#!/usr/bin/env python
# coding: utf-8

# # More about flat corrections

# ## Overview of taking images for flat corrections
# 
# There are a few ways of taking "flat" images:
# 
# + Twilight flats are images of the sky near zenith taken around sunrise or
# sunset.
# + Dome flats are images of the inside of the dome (typically of a smooth
# surface, not of the dome itself),  illuminated by some light source in the dome.
# For smaller telescopes an electroluminescent or LED illuminated panel can be
# used as the light source.
# + Sky flats are composed of several science images.
# 
# Ideally the flat images have fairly high counts (roughly half the maximum counts
# of the detector) so that the *only* important source of error is Poisson error
# due to the light in the flat images, and so that the signal-to-noise ratio in
# those images is essentially zero.

# ## Calibrating and combining flat images
# 
# The process of calibrating and combining flat frames is largely the same
# regardless of the light source being used.
# 
# It is useful to think of flat frames as just like science images of stars or
# galaxies. The telescope is taking a picture of a light source, so bias and dark
# need to be removed from the individual images.
# 
# When combining the images there is a new step we have not discussed yet:
# normalizing (also called rescaling) the calibrated flat frames to a common mean
# or median before combining them. In both sky and twilight flats the illumination
# varies naturally from frame-to-frame. If the images are not scaled to a common
# value before combining, then the ones taken while the sky is brighter will
# inappropriately dominate the result. Dome flats ought to be, in principle,
# perfectly stable with no time variation in their illumination. In practice,
# every light source varies at some level; if you are trying to correct 1%
# differences in illumination, then 1% fluctuations in the light source matter.
# 
# Typically the mean or median is scaled to 1.0 before combining so that when the
# science images are divided by the calibrated, combined flats, the science image
# values do not change too much.