A new method of the representation of a scalar light field is proposed in this pa-per.It is also shown that this method can be adopted for representing the scalarlight field over a very extensive range.In comparison with the previous methodsthe advantages of the present method are as follows:It may be more con-veniently used in an extensive range.It can be surely concluded that in generalcases the matrix characterising the action of the optical system can be truncatedto finite order within any given errors.It can display explicitly the symmetries andrestrictions on space range of the light field distribution and may be also usedto represent the three dimensional distributions of the field in the free space.In this representation

the light field distribution in a plane orthogonal to thelight propagation axis expressed by an element in the sequence space 11

and theoptical system therefore may be represented by an action matrix.In the scope oflinear optics

this matrix is independent of the incident and the diffraction field.In this paper the relations between the action matrix of the resultant optical sy-stem and the action matrices of constituent systems are also given.