This article could also be called cell memebrane integrity factor.
Astaxanthin is a member of the carotenoid family. ref They are found in marine animals like shrimp and salmon, and also in microorganisms, such as algae and yeast, plus in red color plants. The marine animals eat algae to get astaxanthin. Functions include healthy skin, heart health, brain support, and help with joint pain. Taking an excess will turn the stools red. Supplement amounts are between 5-10 mcg. 
Astaxanthins act as a fat soluble antioxidant with anti-inflammatory actions. Check out this picture of a section of a cell membrane that reveals how astaxanthin protects the cell membranes fatty acids against lipid peroxidation.
You will see vitamin C, Beta carotene, and cholesterol are also present.
Cell membranes are made up of two roles of phospholipids that look like balloons on a string. Astaxanthins along with luteins are especially found in the membranes of the retina of the eyes with many benefits. But, only small amounts are needed and maybe not everyday.
Immune system and brain health are also areas where astaxanthin shines.
D. Salina algae, found in top tier multi-vitamin formulas as a source for beta carotene with later conversion into vitamin A when needed, is recommended since it contains the different forms of beta carotene, all-trans, 9-cis, and 13-cis, plus alpha carotene with a small amount of other natural mixed carotenoids. But any amount of astaxanthin would be quite small since D. Salina lacks the enzyme needed to build astaxanthin. Thus, either eating natural food sources is a must or taking a separate supplement. The natural green algae used for supplements is H. pluvialis. Plus Phaffia yeast might also be found. Krill oil contains some as well as chlorella zofiingiensis. Make sure natural sources are listed on labels because a synthetic source is also available.
Foods include shrimp, red yeast, microalgaes such as chlorella and spirulina, egg yolk (darker the better), and red fish like salmon and trout. Plants are poor sources if any. Taking astaxanthin with a fish oil increases absorption.