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In <angular differential imaging>, the instrument is operated in pupil tracking: its pupil and associated quasi-static <speckle patterns> remain nearly fixed on the detector, while the sky rotates with the <parallactic angle>. A reference stellar <point spread function> is formed from other exposures, preferably excluding frames where a companion remains at almost the same location. Subtract the reference from each exposure, then derotate the residuals into the sky frame and combine them. A companion adds coherently after derotation; the stellar residuals are reduced. This is the technique described in the https://arxiv.org/abs/astro-ph/0512335[original angular-differential-imaging analysis]. At angular separation $\rho$, the approximate displacement is $\rho\Delta\psi$, so useful diversity normally requires $\rho|\Delta\psi|\gtrsim\lambda/D$.
In <simultaneous spectral differential imaging>, acquire nearby spectral-band images simultaneously, for example with a <beam splitter> and filters or an <integral field spectrograph>. Stellar <speckle patterns> approximately move radially in proportion to <wavelength>. Rescale each image by $\lambda_0/\lambda$ and normalize the stellar flux before subtracting bands. The speckles then approximately align, while a companion at a fixed sky position moves in the rescaled coordinates. A companion absorption band can also distinguish its spectrum from the star: methane bands are useful for cool companions, as in the https://arxiv.org/abs/astro-ph/0212033[TRIDENT instrument description], but methane is not a universal companion property. Positional diversity scales as $\rho|\Delta\lambda|/\lambda$.
\b[ADI uses sky rotation; SSDI uses simultaneous spectral diversity and wavelength scaling of stellar speckles.]
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