Angular and Spectral Differantial Imaging

SDI is the base mode of the NICI instrument. Each exposure produces two frames, one for each of the two channels. Usually, each channel is operated with a different filter, one off the absorption feature (usually on the blue side), and one on the feature (usually redward of the first filter). Whether SDI is combined with ADI or used at discrete roll angles is the choice of the observer, and is not necessarily a straightforward choice.

Both SDI and ADI techniques seek to separate real objects from speckles. SDI achieves this by exploiting a spectral feature in the desired target (common implementations utilize the 1.6 um methane absorption feature robustly observed in substellar objects cooler than 1400 K). Images are taken simultaneously both within and outside the chosen absorption feature.  Due to the simultaneity of the observations, the star and the coherent speckle pattern are largely identical in both filters, while any faint companion with that absorption feature is bright in one filter and faint in the other. Subtracting the two images thus removes the starlight and speckle patterns while a real companion with the chosen absorption feature remains in the image. In other words, the off-absorption band image acts as an ideal reference point spread function for the absorption band image. Utilizing a signature spectral feature of substellar objects greatly reduces the number of false positives detected (e.g. a background object, while real, still will drop out of the SDI subtraction since it will not have methane absorption).

SDI can be used at two discrete rotator angles for each object. A real object on the sky will rotate with a change of rotator angle; however, speckles which are instrumental phenomena will not. By subtracting data taken at multiple roll angles, speckles are further attenuated and any real object in the frame will display a characteristic jump in roll angle.

ADI employs a similar strategy to build a high quality reference PSF to remove speckles. Instead of observing at discrete roll angles, ADI leaves the rotator off and allows the telescope optics to rotate on the sky. In a sequence of images taken at different parallactic angles, a real companion will track on the sky with the parallactic angle, while speckles will move randomly. From a series of images, a reference PSF can be constructed for and subtracted from each individual image, attenuating quasi-static speckle structure. The main advantage of ADI against just using  discrete roll angles is that the pupil is not moved for the referece PSF image, since the cassegrain rotator is off. The moving M2 support arms (or correspondingly the spider mask are influencing the speckle pattern. An ideal PSF references in this sense only can be optained with the cassegrain rotator not following (ADI).

Combining both SDI and ADI techniques thus allows an even greater degree of speckle supression.

Rotator fixed versus follow

While it is clear that the combination of ADI and SDI (ASDI) is very powerful, the ADI mode of observing has important penalties.  ADI allows the science field to rotate at the science detector plane by observing with a fixed Cassegrain rotator. This field rotation introduces a field dependent blurring that reduces the Strehl and hence the planet detection sensitivity at large radii. This effect can be limited by setting a maximum exposure time per image and/or by observing in positions of the sky when the field rotates slowly, however, these must be traded against the increased contribution from read noise and the degraded performance of the adaptive optics system due to the larger observing zenith distances.

However, ADI (Cassegrain fixed) is not necessarily possible on all objects. To successfully perform ADI on an object, two conditions must be satisfied:

1) During the observing period, the target must rotate on the sky by at least 20 deg (corresponding to a rotation on the chip of 2 pixels at 1"). In ADI mode, a sequence of images is taken while the object moves through a variety of parallactic angles. For each image in the sequence, a reference PSF is built from the remaining images in the sequence. If the target has not rotated through a large enough angle, no images in the series will be appropriate for using as a reference PSF, because a companion object will not move sufficiently to prevent self-subtraction.

2) At the same time, the target must not rotate too much. For a given exposure time (e.g. 1 minute), if sky rotation is too much, an object on the sky at separation of greater than 2” will shear in each image in the series, also leading to lost companion flux. Thus, only objects with enough total sky rotation (>20 deg) but not too high a rate of sky rotation (thus causing shear), are appropriate for rotator-off observations.

For any ADI observation the sky rotation needs to balanced vs. the acceptable shear per image. The available sky rotation as a function of declination and hour angle is shown in Fig 1.

For an object separated by 1" from the parent star, a sky rotation of 20 deg corresponds to a rotation on the chip of two pixels. With typical PSF FWHM approx. 4 pix, this corresponds to about 1/2 FWHM of the PSF and is the minimum rotation necessary to ensure that a good reference PSF can be made. Therefore, only select portions of the sky are available to ADI at any given point in the night.  ADI time can be doubled by observing both before and after transit, omitting the period of highest sky rotation over transit.
A map of shear at 1" from the primary in a 1 minute exposure is shown in Fig. 2.  Thus, observing an object at -35 deg declination starting right after a transit will provide > 30 deg of sky rotation, but also up to two pixels shear for an object at 1" in a 1 minute exposure.

In contrast, for SDI at discrete roll angles only the airmass will constraint the observable sky.

Figure 1: Rotation map on the sky (hour angle vs. declination) for a 1 hour observation. Hour angle plotted on the X axis of this figure is the hour angle at the start of the observation. Contours are given at sky rotations of 60, 40, 30, 20, 15, 10, and 5 deg. Targets with sky rotation of greater than 20 deg in an hour are observable with the ADI technique. Figure from Biller et al., 2008, SPIE.

Figure 2: Map of shear as a function of sky position in a 1 minute exposure for an object 1" from the target. Contours are shown at shear levels of .1, .2, .5, 1, 2, and 5 pixels. Figure from Biller et al., 2008, SPIE.

Created: Sep 1, 2008; Markus Hartung