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A dual-wavelength digital holographic microscopy with premagnification is proposed to obtain the object surface measurements over the large gradient. The quantitative phase images of specimens are captured in high precision by the processing of filtering and phase compensation. The phase images are acquired without phase unwrapping, which is necessary in traditional digital holographic microscopy; thereby the proposed system can greatly increase the speed of reconstruction. The results of numerical simulation and optical experiments demonstrated that the reconstructed speed increased by 37.9 times, and the relative error of measurement is 4% compared with the traditional holographic microscopy system. It means that the proposed system can directly acquire the higher quality quantitative phase distribution for specimens.

Digital holographic microscopy (DHM) is a powerful technology for the measurement of microscopic samples by recording and reconstructing the amplitude and phase of the wave. The dual-wavelength digital holographic microscopy uses two different wavelength lasers to simultaneously record the hologram and numerically reconstruct the phase information according to phase distribution under two wavelengths. As early as 1998, a new method for the extraction of quantitative phase imaging by using partially coherent illumination and an ordinary transmission microscope was proposed by A. Barty et al., which can recover a phase even in the presence of amplitude modulation [

If the optical path difference is less than the equivalent wavelength, the real phase distribution of object can be directly obtained without phase unwrapping by the dual-wavelength digital holographic interferometry. If the optical path difference is greater than the equivalent wavelength, the phase unwrapping process will be simplified by dual-wavelength digital holographic interferometry. The noise immunity and the scope of phase unwrapping algorithms will be improved and expanded, respectively [

A system of dual-wavelength DHM with premagnification, which can directly and accurately obtain quantitative phase images, is presented. The principle of surface topography measurement and phase unwrapping method based on dual wavelength digital holography is introduced. The effectiveness of the system is verified by computer simulations and optical experiments using the 1951 USAF target and the standard groove object. Compared with the traditional single wavelength DHM, the system can not only obtain the phase information without phase unwrapping, but also get the low noise and high precision quantitative phase images.

In dual-wavelength digital holographic microscopy, two laser beams in different wavelengths from separated laser sources are coupled into one beam, and the optical assemblies are shown in Figure

The schematic diagram of dual-wavelength digital holographic microscopy. SF, spatial filter; M, mirrors; BS, beam splitters; S, sample; MO, microscope objective; CCD, charge-coupled devices; PC, personal computer.

The dual-wavelength composite digital hologram will be acquired on the CCD, and the interference pattern can be expressed as

where

The interferometric phase can be extracted by the spatial filtering method and shifted to the center position to perform the Fourier transform. The complex amplitude distribution of the reproducing light field can be obtained as follows:

The intensity and the wavefront phase distribution of optical field can be calculated according to the following expressions:

In order to overcome the issue of phase ambiguity produced by single wavelength approach, a synthetic beat-wave-length is used and expressed as follows:

where

If the optical path difference is less than the equivalent wavelength, the real phase of specimens can be directly obtained without unwrapping. Otherwise, the phase distribution is wrapped between

In summary, the dual-wavelength digital holographic microscopy to measure the large gradient of specimens can solve the problem of phase unwrapping with single-wavelength digital holographic microscopy. As the range of measurement increases, the noise of the phase distribution in the single-wavelength digital holographic microscope also increases. Therefore, the reasonable choice of wavelength and the method of noise reduction are key points in the dual-wavelength holographic microscopy.

The experiments were conducted in a DHM developed by our team. The schematic diagram and the setup are shown in Figure

(a) The schematic diagram of the dual-wavelength DHM system. SF, spatial filter; BS, beam splitters; M, mirrors; ND, neutral density; DS, displacement stage; S, sample; MO, microscope objective; ATT, adjustable tilting stage; BO, beam obstacle. (b) Real picture of DHM.

In order to illustrate that the phase image of sample whose optical path difference is less than the equivalent wavelength can be obtained directly and quickly by dual-wavelength DHM; a numerical simulation experiment is carried out. The computer-generated cone is a phase object with a maximum phase height of

Simulation results for slope: (a) phase distribution for

To demonstrate the advantages and compare the unwrapping speed of the dual-wavelength DHM and traditional single-wavelength DHM, a

3D view of dual-wavelength phase distribution.

The height distributions of cone by dual-wavelength DHM and quality-guided phase unwrapping method are compared. And the results are shown in Table

Comparison of two methods.

Method | Maximum phase ( | Time ( |
---|---|---|

Quality-guided phase unwrapping | 2.5749 | 716.61 |

Dual-wavelength DHM (in the system) | 2.5971 | 18.93 |

Based on the dual-wavelength phase imaging system, the surface of an USAF 1951 target was measured. At the same time, the target was also measured by the scanning three-dimensional profiler (NanoMap 500LS, AEP Technology Inc., USA) and the results showed that the height was about

Experimental results with single wavelength measurement. (a) Phase image for

Experimental results for equivalent wavelength. (a) Phase image for equivalent wavelength, (b) 3D view of dual-wavelength height distribution.

In the reconstruction process, filtering and secondary phase distortion compensation processing are performed [

The comparison of the height distribution curve along the middle symmetrical line of phase with different wavelength (in Figures

The comparison of the height distributions.

Wavelength( nm) | Absolute height | Relative error (compared with the scanned value) | Variance |
---|---|---|---|

632.8 | 61.8 | 14.4% | 1.925× |

532 | 99.3 | 83.8% | 3.188× |

equivalent wavelength | 47.5 | 13.8% | 1.504× |

The comparison of the height distribution values along the middle symmetrical line of sample in pane Figures

Table

The transparent groove standard plate, which is artificially designed, was used as an experimental sample to measure its three-dimensional appearance. The width of groove is

Experimental results with single wavelength measurement. (a) Phase image for

Results for equivalent wavelength. (a) Phase distribution, (b) three-dimensional height distribution.

The height distribution of the middle symmetrical line of the groove (Figure

Height distribution values along the middle symmetrical line of groove in Figure

In order to solve the quantitative phase imaging problem of traditional digital holographic microscopy system for the large gradient of object surface, a dual-wavelength preamplification digital holographic microscopy optical system is proposed. The numerical simulation and experiments are carried out and the effectiveness of the system is verified. The experimental results of the sample phase imaging of the traditional DHM and dual-wavelength preamplification DHM system are compared. The results show that the experimental system can effectively overcome the limitations of the single-wavelength method in the imaging of complex surface objects, increase the observation speed, and simplify the reconstruction process, which further validates the effectiveness of the experimental system for quantitative phase imaging.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work has been supported by the National Natural Science Foundation of China (Nos. 11272368 and 51875068), the International Cooperation Special Project in Science and Technology of China (No. 2015DFR70480), the Chongqing Municipal Education Commission’s science and technology research project (KJ1600929), and the Graduate Innovation Foundation of Chongqing University of Technology (No. ycx2018216).