Elsevier

Optics Communications

Volume 260, Issue 1, 1 April 2006, Pages 117-126
Optics Communications

A new method of three-dimensional measurement by differential interference contrast microscope

https://doi.org/10.1016/j.optcom.2005.10.079Get rights and content

Abstract

Based on weak phase approximation and the partial coherence theory, we analyze the image characteristics of a phase object using a microscope. We show that the image of the phase object is formed by the interplay between the phase distribution and the defocus.

Using this theory, we also show the image characteristics of a differential interference contrast (DIC) microscope.

We develop a method for extracting the phase component from the DIC image using two images with different retardation to reconstruct the phase distribution of the object. We call our new microscope a “retardation-modulated DIC (RM-DIC) microscope”. We describe the RM-DIC microscope and confirm our method using grating samples with depths of 20 and 50 nm.

To measure the three-dimensional (3D) figures of the microstructures on the object using a DIC microscope we need to extract the phase component from the DIC image and to deconvolute the phase component by means of the modulation transfer function (MTF) of the DIC microscope.

We conclude that our RM-DIC microscope can take quantitative measurements of the phase distribution, making it a very useful tool for 3D measurement of an object’s microstructures.

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]I(x,y)=-R(fx,fy,fx,fy)O(fx,fy)O(fx,fy)exp[-2πi{(fx-fx)x+(fy-fy)y}]dfxdfydfxdfy,where R(fx,fy,fx,fy) means the transmission cross-coefficient (TCC) and is expressed asR(fx,fy,fx,fy)=-Q(ξ,ς)p(ξ+fx,ς+fy)p(ξ+fx,ς+fy)dξdς.

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 asI(x)=C[R(0,0,0,0)-i-{R(fx,0,0,0)-R(0,0,-fx,0)}Φ(fx)exp(-2πifxx)dfx].

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

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