SDN0019a

SYSTEM DESIGN NOTE

SDN0019 - Differential Refraction

Prepared by	Date	Approved by	Date	Rev.	Rev Date
Jay Elias	4/8/99	N. Gaughan	4/9/99

SDN0019 - Differential Refraction

1. Introduction

"Differential refraction" is a term used to cover two situations. One is relative differences in position due to the fact that two objects will generally be observed through slightly different atmospheric paths. The second is differences in position as a function of wavelength.

Although differential refraction in the near-infrared is a relatively small effect, the very fine plate scales to be used with the GNIRS long cameras make both effects significant.

2. Guide Stars

The principle effect of spatial differential refraction is that the position of the object to be observed will change slightly relative to the guide star over the duration of a long observation. The differential refraction between two objects is given approximately by

where d z is the differential refraction, in arcsec, and dz is the difference in zenith distance, in arcmin. The zenith distance, z, is an average for the two positions. The coefficient applies to typical conditions on Mauna Kea. Over a four-hour observation, the zenith distance can vary from nearly zero to almost 60 degrees, so the maximum relative shift can approach 1 pixel with the long cameras (0.05 arcsec).

Although this is a potential problem if neglected, the telescope control system (TCS) will provide the appropriate offsets to the OIWFS, which will slowly adjust for this effect for lengthy observations.

3. Wavelength Effects

Differential atmospheric refraction as a function of wavelength affects the spectrometer in two ways. Both are due to the fact that the apparent position of an object is a function of the wavelength at which it is observed.

First of all, the OIWFS will not necessarily be guiding through the same filter passband as that used for spectra. Typically, the OIWFS will use either a J or H filter, or a custom filter covering the combined J and H bands. It may occasionally be used with a K filter, but night-time performance is significantly worse.

Spectra will often be taken at longer wavelengths, which means that the offset between the guide star and the object will change, since the magnitude of the differential refraction is proportional to tan(z). Note that any initial offsets are corrected for during acquisition (provided it is done at the same wavelength as the spectra will be taken at).

It is not clear whether the TCS or OCS are capable of adjusting for this effect. As can be seen from the table (Appendix, below), during the course of a observation of several hours, the K-band position of an object may shift by a full slit width relative to its J-band position.

The second effect mainly affects cross-dispersed spectra: the object will be "smeared" by differential refraction over the wavelength range covered by the spectrum. For example, at a zenith distance of 45°, the difference in position between the object at 0.9 m m and at 2.5 m m is a bit more than 0.2 arcsec – double the slit width. At shorter wavelengths and larger zenith distances, this effect can become significant even for single spectral orders.

This second effect cannot be corrected (unless one adds additional optics to the instrument). The best solution is to orient the slit so that it is oriented in the direction of dispersion (the parallactic angle) so that the different wavelengths will still be transmitted. This will also deal with any differential effects between the guide star and the object that the OCS/TCS don’t take care off.

For point sources, the ideal situation is one in which the slit maintains the parallactic angle. This can be accomplished by holding the instrument rotator fixed, but it then requires the OIWFS to adjust position continuously in order to correct for apparent rotation. The guide star may be occulted at some locations in the field, and the OIWFS may not be capable of adjusting over the full range of angle required.

An alternative solution is one in which the slit is set to a specific value and only adjusted at one-hour intervals; this procedure will keep light losses to acceptable levels under most circumstances.

For extended objects, where the slit angle on the sky may be relevant, it may be necessary to program the observations so that the desired slit angle is close to the parallactic angle – or to use the integral field unit and apply corrections to the resulting data cube.

Note that in any case it will be difficult to produce precise relative spectrophotometry with a narrow slit in cross-dispersed mode, since the image profile itself will vary over such a large wavelength range. Observations with a wider slit and/or comparison with a standard star nearby in the sky will be helpful.

Appendix

Mauna Kea Differential Refraction

Relative to 1.1 m m, in arcsec

z	sec(z)	Wavelength (m m)
z	sec(z)	0.90	1.20	1.40	1.60	1.80	2.00	2.20	2.50	3.50	4.80
0	1.00	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
5	1.00	0.007	-0.002	-0.006	-0.008	-0.009	-0.010	-0.011	-0.012	-0.013	-0.014
10	1.02	0.015	-0.005	-0.011	-0.015	-0.018	-0.020	-0.022	-0.024	-0.026	-0.028
15	1.04	0.022	-0.007	-0.017	-0.023	-0.028	-0.031	-0.033	-0.036	-0.040	-0.042
20	1.06	0.030	-0.010	-0.023	-0.032	-0.038	-0.042	-0.045	-0.049	-0.054	-0.057
25	1.10	0.038	-0.012	-0.030	-0.041	-0.048	-0.054	-0.058	-0.062	-0.070	-0.073
30	1.15	0.048	-0.015	-0.037	-0.051	-0.060	-0.067	-0.072	-0.077	-0.086	-0.091
35	1.22	0.058	-0.019	-0.045	-0.061	-0.073	-0.081	-0.087	-0.094	-0.104	-0.110
40	1.31	0.069	-0.022	-0.053	-0.073	-0.087	-0.097	-0.104	-0.112	-0.125	-0.132
45	1.41	0.083	-0.027	-0.064	-0.088	-0.104	-0.116	-0.124	-0.134	-0.149	-0.157
50	1.56	0.098	-0.032	-0.076	-0.104	-0.124	-0.138	-0.148	-0.159	-0.178	-0.187
55	1.74	0.118	-0.038	-0.091	-0.125	-0.148	-0.165	-0.177	-0.191	-0.213	-0.224
60	2.00	0.143	-0.046	-0.110	-0.152	-0.180	-0.200	-0.215	-0.231	-0.258	-0.272
65	2.37	0.177	-0.057	-0.136	-0.188	-0.223	-0.248	-0.266	-0.286	-0.320	-0.336
70	2.92	0.227	-0.073	-0.175	-0.240	-0.285	-0.318	-0.341	-0.367	-0.410	-0.431
75	3.86	0.308	-0.099	-0.237	-0.327	-0.388	-0.431	-0.464	-0.498	-0.557	-0.585