Non-linear solution for 2D phase shifting

A method of reconstructing a representative detailed phase image from a set of fringe pattern interferogram images of an object captured by an x-ray interferometer having a crossed diffraction grating, said method comprising:

• providing a set of captured images;
• providing a reconstruction technique capable of reconstructing the image from no more than eight images by relating cross components associated with the fringe pattern to the principle components associated with the fringe pattern;
• and
• reconstructing the representative detailed phase image from the provided set of captured images using the provided reconstruction technique.

A computer readable storage medium having a program recorded thereon, the program being executable by a computer to reconstruct a representative detailed phase image from a set of fringe pattern interferogram images of an object captured by an x-ray interferometer having a crossed diffraction grating, said program comprising:

• code for providing a set of captured images;
• code for providing a reconstruction technique capable of reconstructing the image from no more than eight images by relating cross components associated with the fringe pattern to the principle components associated with the fringe pattern;
• and
• code for reconstructing the representative detailed phase image from the provided set of captured images using the provided reconstruction technique.

Apparatus comprising:

• an X-ray interferometer system having a crossed diffraction grating;
• a computer system coupled to the interferometer system and configured with the interferometer system to:
• capture a set of fringe pattern interferogram images from the interferometer system, said set comprising no more than eight captured fringe pattern interferogram images;
• determine an estimate of an absorption parameter, two-dimensional amplitude modulation parameters, and two-dimensional phase modulation parameters from a closed-form solution using the received set of captured fringe pattern interferogram images;
• reconstruct the representative detailed phase image using the parameter estimates;
• and
• display the phase image upon a display device.

Apparatus comprising:

• an X-ray interferometer system having a crossed diffraction grating;
• a computer system coupled to the interferometer system and configured with the interferometer system to:
• provide a set of captured images including fringe patterns;
• provide a reconstruction technique capable of reconstructing the image from no more than eight images by relating cross components associated with the fringe pattern to the principle components associated with the fringe pattern;
• reconstruct the representative detailed phase image from the provided set of captured images using the provided reconstruction technique;
• and
• display the phase image upon a display device.