General conditions for thermal compensation in optical systems

Based on the paraxial imaging formula, the differential conditions of thermal compensation for optical systems with the object planes at random distance are derived in the cases of single lens, touched multilens system and separated multilens system. It is assumed that the object distance and the incident height of each lens do not change with temperature. The relationship between the normalized temperature variation of image distance and the optothermal expansion coefficient of each lens is established with the derived conditions, which is very useful in the design of mechanical and servo systems for an athermalized optical system. The conditions obtained for single lens and touched multilens system are coincided with the regular conditions of thermal compensation when the object plane is at infinity, i.e., the optothermal expansion coefficient of the optical system is equal to the housing expansion coefficient.