| Metalens utilizes an array of sub-wavelength unit cells to engineer the wavefront of incident EM waves.Compared to traditional bulky lens,metalens outperforms in terms of volume,weight,planar integrity,etc.However,its imaging quality still falls behind that of traditional lens.Digital image restoration techniques have been developed since the 1960 s.Its main idea is to use prior knowledge such as point spread function to solve the restored image from the degraded image,corresponding to the inversion of the convolution process.Up to now,the application of image restoration techniques in metalens imaging is still lacking,and it is mainly aimed at the visible spectrum while there is a lack of research in the long-wavelength infrared spectrum.Combining image restoration techniques with long-wavelength infrared metalens can improve the imaging quality of metalens in this spectrum and provide help for the further application of metalens.The research content of this thesis mainly includes:(1)The imaging model formula as the basis of the restoration method is described in detail.The linear algebraic form corresponding to the imaging model formula is deduced and programmed.The degradation and restoration of the imaging process is simulated in the spatial domain.And the problems existing in the image restoration by the direct inverse method in the spatial domain are illustrated.(2)Through the extension and element filling of the point spread function induced matrix in the linear algebraic form,the block circulant matrix is constructed by programming.The spatial domain computation of image restoration is transformed to the frequency domain by performing decomposition on the block circulant matrix.Derivation and calculation verify the equivalence of frequency domain conversion using discrete Fourier transform and the conversion method mentioned above.Furthermore,problems such as circular shift of point spread function,circular convolution’s effect on image boundary,ringing effect,etc.are illustrated.(3)In the frequency domain,four restoration methods are implemented by programming.They are inverse truncated filter in the frequency domain,minimum square error filter,constrained least squares filter,and iterative method based on Bayes theorem.After verification by simulation,four methods are applied to the images obtained by experiments.To a certain extent,some details that are difficult to distinguish in the degraded images are restored.(4)The point spread function of the metalens under the experimental setting is calculated by programming using the far-field scalar diffraction formula,which is used in the four restoration methods.(5)The restoration effects using different methods are compared and analyzed perceptually and quantitatively.And the applicability of restoration methods to different types of images is tested. |
