Correction of aberrations in in-line electron holography
Embodiments herein relate to a process for electron holography image aberration reduction. A system can comprise a memory that stores, and a processor that executes, computer executable components. The computer executable components can comprise a propagating component that reduces hologram aberration of an electron hologram (EH) image by modifying of a pair of sequenced parameters of an array upon which the EH image is constructed, resulting in a modified array, and a generating component that generates a propagated EH image using a propagator comprising the modified array.
1 . A system, comprising:
a memory that stores computer executable components; and
a processor that executes the computer executable components stored in the memory, wherein the computer executable components comprise:
a propagating component that reduces hologram aberration of an electron hologram (EH) image by modifying of a pair of sequenced parameters of an array upon which the EH image is constructed, resulting in a modified array; and
a generating component that generates a propagated EH image using a propagator comprising the modified array,
wherein the propagator is a function of an exponential of a distance between an object and an emitter having been employed to generate the EH image of the object, a physical size of a detector having been employed to receive electrons from the emitter, and a wavelength of the electrons.
2 . The system of claim 1 , wherein the pair of sequenced parameters comprise sequences of consecutive integers having ranges from −N/2 to N/2, which ranges correspond to a sensor having −N/2 by N/2 pixels, the sensor having been employed to generate the EH image.
3 . The system of claim 1 , wherein the computer executable components further comprise:
an aberration component that determines an astigmatism angle and an astigmatism magnitude associated with the EH image,
wherein the propagating component modifies the pair of sequenced parameters using the astigmatism angle and the astigmatism magnitude.
4 . The system of claim 1 , wherein the propagator further is a function of a summation of squares of a modified pair of sequenced parameters resulting from the modifying.
5 . The system of claim 1 , wherein the computer executable components further comprise:
a reconstruction component that generates a reconstructed EH image, based on the propagated EH image, using a fast Fourier transform (FFT) function of a product of the propagator and of an inverse fast Fourier transform (IFFT) function of a normalization of the EH image.
6 . The system of claim 1 , wherein the computer executable components further comprise:
an aberration component that determines an astigmatism angle and an astigmatism magnitude associated with the EH image,
wherein the propagator further is a function of a summation of squares, of an initial pair of sequenced parameters, with the summation of the squares multiplied by an aberration correction function comprising an astigmatism adjustment using the astigmatism angle and the astigmatism magnitude.
7 . The system of claim 1 , wherein the computer executable components further comprise:
an aberration component that determines an astigmatism angle and an astigmatism magnitude associated with the EH image,
wherein the propagator further is a function of a summation of squares, of an initial pair of sequenced parameters, with the summation of the squares summed with an aberration correction function comprising an astigmatism adjustment using the astigmatism angle and the astigmatism magnitude.
8 . The system of claim 1 , further comprising:
a forward propagation component that directs execution of a series of forward propagations in alternation with backward propagations,
wherein use of the propagator by the propagating component to reduce the hologram aberration of the EH image provides for a backward propagation of the backward propagations, and
wherein a forward propagation of the series of forward propagations also comprises use of the modified array.
9 . The system of claim 1 , wherein the computer executable components further comprise:
a notifying component that generates a notification corresponding to a determination that the propagated EH image comprises a reduced level of aberrations as compared to an original level of aberrations of the EH image.
10 . A computer-implemented method, comprising:
reducing, by a system operatively coupled to a processor, hologram aberration at an electron hologram (EH) image by modifying, by the system, a pair of sequenced parameters of an array upon which the EH image is constructed, resulting in a modified array; and
generating, by the system, a propagated EH image using a propagator comprising the modified array,
wherein the propagator is a function of an exponential of a distance between an object and an emitter having been employed to generate the EH image of the object, a physical size of a detector having been employed to receive electrons from the emitter, and a wavelength of the electrons.
11 . The computer-implemented method of claim 10 , wherein the pair of sequenced parameters comprise sequences of consecutive integers having ranges from −N/2 to N/2, which ranges correspond to a sensor having −N/2 by N/2 pixels, the sensor having been employed to generate the EH image.
12 . The computer-implemented method of claim 10 , further comprising:
determining, by the system, an astigmatism angle and an astigmatism magnitude associated with the EH image; and
modifying, by the system, the pair of sequenced parameters using the astigmatism angle and the astigmatism magnitude.
13 . The computer-implemented method of claim 10 , wherein the propagator further is a function of a summation of squares of a modified pair of sequenced parameters resulting from the modifying.
14 . The computer-implemented method of claim 10 , further comprising:
determining, by the system, an astigmatism angle and an astigmatism magnitude associated with the EH image,
wherein the propagator further is a function of a summation of squares, of an initial pair of sequenced parameters, with the summation of the squares multiplied by an aberration correction function comprising an astigmatism adjustment using the astigmatism angle and the astigmatism magnitude.
15 . The computer-implemented method of claim 10 , further comprising:
determining, by the system, an astigmatism angle and an astigmatism magnitude associated with the EH image,
wherein the propagator further is a function of a summation of squares, of an initial pair of sequenced parameters, with the summation of the squares summed with an aberration correction function comprising an astigmatism adjustment using the astigmatism angle and the astigmatism magnitude.
16 . The computer-implemented method of claim 10 , further comprising
directing, by the system, execution of a series of forward propagations in alternation with backward propagations,
wherein use of the propagator to reduce the hologram aberration of the EH image provides for a backward propagation of the backward propagations, and
wherein a forward propagation of the series of forward propagations also comprises use of the modified array.
17 . A computer program product facilitating a process for electron hologram aberration reduction, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, and the program instructions executable by a processor to cause the processor to:
reduce, by the processor, the hologram aberration at an electron hologram (EH) image by modifying, by the processor, a pair of sequenced parameters of an array upon which the EH image is constructed, resulting in a modified array; and
generate, by the processor, a propagated EH image using a propagator comprising the modified array,
wherein the propagator is a function of an exponential of a distance between an object and an emitter having been employed to generate the EH image of the object, a physical size of a detector having been employed to receive electrons from the emitter, and a wavelength of the electrons.
18 . The computer program product of claim 17 , wherein the pair of sequenced parameters comprise sequences of consecutive integers having ranges from −N/2 to N/2, which ranges correspond to a sensor having −N/2 by N/2 pixels, the sensor having been employed to generate the EH image.
19 . The computer program product of claim 17 , wherein the program instructions are further executable by the processor to cause the processor to:
determine, by the processor, an astigmatism angle and an astigmatism magnitude associated with the EH image; and
modify, by the processor, the pair of sequenced parameters using the astigmatism angle and the astigmatism magnitude.
20 . The computer program product of claim 17 , wherein the propagator further is a function of a summation of squares of a modified pair of sequenced parameters resulting from the modifying.