Generalized sine condition for image-forming systems with centering errors

Abstract

The generalized sine condition for an image-forming system with centering errors but allowing for one symmetry plane is derived according to the Fourier optics approach. The variation of the wave-front-aberration function associated with a small displacement of field coordinates is given. The symmetry properties of aberrations are discussed.͓(x o Ј , y o Ј)͔, coordinates at the entrance (exit) pupil with origin at Ẽ o (Ẽ o Ј).

Analysis of pupil and corneal wave aberration data supplied by the SN CT 1000 topography system

“…For any image-forming system [3][4][5][6][7][8], we consider cartesian coordinates (x,Z) and (x 0 ,Z 0 ) in the object and image planes, cartesian coordinates (X, Y) and (X 0 , Y 0 ) in the reference spheres at the entrance and exit pupils respectively, and, at image space, we take into account a convenient axis termed z 0 (Fig. 1).…”

“…Wavefront aberration [3][4][5][6][7][8] is one of the important factors affecting retinal image quality and eyes can suffer not only from conventional or lower-order aberrations but also from higher order ones , specially in old normal or abnormal subjects even with small pupils and in young subjects with large pupils [14]. Ocular aberrations are usually evaluated by tracing rays and describing the wavefront aberration as a superposition (up to a convenient order) of Zernike polynomials.…”

Alternative uses of Coddington's equations in optical design

“…x ¡¸x=mˆ¯¸0 x is the oå ence against the sine condition in the language of Fourier Optics [12] and equation (14) is the same as equation (33) of our former paper [13].…”

“…We have employed this approach in various papers [10][11][12] for rst-order patches, i.e. patches so small that in both the object and the image we can associate with the Fourier expansion a superposition of plane waves (see Section 3 of our previous paper [12]). Recently we extended the Fourier Optics approach for second-order patches [13] (i.e.…”

Alternative uses of coddington's equations in optical design

“…We have employed this approach in various papers [lo-121 for first-order patches, i.e. patches so small that in both the object and the image we can associate with the Fourier expansion a superposition of plane waves (see Section 3 of our previous paper [12]). Recently we extended the Fourier Optics approach for second-order patches [13] (i.e.…”