How does the Cuttlefish camouflage itself accurately despite being color-blind?
The reason why the cuttlefish is colour blind is because 


  it just has one type of cone cell. Humans have three different types,
  each sensitive to a different color of light. With only one cone type,
  you couldn’t differentiate between different colors (reference).


A study was conducted in the lab of Dr Lydia M. Mäthger where two different checkerboards were used to test their colorblindness. 


  1) Gray – Green. One green shade, matched to the maximum absorption
  wavelength of cuttlefish, was combined with 16 different shades of
  gray. As supposed some shades of gray couldn’t be distinguished from
  the green by the cuttlefish, which didn’t adapt the body pattern.
  Experiment one was successful.
  
  2) Blue – Yellow. A checkerboard of blue and yellow matching in
  intensity was used for the second experiment. The skin color of the
  test species didn’t change either and therefore experiment two was
  also successful (reference).


These experiments concluded that it was indeed colourblind.

To confirm the effectiveness of the camouflage, HyperSpectral Imaging (HSI) was used to measure the colour match between the cuttlefish and its background. Using this technology it was perceived as to how a predator would view a camouflaged cuttlefish. It was found that


  Cuttlefish can produce color-coordinated camouflage on natural
  substrates despite lacking color vision, and that the color aspect of
  cuttlefish camouflage is highly effective against fish predators. Much
  of the contrast information (which allows a predator to "pick out" a
  cuttlefish from the background environment) resides in the brightness
  (luminance) rather than in the color (chromatic) aspect of the
  reflected light. What this means is that cuttlefish camouflage
  strategies take away a tool from predators in their ability to pick
  out their prey from the background and instead leave them with only
  brightness as a method for prey identification (reference 1 and reference 2).


And now we get to the main question as to how they do it. Cuttlefish are apparently able to detect the intensity of light reflected from objects in its surroundings. It is able to perceive even a 15% change in contrast. In an experiment, it was found that 


  The animals did not respond to the checkerboard pattern when placed on
  substrates whose color intensities were matched to the Sepia visual
  system, suggesting that these checkerboards appeared to their eyes as
  uniform backgrounds (reference).


In another bit of interesting research done on the ability to copy the patterns on checkerboards (reference), three inferences were drawn 


  The first find was that the range (relative to the size of the
  cuttlefish ‘white square’) for the animal to exhibit disruptive skin
  patterning had to be withing a certain  narrow range. Secondly, given
  the appropriate size of checker, cuttlefish regulated their disruptive
  skin patterns according to the contrast between white and black
  squares. Third, by manipulating the number of white squares on a board to just  4
  among 316 black squares (or 1.25 %) produced disruptive patterning,
  yet increasing the number of white squares to 20, 40 or 80 did not
  increase the frequency of appearance of the cuttlefish ‘white square’,
  but only its clarity of expression.


This study shows that the number of white objects in the background significantly influence cuttlefish skin patterns further putting stress on its ability to view the polarization of light (reference). 




Some cuttlefish camouflage examples