The modal expansion of the field diffracted by a spherical object is transformed to an angular spectrum representation. Outside the object the angular spectrum representation yields the same diffracted field as that from the modal expansion. By neglecting the inhomogeneous plane waves in this representation, we also obtain the virtual, or backpropagated, fields for planes within or behind the object. These virtual fields are the fields that, to an external observer, appear to exist in free space within or behind the object. Thus these virtual fields are different from the actual fields existing in these regions. The image field model is obtained by including aperture limitations to the angular spectrum representation. These image fields could have been obtained by the more cumbersome approach of first computing the field in the entrance pupil of the imaging system by using the modal expansion and then propagating it back to a plane within or behind the object. The physical properties of images of the center plane of spheres are derived for the scalar case. The conditions for representing a sphere with an equivalent thin-object model are derived along with the criteria for directly representing this thin-object model by the modal coefficients. The usefulness of the image field model for numerical field calculations is illustrated by several examples. Diffraction effects that are present only in imaging situations are presented along with field calculations in the Fresnel region, where both the image field model and the modal expansion yield the same results.
© 1998 Optical Society of America
Original Manuscript: September 12, 1997
Manuscript Accepted: October 15, 1997
Published: March 1, 1998
Knut Kvien, "Angular spectrum representation of fields diffracted by spherical objects: physical properties and implementations of image field models," J. Opt. Soc. Am. A 15, 636-651 (1998)