Principles of Operation of the QUEST Camera

The properties of the camera are summarized in table 1. The camera has been designed to operate in drift scan mode,¹ which is also referred to as time-delay integration (TDI) mode. In this mode the telescope is locked into a fixed position at a given declination angle. The CCD array is oriented with the columns of pixels in the clocking direction lined up precisely in the East-West direction, and the CCDs are clocked synchronously with the motion of the star images across each CCD. Each star image thus crosses four CCDs, one in each row of CCDs. Each row of CCDs can have a filter of a different color in front of it so the camera can collect images in each of four colors essentially simultaneously. The camera thus has a 100% duty cycle (i.e., data is collected continuously) and no time is lost due to readout time or telescope slewing time. Since the telescope is locked into fixed position and is not tracking, the system is very stable and produces more accurate photometric measurements. Photometric precision is further enhanced because each point in the sky is imaged by averaging over an entire column of pixels and thus pixel-to-pixel variations in sensitivity are minimized.

Table 1: Properties of the QUEST camera

Parameter	Value
Number of CCDs	112
Array size, CCDs	$28 \times 4$
For each CCD:	$9mm \times 32mm$
pixel size	$13\mbox{$\,\mu{\rm m}$}\times 13\mbox{$\,\mu{\rm m}$}$
Number of pixels	$600 \times 2400$
Pixel size on sky	$0.85\mbox{$^{\prime\prime}$}\times 0.85\mbox{$^{\prime\prime}$}$
Array size, pixels	$16,800 \times 9,600$ pixels
Total no. of pixels	$161 \times 10^6$
Array size, cm	$25.0\mbox{$\:{\rm cm}$}\times 19.3\mbox{$\:{\rm cm}$}$
Array size, on sky	$4.6\mbox{$^{\circ}$}\times 3.6\mbox{$^{\circ}$}$
Effective area	$\sim$10 square degrees

During a clear night, a 4.6$^{\circ}$ wide by 120$^{\circ}$ long strip, or approximately 500 square degrees, can be covered in each of four colors. The camera was built at Yale University and Indiana University. It was installed at the prime focus of the telescope in early 2003 and will start science quality data taking later that year.

In the following sections, we will describe the principles of operation of the camera.

If the camera were used to drift scan along the equator, the images of stars would follow straight lines and move at the same rate across the image plane. However, at declinations other than the equator, the stars will follow arcs of circles and stars at different North-South positions will move at different rates. In drift scanning, the sagittas due to the first effect will smear the images in the North-South direction, and due to the second effect some of the stars will not be exactly synchronous with the CCD clocking rates and thus will be smeared in the East-West direction. In order to keep these effects at an acceptable level, i.e. to keep the smearing of the point spread function below about one arc second in any direction, we rotate each CCD by an amount dependent on the declination being scanned in such a way that the clocking direction of each CCD is tangential to the arcs that the stars are moving in at that location in the array. This is accomplished by mounting each of the four CCDs in a North-South row on an Invar² bar, which we call a ``finger.'' Each of the four fingers can be rotated by a different amount by cams which are driven by external, computer controlled stepper motors. An exaggerated sketch of this scheme is shown in figure 1. For convenience, we label the fingers A, B, C, and D, and the columns of CCDs 1, 2, 3 ... 28 as shown in figure 2. This figure also shows the pivot points and the cams used to rotate the fingers. In addition, each column of CCDs is scanned along a slightly different declination, and therefore, the parallel clocks reading out the CCDs are synchronized at slightly different rates.

Figure 1: Schematic diagram of the CCD rotation to keep each CCD lined up along the line of motion of the star images.

Figure 2: Layout of the CCDs on the image plane. Also shown are the Invar fingers supporting the CCDs, their pivot points and the finger rotating cams.

The radius $r_{\delta}$ of the star tracks (i.e. the arcs of circles along which the image of a star moves in drift scanning) on the image plane of a telescope with focal length f at a declination $\delta$ is to a good approximation given by:

$$r_{\delta}=\frac{f}{\tan \delta}.$$

The parallel clock rate $\nu_{\delta}$ for reading out a CCD in such a way that the motion of the charge is synchronous with the motion of the star image across the CCD at a declination $\delta$ is given by:

$$\nu_{\delta} = \frac{\Omega f}{a}\cos \delta.$$

where $\Omega=72.7 \mu{\rm radians/sec}$ is the rotation rate of the Earth, $f$ is the focal length of the telescope, and $a$ is the pixel size on the CCD. For the Oschin Schmidt telescope and our pixel size, this gives:

$$\nu_{\delta} = 17 \cos \delta \qquad {\rm lines/second}.$$

In drift scanning along the equator, the readout parallel clocks are thus synchronized at approximately 17 lines/second. At this rate, a star image takes 140 seconds to cross a CCD. This gives an integration or exposure time of 140 seconds. At higher declinations, the clocking rate is somewhat slower giving a slightly longer exposure time. In drift scan mode, this exposure time is governed by the rotation of the earth and can not be changed. However, since each star crosses four CCDs, these can be added for an effective exposure time of 560 seconds. In cases where even longer exposure times are desirable, repeated scans of the same area of sky can be performed and co-added.

The angle by which the CCD support fingers (see figure 1) have to be rotated to keep the clocking direction of the CCDs tangent to the star tracks on the image plane at a declination $\delta$ is:

$$\Delta\theta = \frac{d}{f}\tan\delta$$

where $d$ is the distance of the pivot point of each finger from the camera centerline ( $d = \pm 7.5\mbox{$\:{\rm cm}$}$ for fingers 1 and 4 and $\pm 2.5\mbox{$\:{\rm cm}$}$ for fingers 2 and 3). Thus, for example, the top finger (1) has to be rotated about $0.15\mbox{$^{\circ}$}$ for $\delta=6\mbox{$^{\circ}$}$, which is very small but nevertheless quite important to keep the image sizes small. As mentioned above, the 28 columns of CCDs scan along slightly different declinations and thus have to be clocked at slightly different rates. For example, with the camera scan centered at $\delta=6\mbox{$^{\circ}$}$, the four columns have to be clocked at 17.638, 14.726, 17.613, and 17.598 lines/second, respectively. Again this variation is very small but nevertheless quite important. The detailed implementation of this scheme is to clock all four columns at the same rate but drop clock pulses at different rates in the four columns to produce the average clock rates required. The fast serial readout clock is 100 kHz for all of the CCDs in the array.

The scheme described above for varying the rotation and clock rate synchronization of the different CCDs in the array removes the dominant effects that smear the images. There are, however, residual effects due to the sagitta of the image motion and spread in the rate of motion of the images across the finite width of a single CCD, as illustrated in figure 3. For a CCD with length l (in the E-W direction) and width w (in the N-S direction), the residual smearing of the image size $\Delta x$ and $\Delta y$, in the E-W and N-S directions respectively, scanning at a declination $\delta$, is given by:

$$\Delta x = \frac{1}{8} \frac{l^{2}}{f}\tan \delta$$

$$\Delta y = \frac{1}{2} \frac{lw}{f}\tan \delta$$

where f is the focal length of the telescope. This residual smearing limits the range of declinations at which this camera can be used in the drift scanning mode without intolerable degradation of the image sizes.

Figure 3: Sagitta ($\Delta x$) and path length difference ($\Delta y$) on a single CCD.

The design has been optimized in such a way that the residual image smearing is kept below 1 arcsec for declinations up to $\pm 25\mbox{$^{\circ}$}$. Given the typical seeing at the Palomar site, we can drift scan at declinations up to these declinations with no appreciable degradation of image quality. This is sufficient for the equatorial survey for which the camera has been designed. Of course, the camera can be operated in a conventional point and stare mode to cover regions of the sky above these declinations.

Another complication of the design was due to the fact that the image plane of a Schmidt telescope is not flat but has the shape of a convex spherical surface. To arrange the CCDs in such a shape would have been cumbersome. Instead, we designed, and had built, a 36$\:{\rm cm}$ diameter field flattener lens that covered the entire image plane. This lens produced a flat image plane and, in addition, corrected for the pincushion distortion inherent in the telescope to a level where the degradation of the image shapes were negligible.

The depth of field of the Schmidt telescope is quite shallow. For this reason, the front surfaces of the 112 CCDs, including the motion of the finger mounts, had to be kept in a plane to a tolerance of less than $\pm 25$$\,\mu{\rm m}$. It required great care in the precision machining and the alignment procedures to achieve this precision.

During the commissioning period, after the camera had been installed in the telescope, a great deal of effort was expended to align the plane of the CCDs with the focal plane of the telescope. Once this had been achieved, however, it was quite stable and required no further adjustment. Typically, before each nights' data taking the focus of the telescope, the rotational position of the fingers, and the synchronized read out rate, which have been set by the control computers for the appropriate declination, were checked by looking at the shape and size of stellar images.

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Footnotes

... mode,¹

We thank Steve Shectman for many interesting discussions concerning the technique of drift scanning.

... Invar²

Invar is a stainless steel alloy that has a relatively low coefficient of thermal expansion.