Claus Daniel, Rodenburg John Marius
Appl Opt. 2015 Mar 10;54(8):1936-44. doi: 10.1364/AO.54.001936.
The reconstruction of the smallest resolvable object detail in digital holography and coherent diffractive imaging when the detector is mounted close to the object of interest is restricted by the sensor's pixel size. Very high resolution information is intrinsically encoded in the data because the effective numerical aperture (NA) of the detector (its solid angular size as subtended at the object plane) is very high. The correct physical propagation model to use in the reconstruction process for this setup should be based on the Rayleigh-Sommerfeld diffraction integral, which is commonly implemented via a convolution operation. However, the convolution operation has the drawback that the pixel size of the propagation calculation is preserved between the object and the detector, and so the maximum resolution of the reconstruction is limited by the detector pixel size, not its effective NA. Here we show that this problem can be overcome via the introduction of a numerical spherical lens with adjustable magnification. This approach enables the reconstruction of object details smaller than the detector pixel size or of objects that extend beyond the size of the detector. It will have applications in all forms of near-field lensless microscopy.
当探测器安装在靠近感兴趣的物体时，数字全息术和相干衍射成像中最小可分辨物体细节的重建受到传感器像素大小的限制。由于探测器的有效数值孔径（NA）（其在物平面所张的立体角大小）非常高，所以非常高分辨率的信息本质上已编码在数据中。在此设置的重建过程中应使用的正确物理传播模型应基于瑞利 - 索末菲衍射积分，通常通过卷积运算来实现。然而，卷积运算的缺点是在物体和探测器之间传播计算的像素大小保持不变，因此重建的最大分辨率受探测器像素大小限制，而非其有效数值孔径。在此我们表明，通过引入具有可调放大倍率的数值球面透镜可以克服这个问题。这种方法能够重建小于探测器像素大小的物体细节或延伸超出探测器大小的物体。它将在所有形式的近场无透镜显微镜中得到应用。
