Bipolar projectivity of gaussian points in optical systems with curvilinear axis

Specific off-axis geometrical points of optical systems with curvilinear optic axis and a new fundamental projective property of conjugate gaussian points are found. This property is called by author a bipolar projective correspondence (BPC); specific off-axis points are called optical poles. Last ones provide the BPC property of gaussian points. Their existence is proved for any optical systems with curvilinear optic axis in case if the optic power of the system is not equal to zero and the deflection angle is not equal πn, where n = 0, 1,... It's proved that optical poles are placed on the specific straight lines, called foctrices. These specific lines pass through optical foci being parallel to the opposite asymptotic arms of the optic system. Positions of optical poles are conjugated accordingly to well-known Newton's optic equation.