| Compared with the traditional optical imaging system,the extended depth of field(EDF)imaging system with odd-symmetric phase plate can give the larger depth of field,correct some defocus-related aberration and simplify the complexity of imaging system.Consequently,the EDF imaging system with odd-symmetric phase plate occupies the important research significance and practical potentials.In this paper,we focused on the characteristics and applications of EDF imaging system with odd-symmetric phase plate,aiming at investigating the new design of odd-symmetric phase plate,effects of the factors influencing the imaging system,intermediate image decoding algorithms and designs and applications of the EDF imaging system.First,a composite phase plate composed with any two cubic phase plates was proposed to tune the depth of field of imaging system.Ray aberration theory was adopted to visually analyse the tunable effect on ray structure around focal plane of the proposed phase plate.The stationary phase method and Fresnel integral method are employed respectively to derive the approximate expression of point spread function(PSF)and analytical expression of optical transfer function(OTF).Based on the expression derived,the cutoff frequency of imaging system was obtained,which was further used to carry out the theoretical range of the depth of field can be tuned with the composite phase plate.Numerical simulations show that the proposed composite phase plate do has the property to tune the depth of field of imaging system.Moreover,although all the analyses conducted above are on the basis of cubic phase plate,the composite phase plate can be composited with any two odd-symmetric phase plates.Second,a new odd-symmetric phase plate-inverse sinusoidal phase plate was presented.The revised Fisher information-based method was used to optimize the phase parameters of the proposed phase plate.Meanwhile,the optimal phase parameters of cubic,sinusoidal and tangent phase plate are also investigated by the same optimization procedure.The mean square error and Hilbert space angle metric between the focused and defocused modulation transfer function(MTF)indicate that the proposed phase plate yields better performance in acquiring defocus-invariant MTF over existing phase plate.The mean structural similarity(SSIM)metrics of decoding image of different phase plates were carried out and the results show that the final decoding image of proposed phase plate has less image artifacts.It is the first time that the influences of high-order terms in OSPP were considered and the result demonstrates that high-order term can increase the defocus tolerance for odd-symmetric phase plate.Third,effect factors such as wavelength,monochromatic aberration,detector sampling,noises and image artifacts in the imaging chain of EDF imaging system with odd-symmetric phase plate are analyzed and the analytical models were developed.The functional relationship between peak position of PSF and wavelength was established theoretically,displaying the necessity for correcting the axial chromatic aberration.It is also the first time that the analytical OTF of cubic phase plate with the presence of spherical aberration,coma,astigmatism,field curvature,distortion and defocus was derived and the corresponding results suggest that cubic phase plate can tolerate some aberration such as coma,astigmatism,filed curvature and spherical aberration.The spurious response ratio was used to analyze the effect of detector sampling and result shows that detector sampling does not affect the characteristics of EDF imaging system.From the analysis of spectral signal-to-noise ratio(SNR)of EDF imaging system,we conclude that noise and the value of MTF are mutual constraints.From the point of the phase transfer function,the phenomena of image artifacts in decoding image were explored theoretically and some methods to alleviate image artifacts were discussed and verified.Fourth,the sparse prior of natural image was introduced to the decoding algorithm for the first time to decode the intermediate coding image with low SNR.Decoding algorithms based on sparse representation were studied and experimentally verified.Experimental results illustrate that these algorithms can effectively improve the image quality and reduce the noise gain of final decoding image.On the basis of previous work,we developed a new decoding algorithm based on the convolutional sparse representation,which can enable the final decoding images to possess more details and high quality.Fifth,the idea of tunable EDF imaging system was proposed for the first time and has been realized by shifting the odd-symmetric phase plate from the pupil center without changing the extension ratio of depth of field.The analytical relationship between the shift value of cubic phase plate and defocus distance was established and experimentally verified by the designed EDF imaging system with cubic phase plate.Sixth,3D imaging system with EDF was studied and designed based on the method of alleviating image artifacts.Experimental results demonstrate that this imaging system can not only obtain the same extended depth of field as EDF imaging system does,but also can gain the signed defocus map.The proposed imaging system further enriches the range of applications of EDF imaging system with odd-symmetric phase plate. |
