Sarkar Saumya J, Ebrahim-Zadeh M, Samanta G K
Physical Research Laboratory, Ahmedabad, Gujarat, 380009, India.
Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat, 382424, India.
Sci Rep. 2024 Dec 28;14(1):30872. doi: 10.1038/s41598-024-81722-2.
Talbot length, the distance between two consecutive self-image planes along the propagation axis for a periodic diffraction object (grating) illuminated by a plane wave, depends on the period of the object and the wavelength of illumination. This property makes the Talbot effect a straightforward technique for measuring the period of a periodic object (grating) by accurately determining the Talbot length for a given illumination wavelength. However, since the Talbot length scale is proportional to the square of the grating period, traditional Talbot techniques face challenges when dealing with smaller grating periods and minor changes in the grating period. Recently, we demonstrated a Fourier transform technique-based Talbot imaging method that allows for controlled Talbot lengths of a periodic object with a constant period and illumination wavelength. Using this method, we successfully measured periods as small as a few micrometers and detected sub-micrometer changes in the periodic object. Furthermore, by measuring the Talbot length of gratings with varying periods imaged through the combination of a thick lens of short focal length and a thin lens of long focal length and large aperture, we determined the effective focal length of the thick lens in close agreement with the theoretical effective focal length of a thick lens in the presence of spherical aberration. These findings establish the Talbot effect as an effective and simple technique for various sensing applications in optics and photonics through the measurement of any physical parameter influencing the Talbot length of a periodic object.
塔尔博特长度是指平面波照射周期性衍射物体（光栅）时，沿传播轴两个连续自成像平面之间的距离，它取决于物体的周期和照明波长。这一特性使得塔尔博特效应成为一种直接的技术，通过精确确定给定照明波长下的塔尔博特长度来测量周期性物体（光栅）的周期。然而，由于塔尔博特长度尺度与光栅周期的平方成正比，传统的塔尔博特技术在处理较小的光栅周期和光栅周期的微小变化时面临挑战。最近，我们展示了一种基于傅里叶变换技术的塔尔博特成像方法，该方法能够在周期和照明波长恒定的情况下，对周期性物体的塔尔博特长度进行控制。使用这种方法，我们成功测量了小至几微米的周期，并检测到周期性物体中小于微米级的变化。此外，通过测量通过短焦距厚透镜和长焦距大孔径薄透镜组合成像的不同周期光栅的塔尔博特长度，我们确定了厚透镜的有效焦距，与存在球差时厚透镜的理论有效焦距高度吻合。这些发现表明，通过测量影响周期性物体塔尔博特长度的任何物理参数，塔尔博特效应是一种在光学和光子学中用于各种传感应用的有效且简单的技术。
