Infrared scanner coordinate system transformation

Sloan Digital Sky Survey Telescope Technical Note 19971102

Walter Siegmund

Contents

• Introduction
• Transformation equations
• Conclusions

Introduction

The Sloan Digital Sky Survey (SDSS) has two components, an imaging survey and a spectrographic survey. The desired photometric accuracy of the imaging survey can only be achieve during excellent photometric conditions. Because of the difficulty of visually detecting thin patches of clouds under dark conditions, an infrared (IR) scanner was constructed in 1993 to monitor nighttime cloud cover at Apache Point Observatory. It has been used routinely since the end of 1995 and has proved to be valuable for monitoring sky conditions at the observatory.

The IR scanner confers the following benefits.

• Thin clouds are readily apparent in the images.
• Animation of a series of frames allow trends to be discerned. Observations can be planned better and telescope time can be used more efficiently.
• Under marginal conditions, deterioration can be detected and the telescope enclosure can be closed before precipitaion falls on the optics.
• The scanner image archive allows an astronomer to examine the condition of the sky at the time of an observation as an aid in the interpretation of the data.

Transformation equations

The scanner operates by moving two mirrors that are mounted in an altitude-altitude configuration. The left diagram (Figure 1) shows the scanner coordinate system. The right diagram is the familiar azimuth-altitude coordinate system. Both are right-handed systems. Azimuth is measured positive to the east from the south, i.e., the same convention that is used in the Apache Point Observatory telescope control computer.

Figure 1: IR scanner and horizon (azimuth-altitude) coordinate systems. Positive axes and angles are labeled.

By inspection,

X = Z'
Y = -X'
Z = -Y'

Consequently,

cos()•cos() = sin(a)
cos()•sin() = -cos(a)•cos(A)
sin() = -cos(a)•sin(A)

The loci of points at 15° intervals in azimuth and altitude are plotted in scanner coordinates (Figure 2). This is the format that an 80°x80° image would have. The distortion is modest except near the east and west points of the horizon. The low distortion makes it relatively easy to interpret the resulting images. The images could be resampled to reduce distortion but this has not proved necessary, so far.

The loci of points at 15° intervals in scanner coordinates are plotted on an azimuth-altitude polar plot (Figure 3). This is the view of an observer looking up at the zenith. The line scan direction is vertical on the page. The frame scan direction is left-right.

Figure 2: Loci of points at 15° intervals in azimuth and altitude are plotted in scanner coordinates. This is the format of a scanner image displayed in a rectangular format. Distortion is modest except near the east and west points on the horizon.

Figure 2: Loci of points at 15° intervals in scanner coordinates are shown on a azimuth-altitude polar plot.

Conclusions

 A simple set of coordinate transformations describe the relationship of the infrared scanner and the altitude-azimuth sky coordinate systems.

Date created: 11/02/1997
Last modified: 02/11/1998