Study On Reconstruction Algorithm Of Optical Coherence Tomography Based On Gradient Refractive Index Field Characteristics

With the continuous development of modern industry,gradient index materials have played an increasingly important role in various applications such as telecommunications,medicine,and biosensing.Accurately understanding the refractive index distribution of gradient index materials is not only important for evaluating their Performance in optics is important,but also very important for controlling product quality.As a non-contact measurement technology,optical coherence tomography has the advantages of high detection depth,no interference with the measured field,harmless and non-polluting,etc.It can perform three-dimensional quantitative measurements of the refractive index distribution of gradient refractive index media.Since the distribution characteristics of the gradient refractive index change continuously along a certain direction,the real phase difference and the refractive index distribution will have piecewise linear characteristics during the digital processing process.Most existing phase unwrapping algorithms and image reconstruction algorithms both Failures to take this feature into account leading to poor quality of phase unwrapping and image reconstruction.Therefore,how to make full use of the relevant features and design the corresponding phase unwrapping algorithm and image reconstruction algorithm to improve the accuracy and quality of optical coherence tomography in measuring gradient refractive index is an important research direction,which has important theoretical significance and application value.According to the distribution characteristics of gradient refractive index,this paper studies the phase unwrapping algorithm in the process of reconstructing gradient refractive index by optical coherence tomography and its image reconstruction algorithm under sparse projection angles.The main research contents are as follows:1.Aiming at the problem that the phase unwrapping algorithm of the intensity transfer equation can achieve effective global unwrapping,but there is a problem that the unwrapping error is not suppressed enough,which leads to the decline of the overall unwrapping effect,this paper proposes a phase unwrapping algorithm for the intensity transfer equation with weighted regularity constraints.Based on the noise distribution characteristics of the wrapped phase,and according to the distribution characteristics of the gradient refractive index field,the iterative algorithm and the establishment of a weighted regularity optimization model are used to correct the phase expansion results of the intensity transfer equation,to suppress the error propagation and reduce the difference between the unwrapped result and the true phase.This algorithm not only makes up for the insufficient error suppression of single-step phase unwrapping but also uses the prior information that the real phase has piecewise linear characteristics to establish a weighted second-order full variational regularization model,which further improves the accuracy of the phase unwrapping in the noise source region.Simulation experiments show that the method proposed in this paper has higher phase unwrapping quality and precision than the traditional intensity transfer equation phase unwrapping method,and the phase unwrapping result is closer to the real phase.2.In the sparse projection perspective,the common first-order TV regularization model assumes that the image gradient modes are sparse,and good image boundaries and flat regions can be maintained for segmented constant feature parts of the image,but step artifacts often appear in segmented linear parts of the image.To address this problem,this paper proposes an image reconstruction algorithm model combining firstorder and second-order full variational constraint minimization,which combines the good reconstruction characteristics of first-order TV regularization in the image segmentation constant feature region and image edge and the advantage of second-order TV regularization in suppressing the step effect in the image linear region according to the different characteristics of the optical coherent laminar technique to reconstruct the gradient refractive index field.Parametrically controlled first-order TV and secondorder TV regularization are used to reconstruct different regions of the image adaptively,and the model is solved using a non-parametric ASD-POCS iterative optimization algorithm.Through simulation experiments,it is verified that the proposed method is better than the first-order TV regularization and the second-order TV regularization in suppressing the staircase effect and maintaining the image boundary,respectively,and the image reconstruction results are closer to the real image.3.In order to verify the effectiveness of the proposed method in optical coherence chromatography gradient refractive index measurement experiments,the measurement experiments were simulated by Zemax software,and the measurement system was a laser phase-shifted polarization interferometric chromatography measurement system,and the sample to be measured was a multimode gradient refractive index fiber,Interference images are acquired according to the experimental principle,and phase expansion is performed after extracting the phase difference by the five-step phase shift method.The phase expansion results show that the improved method has better phase expansion quality and accuracy compared with the traditional intensity transfer equation phase expansion algorithm,and the root mean square error RMSE is reduced by 5%,44%,and 34% for the three cases of no noise and the addition of ±0.5 rad and±1 rad random noise,respectively.Subsequently,30 and 60 angular phase differences were collected uniformly in the range of 0° to 180° as projection data for refractive index reconstruction,respectively.The reconstruction results verify that the improved method can both suppress the step effect and maintain the image boundary,and has better refractive index reconstruction quality and accuracy compared with first-order TV regularization and second-order TV regularization,and the normalized mean square distance is reduced by 4% and 9% compared with first-order TV regularization and 9%and 10% compared with second-order TV regularization at 30 and 60 projection angles,respectively.Finally,the proposed method is used to reconstruct the two-dimensional refractive index distribution of the fiber fault plane in turn,and the three-dimensional refractive index distribution of the multimode fiber is reconstructed by superposition of the fault plane.