Combining Differential Images by Inverse Riesz Transformation

A method of forming a representative high frequency emphasized phase image from a phasor image, the method comprising:

• differentiating the phasor image to produce an intermediate image having two orthogonal components;
• constructing a (complex) image from the two orthogonal components of the intermediate image;
• and
• applying an inverse Riesz transform to the constructed image to form a representative high frequency emphasized phase image, wherein the representative high frequency emphasized image comprises a high pass filtered component and a discrepancy component.

A method of reducing noise in a pair differential images, the method comprising:

• combining the differential images into of a complex image having real and imaginary parts;
• inverse Riesz transforming the complex image to give an intermediate complex image;
• removing the imaginary part of the intermediate complex image;
• forward Riesz transforming the real part of the intermediate complex image to form a complex output image having real and imaginary parts;
• associating the real and imaginary parts of the output image with the real and imaginary differential image inputs.

A method of forming a representative image from a pair of differential input images, the method comprising:

• determining a plurality of spectral lobes from the differential input images;
• selecting from the plurality of determined lobes, two substantially orthogonal sidelobes, said selected sidelobes representing spatial differential phase information of the differential input images;
• blending an orientational distribution of spatial differential phase information of the selected sidelobes by maintaining a power spectrum of the differential input images to form a processed differential phase image;
• and
• forming a representative image emphasising high frequency detail information of the object from the processed differential phase image.

A computer readable storage medium having a program recorded thereon, the program being executable by a computer apparatus to form a representative image from a crossed grating fringe pattern interferogram of an object from an interferometer, the program comprising:

• code for determining a plurality of spectral lobes from the interferogram;
• code for selecting from the plurality of determined lobes, two substantially orthogonal sidelobes, said selected sidelobes representing spatial differential phase information of the interferogram;
• code for applying an inverse Riesz transform to the spatial differential phase information of the selected sidelobes to form a transformed differential phase image;
• and
• code for forming from the transformed differential phase image, a representative image emphasising high frequency detail information of the object.

A computer readable storage medium having a program recorded thereon, the program being executable by a computer apparatus to form a representative high frequency emphasized phase image from a phasor image, the method comprising:

• code for differentiating the phasor image to produce an intermediate image having two orthogonal components;
• code for constructing a (complex) image from the two orthogonal components of the intermediate image;
• and
• code for applying an inverse Riesz transform to the constructed image to form a representative high frequency emphasized phase image, wherein the representative high frequency emphasized image comprises a high pass filtered component and a discrepancy component.

A computer readable storage medium having a program recorded thereon, the program being executable by a computer apparatus to form a representative image from a pair of differential input images, the method comprising:

• code for determining a plurality of spectral lobes from the differential input images;
• code for selecting from the plurality of determined lobes, two substantially orthogonal sidelobes, said selected sidelobes representing spatial differential phase information of the differential input images;
• code for blending an orientational distribution of spatial differential phase information of the selected sidelobes by maintaining a power spectrum of the differential input images to form a processed differential phase image;
• and
• code for forming a representative image emphasising high frequency detail information of the object from the processed differential phase image.

A computer apparatus for forming a representative high frequency emphasized phase image from a phasor image, the apparatus comprising:

• means for differentiating the phasor image to produce an intermediate image having two orthogonal components;
• means for constructing a (complex) image from the two orthogonal components of the intermediate image;
• and
• means for applying an inverse Riesz transform to the constructed image to form a representative high frequency emphasized phase image, wherein the representative high frequency emphasized image comprises a high pass filtered component and a discrepancy component.

An x-ray interferometer system comprising:

• an x-ray device capturing a crossed grating fringe pattern interferogram of an object, and a computer apparatus forming a representative image from the captured crossed grating fringe pattern interferogram, the representative image being formed by:
• determining a plurality of spectral lobes from the interferogram;
• selecting from the plurality of determined lobes, two substantially orthogonal sidelobes, said selected sidelobes representing spatial differential phase information of the interferogram;
• applying an inverse Riesz transform to the spatial differential phase information of the selected sidelobes to form a transformed differential phase image;
• and
• forming from the transformed differential phase image, a representative image emphasising high frequency detail information of the object.