The IDL code observable.pro calculates the airmass, parallactic angle, and amplitude of atmospheric differential refraction that will occur for a slitmask at a given position angle. While airmass and parallactic angle are also available through iraf or the web I couldn't find the amplitude in any easy-to-use form. You are welcome to use the code. It has been tested versus tables available in the literature and web but please give me feedback. Examples/instructions are in comments near the top of the code. The general syntax is observable, month, observatory_dec, object_ra (hours), object_dec.
For imaging, just open idl and call the code with, e.g.,
IDL> observable, 11.7, -30., 3.5, -27.
to see the hourly airmass table for CDF-S (03 30 -27) as viewed from latitude -30 (CTIO) on November 21.
For multislit spectroscopy, you'll want to activate the atmospheric differential refraction calculation by adding /par. Default wavelength range is from 3000 to 10000A but you can specify these with l1 and l2, and you can test a particular position angle using pos. For example,
IDL> observable, 11.7, -30., 3.5, -27., /par, l1=4000, l2=6000, pos=180
outputs the airmass, parallactic angle, and amplitude of atmospheric differential refraction from 4000 to 6000A both along the parallactic angle and perpendicular to slits at position angle 180 (degrees east of north). Default atmospheric conditions are for La Silla and should be good for most observatories, including Tololo/Pachon/Las Campanas. Adding /vlt ensures that typical Paranal atmospheric conditions are used (slightly less refraction). Adding /keck prints out a reminder of the Keck Nasmyth platform limits and ensures that typical Mauna Kea atmospheric conditions are used (the low atmospheric pressure leads to about 30% less differential refraction than at most sites, so that's an important difference).
For multifiber spectroscopy, just leave off pos and see if the light you care about will make it down the fiber.
For single-slit (or aperture pair) spectroscopy with the slit constantly rotated to be at the parallactic angle, again just pay attention to the amplitude along the parallactic angle (i.e. leave off pos) to make sure that your slit is long enough to get all the light you care about.
Note that in all of this it's important to think about what wavelength you will be guiding at. Any differential refraction between the guiding wavelength and the slit(mask) alignment filter wavelength is zeroed out during alignment but this will grow as the exposure continues. So you actually need to calculate the change in differential refraction from lambda_min to lambda_guide and lambda_max to lambda_guide to figure out what wavelengths will make it into your slit(s). Some modern telescopes allow you to simulate guiding at a central science wavelength which effectively removes this concern and lets you just worry about differential refraction from lambda_min to lambda_max. Don't forget to account for astrometric errors when choosing slit widths - it takes high confidence in your astrometry, seeing, and lack of differential refraction to justify using slits narrower than 1" for dim objects.