Optical transfer function: Difference between revisions

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A three-dimensional optical transfer function can be calculated as the three-dimensional Fourier transform of the 3D point-spread function. Its color-coded magnitude is plotted in panels (b) and (d), corresponding to the point-spread functions shown in panels (a) and (c), respectively. The transfer function of the wide-field microscope has a [[support (mathematics)|support]] that is half of that of the confocal microscope in all three-dimensions, confirming the previously noted lower resolution of the wide-field microscope. Note that along the ''z''-axis, for ''x''&nbsp;=&nbsp;''y''&nbsp;=&nbsp;0, the transfer function is zero everywhere except at the origin. This ''missing cone'' is a well-known problem that prevents optical sectioning using a wide-field microscope.<ref name=MaciasGarza88>{{cite book |last1= Macias-Garza |first1= F. |last2= Bovik |first2= A. |last3= Diller |first3= K. |last4= Aggarwal |first4= S. |last5= Aggarwal |first5= J. |title= ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing |chapter= The missing cone problem and low-pass distortion in optical serial sectioning microscopy |conference= ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on, Institute of Electrical & Electronics Engineers (IEEE) |pages= 890–893 |volume= 2 |year= 1988 |doi= 10.1109/ICASSP.1988.196731 }}</ref>
 
The two-dimensional optical transfer function at the focal plane can be calculated by integration of the 3D optical transfer function along the ''z''-axis. Although the 3D transfer function of the wide-field microscope (b) is zero on the ''z''-axis for z≠0''z''&nbsp;≠&nbsp;0; its integral, the 2D optical transfer, reaching a maximum at ''x''&nbsp;=&nbsp;''y''&nbsp;=&nbsp;0. This is only possible because the 3D optical transfer function diverges at the origin ''x''&nbsp;=&nbsp;''y''&nbsp;=&nbsp;''z''&nbsp;=&nbsp;0. The function values along the ''z''-axis of the 3D optical transfer function correspond to the [[Dirac delta function]].
 
==Calculation==