Multi-image focus retrieval technology for biological microscopy based on the transport of intensity equation

CHENG Hong; ZHANG Tianyi; KONG Meng; ZHANG Cheng; BIAN Jinchao

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Multi-image focus retrieval technology for biological microscopy based on the transport of intensity equation

Optical Information Technology | 更新时间：2026-01-05

- Multi-image focus retrieval technology for biological microscopy based on the transport of intensity equation
- OPTICAL TECHNIQUE Vol. 51, Issue 6, Pages: 641-648(2025)
- 作者机构：
  
  1.安徽大学电子信息工程学院，安徽合肥 230601
  2.合肥师范学院电子信息与集成电路学院，安徽合肥 230601
- 作者简介：
- 基金信息：
- DOI：
  CLC： O438.2
- Received：01 April 2025，
  
  Revised：2025-06-17，
  
  Published：20 November 2025
- 稿件说明：
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程鸿,张天一,孔勐等.基于强度传输方程的生物显微多图像聚焦恢复技术[J].光学技术,2025,51(06):641-648.

CHENG Hong,ZHANG Tianyi,KONG Meng,et al.Multi-image focus retrieval technology for biological microscopy based on the transport of intensity equation[J].OPTICAL TECHNIQUE,2025,51(06):641-648.
程鸿,张天一,孔勐等.基于强度传输方程的生物显微多图像聚焦恢复技术[J].光学技术,2025,51(06):641-648. DOI：

CHENG Hong,ZHANG Tianyi,KONG Meng,et al.Multi-image focus retrieval technology for biological microscopy based on the transport of intensity equation[J].OPTICAL TECHNIQUE,2025,51(06):641-648. DOI：

摘要

针对使用显微镜观察生物样本时，视野出现的样本个体对应的聚焦位置不同造成无法全部聚焦成像的问题，提出了一种基于强度传输方程的多图像聚焦恢复技术。通过设计的图像采集装置，两个相机分别拍摄一次获取样本聚焦和散焦强度图，结合强度传输方程求解出相位信息，再利用角谱传播算法恢复不同深度细胞的聚焦状态。技术无需复杂、高成本的硬件改装即可避免传统方法中因机械调节带来的误差，同时可以获得高精度相位信息。模拟的血红细胞实验表明，算法恢复后细胞的聚焦误差降低到恢复前误差值的18.18%。利用植物组织和昆虫组织的实验验证了该技术对于离散和连续生物组织的聚焦位置恢复都有较好的普适性。

Abstract

To address the issue of varying focal positions of individual sample objects in the field of view when observing biological samples under a microscope

which prevents full-focus imaging

a multi-image focus retrieval technique based on the Transport of Intensity Equation （TIE） is proposed. Using the designed image acquisition device

intensity maps of both focused and defocused states of the sample can be obtained without the need for mechanical movement.The phase information is then solved using the Transport of Intensity Equation

and the angular spectrum propagation algorithm is used to retrieve the focused states of cells at different depths. This technique avoids the errors introduced by mechanical adjustments in traditional methods without the need for complex or high-cost hardware modifications

while also providing high-precision phase information. Simulation experiments on red blood cells show that the focus error of the cells is reduced to 18.18% after retrieval. Experiments on plant tissue and insect tissue further validate the applicability of this technique for focus retrieval in both discrete and continuous biological tissues.

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references

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