A new method of three-dimensional measurement by differential interference contrast microscope
Introduction
Differential interference contrast (DIC) microscopes [1], [2] are commonly used for observing objects’ phase distribution. The DIC microscope is a very powerful means of revealing detailed structures in living cells and small steps on the surfaces of semiconductor wafers. Current DIC microscopes have high sensitivity and high resolution. However, DIC microscopes have a drawback in that, they are unable to make quantitative measurements of the phase distribution of the phase object.
Previous researchers have tried to measure surface profiles and have discovered a method of surface slope measurement with a DIC microscope [3], [6], [7], [8], [11]. These methods were very useful for surface slope measurements but could not be extended to the reconstruction of the microstructures of an object because they used only the reflected light component to analyze the phase object. If the object has microstructures, the light used to illuminate it is diffracted at the edges of these surface structures, and the diffracted and the reflected lights interfere with each other and form interference patterns. Under these conditions, the phase information on edges, a DIC microscope is able to acquire from interference patterns, is limited to the average slope of the surface.
To overcome this disadvantage, it is necessary to analyze the images formed by diffracted light. Using the partial coherence theory, we analyzed the image characteristics of a phase object using a DIC microscope.
In this paper, we describe a new method of quantitative measurement using a DIC microscope and show the experimental results of applying this new method to a DIC microscope.
First, we analyze the image characteristics of a phase object under a microscope and theoretically show that the image of the phase object is formed by the interplay between the phase distribution and the defocus. Second, we discuss the image characteristics of the DIC microscope. We explain that the DIC image has four components and each component is analyzed corresponding to the property of the object. Using a blazed grating approximation, we show that light reflected from a gentle slope is replaced with diffracted light from a blazed grating.
Third, we describe the principle and experimental setup of our retardation-modulated DIC (RM-DIC) microscope. Finally, we present the experimental results of three-dimensional (3D) measurements made with the RM-DIC microscope.
Section snippets
Image characteristics of a phase object
To begin with, we discuss an image of a phase object viewed with a microscope to represent the image characteristics of a DIC microscope.
According to the partial coherence theory, the image intensity distribution of a microscope is given by [4], [5], [10]where means the transmission cross-coefficient (TCC) and is expressed as
Principle
We now explain the image characteristics of the DIC microscope above and find that the DIC image consists of the four image components. This means that to reconstruct the 3D structure of the object, we have to analyze each of the image components of the DIC image. Notably, when a phase object has microstructures, it is important to extract a linear image component of the phase distribution from the DIC image and to analyze it.
To measure the 3D structure of the object, we developed a new DIC
Comparing the calculated image of a phase object with the observed data
We compare the calculated image intensity distribution of a phase object with the observed values to confirm the image characteristics expressed in Eqs. (5), (7).
First, using the sample made with depth d = 20 nm, we confirm Eq. (5). Since the depth of this sample is small, we can rewrite Eq. (5) approximately as
We put wavefront aberrations caused by defocus into the pupil function and calculated the {R(fx, 0, 0, 0) − R(0, 0, − fx, 0)}
Conclusion
In the context of the weak phase approximation and the partial coherence theory, we discussed the image characteristics of a phase object and found that DIC images consist of four image components.
When the imaging optics include defocus, an intensity image is formed by interaction between the phase distribution and the defocus. We were able to check the image characteristics of the phase object using a microscope and experimentally confirm the distinctiveness of the phase object.
We showed that
References (11)
J. Phys. Radium Paris
(1955)Progress in Microscopy
(1961)Proc. SPIE, CR
(1992)- et al.
Opt. Acta
(1971) - et al.
Proc. SPIE
(1996)