PMID- 20508699
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20101012
LR  - 20181023
IS  - 1520-8532 (Electronic)
IS  - 1084-7529 (Linking)
VI  - 27
IP  - 6
DP  - 2010 Jun 1
TI  - Two matrix approaches for aerial image formation obtained by extending and 
      modifying the transmission cross coefficients.
PG  - 1311-21
LID - 10.1364/JOSAA.27.001311 [doi]
AB  - This paper physically compares two different matrix representations of partially 
      coherent imaging with the introduction of matrices E and Z, containing the 
      source, object, and pupil. The matrix E is obtained by extending the Hopkins 
      transmission cross coefficient (TCC) approach such that the pupil function is 
      shifted while the matrix Z is obtained by shifting the object spectrum. The 
      aerial image I can be written as a convex quadratic form I = <phi|E|phi> = 
      <phi|Z|phi>, where |phi> is a column vector representing plane waves. It is shown 
      that rank(Z) < or = rank(E) = rank(T) = N, where T is the TCC matrix and N is the 
      number of the point sources for a given unpolarized illumination. Therefore, the 
      matrix Z requires fewer than N eigenfunctions for a complete aerial image 
      formation, while the matrix E or T always requires N eigenfunctions. More 
      importantly, rank(Z) varies depending on the degree of coherence determined by 
      the von Neumann entropy, which is shown to relate to the mutual intensity. For an 
      ideal pinhole as an object, emitting spatially coherent light, only one 
      eigenfunction--i.e., the pupil function--is enough to describe the coherent 
      imaging. In this case, we obtain rank(Z) = 1 and the pupil function as the only 
      eigenfunction regardless of the illumination. However, rank(E) = rank(T) = N even 
      when the object is an ideal pinhole. In this sense, aerial image formation with 
      the matrix Z is physically more meaningful than with the matrix E. The matrix Z 
      is decomposed as B(dagger)B, where B is a singular matrix, suggesting that the 
      matrix B as well as Z is a principal operator characterizing the degree of 
      coherence of the partially coherent imaging.
FAU - Yamazoe, Kenji
AU  - Yamazoe K
AD  - 231 Cory Hall, Department of Electrical Engineering and Computer Science, 
      University of California, Berkeley, California 94720-1770, USA. 
      kenjiy@eecs.berkeley.edu
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Opt Soc Am A Opt Image Sci Vis
JT  - Journal of the Optical Society of America. A, Optics, image science, and vision
JID - 9800943
EDAT- 2010/05/29 06:00
MHDA- 2010/05/29 06:01
CRDT- 2010/05/29 06:00
PHST- 2010/05/29 06:00 [entrez]
PHST- 2010/05/29 06:00 [pubmed]
PHST- 2010/05/29 06:01 [medline]
AID - 199425 [pii]
AID - 10.1364/JOSAA.27.001311 [doi]
PST - ppublish
SO  - J Opt Soc Am A Opt Image Sci Vis. 2010 Jun 1;27(6):1311-21. doi: 
      10.1364/JOSAA.27.001311.