CAJ | 학술논문

在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.
재유격납상공간중,통과장일계광학계통적전수구진분해위좌표선전、비례축방화조추구진적조합,득도료일계광학계통재공역적분수부리협표시.결과표명:임의일계광학계통균가표시위경과비례축방화이차상위조제적분수부리협변환.통과장수입수출광장재상공간중작π/2각선전,득도료일계광학계통재빈역적전수구진화연사적분공식,진이득도료일계광학계통재빈역적분수부리협표시.비교공역화빈역일계광학계통적상공간변환구진,설명2개계통본질상속동일변환재불동기좌표하적표시,병추도출료광학계통재공역화빈역구유상동분수부리협변환적조건.
The fractional Fourier express of the first-order optical system was derived by decomposing the transfer matrices of firstorder optical system into coordinate rotation matrix, scale matrix and chirp matrix in Wigner phase space. The results show that an arbitrary first-order optical system can be expressed as the scaled and chirp modulation fractional Fourier transform. The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field π/2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained. By comparing the transfer matrices of two first-order optical systems in space and frequency domains respectively, it is found that the two first-order optical systems in different domain can be expressed as two different expressions of one and the same transfer based on different coordinates. At last the condition is derived for an optical system to implement the fractional Fourier transform in space and frequency domains with the same order.