Digital Holographic Focusing Imaging Based on Butterworth Feature Function
Objective As we all know,in an ideal optical system,the object and image distances should satisfy the Gaussian formula in order to achieve clear imaging in the optical path.In digital holographic microscopy,clear imaging of the object's light field is required for phase reconstruction.As a result,how to accurately establish the location relationship between objects and images during image capture has become a focus of current research.As the degree of defocusing grows,the image's edge dispersion and brightness both grow,which can result in considerable disparities between defocused and focused photos.The focusing function determination is significantly hampered by holographic interference fringes,which are a component of the image information.Of these,the entire region shows high-frequency noise in both speckle and fringes,which significantly lowers the signal-to-noise ratio of the reconstructed image.Furthermore,it is challenging to identify the defocused image because conventional focusing mechanisms are typically noise-sensitive.Therefore,the key to tackling this challenge is identifying an appropriate focused picture evaluation technique.Methods To address the impact of noise errors introduced by holographic interference fringes during the experimental procedure on determining the ideal focal point,this research offers a digital holographic microscopic focusing imaging approach.This technique creates an off-axis digital holographic microscopic focusing imaging experimental system using transmission technology,based on the Mach-Zehnder interference system.The object optical path is scanned on-axis using a high-precision piezoelectric nano displacement stage to produce three sets of hologram sequences:digital holographic microscopic images,microscopic imaging image sequence,and simulated defocused sequence images.The impact of different speckle noise and interference fringes on the experimental results is ascertained by means of comparative observation.To address this issue,we propose a digital holographic focusing imaging algorithm based on the Butterworth feature function,which is divided into two steps.Firstly,the interference fringes of the hologram are suppressed in the frequency domain to obtain the hologram after inverse Fourier transform,and the eight-neighborhood gradient operator is used to obtain the maximum edge value.Then,different gradient operators are used to perform gradient calculations on the hologram and complete the focusing evaluation.Results and Discussions Using the Butterworth low-pass filter described in this paper,the following conclusion can be reached from the holographic calculation results.The results after suppressing the interference fringes are shown in Fig.6,and the resolution plate morphology details are visible in the image,but with little oblique interference fringes in place of the more noticeable wide fringes.Because the wideband signal generated from the image's Fourier transform is more prominent than the narrow band signal,gradient calculation is utilized to determine the total edge details in the image.When a large area of oblique fringes is suppressed,continuing to suppress small fine fringes will affect the gradient judgment of phase details.Therefore,coarse fringe suppression is only performed once for holograms.Various evaluation indicators are calculated for the results after calculation using five gradient operators,as shown in Table 1.In the same noise environment,the focus evaluation result obtained by the algorithm has a higher articulation ratio R.The sensitivity S of the hologram processed using the algorithm is significantly higher than the calculated result of the original hologram.In the presence of noise,the algorithm proposed can still maintain stability in flat areas,indicating its strong anti-noise performance.From the perspective of algorithm running time t,the algorithm has significantly improved computational efficiency.The R value of the focusing curve obtained by using the algorithm is increased to 13.34 times the original value,the S value is increased to 66.35 times the original value,the flat area volatility V value is decreased by 51.47％,and the t value is shortened by 54.78％.From the above analysis results,it can be seen that the algorithm proposed in this paper has certain advantages in various aspects.From Table 2,it can be seen that the actual measurement result of the focusing position 23 obtained by the algorithm is:the height is 0.3261 μm,which shows a relative error,in comparison with the white light measurement result of 0.3130 μm,of 4.19％;the line width is 6.810 μm,which shows a relative error,in comparison with the white light measurement result of 6.796 μm,of 0.206％.The focusing results obtained by the algorithm in this paper are accurate.Conclusions Through theoretical analysis and experimental verification,the focusing evaluation of the proposed holographic algorithm is completed.The experimental results highlight the advantages of the filtering model in digital holographic microscopic focusing imaging characteristics.By analyzing the calculation results of different gradient operators,it is proved that the algorithm in this paper ultimately leads to a more accurate focus position.From the perspective of reconstructed phase characteristics,the edge of the resolution plate is sharper,the focusing morphology is more prominent,and the stability of traditional operators is improved under the same noise environment.The results of quantitative analysis of the algorithm using different evaluation indicators show that,the focusing curve obtained by the algorithm in this paper has steeper peaks,uniform focus results,intense peak response,and reduced fluctuation in the flat area.The proposed algorithm can meet the requirements of digital holographic microscopy focusing imaging.
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