Several practical problems which arise in optics are related to achieving a desired three-dimensional signal distribution inside a bounded spatial domain. The author deals with harmonic time dependence he finds an example in integrated circuit microfabrication; if time dependence is arbitrary, pulse compression is thought to be in a dispersive media. To all of these problems there is a unifying approach based on axiomatic system theory. This theory is well-known to rely on the state space formulation. The way in which the input acts on the state is quantified by the `controllability' concept. Similarly `observability' relates output data to the state. Strictly related to this approach is the `optimal control problem', where the task is to find an input which minimizes a functional consisting of two addenda: a physical term comparing the obtained output with the desired one by some quadratic criterion, and an economical term related to the cost of a given input. These concepts are widely used in signal processing, control theory, etc. Their application to optical problems requires them to be extended to distributed parameter systems. For the cases discussed in the text controllability results will be given and optimal control problems will be stated.

Crosta, G. (1979). Axiomatic system theory and optical images. In M. Grosmann, & P. Meyrueis (a cura di), Optics and Photonics Applied to Three-Dimensional Imagery - Proceedings of the Society of Photo-Optical Instrumentation Engineers vol. 212 (pp. 54-60). Bellingham, WA : Society of Photo-Optical Instrumentation Engineers [10.1117/12.958384].

Axiomatic system theory and optical images

CROSTA, GIOVANNI FRANCO FILIPPO
Primo
1979

Abstract

Several practical problems which arise in optics are related to achieving a desired three-dimensional signal distribution inside a bounded spatial domain. The author deals with harmonic time dependence he finds an example in integrated circuit microfabrication; if time dependence is arbitrary, pulse compression is thought to be in a dispersive media. To all of these problems there is a unifying approach based on axiomatic system theory. This theory is well-known to rely on the state space formulation. The way in which the input acts on the state is quantified by the `controllability' concept. Similarly `observability' relates output data to the state. Strictly related to this approach is the `optimal control problem', where the task is to find an input which minimizes a functional consisting of two addenda: a physical term comparing the obtained output with the desired one by some quadratic criterion, and an economical term related to the cost of a given input. These concepts are widely used in signal processing, control theory, etc. Their application to optical problems requires them to be extended to distributed parameter systems. For the cases discussed in the text controllability results will be given and optimal control problems will be stated.
No
Scientifica
Capitolo o saggio
bounded spatial domain; wave equation; Helmholtz equation; integrated circuit microfabrication; pulse compression; dispersive media; state space formulation; controllability; duality; adjoint system; optimal control; optical information processing; image formation
English
Optics and Photonics Applied to Three-Dimensional Imagery - Proceedings of the Society of Photo-Optical Instrumentation Engineers vol. 212
0361-0748
Outline of investigation carried out by the author when working as an independent consultant.
Crosta, G. (1979). Axiomatic system theory and optical images. In M. Grosmann, & P. Meyrueis (a cura di), Optics and Photonics Applied to Three-Dimensional Imagery - Proceedings of the Society of Photo-Optical Instrumentation Engineers vol. 212 (pp. 54-60). Bellingham, WA : Society of Photo-Optical Instrumentation Engineers [10.1117/12.958384].
Crosta, G
File in questo prodotto:
File Dimensione Formato  
1979_SPIE-SXB-1.pdf

accesso aperto

Descrizione: presentation slides, part 1
Dimensione 3.65 MB
Formato Adobe PDF
3.65 MB Adobe PDF Visualizza/Apri
1979_SPIE-SXB-2.pdf

accesso aperto

Descrizione: presentation slides, part 2
Dimensione 3.63 MB
Formato Adobe PDF
3.63 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/94844
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
Social impact