关键词: 标量衍射理论, 菲涅耳衍射模型, 4f 系统

Abstract: In the speckle interference image subtraction experiment，we found that the hologram prepared by the standard 4f system could obtain interference fringes，but the 4f single lens system couldn′t achieve the expected results. In this paper， the light field distributions of the object and image planes of the two systems were derived using the Fresnel diffraction model of scalar diffraction theory，which demonstrated the light field distributions of the image planes of the two systems were different. The results showed that the light field on the image plane of both systems contained factors of -exp( j4kf )U₀（ -x，-y）.However，the 4f single lens system had a quadratic phase factor exp[ jk ( x² + y ² ) /( 2f ) ] that varies with different coordinate positions （x，y） of the image plane than the standard 4f system. For direct eye observation and detector detection，the received light intensity was not affected by the phase factor，so there was no difference between the two kinds of imaging， and they were equal inverted real images. However， in a more precise interferometric optical system，the influence of the quadratic phase factor of the image plane light field of the 4f single lens imaging system can′t be ignored.

Key words: scalar diffraction theory, Fresnel diffraction model, 4f system