对数字无透镜傅里叶变换全息图直接采用逆傅里叶变换进行物场的数值重建时,需要满足两个条件：第一,全息图的记录过程必须满足傍轴近似条件,否则再现过程中会产生非傍轴像差; 第二,记录全息图时物平面与参考点光源到全息图记录平面的距离必须相等,否则再现过程中会产生离焦像差。理论分析了非傍轴及离焦记录条件下数字无透镜傅里叶变换全息图的灰度分布特点,并提出了相应的非傍轴及离焦像差的数值校正方法。根据实际的非傍轴或离焦记录情况,分别给所记录的数字全息图灰度分布矩阵乘以适当的非傍轴或离焦校正因子,以消除灰度矩阵中非傍轴或离焦因素的影响,然后再对校正后的全息图灰度矩阵做逆傅里叶变换处理,即可得到准确的数字再现像。实验结果表明,该数值重建方法能够有效地消除无透镜傅里叶变换全息术中数字再现像的非傍轴像差及离焦像差,提高再现像的质量。

In digital lensless Fourier transform holography, performing inverse Fourier transform directly to the digital hologram for the numerical reconstruction of the object field requires two conditions. Firstly, the paraxial approximation condition must be satisfied in the recording process of the hologram, otherwise a nonparaxial aberration will be produced in the reconstruction process. Secondly, the distances from the object plane and the reference point source to the recording plane of the hologram must be equal, or else a misfocus aberration will be produced in the reconstruction process. The grayscale distribution of the digital lensless Fourier transform holograms recorded under the condition of nonparaxiality or misfocus is analyzed in theory, and corresponding numerical correction methods for nonparaxial or misfocus aberration are introduced, respectively. According to the actual recording conditions, if using proper correction factors for nonparaxiality or misfocus to multiply the grayscale distribution matrix of the recorded digital hologram, the influence of the nonparaxialty or misfocus can be removed. Accurate digital reconstructed image will be obtained by performing inverse Fourier transform directly to the corrected hologram grayscale matrix. The experimental results show that the introduced numerical reconstruction methods can well correct the nonparaxial or misfocus aberration and thus improve the quality of the digital reconstructed image in digital lensless Fourier transform holography.