Ptychography imaging systems and methods with convex relaxation

Abstract

Certain aspects pertain to ptychographic imaging systems and methods with convex relaxation. In some aspects, a ptychographic imaging system with convex relaxation comprises one or more electromagnetic radiation sources, a digital radiation intensity detector, and a processor in communication with the digital radiation detector. The electromagnetic radiation provides coherent radiation to a specimen while the digital radiation intensity detector receives light transferred from the sample by diffractive optics and captures intensity distributions for a sequence of low resolution images having diversity. The processor generates a convex problem based on the sequence of low resolution images and optimizes the convex problem to reconstruct a high-resolution image of the specimen. In certain aspects, the convex problem is relaxed into a low-rank formulation.

What is claimed is: 
     
         1 . A ptychographic imaging system with convex relaxation, the system comprising:
 one or more electromagnetic radiation sources configured to provide coherent radiation to a specimen;   a digital radiation intensity detector configured to receive light transferred from the sample by diffractive optics and to capture intensity distributions for a sequence of low resolution images of the specimen; and   a processor in communication with the digital radiation detector to receive the intensity distributions the sequence of low resolution images, the processor configured to:
 generate a convex problem based on the sequence of low resolution images; and 
 optimize the convex problem to reconstruct a high-resolution image of the specimen. 
   
     
     
         2 . The ptychographic imaging system with convex relaxation of  claim 1 ,
 wherein the one or more electromagnetic radiation sources are configured to provide coherent radiation to a specimen from a plurality of incidence angles at a sequence of sample times; and   wherein the sequence of low resolution images is associated with the plurality of incidence angles.   
     
     
         3 . The ptychographic imaging system with convex relaxation of  claim 1 ,
 wherein the diffractive optics comprises a spatial light modulator configured to provide a pattern at a plurality of locations at a Fourier plane of the specimen; and   wherein the sequence of low resolution images is associated with the plurality of locations.   
     
     
         4 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein the processor generates the convex problem by:
 stacking image data from the low-resolution images into a combined image matrix;   constructing measurement matrices; and   generating the convex problem using convex relaxation.   
     
     
         5 . The ptychographic imaging system with convex relaxation of  claim 1 , where the convex problem comprises a minimization function and solution restraints. 
     
     
         6 . The ptychographic imaging system with convex relaxation of  claim 5 , wherein the minimization function has no local minima. 
     
     
         7 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein the diffractive optics comprises a low NA objective lens. 
     
     
         8 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein the processor optimizes the convex problem by:
 relaxing the convex problem into a low-rank formulation; and   reconstructing the high-resolution imaging of the specimen using a low-rank ptychography process.   
     
     
         9 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein if the convex problem is large scale, then the processor optimizes the convex problem by:
 relaxing the convex problem into a low-rank formulation; and   reconstructing the high-resolution imaging of the specimen using a low-rank ptychography process.   
     
     
         10 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein the convex problem is large scale if the number of low resolution images is above 200 or each low resolution image has a resolution of more than 50×50 pixels. 
     
     
         11 . The ptychographic imaging system with convex relaxation of  claim 1 , wherein the one or more electromagnetic radiation sources are in the form of an LED array. 
     
     
         12 . A ptychographic imaging method with convex relaxation, the method comprising:
 collecting a sequence of low resolution images of a specimen;   generating a convex problem based on the sequence of low resolution images; and   optimizing the convex problem to reconstruct a high-resolution image of the specimen.   
     
     
         13 . A ptychographic imaging method with convex relaxation of  claim 10 , wherein collecting a sequence of low resolution images of a specimen comprises:
 providing coherent radiation to the specimen from a plurality of incidence angles at a sequence of sample times;   transferring light from the specimen through diffractive optics to a digital radiation intensity detector; and   sampling a sequence of low resolution images associated with the plurality of incidence angles.   
     
     
         14 . A ptychographic imaging method with convex relaxation of  claim 10 , wherein collecting a sequence of low resolution images of a specimen comprises:
 illuminating the specimen;   providing a pattern at a plurality of locations on a display of a spatial light modulator located at the Fourier plane of the specimen;   transferring light from the specimen using diffractive optics with the spatial light modulator to a digital radiation intensity detector; and   sampling a sequence of low resolution images associated with the plurality of locations of the pattern.   
     
     
         15 . The ptychographic imaging method with convex relaxation of  claim 10 , wherein generating the convex problem comprises:
 stacking image data from the low-resolution images into a combined image matrix;   constructing measurement matrices; and   generating the convex problem using convex relaxation.   
     
     
         16 . The ptychographic imaging method with convex relaxation of  claim 10 , where the convex problem comprises a minimization function and solution restraints, wherein the minimization function has no local minima. 
     
     
         17 . The ptychographic imaging method with convex relaxation of  claim 10 , wherein optimizing the convex problem comprises:
 relaxing the convex problem into a low-rank formulation; and   reconstructing the high-resolution imaging of the specimen using a low-rank ptychography process.   
     
     
         18 . The ptychographic imaging method with convex relaxation of  claim 10 , further comprising:
 if the convex problem is large scale, optimizing the convex problem by relaxing the convex problem into a low-rank formulation and reconstructing the high-resolution imaging of the specimen using a low-rank ptychography process.   
     
     
         19 . The ptychographic imaging method with convex relaxation of  claim 15 , wherein the convex problem is large scale if the number of low resolution images is above 200 or each low resolution image has a resolution of more than 50×50 pixels.