Information capacity and resolution in an optical system

On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

“…We also suggested an alternative derivation of an 'incoherent' version (20) of the Heisenberg uncertainty inequality (which may be termed the Laue inequality [8]). Finally, we obtained an estimate for the information capacity of imaging (scattering) systems which appears complementary to results of Shannon [18], Gabor and others [11,5] concerning the information capacity of communication and imaging systems. According to this last result, the number of bits of information about the sample that can be obtained in an imaging (scattering) experiment cannot exceed the total number of the imaging quanta (probing particles) used in the experiment, while the spatial resolution (number of effective voxels) and the signal-to-noise ratio can be traded-off against each other.…”

“…We derived several forms of uncertainty inequalities which are related to the Heisenberg uncertainty principle [12] and the information capacity of communication and imaging systems described by Shannon [18] and others [11,5]. We showed that our inequality (14) potentially provides a more accurate lower bound for the phase-space volume (which quantifies the Heisenberg uncertainty) than the conventional uncertainty relationship (7).…”

“…Inequality (23) is related to expressions for the information capacity (limits) obtained by Shannon for communication systems [18] and by Gabor and others for imaging and electromagnetic fields [11,5]. According to Shannon [18], the number of bits N bits that can be transmitted within a time interval A t over a communication channel with bandwidth W t = 1/∆t is limited by N bits A t W t log snr .…”

Diversity and degrees of freedom in wireless communications

“…The concept of degrees of freedom has been well studied in the optical community [1,5,6]. The author in [6] calls DOF the number of independent parameters needed to represent the output of the channel.…”

Information and resolution in electromagnetic optical systems

“…Polarization encoding is also possible; however, it is almost exclusively considered in the context of only two orthogonal states of polarization (see, e.g., [24]). Such analysis is perhaps natural in the sense that crosstalk between the two degrees of freedom is zero in the ideal case, but it automatically forsakes the possibilities afforded by encoding over the entirety of Poincaré space (or Stokes space if amplitude modulation is also employed).…”