Digital holographic microscopy based on a modified lateral shearing interferometer for three-dimensional visual inspection of nanoscale defects on transparent objects
© Seo et al.; licensee Springer. 2014
Received: 17 July 2014
Accepted: 26 August 2014
Published: 4 September 2014
A new type of digital holographic microscopy based on a modified lateral shearing interferometer (LSI) is proposed for the detection of micrometer- or nanometer-scale defects on transparent target objects. The LSI is an attractive interferometric test technique because of its simple configuration, but it suffers from the so-called 'duplicate image’ problem, which originates from the interference of two sheared object beams. In order to overcome this problem, a modified LSI system, which employs a new concept of subdivided two-beam interference (STBI), is proposed. In this proposed method, an object beam passing through a target object is controlled and divided into two areas with and without object information, which are called half-object and half-reference beams, respectively. Then, these two half-beams make an interference pattern just like most two-beam interferometers. Successful experiments with a test glass panel for mobile displays confirm the feasibility of the proposed method and suggest the possibility of its practical application to the visual inspection of micrometer- or nanometer-scale defects on transparent objects.
Digital holographic microscopy (DHM) is a technique which enables the numerical reconstruction of recorded holograms with a computer [1, 2]. In DHM, amplitude and phase information of a target object is recorded on a charge-coupled device (CCD) camera as an interference pattern, which is called hologram, through an objective lens. Then, similar to an optical holography, the diffraction of wavefronts from the recoded hologram is computed and numerically propagated along the reconstruction distance to any chosen observation plane with a computer system. Thus, based on this numerical knowledge of the propagated complex wavefront, the amplitude and the phase of a target object can be computed, which can lead to micrometer- or nanometer-scale quantitative measurements of the target object [3–6].
When investigating, DHM obtains the depth information of a specimen and resolves phase differences corresponding to depth differences as price as several nanometers. Thus, it would be well suited for detection of nanometer- or micrometer-scale defects on transparent objects [7–9]. Furthermore, since the phase information provided by DHM allows us to visualize the detailed topological shapes of those defects, DHM attracts the attentions of various information technology industries .
In general, DHM can be implemented with an interferometer system. There are two kinds of interferometer systems which are two-beam and single-beam interferometers, which include the Michelson and the Mach-Zehnder interferometers and shearing interferometer, respectively [1–6]. Here, the recorded hologram by DHM is usually composed of three components which are DC bias and real and virtual images, in which DC bias and virtual image are undesired terms in the numerical reconstruction process. Thus, these terms need to be eliminated because their elimination results in an enhancement of image quality.
Kim et al. suggested a modified Cochran interferometer for removing DC bias and virtual image by using a phase shifting method . Cuche et al. also proposed a Fresnel diffraction method for removing DC bias and virtual image in the frequency domain with a low-pass filter . Based on these interferometers, various DHM systems have been proposed for defect detection on transparent materials. Xu et al. presented an in-line DHM system for testing micro-structures with a long-distance microscope . Schulze et al. also proposed another DHM system based on a modified Mach-Zehnder interferometer to detect defects on semiconductor wafers . Kuhn et al. obtained 3-D information of the transparent microstructure from the depth data detected by DHM . In addition, Wahba and Kreis measured the refractive index of optical fibers by DHM , and Colomb et al. proposed a digital holographic reflectometry based on a modified Mach-Zehnder interferometer .
In addition, a single-beam lateral shearing interferometer (LSI) has been also applied for DHM because of its simple optical configuration. Sen and Puntambekar suggested shearing interferometers for prism testing under manufacturing . Nyyssonen et al. presented a simple wavefront shearing interferometer for lens testing . In addition, Merzkirch generally analyzed the shearing interferometer . Matsuda et al. suggested a holographic LSI system for the real-time measurement of large liquid surface deformations . Moreover, Choi et al. presented wedge-plate shearing interferometers for collimating testing of laser beam using a moiré technique . In addition, Singh et al. suggested a LSI-based DHM system for imaging small biological specimens .
In most LSI systems, hologram patterns are formed by two laterally sheared object beams. This is unlike the conventional two-beam interferometer, where a hologram pattern is generated by the interference of two separate object and reference beams. In other words, the conventional LSI system has no obvious reference beam. Thus, the recorded hologram inevitably includes not only DC bias and twin images like in most two-beam interferometers but also undesired images, so-called duplicate images which result from the two sheared object beams getting involved in interference. This deteriorates the operational performance of the conventional LSI system.
In order to alleviate this drawback, in this paper, a modified LSI system employing a new concept of subdivided two-beam interference (STBI) is proposed, and several key parameters for this proposed system are derived based on ray optics. Here, the object beam passing through a transparent target is divided into two areas with and without object information, which is called half-object and half-reference beams, respectively. Thus, these two half-beams make an interference pattern without the aforementioned duplicate images . Additionally, a new type of DHM system based on this modified LSI is also implemented for visual inspection of micrometer- or nanometer-scale defects on transparent objects. For confirmation of the feasibility of the proposed method, experiments with a simple touch-glass panel for mobile displays are carried out, and the results are comparatively analyzed with those of the conventional method in terms of the effects of duplicated images.
Modified lateral shearing interferometer
where O F denotes the object beam reflected from the front surface of an optical window glass, which is assumed to be composed of O1 and R1 with and without object information, respectively. Likewise, the object beam reflected from the back surface of an optical window glass is denoted as O B , which is also assumed to consist of O2 and R2. In addition, , , and represent the intensities of O1, R1, O2 and R2, respectively.As seen in Equation 1, the first and second square brackets in Equation 1 represent the DC bias and the twin (real and virtual) images, respectively. Here, the second term in Equation 1 is referred to as 'Area 2’ in Figure 2. These two terms look very similar with those of most two-beam interferometers. However, the third term in Equation 1, which is referred to as 'Area 1’ in Figure 2, represents undesired images, which are called duplicate images. These may be generated only in the LSI system due to the interference of two sheared object beams. Since the 'Area 1’ in Figure 2, which is referred to as the third term, is partially overlapped with those of twin images, these images are excessively reconstructed together with twin images. Thus, these images must be removed because they degrade the quality of reconstructed images.
Hologram formation with half-object and half-reference beams
As shown in Figure 4, the object and reference beam areas of O1 and R1 with and without object information, respectively, are reflected from the front surface of the optical window glass. In addition, another object and reference beam areas of O2 and R2 are also reflected from the back surface of the optical window glass. Thus, a hologram pattern can be partially formed between the object-beam area O1 and the reference-beam area R2 just like in most two-beam interferometers.
As mentioned above, in the proposed method, O1 and R2 make an interference pattern, which is composed of two areas including 'Area 2′’ and 'Area 3′’ as shown in Figure 4. Here, the 'Area 2′’ and the 'Area 3′’ represent twin (real and virtual) images and DC bias, respectively, just like those of the conventional two-beam interferometer.
Lateral shearing distance by two object beams
where t and θ i denote the thickness of an optical window glass and the incident angle of the object beam onto the optical window glass, respectively. Also, n1 and n2 represent the refractive index in the air and in the optical window glass, respectively.
Effective interference area
According to Equation 3, θ t is calculated to range from 0° to 60° as shown in Figure 6. Of course, the optimum value of θ t becomes 60°, in which two halves of each object beam can interfere in the largest beam areas. However, if θ t is larger than 60°, duplicate images begin to generate because more than the halves of each object beam are overlapped. Thus, θ t must be controlled to be 60° in the proposed LSI system.
In the conventional LSI system, the LSD is estimated to be in the range of 0 to 0.76 mm depending on the incident angle θi, which varies from 0° to 90° when the thickness of the optical window glass and the radius of the object beam are given by 1 and 5 mm, respectively. Then, from Equation 3, θ t is calculated to range from 85.72° to 90°, which means that the EIA may be much reduced.
On the other hand, in the proposed method, the LSD is calculated to be in the range of 0 to 9 mm in case the thickness of the optical window glass and the radius of the object beam are 12 and 5 mm, respectively. Moreover, θ t is ranged from 23° to 90°, and the EIA is calculated to be about 3.07 × 10-4 mm2 for θ t = 60°.
Digital reconstruction of the recorded hologram pattern
The hologram pattern recorded by the proposed system of Figure 3 contains both intensity and phase information of a target object. Thus, from this hologram pattern, phase data of the target object can be extracted, and a 3-D image can be numerically reconstructed with the quantitative phase contrast method .
For extracting depth data of a target object, Fresnel diffraction approximation and the angular spectrum method are mostly used . Here, in this paper, the recorded hologram is transformed into the image plane domain by using the angular spectrum method and then the complex amplitude on the image plane is converted into the phase data. With this phase data, the 3-D object image is numerically reconstructed.
Results and discussion
Figure 3 shows an optical setup of the proposed DHM system based on a modified LSI. In the experiment, a random linearly polarized He-Ne laser with the continuous wave (CW) output power of 2 mW at 632.8 nm is used as a light source, which has been collimated in the experiments. A transparent touch-glass panel with defects of scratches and digs whose sizes ranged from 100 to 180 μm is used as the test object. The optical beam from the He-Ne laser passes through the test object and magnifies with an objective lens (×20, NA = 0.40). Here, the hologram pattern is generated by controlling the sizes of the object beams which are reflected from the front and back surfaces of the optical window glass. The window glass plate used in the experiment has a dimension of 100 mm × 100 mm × 12 mm. For efficient interference of two object beams, the LSD is optimized by combined use of the incident beam angle and the thickness of the optical window glass.
To confirm the feasibility of the proposed method, experiments with a test touch-glass panel with defects of scratches and digs are carried out. For detection of scratches and digs of the test object, hologram patterns of two sheared object beams of the test object are captured by the CCD camera using a × 20 objective lens. Then, 3-D images are reconstructed from these recorded holograms, and the results are compared to those of the conventional LSI system.
Detection of scratches on the test touch-glass panel
Imaging of micrometer-scale scratches with the conventional LSI system
Imaging of micrometer-scale scratches with the proposed system
Detection of digs on the touch-glass panel
Digs as well as scratches on a touch-glass panel make errors in the production process of smart phones. Thus, detection of dig defects is very important for discrimination of high-quality panels compared to those of low quality. Here, digs on the test object are also detected by both the conventional and proposed LSI systems. Moreover, for their performance comparison, a dig with a relatively large dimension is detected.
Imaging of micrometer-scale digs with the conventional LSI system
As mentioned above, in the conventional system, the thickness of the optical window glass and the object beam's radius are set to be 3 and 5 mm, respectively. Under this circumstance, the LSD and the TIA are calculated to be 100 μm and 89.47°, respectively, which means that the effective interference area cannot be optimally formed. In other words, the shearing distance of two object beams seems very small compared to the dig having a size of about 100 to 180 μm; thus, real and duplicated images cannot be separated. Even though the depth data of the dig is estimated to be about 2.52 μm from the mixed image, this value may not be valid data for the real depth of the dig. Hence, the dig's surface area cannot be detected because two real and duplicate images have been partially overlapped to each other as shown in Figure 14b. Thus, the conventional LSI system has a limitation in application to detection of relatively large defects since the EIA cannot be sufficiently formed for the interference of two object beams without duplicate images.
Imaging of micrometer-scale digs with the proposed system
From a real image, the depth value of the dig is estimated to be 1.45 μm on the average, and its surface area is also measured to be about 180 μm × 100 μm. Here, it is found that there exists a 1.07 μm difference between two estimated depth data of the conventional and the proposed systems, but it does not mean anything because two real and duplicate images have been mixed up together. In other words, the real image has been heavily influenced by the duplicate image in the reconstructed process in the conventional LSI system. On the other hand, in the proposed method, only the real image has been reconstructed without the duplicate image; therefore, exact detection of depth and shape data of the dig can be possible even though the dimension of dig relatively looks large.
In this paper, a new type of the DHM system based on a modified LSI has been proposed for detection of micrometer- or nanometer-scale defects on transparent target objects. In the proposed system, the so-called duplicate image problem of the conventional LSI has been alleviated by employing a new concept of STBI. It means that the proposed system can operate just like most conventional two-beam interferometer systems. Successful experiments with the test object of a touch-glass panel for mobile displays confirm the feasibility of the proposed method and the possibility of its practical application to three-dimensional visual inspection of micrometer- or nanometer-scale defects on transparent objects by taking advantage of its simple optical configuration as well as its two-beam interferometer operation.
This work was supported by the National Research Foundation of Korea (NRF) through a grant funded by the Korean government (MEST) (No. 2013-067321). The work reported in this paper was conducted during the sabbatical year of Kwangwon University in 2012.
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