac{\text{Ghost}\hspace{0.17em}\text{amplitude}}{\text{Parent}\hspace{0.17em}\text{amplitude}}={\mathrm{\pi}\mathrm{\sigma}}_{0}\mathrm{\alpha}\mathrm{\Delta}~\mathrm{\alpha}.$$
(3)
$$\mathrm{\delta}(\mathrm{\Delta}x)=\mathrm{\Delta}t(\mathrm{\delta}v).$$
(4)
$${I}_{\text{out}}=\mathrm{\alpha}{I}_{\text{in}}+\mathrm{\beta}{{I}_{\text{in}}}^{2}+\mathrm{\gamma}{{I}_{\text{in}}}^{3}+\cdots .$$
(5)
$$\mathrm{\delta}\mathrm{\varphi}\le 1/(\text{SNR}).$$
(6)
$$I(x)[1+\mathrm{\u220a}(x)]=I(x)+I(x)\mathrm{\u220a}(x)\iff S(\mathrm{\sigma})+S(\mathrm{\sigma})*E(\mathrm{\sigma}),$$
(7)
$$\mathrm{\u220a}(x)={\mathrm{\u220a}}_{e}(x)\hspace{0.17em}+{\mathrm{\u220a}}_{o}(x)\iff E(\mathrm{\sigma})={E}_{e}(\mathrm{\sigma})+i{E}_{o}(\mathrm{\sigma}),$$
(8)
$${S}_{\text{obs}}(\mathrm{\sigma})=S(\mathrm{\sigma})+[S(\mathrm{\sigma})*{E}_{e}(\mathrm{\sigma})].$$
(9)
$$I[x+\mathrm{\u220a}(x)]\approx I(x)+{I}^{\prime}(x)\mathrm{\u220a}(x).$$
(10)
$$I(x)\iff S(\mathrm{\sigma}),$$
(11)
$${I}^{\prime}(x)\iff 2\mathrm{\pi}i\mathrm{\sigma}S(\mathrm{\sigma}).$$
(12)
$$I(x+\mathrm{\u220a})\iff S(\mathrm{\sigma})+[2\mathrm{\pi}i\mathrm{\sigma}S(\mathrm{\sigma})]*E(\mathrm{\sigma}).$$
(13)
$$\begin{array}{l}{S}_{\text{obs}}(\mathrm{\sigma})=S(\mathrm{\sigma})-2\mathrm{\pi}[\mathrm{\sigma}S(\mathrm{\sigma})]*{E}_{o}(\mathrm{\sigma})\\ \approx S(\mathrm{\sigma})-2\mathrm{\pi}\mathrm{\sigma}[S(\mathrm{\sigma})*{E}_{o}(\mathrm{\sigma})].\end{array}$$