To what degree is emotional state visible in a person's eyes? Is it true that a person's emotional state (such as arousal, fear, etc) can be determined by looking solely at the persons eyes?

Here I am assuming that this may be the case only in limited circumstances (specific scenarios or specific basic emotions such as fear) but if emotional state can be determined from the eyes, is there any research on the extent to which this is possible?
This question has mostly been asked in reverse in the research literature--not whether the eyes can show emotion (which is often called affect by psych researchers), but whether humans can accurately judge affective state based only on the eyes.  That ability varies somewhat depending on demographic parameters (age, gender, and socioeconomic class, as well as autism spectrum disorder status).

The "Reading the Mind in the Eyes" test, developed by Simon Baron-Cohen, tests exactly that, using stimuli like these.



Participants are asked to choose the most applicable emotion word for a picture restricted to the eye area.  Neurotypical controls are more successful at this task than autism spectrum participants; since most of the research has focused on showing differences between populations on this task and not on quantifying normal performance, the reported data on controls alone is difficult to interpret by itself. The test has fairly good test-retest reliability, but it has been criticized for gender bias since there are considerably more male eyes in the stimuli set than female eyes.  This is particularly problematic in light of Baron-Cohen's "extreme male brain" theory of autism.