The tilt aberration and lense phase aberration seem difficult to reduce completely. Could you give me some suggestions? Thank you in advance.
Dear Mingqing
Simply by removing the phase you get when your record the hologram witout any object in the object beam (in a transmission microscope).
best
Pascal PICART
Hello Mingqing,
Assuming you have extracted the virtual (or real) image from your hologram, there are two ways to correct the phase aberration:
- with a model of the aberration ("Numerical Parametric Lens"): choose a part of the reconstructed object that is known to be "perfectly flat", but is affected by the phase aberration. Find the coefficients of a model that fits the phase in this region, for example for a tilt it will be a linear function in x and/or y, for a lens aberration it will be a quadratic function, etc. There are fitting functions in Matlab/Octave for that purpose. Then, once you have the coefficients you calculate a 2D phase map for the whole image that corresponds to the coefficients found in the smaller region, and you withdraw it from the original phase map. The subtraction operation is better done with a multiplication with the complex conjugate, to avoid problems with phase jumps.
- with the actual phase aberration ("Reference Conjugated Hologram"): as mentioned by Prof. Picart, you need a reference hologram recorded with no object present in the object beam. The phase extracted from this hologram corresponds to the overall phase aberration due to contributions of the object beam and the reference beam (the phase difference between the two beams). When you record a hologram with an object inserted, you can then easily suppress the phase aberration at the plane of the hologram by subtracting the phase of the reference hologram from the phase extracted from that hologram. As previously, phase subtraction is done by multiplication with the complex conjugate, hence the name. The advantage of this technique is that you don't need to have an object with a known flat area, as long as you have recorded a reference hologram previously.
There is a PhD thesis providing more details about aberration compensation, especially chapters 3 and 4 (link below).
Good luck!
https://infoscience.epfl.ch/record/64346
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