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Metrology pp 1-34 | Cite as

Confocal Microscopy for Surface Profilometry

  • Liang-Chia ChenEmail author
Living reference work entry
Part of the Precision Manufacturing book series (PRECISION)

Abstract

The application of automated optical inspection (AOI) to advanced manufacturing processes with tight takt time and specifications is critical in winning today’s global competition. In the past decades, great effort had been devoted to developing novel solutions for in-line optical inspection of surfaces and the dynamic characteristics of tested components or devices. Conventional approaches to microscale 3D surface profilometry have adopted novel optics or concepts in confocal microscopy for measuring 3D surface characteristics with high speed and precision. One-shot measurement capability is demanded to minimize measured uncertainty from environmental vibration or system instability. Nevertheless, extremely high-speed microscopic 3D confocal profilometric methodologies for 100% full-field inspection are yet to be developed. This chapter intends to provide the measurement principle and development of confocal optical profilometry in overcoming bottlenecks and developing feasible solutions for novel manufacturing technologies, such as roll-to-roll nanoimprinting or semiconductor processes. It contains the basic optics, the measuring algorithms and industrial applications in optical confocal microscopy required for surface profilometry.

Keywords

Microscopy Confocal microscopy Optical metrology Automated optical inspection (AOI) Microscopic confocal profilometry 3D measurement Optical profilometry In situ inspection Precision manufacturing One-shot imaging 

Basic Theory

Confocal microscopy was first proposed by Minsky in 1961 for its main application in biological investigation by using fluorescence and in-focus contrast (Minsky 1961). For industrial inspection, the main difference is the use of illumination light source and emitted light reflection or backscattering for nonfluorophores and excitation. In confocal microscopy, axially segmented images of the tested sample are generally achieved by confining the illuminating area by the use of an illumination aperture and detecting the reflected light using a pinhole, slit, or other structured patterns for clearly distinguishing in-focus light from out-of-focus one. A confocal microscope works by geometrically matching two conjugate focal points in image space. As the sample is scanned through the focal point, peak intensity can be detected only when the focal point lies directly on the surface of the sample. Vertically scanning along the optical axis of the objective or tested sample is essential to generate a series of optically sectioned image, in which a depth response curve can be produced to detect the best focus position by the means of finding the peak intensity and the surface height of the tested sample can be determined.

Scanning confocal microscopy is a well-known and useful measurement technique for surface topography measurement due to its superior lateral and vertical resolution over conventional microscopy in in situ automatic optical inspection (AOI) for microstructures (Chen et al. 2016). Confocal microscopy can achieve high resolution, depth discrimination, and excellent sectioning capability in 3D profile measurement (Chen et al. 2012).

In a point-scanned confocal microscope, illumination light source lightens the tested object using an objective and the reflected or backscattered light is received coaxially by an optical detector for sizing intensity of the reflected light. The detection is achieved using a pinhole or slit in front of the detector. A basic configuration of traditional confocal microscope is illustrated in Fig. 1. Only the light that is reflected from the focal plane of the system can precisely pass through the pinhole or slit and is detected by the detector. This optical conjugate configuration generates a strong optical sectioning property for vertically scanning 3D profiles of the tested object. A vertical scanning along the optical axis of the microscope can be used to generate a depth-response curve (DRC), in which the depth associated with the maximum light intensity of the curve can represent the depth of the scanned surface. A complete volumetric structure or surface topography of the tested object can be scanned by a spatially lateral scanning (X, Y direction) in cooperating with a vertical scanning along the optical axis for each scanned object’s point. Traditional confocal microscopes generally use a linear translation stage for lateral scanning and piezoelectric transducer (PZT) for vertical scanning.
Fig. 1

Structure of traditional confocal microscope

A schematic illustration of a basic optical confocal configuration is shown in Fig. 2. As the configuration illustrates, a coherent or incoherent illumination light intensity, S(v, w), is projected through an illumination aperture and a microscope’s objective having a pupil function, P(ξ, η), and then focused onto a tested sample having a reflectance distribution defined as r before it is reflected or backscattered to the objective and then focused onto an imaging pinhole or a slit by following an optical detector having sensitivity, defined as D(v, w) for photon detection using a photon multiplexer transducer (PMT) or a charge couple device (CCD) (Artigas 2011).
Fig. 2

Basic optical confocal microscopic configuration

When the incident light is projected through an illumination aperture with out-of-focus by a quantity, defined as u along the optical axis, i(u, v, w) represents the illumination light pattern being out-of-focus by a quantity, u along the optical axis on the object plane, given by
$$ i\left(u,v,w\right)=S\left(v,w\right)\otimes {\left|h\left(u,v,w\right)\right|}^2 $$
(1)
where h(u, v, w) is the transfer function in representation of the Fourier transform of the pupil distribution to be expressed as follows:
$$ h\left({x}_2,{y}_2\right)=\int {\int}_{-\infty}^{\infty }P\left({x}_1,{y}_1\right){e}^{\frac{jk}{f}\left\{{x}_1{x}_2+{y}_1{y}_2\right\}}{dx}_1{dy}_1 $$
(2)
where x1 and y1 are the spatial coordinates on the first propagation plane; x2 and y2 are the spatial coordinates on the second propagation plane.
In general, the parameters x and y are expressed in the normalized optical coordinates; the above transfer function can be rewritten in a more expressive format as follows:
$$ h\left(u,v,w\right)=\underset{-\infty }{\overset{\infty }{\int }}P\left(\xi, \eta \right){e}^{i\left(\xi v+\mu w\right)}{e}^{i\Delta W\left(u,v,w\right)} d\xi d\eta $$
(3)
where ξ and η are the pupil coordinates, which are perpendicular to the aperture radius of the pupil; sinα is the objective’s numerical aperture; ΔW(u, v, w) is the wavefront consisting of two terms in focusing and aberration; the parameters v and w are defined as the normalized optical coordinates, given by
$$ {\displaystyle \begin{array}{l}v=\frac{2\pi }{\lambda }x\sin \alpha \\ {}w=\frac{2\pi }{\lambda}\mathrm{y}\sin \alpha \end{array}} $$
(4)
For a circular pupil, the pupil coordinates, ξ and η are defined as:
$$ \xi =\frac{x}{a} $$
(5)
$$ \eta =\frac{y}{a} $$
(6)
$$ \xi =\eta =\rho \sin \theta $$
(7)
Using Eq. (7), Eq. (3) can be further simplified as:
$$ h\left(u,v\right)=\underset{0}{\overset{1}{\int }}P\left(\rho \right){J}_0\left( v\rho \right){e}^{i\Delta W\left(u,\rho \right)}\rho d\rho $$
(8)
where J0(x) is a first-order Bessel function of the first type.
The defocus term for the wavefront in the pupil region is expressed as
$$ \Delta W\left(u,\rho \right)=-\frac{1}{2}u{\rho}^2 $$
(9)
where
$$ u=\frac{8\pi }{\lambda }z{\sin}^2\left(\alpha /2\right) $$
(10)
Eq. (8) can then be simplified to
$$ h\left(u,v\right)=\underset{0}{\overset{1}{\int }}P\left(\rho \right){J}_0\left( v\rho \right){e}^{-i\frac{1}{2}u{\rho}^2}\rho d\rho $$
(11)
Thus, when i(u, v, w) is reflected or backscattered to the objective and focused through an imaging pinhole then onto an optical detector, the detected light intensity can be given as follows:
$$ {\displaystyle \begin{array}{l}I\left(u,v,{v}_d\right)=\\ {}{\left|2\underset{0}{\overset{1}{\int }}P\left(\rho \right)\exp \left(\frac{1}{2} ju{\rho}^2\right){J}_0\left(\rho v\right)\rho d\rho \right|}^2\underset{0}{\overset{v_d}{\int }}{\left|2\underset{0}{\overset{1}{\int }}P\left(\rho \right)\exp \left(\frac{1}{2} ju{\rho}^2\right){J}_0\left(\rho v\right)\rho d\rho \right|}^2 vdv\end{array}} $$
(12)
where vd is the normalized aperture size of the pinhole, \( {v}_d=\frac{2\pi }{\lambda }r\sin \alpha \), in which r is the radius of pinhole and sinα is the numerical aperture of the objective.
Equation (12) can be also simplified and expressed in a convolution form as follows:
$$ I\left(u,v,w\right)=\left(S\left(v,w\right)\otimes {\left|h\left(u,v,w\right)\right|}^2\right)\left(D\left(v,w\right)\otimes {\left|h\left(0,v,w\right)\right|}^2\right) $$
(13)
When vd = 0, the optical configuration can be called an ideal confocal microscope with a pinhole having an infinite tiny point size. The light intensity being detected can be simplified and expressed as
$$ I\left(u,v,0\right)={\left|2\underset{0}{\overset{1}{\int }}P\left(\rho \right)\exp \left(\frac{1}{2} ju{\rho}^2\right){J}_0\left(\rho v\right)\rho d\rho \right|}^4 $$
(14)
In contrast, when vd → ∞, the optical configuration can be called a conventional optical microscope. Figure 3 illustrates the normalized light intensity responding to various normalized pinhole sizes, in which the pinhole size significantly affects the light intensity distribution.
Fig. 3

Schematic diagram of the normalized light intensity responding to various normalized pinhole sizes

Virtual Confocal Microscopy

Optical Configuration

The greatest difference of a virtual confocal microscope from a conventional one lies in the fact that no pinhole or slit is being used at the image focus plane. The object focus plane is searched by measuring the focus degree of a projected structured pattern and is detected when the image focus reaches to its maximum. This makes the technique being called virtual or pseudo confocal measurement. As the depth information is measured by the focus degree in the image plane, people also call it shape from focus (SFF).

The schematic diagram of a typical virtual confocal microscope is illustrated in Fig. 4 (Chen et al. 2014). When the tested sample is with a kind of textureless surface, a light source with a designed wavelength with selected bandwidth is employed as an active illumination and is projected through a structured pattern as the illumination aperture. When the tested sample is with a kind of surface texture possessing certain roughness, the active illumination can be replaced by using a normal optical aperture when the light is incident into the microscope. A set of focus lenses is usually used to collimate and focus the structured light into a microscope objective. A vertical linear scanner using either a piezoelectric transducer (PZT) or precise translation stage is integrated with the objective for vertical scanning. The reflected or backscattered light is collected by the objective and passes through the beam splitter and then focuses on an area-scan image sensor at its image plane.
Fig. 4

Schematic diagram of a typical virtual confocal microscope

Considering the reflectance characteristics of the tested sample, the design of light transmittance and grating size of the pattern are generally optimized to achieve best lateral measurement resolution. In general, the smaller the structured pattern is, the higher measuring resolution can be achieved. However, this will be restricted by the image detection limit. The structured pattern can be made by chrome coating, holography, or other printing techniques. A different size and pitch of structured pattern can be designed to achieve required lateral resolution. For example, a glass grating with checkerboard patterns having various pitch sizes can be employed in structured projection. When an optical aperture is used to measure a tested sample with surface texture, the measuring spatial resolution can normally reach to the image detection limit. In contrast, the active illumination method can only achieve the scanning up to the pattern resolution. Its full-field image can be realized by shifting the illumination pattern for lateral scanning but this normally consumes more time in inspection.

Measuring Principle

Figure 5 illustrates the brief operation principle of the virtual confocal microscopy. Two conjugate points located in the object and image planes of the virtual confocal microscope are matched by searching for its maximum degree of image focus. When the object point scans at the focus plane, the image focus detected on its corresponding conjugate point in the image plane can reach a maximum along its scanning axis. Depth map can be reconstructed by defining a focus operator and depth estimation algorithm.
Fig. 5

Confocal vertical scanning principle

The intensity of defocused image on the image plane, Id(x, y), is given by convolution of the focused image, If(x, y), with the point spread function (PSF) of the image system, h(x, y), as follows:
$$ {I}_d\left(x,y\right)=h\left(x,y\right)\ast {I}_f\left(x,y\right) $$
(15)
$$ h\left(x,y\right)=\frac{1}{2{{\pi \sigma}_h}^2}{e}^{-\frac{x^2+{y}^2}{2{\sigma_h}^2}} $$
(16)
where σh is the spread parameter, which is proportional to the radius of the circular patch on the object surfaces.

To precisely measure the focus degree of a detecting image pixel, a high-pass focus measure operator o(x, y) is used to evaluate the image consisting of the pixel with its neighboring pixels as a subimage (Nayar and Nakagawa 1990). A sum-modified-Laplacian (SOL) operator, used as the focus index, can quantify the degree of the focus on the detecting image, given as

$$ {\displaystyle \begin{array}{ll} ML\left(x,y\right)=& \left|2I\left(x,y\right)-I\Big(x-\mathrm{step},y\left)-I\right(x+\mathrm{step},y\Big)\right|\\ {}& +\left|2I\left(x,y\right)-I\Big(x,y-\mathrm{step}\left)-I\right(x,y+\mathrm{step}\Big)\right|\end{array}} $$
(17)
$$ F\left(i,j\right)=\sum \limits_{x=i-N}^{i+N}\sum \limits_{y=j-N}^{j+N} ML\left(x,y\right)\qquad \mathrm{for}\ ML\left(x,y\right)\ge T $$
(18)
where the parameter N is the window size and T is a threshold set to filter image noise.
To make the measurement principle clear, a measurement flow chart, shown in Fig. 6, is illustrated and described. A system calibration is performed to determine best measuring parameters, such as the pitch and size of illumination pattern, sensor exposure time, and vertical scanning pitch to satisfy required measurement resolution and precision. During the vertical scanning operation, a series of sectioned images are acquired by actuating the linear motion stage. The signal-to-noise ratio of the scanned image is enhanced by adequate image preprocessing algorithms. The focus index is determined using the SML operator for each tested pixel. With focus index along the depth axis, a depth response curve (DRC) is established for peak detection on the maximum focus index. An effective peak search algorithm is needed to determine the depth of each measured point. A full-field surface contour of the tested surface can be reconstructed for quality insurance purposes.
Fig. 6

Flow chart diagram of virtual confocal measuring method

Measuring Examples

A precalibrated standard gauge block with a step height of 32.54 μm was employed to verify measurement accuracy of the developed system. A structured grating with black and white checkboard pattern of a pitch size of 60*60 μm2 was used for active light illumination. By performing the measurement procedure described above, the 3D profile of the sample was reconstructed. Figure 7 shows the reconstructed 3D contour of the tested object. The repeatability of the measurement can reach less than 0.2 μm at a confidence level of three standard deviations.
Fig. 7

Reconstructed 3D contour for a precalibrated precision gauge block

Using the method for IC dicing inspection, Fig. 8 shows a typical example of chipping defect which appeared on the IC dicing process. By using the developed measurement method with IR light source of 1100 nm, the 3D profile of the IC chip with a defect can be measured.
Fig. 8

A typical example of IC chipping defects: (a) 2D image of chipping defect captured with IR camera and (b) the 3D profile

Lateral Scanning Confocal Microscopy

Optical Configuration

To expedite in situ three-dimensional shape measurement, lateral confocal scanning (LCS) microscopy provides an effective method, since it can skip vertical scanning operation normally required by traditional confocal microscopy in contour scanning. Optically, the LCS is different from the traditional confocal microscopy, in which one angle between the lateral scanning plane and the focus plane is configured, so that the optical inspecting axis is tilting with the sample, shown in Fig. 9. Fantastically, with such configuration, one detected image can include all focus information acquired from different vertical scanning depths. Essentially, the imaging sensor observes one inspecting point by using a line array of optical pixels, so all the focus information along the tilting axis, which locate in different depth sections, can be detected by the sensor simultaneously. Consequently, when the microscope scans along the tested sample laterally, all the focus information existing in three-dimensional space can be detected and the vertical scanning operation can be totally skipped. Obviously, the penalty of the LSC will be considerable increase of the sensing elements, so the imaging detection rate can be less efficient. Moreover, the lateral scanning is suggested to be performed on a precise scanning stage, so the line scanning does not introduce substantial positioning errors into the measurement result.
Fig. 9

Schematic diagram of lateral confocal scanning microscopy

To inspect a sample with spectacular light property or textureless condition, the LSC system generally employs an illumination structured pattern which goes through an optical filter and an optical grating for generation of high-quality structured grid patterns. To suit various kinds of the object’s surface characteristics, the light intensity needs to be controlled to produce good image contrast of the projected pattern. With this design, it is capable of profiling microstructures having low reflectivity and high slope surfaces.

Illuminated in Fig. 10, for the purpose of the lateral scan measurement, the optical objective is orientated two angles, α and β, with the scanning axis Y and the vertical Z axis, respectively (Chen et al. 2010). The first angle α is designed to set the image focus plane to be parallel with the tested microstructure surface, in which the projected structure pattern is focused on the tested surface, shown in Fig. 10a. As illustrated in Fig. 10b, β is designed to generate a focusing-and-defocusing process along the Y-axis during the lateral scanning operation, in which the structured light being projected on the tested surface has a focus variance trend along the scanning direction. In the method, LCS is performed by synchronizing a linear moving stage with the full-field image acquisition, in which the maximum resolution of the scanning step is defined as the finest resolution of the stage. A depth response curve (DRC) of each detected pixel can be obtained along its scanning direction. It is clear to see that a modulated focusing function is obtained along the scanning direction, in which a focus measure signal is peaked at the corresponding confocal scanning depth of the detected surface point.
Fig. 10

Optical configuration of the developed LCS system: (a) tilting angle of α with respect to the scanning direction, Y-axis; (b) yaw angle of β with respect to the vertical direction, Z-axis

Measurement Principle and Algorithm

In the LSC, the optical system is inclined by an adequate angle, β, with the vertical axis, thus orientating its focus plane to be tilted one angle with its lateral scanning plane. Figure 11 shows the image formation geometry associated with the LCS being developed here.
Fig. 11

Image formation geometry of the LCS optical configuration

The optical relationship between the object distance, o, the image distance, i, and the effective focal length, f, are given by Gaussian lens law as follows:
$$ \frac{1}{o}+\frac{1}{i}=\frac{1}{f} $$
(19)
When the sample surface and the focus plane are not parallel, only some portion of the tested surface is located within the focus range of the image plane and can be captured by an imaging sensor. The focus range, Fr, is given by:
$$ {F}_r=\frac{\mathrm{DOF}}{\tan \beta } $$
(20)
In Fig. 12, Point o(xr, yr) is a cross position between the focus plane and the tested surface. A maximum light intensity can be only obtained on this position while the intensity of other positions is attenuated. Illustrated in Fig. 13, the light intensity of the detected modulated DRC is similar to a sin-modulated Gaussian function along the lateral scanning direction. Thus, the intensity, I(i, j), of the DRC can be modeled as follows:
$$ I\left(i,j\right)=\sin \left(\frac{2\pi }{f}\cdot i\right)\left(a\cdot {e}^{\left(-\frac{{\left(1-M\right)}^2}{2{\left(1,/,\beta \right)}^2}\right)}\right) $$
(21)
where
  • \( \sin \left(\frac{2\pi }{f}\cdot i\right) \) is the structured light distribution

  • f is the period of the structured light pattern

  • i is the pixel position of the image detection

  • a is the modulation amplitude

  • M is the peak position of the Gaussian curve

  • β is the yaw angle with respect to Z-axis

Fig. 12

Relationship between the focus range and the DOF in the developed optical configuration

Fig. 13

Light intensity of the detected DRC

To determine the peak accurately, a peal detection algorithm of a DRC is described. A block diagram of the algorithm is shown in Fig. 14. Low frequency components, such as the DC term of the DRC are first removed from the DRC by taking the first derivative operation, and the signal is then rectified by square-law detection and low-pass filtering. As a result, the peak of the low-pass filter output is located and the vertical position that corresponds to the peak is detected.
Fig. 14

Peak detection algorithm for DRC

Meanwhile, in the surface measurement process, the horizontal interval (Sp) of scanning is critical to the detection resolution. It depends on the angle β and the scanning resolution (k) and can be defined as follows:
$$ {S}_p=k/\cos \beta $$
(22)
Space resolution k is generally determined by the CCD pixel size. Figure 15 shows that Sp varies against β ranging from 0° to 60°. The system’s depth resolution Dr can be controlled by adequately controlling α and β. The depth resolution Dr can be described as follows:
$$ {D}_r=k\left(\sin \alpha +\cos \alpha \cdot \sin \beta \right) $$
(23)
Fig. 15

Relationship between the tilted angle β and scan pitch Sp

Measurement Examples

A measurement on a precalibrated step height surface is performed for measurement accuracy evaluation. Its lateral scanning process is shown in Fig. 16, in which its step height of 5.14 μm is evaluated. By performing the measurement procedure as described, Fig. 17a, b demonstrates the 3D map and cross-section profile being reconstructed from the step-height surface, respectively. From the analysis of the measured result, the average height of the step height was 5.14 μm and the standard deviation was 0.033 μm. Table 1 illustrates the measurement accuracy and repeatability by a 30-time repeatability test.
Fig. 16

LCS process of a calibrated standard step height

Fig. 17

Measurement results of calibrated step height: (a) 3D map and (b) cross-section profile

Table 1

Accuracy and repeatability obtained from 30-time repeatability test of the calibrated step height

Measurement results

Number of scanned images

Standard height

Measured result

Standard deviation

1300

5.14 μm

5.13 μm

0.033 μm

Meanwhile, an industrial sample having 30° V-groove microstructures, which was made by roll-to-roll nanoimprinting process, was measured by the LSC method. As shown in Fig. 18, to measure both the slit sides of the V-groove simultaneously, the measuring optical design employs two microscopic probes to project structured light patterns and two imaging sensors to acquire reflected light from the detected object’s surface from two adequate tilting angles, in which the probe is aligned with the detected surface to obtain maximum reflected light (Fig. 19). An optical objective with magnification of x50, NA of 0.95, and an illumination grating pattern of 50 μm were used for the task. By using the LSC method, the 3D map was reconstructed and the cross section was evaluated by comparison with the reference values, in terms of the height, angle, and width of the V-groove, shown in Fig. 20. From a 30-time repeatability test, Table 2 illustrates the measurement repeatability being obtained from a 30-time repeatability test
Fig. 18

Schematic diagram of optical configuration of LSC system developed for measuring microscopic V grooves

Fig. 19

LCS process of standard angle target: (a), (b), and (c) are obtained by left side CCD; (d), (e), and (f) are obtained by right side CCD

Fig. 20

Measurement result of the reference target: (a) top view; (b) 3-D map; and (c) cross profile

Table 2

Measurement repeatability being obtained from a 30-time repeatability test of the 30°V-groove microstructures

Measurement results

 

Average value

Standard deviation

Height

14.65 μm

0.23 μm

Width

48.79 μm

0.54 μm

Angle

119.55°

0.78°

Chromatic Confocal Microscopy

Basic Optical Configuration and Theory

Traditional confocal microscopy is by means of vertical scanning to establish a depth response curve of the light intensity, which primarily depends on the light wavelength and the numerical aperture of the objective. To avoid vertical scanning and increase measurement efficiency, a spectrum scanning confocal measurement method employs a chromatic objective to disperse the light vertically according to light wavelength and focus on various depth positions. This kind of microscope generally equips with a predefined broadband light source in combination with a diffractive lens as well as wavelength-to-depth coding for instantaneous point-scanned or line-scanned profile measurement of a three-dimensional surface. This technology takes the advantage of chromatic light dispersion to completely skip vertical scanning operation, which is required for establishment of the depth response curve. Figure 21 illustrates the schematic diagram of a chromatic confocal microscope utilizing a chromatic objective for multi-wavelength light dispersion and a pinhole to precisely filter a light wavelength corresponding to the object’s test height (Chen et al. 2011a, b).
Fig. 21

Schematic diagram of chromatic confocal microscopy

In Fig. 21, when one chromatic objective is used as both the illuminating and imaging lens, the light intensity function of acquired signals is given as:
$$ I\left(u,v\right)={\left|2\underset{0}{\overset{1}{\int }}P\left(\rho \right){e}^{\left( ju{\rho}^2/2\right)}{J}_0\left(\rho v\right)\rho d\rho \right|}^4 $$
(24)
where P(ρ) denotes the pupil function of objective; J0 is the zero-order Bessel function; u and v are the normalized optical radii.
$$ v\approx \frac{2\pi }{\lambda }r\sin {\alpha}_0\, u\approx \frac{8\pi }{\lambda}\mathrm{z}{\sin}^2\left(\frac{\alpha_0}{2}\right) $$
(25)
Moreover, when using a finite pinhole with a fixed size, the axial response function of the system is given
$$ I\left(u,v\right)=\underset{0}{\overset{v_D}{\int }}{\left|2\underset{0}{\overset{1}{\int }}P\left(\rho \right){e}^{\left( ju{\rho}^2/2\right)}{J}_0\left(\rho v\right)\rho d\rho \right|}^4 vdv $$
(26)
where vD is the normalized aperture size of a pinhole.
Using Eq. (26), the axial light intensity for various pinhole sizes is illustrated as Fig. 22.
Fig. 22

Axial light intensity distribution for various pinhole sizes

Line-Scanned Chromatic Confocal Microscopy

Line-scanned chromatic confocal microscopy is generally more efficient as one sectioned-line profile can be measured by one image exposure (or one shot imaging). However, the vertical measuring resolution and precision is usually decreased due to the signal cross talk between adjacent detection points. The diffraction coupling problem between two incident light beams along the slit direction has been regarded as one of significant problems in restraining slit-scan chromatic confocal measurement from possessing high measurement accuracy. The signal cross talk can potentially increase the full width at half-maximum (FWHM) of the depth response signal and potentially decrease the depth detection resolution for more than 10%. To address this, a common strategy is to increase the scanning pitch between two neighboring points, so the cross-talk phenomenon is minimized. However, by doing so, the lateral measuring resolution is decreased as the measuring points are sparser. In general, an adequate selection is made to make the best trade-off between measurement efficiency and precision according to various measurement requirements in AOI.

Shown in Fig. 23, a fiber-based line-scanned chromatic confocal microscope is introduced. It uses a chromatic dispersive objective for vertical light dispersion in a designed depth range. A pair of linear coherent image fiber arrays are employed and integrated in a multi-wavelength line-slit optical configuration in consideration of minimizing the signal cross-talk effect, illustrated in Fig. 23a. Using the chromatic objective, the incident light is dispersed according to a predefined depth ranging from a few micrometers to even several millimeters. Each fiber is arranged in a one-to-one conjugate relationship between each incident light and its corresponding detected object point; the cross-talk effect is minimized, in which unfocused light spatially and other possible stray lights are filtered away from the corresponding spectrometer.
Fig. 23

Schematic diagram of line-scanned chromatic confocal microscope: (a) optical configuration and (b) prototype system

A hardware setup of the microscope is shown in Fig. 23b. The developed optical system setup employs a pair of linear coherent fiber arrays at the incident and imaging conjugate focal plane positions, respectively. The light source used is a broadband light source generated by either a xenon arc lamp, halogen light, or light-emitting diodes (LED). The light first focuses and passes through a slit with aid of a set of optical lenses. The axial dispersion of light is generated by a chromatic confocal objective in which light having a specific wavelength can be focused on a corresponding depth position at the tested sample’s surface. In the above configuration, the dispersive objective is designed to modulate an incident broadband light for generation of a predefined axial chromatic light dispersion along the object-focusing zone. Each image fiber is spatially configured and employed to match a detecting incident light beam from the light source with its corresponding reflected light from an object underlying inspection, in which a spatially conjugate one-to-one relation between each incident light and its matching detected object point can be formed accurately. Meanwhile, another conjugate one-to-one optical relation between each detected object point and its matching image pixel is also established through the above image-fiber mapping. Each fiber is designed to spatially remove the unfocused light and other possible stray lights, thereby minimizing the potential lateral cross talks between the detected image sensors. Then, the one-to-one conjugate relationship between the incident fiber point and its corresponding detected fiber point can be established. Meanwhile, the chromatic optical objective with various optical magnification can be used to disperse the incident white light with a spectrum range onto a series of focal distances with respect to the corresponding wavelength. Figure 24a illustrates an example of vertical light dispersion between 400 and 700 nm by a chromatic optical objective, while its chromatic spectral light distribution and calibrated mapping curve between a light wavelength range of 300 nm and a detected depth of 90 μm are shown in Fig. 24b, c, respectively. The linearity of the curve represents the degree of a uniform vertical resolution of the depth measurement. More linear the curve is, the uniform the vertical resolution is. The design of the chromatic objective can significantly influence the uniformness of the vertical resolution along the measurement depth range.
Fig. 24

Dispersion of chromatic light: (a) illustration of axial chromatic light dispersion generated by the chromatic objective; (b) chromatic spectral light distribution; and (c) calibration-mapping curve between light wavelength and measuring depth

To obtain a reasonably accurate model of the above calibration-mapping curve, a least-squares second-order polynomial approximation can be used to perform the best fit and the model is given as:
$$ z\left(\lambda \right)=a{\lambda}^2+ b\lambda +c $$
(27)
A longitudinal chromatic aberration relationship between wavelength and depth can be further simplified and expressed as follows:
$$ I\left(\lambda \right)=C{\left[\frac{\sin \left(u/2\right)}{\left(u/2\right)}\right]}^2 $$
(28)
where \( u=\frac{2\pi }{\lambda }{NA}^2\left(a{\lambda}^2+ b\lambda +c\right) \).

Analysis of Sensor Cross Talks

In general, the traditional confocal system usually employs a micro pinhole or slit to minimize the potential light cross talk between the neighboring detecting sensors. The cross-talk problem is mainly generated by the general optical point spread phenomenon, in which it potentially reduces the image quality. The FWHM of the depth response curve for three different measurement methods, in terms of point, slit, and area types, are shown in Fig. 25. It is clear to see that the FWHM is significantly increased when the pinhole or slit is removed from its conjugate position, in which a detecting pixel can cross talk (or convolute in Mathematics) with many of its neighboring pixels. Without employment of a pinhole or slit, the resultant light intensity of a single detecting sensor from its cross talk neighboring region can be expressed by the following equation:
Fig. 25

Schematic diagram of cross-talk phenomenon: (a) two reflection light beam focusing on two neighboring pixels; (b) light cross-talk phenomenon; and (c) the depth response curve for three different confocal measurement methods, in terms of pinhole, slit, and area types

$$ I\left(i,j\right)=2\sum \limits_{p=0}^{\infty}\sum \limits_{q=0}^{\infty}\left[{C}_{i+p,j+q}\cdot {I}_{i,j}\left(i+p,j+q\right)\right] $$
(29)
where Ci + p, j + q is the surface reflection coefficient at Pixel (i + p, j + q).
To minimize the above cross-talk effect, a set of spatially matching image fiber pairs can be used to establish one-to-one conjugate relationship between the incident fiber point and its corresponding detected pixel. Figure 26 elucidates an optical conjugate design using a fiber core diameter and a fiber pitch for accurate corresponding matching between the object and the image planes. The fiber is designed to spatially filter unfocused light and other possible stray lights from the corresponding detection sensors, in which an adequate pitch of the fiber array is designed in consideration of the point spread function (PSF) of the optical focusing lens used in the optical fiber array.
Fig. 26

Schematic diagram of the spatially matching image fiber pairs: (a) optical configuration of fiber pairs and (b) optimal design of the fiber core diameter and fiber pitch

Measurement Examples and Analyses

The flow chart diagram of the chromatic confocal measuring method is illustrated in Fig. 27. A system calibration procedure including light intensity optimization, positioning verification of the translation stage, and optimal control of light exposure time for best image contrast is performed to ensure an optimal spectrum imaging condition for chromatic scanning. Following this, implementation of a vertical scanning calibration using a precalibrated target surface and precise linear moving stage is performed to establish accurate mapping between profile depth and light wavelength. With the calibrated function, the tested sample can be scanned to produce line-sectioned profiles and further reconstruct 3D map by performing lateral scanning.
Fig. 27

Flow chart of the chromatic confocal measuring method

To evaluate the effect of the fiber size on the FWHM of the depth response curve, a standard calibrated flat mirror was mounted on a precalibrated PZT linear stage for performing vertical scanning. In the test, four setup using a continuous slit with an opening width of 60 μm, a single fiber with a diameter of 62.5 μm for simulating a pinhole, a linear fiber array with a diameter 9 μm having a pitch of 125 μm and a linear fiber array with a diameter of 62.5 μm, and a pitch of 125 μm were employed to perform a 30-time repeatability test on the same depth position of the tested target. The experimental results are shown in Fig. 28, in which the fiber array with a diameter of 9 μm and a pitch of 125 μm has a comparable result in comparison with the single pinhole with a diameter of 62.5 μm. It is also clear to see that the linear fiber array with a diameter 62.5 μm and a pitch of 125 μm has a narrower spectral response curve (SRC) than the continuous slit with an opening width of 60 μm. Figure 29 illustrates the 30-time repeatability measurement results on the FWHM of the SRC obtained from the four experimental setups. It is clear to observe that the linear fiber array employed in the tested system has significantly reduced the cross-talk effects. As seen, the reliability of the measurement has been significantly improved when the result using the linear fiber array is compared with the continuous slit having a similar opening width. By detecting the peak of the SRC, the reliability of the depth measurement on the same calibrated target surface can be shown in Table 3. The listed results have reasonably confirmed with the above outcome. As seen, it is observed that the result of the slit with a 60 μm opening width has much higher standard deviation on FWHM than the other three tests. This clearly indicates that the measuring performance of this setup is not as precise as the others.
Fig. 28

Spectral response curve (SRC) obtained by using various confocal filters: (a) continuous slit having an opening width of 60 μm; (b) a linear fiber array with a diameter 9 μm and a pitch of 125 μm; (c) a linear fiber array with a diameter 62.5 μm and a pitch of 125 μm; and (d) a single fiber with a diameter of 62.5 μm

Fig. 29

FWHM of the spectral response curve (SRC) using various confocal filters in a 30-time repeatability test

Table 3

30-time repeatability test results of SRC using various confocal filters

 

Slit

(60 μm)

Fiber

(62.5 μm)

Fiber

(9 μm)

Pinhole

(60 μm)

Standard deviation of peak position (nm)

0.8045

0.0595

0.0305

0.0144

Mean FWHM (nm)

30.200

31.853

25.570

21.140

Standard deviation of FWHM (nm)

3.214

0.836

0.693

0.667

Meanwhile, to verify the measurement accuracy of the chromatic confocal measuring method, a 25.4 μm standard step-height target was employed to perform step-height profile measurement. Figure 30a exhibits the step measurement result using the continuous slit having an opening width of 60 μm, in which the average height and standard deviation were 24.98 μm and 0.066 μm, respectively, in a 30-time repeatability test. By using the linear coherent fiber array with a diameter 62.5 μm and a pitch of 125 μm, the standard deviation was slightly decreased to 0.061 μm, as seen in Fig. 30b. Significantly noticed in Fig. 30c, the standard deviation was considerably decreased to 0.009 μm when employing the linear fiber array with a diameter 9.0 μm and a pitch of 125 μm. Moreover, it is also importantly noted that the measurement of this kind of linear fiber array has been very close to the one to be achieved by the single pinhole. Table 4 lists the measurement results achieved by the four tested different filters. From the experimental results, it confirms that the method using linear fiber arrays is capable of minimizing the cross-talk errors and enhancing the measurement accuracy for chromatic confocal measurement by more than 16-folds. The measurement result by using the developed system was comparably close to the one achieved by the single-pinhole confocal measurement method, while the measurement efficiency can be enhanced due to its multiple-point measuring configuration. Unquestionably, the lateral measuring resolution of the fiber array is inferior than the one achieved by the slit type. This is always a trade-off decision to be made by the technology users in consideration of various in situ measurement requirements.
Fig. 30

Measurement repeatability results on a 25.4 μm standard step-height target: (a) continuous slit having an opening width of 60 μm; (b) a linear fiber array with a diameter 62.5 μm and a pitch of 125 μm; (c) a linear fiber array with a diameter 9.0 μm and a pitch of 125 μm; and (d) a single fiber with a diameter of 62.5 μm

Table 4

30-time repeatability test results on measuring a 25.4 μm step-height target using various confocal filters

 

60 μm slit

62.5 μm fiber

9 μm fiber

60 μm pinhole

Average height (μm)

24.98

25.56

25.41

25.406

Standard deviation (μm)

0.066

0.061

0.009

0.0076

An industrial sample of a printed circuit board (PCB) with micro round bumps having a nominal height of 25 μm was tested to measure profile of the bumps. A line-scan chromatic measuring method inspection was performed to measure the bumps. Figure 31a, b present 3D reconstructed map and cross-section contours of the measured bumps, correspondingly. The measurements result indicate that the method is capable to measure industrial microstructures with highly varying surface reflectance on the tested sample. The measuring repeatability from a 30-times run was verified to be within a submicrometer scale.
Fig. 31

Measurements of a micro round bump in a printed circuit board (PCB): (a) reconstructed 3D map and (b) cross-sectional profile

Conclusions

A confocal microscopic profilometer is extremely important and useful to achieve in situ surface profilometry and automated optical inspection (AOI) of microstructures in modern advanced manufacturing. Based on confocal microscopy, various kinds of optical configuration and techniques have been quickly developed to satisfy demanding measurement requirements in tight tolerance and high precision, as well as efficiency. The developed measurement method and system can be widely employed to in situ microstructure profile measurement. It is worth noting that, using the confocal method, the detection resolution of surface profilometry can reach below 0.03% of the overall detection range. Nonetheless, there is still huge potential in the field to be further developed to satisfy demanding needs in the fast developing world. Novel optics and modern computer technologies such as artificial technology can be utilized to break through the current measuring limits, especially in greatly shortening of takt time consumed by the confocal method. The developed system can be further developed with advancement of the hardware performance such as the imaging sensor for its optimal performance in in situ AOI.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Taiwan UniversityTaipeiTaiwan

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