Il Nuovo Cimento (1943-1954)

, Volume 6, Issue 1, pp 57–61

# Sopra una teoria generale dell'immagine nei sistemi ottici aventi un piano di simmetria

• M. Di Jorio
Article

## Riassunto

Per una variazionedΩ del campo si introduce il concetto di deformazione, col quale è possibile fondare una teoria per la formazione generale dell'immagine ottica. Si introduce poi, facendo riferimento alla condizione generale dell'isoplanatismo, una misuradD razionale di questa deformazione, che viene infine calcolata ricorrendo alla legge differenziale generale per due onde indipendenti. L'integrazione permette di riferire la deformazione di un campo generico Ω a quella di un campo Ω0 scelto come origine.

## Summary

In the present paper the basic ideas for a general theory of the formation of the optical image are outlined and the main theorem for such a theory is given. The only condition for its validity is for the optical system to have one simmetry plane, the principal rays laying upon it.

We did separate the aberrations strictly said, from the additional conditions for the field curvature and the distorsion, so following some modern authors. We have thought such a distinction to be rational, both for the logic development of the concepts and for the fact that a general theory of the field curvature already exists (2).

When two image bundles, corresponding to a variationdΩ of the field, are congruent, we say that the variation of the deformation is zero, by passing from the field Ω to the field Ω+dΩ. We call isoplanatic two such bundles; this happens when a particular equation, which is called the general condition for isoplanatism, is satisfied. Such isoplanatic structure, however, subsists only for particular systems. In the general case the bundles corresponding to a variationdΩ are not congruent and therefore a relative deformation exists. The new image theory is based on the possibility to define a measure for such a deformation. The measure is quite naturally defined as the variationdD between the values of the characteristic optical lenghth, for the actual deformed wave surfaces and for the corresponding isoplanatic ones. The calculation ofdD is effected by having recourse to the general differential law for two independent wave surfaces (5), which is valid whatever the structure of the two waves may be. From such a calculation the basic theorem of the theory follows, the result being analytically expressed (5).

A first formal transformation of the general deformationdD is also shown, to make the integration easier. After such transformation the deformation of a field Ω can be referred to that of a field Ω0 taken as origin. In centered systems it is natural to assume Ω0=0, that is to take the optical axis as origin. The initial bundle is then a revolution one. The two conditions thatD=0 and that the spherical aberration on the optical axis be zero, taken together, define a system free from aberrations strictly said, that is stigmatic.

## References

1. (1).
M. Di Jorio:Il Nuovo Cimento,5, 447 (1948).
2. (2).
M. Di Jorio:Teoria generale della curvatura del campo dei sistemi ottici, Comunicazione presentata al Congresso di Fisica in Lecco (8–12 November 1948) della Società Italiana di Fisica.Applications de la théorie générale de la courbure de champ des systèmes optiques aux problèmes de photogrammétrie, Comunicazione presentata al VI Congresso Internazionale di Fotogrammetria a L'Aia, 1948;Ottica,2, 13 (1948).Google Scholar
3. (3).
Per es.M. Herzberger:Ottica,1, 83 (1947).
4. (4).
F. Scandone:La Rivista del Nuovo Cimento,3, 144 (1947).Google Scholar
5. (5).
M. Di Jorio:Ottica,1, 3 (1947).Google Scholar