Effects of defocus on the transfer function of coherence scanning interferometry.

Rong Su,Richard Leach,Matthew Thomas,Jeremy Coupland

doi:10.1364/ol.43.000082

Abstract

Coherence scanning interferometry (CSI) offers three-dimensional (3D) measurement of surface topography with high precision and accuracy. Defocus within the interferometric objective lens, however, is commonly present in CSI measurements and reduces both the resolving power of the imaging system and the ability to measure tilted surfaces. This Letter extends the linear theory of CSI to consider the effects of defocus on the 3D transfer function and the point spread function in an otherwise ideal CSI instrument. The results are compared with measurements of these functions in a real instrument. This work provides further evidence for the validity of the linear systems theory of CSI.

Highlights

In two-dimensional imaging systems, such as those used in wide-field microscopy, the effects of defocus generally degrade image quality, in certain circumstances one or more defocused images have been used as a means of edge enhancement [1] and to retrieve phase information from intensity images [2]
In a way that is analogous to confocal microscopy, it is the relative defocus between the object and reference arms that is important in this case, and the effect of defocus on the transfer function (TF) and point spread function (PSF) that characterize the 3D performance in coherence scanning interferometry (CSI) is determined
Michelson objectives are mostly used for low numerical aperture (NA), low-magnification systems (10× and lower) while Mirau objectives are more useful at higher NA and higher magnification (10× to 100×)

Summary

Introduction

Defocus in CSI means that the reference mirror is not accurately positioned at the conjugate focal plane of the lens, Fig. 1. The linear systems theory shows that the interference term of the CSI signals in the spatial frequency domain (k-space), I k, can be expressed as the multiplication of the object spectrum, O k, and the TF ( understood as the linear shift-invariant filter), H k, as

Results

Conclusion