2.5-m Telescope Pointing Error Budget

Sloan Digital Sky Survey Telescope Technical Note 19970527

Contents

• Introduction
• Pointing Error Budget

Introduction

The Sloan Digital Sky Survey imaging survey consists of 90 strips that are produced by scanning a great circle with the telescope. Each pair of strips make a filled stripe 2.5° wide. Thus, it is correct to say that the imaging survey consists of 45 stripes. The data are saved as 2048 x 1362 pixel frames

The interleaved strips and adjacent stripes overlap about 1 arc minute. It is desirable that large extended objects, i.e., nearby galaxies, be contained wholly within one strip or its neighbor. This will not always be possible, especially for galaxies with large angular diameters. However, a 2-D pointing accuracy of 3 arc seconds RMS leads to acceptibly uniform overlap and minimises the number of cases that require special handling (Table 3).

The requirement of efficiency in acquiring the guide stars in the setup for spectroscopy runs leads to the same number (Table 1). A guide fiber bundle diameter of 16.5 arc seconds and a pointing accuracy of 3 arc sec RMS results in 99% initial success in acquiring guide stars. This assumes that additional errors due to rotator angle, plate scale, star position, etc., are negligible.

Table 1: Pointing accuracy criterion needed for efficient spectroscopic operation.

Component	Value	Unit	Notes
Guide fiber bundle diameter	1	mm	1
Guide fiber bundle diameter	16501	mas	2
Image diameter	1000	mas	3
Max radius for acquisition	7751	mas	4
Number of standard deviations	2.58		5
Pointing accuracy (RMS)	3004	mas	6

Notes:

1. One of the ten guide bundles will be 1.0 mm in diameter. The balance will be 0.5 mm in diameter.
2. The telescope scale is 60.6 microns/arc second.
3. We assume that the guiding algorithm will converge if the image center is 500 mas or more from the edge of the fiber bundle.
4. See previous note.
5. This corresponds to a 99% success rate for a Gaussian distribution.
6. See previous note.

Pointing error budget

Table 2: Pointing error budget.

Component	2-D error (mas RMS)	Notes
Tracking error (300 > f > 1 mHz)	100	1
Magnetic fiducial error	1500	2
Encoder error between fiducials (f < 1 mHz)	1000	3
Pointing model error	1000	4
Flexure (not in model)	1000	5
Mechanical Hysteresis	1000	6
Thermal deformation	1000	7
Refraction error (z = 45 deg)	400	8
Primary nonrepeatability	800	9
Secondary nonrepeatability	20	10
Camera nonrepeatability	200	11
Coordinate transformation error	10	12
Total	2846	13

Notes:

1. This number is for the tracking error budget (Sloan Digital Sky Survey Telescope Technical Note 19970523). It is applicable over the listed frequency range. The unit mHz is millihertz.
2. Assumes a specification for the magnetic fiducials of +/-15 microns worst case over the temperature range -20 to +20 deg C.
3. Over several days, on the 3.5-m the locations of the fiducials repeat to 8 arc sec P-V. This includes magnetic fiducial error and encoder error.
4. This only includes errors in determining model coefficients. The values of this and the three following items are set to a level that should allow rapid debugging of these effects. The major limitation, position noise from seeing should be below 100 mas RMS and should not contribute significantly.
5. This includes all mechanical flexure that is not in the telescope model.
6. This includes all mechanical hysteresis.
7. This includes all errors due to temperature gradients in telescope components.
8. The total refraction at this zenith angle is 60 arc sec. This varies by perhaps +/-1 arc sec during clear weather. The assumption here is that all but 100 mas RMS can be compensated using surface pressure, humidity and temperature measurements.
9. Assumes use of linear stepper motors with an error of 0.6 microns RMS and that quantization error dominates.
10. Assumes measured performance of the 3.5-m secondary.
11. The kinematic mount for the 3.5-m optics test interferometer repeated to 1 micron. The camera is more massive and the mount more complex so a more conservative number is suggested. Gunn believes that 1 micron can be achieved.
12. From Russell Owen.
13. Statistical independence assumed.

    Table 3: Overlap error of adjacent or interleaved strips.

    Component	2-D error (mas RMS)	Notes
    1-d error	2012	1
    Strip overlap error	2845	2
    Peak-valley overlap variation (6 sigma)	17070	3

Notes:

1. Only the error normal to the strip direction affects strip overlap.
2. The error from two pointings determines strip overlap.
3. Only 1 in 1000 overlaps will be worse than this. Each of the 90 strips will likely be observed in several segments. Consequently, several hundred pointing operations will be required.

Discussion

I believe this to be a conservative error budget that should be straightforward to satisfy initially. Also, it should be reasonable to maintain telescope pointing at this level. Should this prove impractical for some unforeseen reason, alternatives exist.

• We can imagine doing real-time updates of the tracking, by, e.g., noticing when and where a given astrometric standard crosses the array.
• We can perform an initial on-sky pointing correction. Since the scan loci in alt-az space are rather compact over most of the sky, this would provide most of the benefit of real-time updates but may be easier to implement.

Date created: 05/27/97
Last modified: 05/28/97
Walter A. Siegmund