The light of thy countenance— This expression here seems to signify the special, the majestic presence of God, visibly presiding over the army of the Israelites, by a light shining cloud going before them and conducting them; so that the words here will be best rendered by the light of thy presence, and not by the light of thy countenance; which is the same with God's favour, the mention whereof follows in the next words, as the ground or reason of this his shining presence, and not as the thing itself.
Related Commentaries of Psalms 44:3
Psalms 44:3
3 For they got not the land in possession by their own sword, neither did their own arm save them: but thy right hand, and thine arm, and the light of thy countenance, because thou hadst a favour unto them.