Variable focusing of electron microscopy image data utilizing origin-centered discrete fractional fourier transform

1. A computer-implemented method for adjusting the focus in original electron microscope image data, the method comprising:

obtaining original electron microscope image data comprising a plurality of spatially-indexed amplitude values, and further comprising a center located relative to the plurality of spatially-indexed amplitude values;

providing a fractional power parameter associated with a fractional Fourier transform operation;

calculating approximated centered two-dimensional discrete phase restoration information responsive to the fractional power value;

calculating an approximated centered two-dimensional fractional Fourier transform operation responsive to the fractional power value;

operating on the original electron microscope image data with the approximated centered two-dimensional phase restoration information and the approximated centered two-dimensional fractional Fourier transform operation to produce computationally-focused image data;

wherein the focus plane of the computationally-focused image data is responsive to the fractional power parameter.

2. The method of claim 1 , further comprising adjusting the fractional power and operating on the original electron microscope image data with another resulting approximated centered two-dimensional phase restoration information and the approximated centered two-dimensional fractional Fourier transform operation responsive to the adjusted fractional power.

3. The method of claim 2 , the method further comprising: producing additional computationally-focused image data for the adjusted fractional power.

4. The method of claim 2 , further comprising: adjusting the fractional power in response to a user input.

5. The method of claim 2 , further comprising: adjusting the fractional power in response to an output of a control system.

6. The method of claim 1 , wherein the centered two-dimensional fractional Fourier transform comprises a numerical algorithm.

7. The method of claim 1 , wherein the centered two-dimensional fractional Fourier transform operation is approximated by any from the group of a Taylor series expansion, a Hermite function expansion, a perturbation approximation, a singular integral approximation, or an infinitesimal generator computation.

8. The method of claim 1 , wherein the original electron microscope image data represents data from a first subset of larger electron microscope image data, the method further comprising: producing additional computationally-focused image data for a second subset of the larger electron microscope image data.

9. The method of claim 1 , further storing the original electron microscope image data as a digital image.

10. The method of claim 1 , further storing the computationally-focused image data as a digital image.

11. A system for adjusting focus in original electron microscope image data, the system comprising:

a numerical centered two-dimensional phase restoration operation for approximately restoring phase information associated with the original electron microscope image data to produce computationally-focused image data, the centered two-dimensional phase restoration operation responsive to a fractional power;

a numerical centered two-dimensional fractional Fourier transform operation for applying at least one approximated centered two-dimensional fractional Fourier transform operation responsive to the fractional power;

a parameter adjuster for providing a range of variation of the at least one fractional power;

wherein the numerical centered two-dimensional phase restoration operation and numerical centered two-dimensional fractional Fourier transform operation are applied to the original electron microscope image data, resulting in computationally-focused image data.

12. The system of claim 11 , the parameter adjuster to adjust the fractional power, and the numerical centered two-dimensional fractional Fourier transform operation to operate on the original electron microscope image data with another resulting approximated centered two-dimensional fractional Fourier transform having determined by the adjusted fractional power.

13. The system of claim 12 , wherein the numerical centered two-dimensional fractional Fourier transform operation to produce additional computationally-focused image data for the adjusted fractional power.

14. The system of claim 12 , the parameter adjuster to adjust the fractional power in response to a user input.

15. The system of claim 12 , the parameter adjuster to adjust the fractional power in response to an output of a control system.

16. The system of claim 11 , wherein the parameter adjuster to adjust fractional Fourier transform comprises a numerical algorithm.

17. The system of claim 11 , wherein the centered two-dimensional fractional Fourier transform operation is approximated by any from the group of a Taylor series expansion, a Hermite function expansion, a perturbation approximation, a singular integral approximation, or an infinitesimal generator computation.

18. The system of claim 11 , wherein the original electron microscope image data represents data from a first portion of larger electron microscope image data, the system produce additional computationally-focused image data for a second portion of the larger electron microscope image data.

19. The system of claim 11 , further comprising: memory for storing the original electron microscope image data as a digital image.

20. The system of claim 1 , further comprising: memory for storing the computationally-focused image data as a digital image.