## Abstract

For digital phase detection, the characteristic polynomial method permits
algorithms that are insensitive to the harmonic content of the signal and
insensitive to miscalibration to be designed easily. It is shown here that
this method can also be used to design algorithms that are insensitive to a
possible bias modulation of the intensity.

© 1997 Optical Society of America

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### Equations (10)

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(1)
$${I}_{k}=A\left[1+\mathrm{\gamma}\mathrm{frng}\left(\mathrm{\phi}+k\mathrm{\delta}\right)\right],$$
(2)
$$\mathrm{\phi}*=\mathrm{arctan}\left(\frac{\mathrm{\sum}_{k=0}^{M-1}{b}_{k}{I}_{k}}{\mathrm{\sum}_{k=0}^{M-1}{a}_{k}{I}_{k}}\right),$$
(3)
$$S\left(\mathrm{\phi}\right)=\mathrm{\sum}_{k=0}^{M-1}{c}_{k}{I}_{k},$$
(4)
$$P\left(x\right)=\mathrm{\sum}_{k=0}^{M-1}{c}_{k}{x}^{k}.$$
(5)
$$exp\left(\mathit{im}\mathrm{\phi}\right)\mathrm{\sum}_{k=0}^{M-1}{c}_{k}{\left[exp\left(\mathit{im}\mathrm{\delta}\right)\right]}^{k}=exp\left(\mathit{im}\mathrm{\phi}\right)P\left[exp\left(\mathit{im}\mathrm{\delta}\right)\right].$$
(6)
$$\mathrm{\sum}_{k=0}^{M-1}{c}_{k}=0,$$
(7)
$$\mathrm{\sum}_{k=0}^{M-1}{c}_{k}k=P\prime \left(1\right).$$
(8)
$$\mathrm{\phi}*=\mathrm{arctan}\left(\frac{3{I}_{0}-5{I}_{1}+5{I}_{4}-3{I}_{5}}{-{I}_{0}-3{I}_{1}+4{I}_{2}+4{I}_{3}-3{I}_{4}-{I}_{5}}\right)$$
(9)
$$\mathrm{\phi}*=\mathrm{arctan}\left(\frac{-{I}_{0}+2{I}_{1}-2{I}_{3}+{I}_{4}}{-2{I}_{1}+4{I}_{2}-2{I}_{3}}\right).$$
(10)
$$\mathrm{\sum}_{k=0}^{M-1}{c}_{k}{k}^{s}={\mathbf{D}}^{s}P\left(1\right),$$