Synthetic wavelength to increase the snapshot optical sensor’s elevated vertical measurement ranges

Mothana A. Hassan; Haydn Martin; Liam Blunt; Xiang Jiang

doi:10.1364/AO.58.009051

1. INTRODUCTION

The continued enhancement of optical digital methods of surface profile measuring is advantageous for numerous industries and applications. It is particularly valuable within high-precision manufacturing processes, as it allows production to be completed faster and with an increased degree of accuracy [1,2]. Furthermore, the cost is significantly lower. The technology is desirable because it uses sensors to scan and analyze surfaces without requiring direct contact. The process is exceptionally fast when compared to less sophisticated methods such as phase shift interferometry (PSI). It captures all the data in one instance to generate a single-shot interference calculation [3]. However, for the method to work, certain specific criteria must be met. As stated previously, there should be no direct contact with the surface. The process must happen reasonably fast and use suitably sized sensors. The equipment cannot be overly sensitive to external environment noise. Whether the measurement is precise or relatively broad, the embedded sensor should provide the same level of accuracy. Currently, the most common optical metrology sensors are expensive to operate, slow to function, and large in dimension [4,5]. As a result, extensive time and research have been invested in developing optical methods of embedded surface topography measurement. The term “embedded metrology” refers to the process of testing industrial machine platforms without the need to extract or withdraw materials first. This involves the use of highly specialized equipment [6,7]. Tools need to be extremely accurate, stable, and capable of operating at fast speeds. There is a significant amount of research on the topic of online and inline measurement techniques. The existing literature spans several countries and focuses on diverse contexts. In most cases, the methods analyzed include the use of speckle assessment and diffuse light [8,9]. Both processes are efficient methods of examining the microscopic characteristics of surface textures. There are weaknesses in both, however, with one of the biggest being the fact that they have a testing limit. Though they are a good choice for microscale investigations, they are unable to analyze submicroscale textures [10,11]. Nevertheless, this type of optical profilometry remains valuable because it is skilled at assessing fine surfaces without the need for contact [12,13]. With this method (optical as noncontact method), it is possible to conduct accelerated data collection and eliminate the risk of interference from external effects. As discussed, the success of this method is dependent on certain criteria or conditions: the sensors must be appropriately sized; the testing tools cannot be overly vulnerable to environmental interference; and the measurement must be taken at high speed as one quick data collection. Therefore, not all scenarios lend themselves well to embedded metrology. Moreover, dynamic applications are often incompatible. Deficiencies cannot be easily identified or assessed because, in this case, the substrate is moving. When paired with a stationary objective lens, it is impossible to make a calculation. Hence, dynamic applications are also very challenging in terms of roll-to-roll production. Fortunately, it is usually enough to analyze the inline surface only and deduce the remaining lateral axis calculation from the rate at which the substrate is moving [14,15]. It is significantly more compatible concerning fast modulate signal processing than any of the counting techniques originally created for fringe calculations. For all of the methods mentioned, precision and consistency are vital. They must adhere to an optimal working point as far as possible in order to ensure accurate results. Often, this requires a concession, an offset between accuracy and speed. The more precise and stable the process, the longer it usually takes to complete. It works in the opposite direction, too. For instance, the operating process can be substantially accelerated if the traveling speed of the laser beam and its overall power are increased. Therefore, the problem is that this can result in loss of quality of surface measurement. There is a limit to how much degradation can be tolerated before the process surface begins showing severe aberrations [16]. For rapid calculations that are not dependent on direct contact with the processing surface, the best option is an optical method of extracting embedded surface measurements. This allows for the use of sensors that analyze and examine the surface but do not touch it. It should, however, be noted that some applications require the use of less common approaches, such as the micropolarizer array phase shift [17,18]. There is no shortage of optical metrology sensors on the market. However, the most commonly used tend to be expensive, inefficient, and unable to handle accelerated detection speeds. This is why single-shot interference-based measurements were developed, as they represent a novel approach to a persistent problem and provide operators with a way to overcome the limitations of older equipment. With a single-shot interference-based measurement, all the information required for analysis must be captured in a single, fast process. The data is presented in an interferogram pattern [19,20]. According to some researchers, this technique is also a great way to eliminate the impact of unwanted noise and external vibrations. The spectral phase interferometry is based on a single-shot measurement mechanism that is designed to capture data at a high rate of resolution in real-time surface investigations. Furthermore, single-shot measurements methods are unable to capture multiple analyses when working with complex physical samples. While single-shot approaches have significant potential, they are also limited in some ways. For example, they rely on a fairly restrained presumption of smoothness within the surface profile in the band limit. This makes it extremely difficult to analyze objects that contain sharp edges [21]. Image data captured from the $x$ domain is a necessary part of calculating the surface profile [22]. Moreover, multiple calculations are often needed for continuous applications, and they cannot be generated with single-shot discrete image data. Thus, they must be swapped for discrete transforms with the ability to record difficult approximations. The continued development of snapshot spatial dispersive interferometry techniques enables the production of vertical range measurements that are more precise than ever before. This is fortunate, because there is need for a more reliable method of analyzing the modulation frequency. It must also be centered on a snapshot (single-shot line scanning) measurement process such as the Fourier transform profilometry (FTP) technique. With FTP, it is possible to complete accelerated data extractions within a single complete process cycle [23–26]. As discussed, all the data are presented in one complete interferogram pattern. Employing one grating in the measurement arm to generate line/profile, the broadband-dispersed measurement interferometer can facilitate the practicality and efficiency of spatially dispersed short-coherence interferometry (SDSCI) sensor. The snapshot dispersive interferometry sensor is the first type of optical instrumentation to achieve most of the embedded measurements requirements; the snapshot interferometer is capable of submicrometer scale measurement of surface topography by using wavelength division multiplexing with a dispersive probe for single-line measurement. Instead of using a standard scanning mechanism, it uses a ${10\times}$ objective scan lens to produce instant wide-profile measurements up to 2 mm in range. As a result, the interferometric method can be beneficial in single-shot measurement applications, in which one exposure time of spectrometer camera speed acts as speed control. The present work suggests the use of the SDSCI sensor for FTP application, with a superluminescent diode (SLD) supplying a broadband light source. The FTP technique was applied for signal analysis of results, entailing subtraction of the phase shift slope from the interference intensity for every pixel. Furthermore, a spectrally resolved broadband interferogram was employed for thorough evaluation of the SDSCI sensor. This approach helped obtain a baseline for identifying the surface profiles at nanoscale level. Addressing certain difficulties encountered in this investigation, a compact inner configuration was developed for the SDSCI sensor. It is considered that the proposed SDSCI sensor can aid in creating a new and highly accurate compact device that is compatible with embedded surface and dimensional metrology applications that depend on the SDSCI sensor. The interferogram derived from a single-shot/snapshot profilometry technique was assessed on the basis of a compact SDSCI layout arrangement. Additionally, based on its performance, it was concluded that the SDSCI sensor shortened the irregular optical path length (OPL) between the reference and measurement arms of the interferometer, thus improving the ability to repeat procedures.

2. PRINCIPLE OF OPERATION

Applications to optical metrology analyses that involved using single-shot line-scanning interferometers can benefit from examining snapshot dispersive optical interferometry. The primary function of a snapshot dispersive optical interferometry sensor is presented by the same layout of SDSCI sensor in previous papers [27,28]. The components of the suggested arrangement include a Michelson interferometer with light provided by a SLD (Exalos EXS831908411) with the operational parameters of 820-nm central wavelength and 25-nm broadband laser diode (LD) (CPS635R, Thorlab) with operational wavelength 636 nm used for aligning the setup. The diffraction grating and objective scan lens (dispersive optical probe) enables the spatiality of the broadband light source to encompass the profile on the examined sample. Spatial dispersiveness is displayed by the interferometer, and measurement of the optical phase is undertaken for all sampled wavelengths at the same time. Exploiting the correlation between topography and an optical path difference (OPD) in the interferometer, an interferometric extraction of the surface topography information can be undertaken based on the spectrally resolved phase data. The dispersed profile over the examined sample can facilitate the acquisition of the surface topography information. The line-dispersed scanning profile is an important factor for snapshot spatial dispersive interferometry. This factor can be calculated in terms of special characteristics of diffraction grating for optical probe, spectrometer design, and the particular design of the numerical aperture (NA) for the objective scan lens. Any changes in the OPD at the reference arm of the spectrometer will be recorded incrementally as the output signal. Every single wavelength at each position $x$ for the sample under test will be analyzed through the spectrometer along with line scanning for a dispersive optical probe.

Any phase of the interferogram signal at each precise wavelength was introduced by the OPD. Consequently, the surface height $h$ is introduced at the same actual surface location $x$ in the sample. The general function of the spatial dispersive interferometry technique is as follows:

(1)$$I\left( {x,{\lambda _s}} \right) = {I_r}\left( \lambda \right)\, + {I_m}\left( {{x_\lambda }} \right)\cos \phi \left( {x,{\lambda _s}} \right).$$

The intensities for the reference and measurement arms can be expressed generally by $ {I_r}( \lambda ) $ and $ {I_m}( {{x_\lambda }} ) $, respectively. The phase difference is directly associated with surface height ${h}$, as shown in Eq. (2),

(2)$$\phi \left( {x,{\lambda _s}} \right)\, = \frac{{4\pi }}{{{\lambda _s}}}{h_x},$$

where $ {\lambda _s} $ is a synthetic wavelength that is defined as follows:

(3)$${\lambda _s} = \frac{{{\lambda _{\rm end}}{\lambda _{\rm start}}}}{{{\lambda _{\rm end}} - {\lambda _{\rm start}}}}.$$

The synthetic wavelength theory is based on using two wavelengths, $ {\lambda _{\rm start}} $ and $ {\lambda _{\rm end}} $ [29,30]. With FTP, it is possible to isolate the phase from the spatial interferometry mechanism, although for this to be successful, it needs to be calibrated in a specific manner so that background intensity is analyzed in the space left by the obstructed measurement arm. Following this, a single spectral interferogram pattern can be generated. The interferogram pattern is produced by the dispersive wavelength, which is an effective method of identifying the phases encoded within targeted wavelengths. As mentioned, this is advantageous because the data can be gathered and recorded in a single process. Consequently, they are also an indicator of surface height locations. At this stage of the study, a complete Fourier transform algorithm process had been used to identify the wavelength phase. The results are as follows:

(4)$$\begin{split}I\left( {x,{\lambda _s}} \right) & ={I_r}\,\left( \lambda \right) + \frac{1}{2}{I_m}\,\left( {{x_{{\lambda _s}}}} \right)\exp \,\left[ {i\phi \,({x_{{\lambda _s}}})} \right]\\ &\quad+ \frac{1}{2}{I_m}\,\left( {{x_{{\lambda _s}}}} \right)\exp \,\left[ { - i\phi \,({x_{{\lambda _s}}})} \right].\,\end{split}$$

The mid-term of Eq. (4) can be modeled by the following expression:

(5)$$c( {{x_{{\lambda _s}}},{\lambda _s}} ) = \frac{1}{2}{I_m}( {{x_{{\lambda _s}}}} )\exp[ {i\phi \,({x_{{\lambda _s}}})} ].$$

By using discrete Fourier transform (DFT) in Eq. (5), the new emerging equation is expressed as follows:

(6)$$I( {{x_{{\lambda _s}}},{\lambda _s}} ) = A( {{\lambda _s}} ) + C( {{x_{{\lambda _s}}}} ) + {C^*}( {{x_{{\lambda _s}}}} ).$$

The $ {C^*}( {{x_{{\lambda _s}}}} ) $ demonstrates the complex conjugate of $ C $. By subsequently applying the inverse DFT to the conjugated term in Eq. (6) in order to retrieve the actual phase, we choose the complex logarithm. Consequently,

(7)$$\begin{split}\log \left\{ {\frac{1}{2}{I_m}\left( {{x_{{\lambda _s}}}} \right)\exp \left[ {i\,\phi \left( {{x_{{\lambda _s}}}} \right)} \right]} \right\} = \log \left[ {\frac{1}{2}{I_m}\left( {{x_{{\lambda _s}}}} \right)} \right] + i\,\phi \left( {{x_{{\lambda _s}}}} \right).\end{split}$$

At this point, the wavelength phase is extracted and isolated within the imaginary part. When required, it can be “unpacked” and revealed by using a compatible algorithm. In accordance with the wavelength scanning interferometry mechanism, the resolution of the optical measurement is based on the shortest synthetic wavelength that relates to the maximum tuning ranges ($ \Delta \lambda $) as follows:

(8)$${ \wedge _{\min }} = \,\frac{{{\lambda ^2}}}{{\Delta \lambda }},$$

where $ { \wedge _{\min }} $ is the light source coherence length, $ \lambda $ is the light source wavelength (825 nm of SLD), and $ \Delta \lambda $ is the light source broadband (25 nm of SLD),

(9)$$\phi = \frac{{2\pi }}{{{\lambda _s}}}\Delta x = \frac{{2\pi }}{{{\lambda _s}}}2h.$$

When $L = h$, height ($h$) is correlated with half of the total OPD in the interferometer pattern. Thus, the calculation may be executed by identifying the absolute of the phase change throughout the entire wavelength scanning range. Refer to Eq. (10):

(10)$$\Delta \phi = \frac{{4\pi h}}{{{\lambda _s}}} = 4\pi {L_{\rm ref}}\,\left(\frac{1}{{{\lambda _{\rm start}}}} - \frac{1}{{{\lambda _{\rm end}}}}\right),$$

where $ {\lambda _{\rm start}} $ (790 nm), $ {\lambda _{\rm end}} $ (836 nm) are the starting and ending wavelengths of the broadband light source, respectively. By considering the phase difference $ \Delta \phi = 2\pi $, and by substitution in Eq. (10), the $ {L_{\rm ref}}\, = h $ is about ($8\,\,\unicode{x00B5}{\rm m}$). When utilizing spatial dispersive interferometry, it is necessary to accommodate various constraints such as diffraction grating (1200 L/mm), spectrometer resolution rate, resolution of the device, and the limitations of the scanning objective lens. Once the light beam from the SLD has reached the diffraction grating, the first order can be calculated and distributed throughout the sample. It is then possible to identify the coherence length being employed. The resolving power of a diffraction grating (R) can be expressed as follows:

(11)$$R = \frac{\lambda }{{\Delta \lambda }}.$$

For SLD, the beam size is $({8.3}\,\,{\rm mm})\,{\rm = }D = N$,

(12)$$R = m\times N,$$

when ($m$) represents the number of illumination grooves for the first order ($R = 1200 \times 8.3\,\,{\rm mm} = 9960$). Consequently, the spectral resolution ($ \Delta \lambda $) is identified in the following way: $ \Delta \lambda = ( {825\,\,{\rm nm}/9960} ) = 0.0828\,\,{\rm nm} $. The quantity of points of spatial dispersive interferometry sensor that may be determined is $N = \;({25}\;{{\rm nm}/0.0828}\;{{\rm nm}})= {302}$ points. Lastly, the spatial dispersive interferometry mechanism generates a coherence length calculation, $ {L_c} = {\rm [}0.66 \times \,{\lambda ^2}/\Delta \lambda ) = { [}0.66\,\, \times \,{(825\,\,{\rm nm})^2}/0.0825\,\,{\rm nm}] $, as regards the surface height of the targeted profile. This is identified by calculating the wavelength phase and analyzing how it relates to the other measurements. In this instance, for example, the calculation of coherence length on both sides is $ 2{L_c} = 10.84\,\,{\rm mm} $ for the spatial dispersive interferometry sensor. Figure 2 shows the full description Michelson interferometer setup for the ordinary and dispersive configurations (a and b, respectively).

Fig. 1. Snapshot dispersive optical interferometry sensor based on Michelson configuration.

Download Full Size | PDF

Fig. 2. Michelson interferometers. (a) Ordinary interferometer setup; (b) dispersive interferometer configuration.

Download Full Size | PDF

These computed results highlight the increasing vertical scanning range of dispersive optical probe orientation from 200 nm ($ \lambda /4 $) to 18 µm. These results support the dispersive optical probe sensor’s ability to measure the different profile sample types that meet the embedded metrology requirement. The concept of snapshot optical sensor analysis information under test using a synthetic wavelength approach has been described in the flow chart steps given in Fig. 3.

Fig. 3. Snapshot optical sensor analysis data steps flow chart.

Download Full Size | PDF

3. EXPERIMENTAL SETUP

Figure 1 illustrates the configuration of the initial SDSCI sensor and its elements. The beam of the light source penetrated the beam splitter to the dispersive optical probe, followed by its projection on the examined sample. A unique design for the objective scan lens (LSM02-BB, Thorlabs), a ruled reflective diffraction grating (GR25-1210, Thorlabs), and the examined specimen (ROBERT-511-single groove, ${\rm depth} - d = 1\,\,\unicode{x00B5}{\rm m}$ and ${\rm width} - w = 100\,\,\unicode{x00B5}{\rm m}$) constituted the components of the unique structure of the dispersive probe. The dispersive probe is responsible for receiving the reflection of the dispersed light from the specimen being tested. Furthermore, a Michelson interferometer arrangement represented the FTP that was the interferometer layout. The examined sample reflected the wavefronts that provided the spectral interferogram, while the compact spectrometer (S150, Solar Laser Systems, Minsk, Belarus) was employed for analysis purposes with the reference mirror. The zero-order beam reflected from the optical probe diffraction grating served as the reference beam in the amended scheme as an alternative to employing a distinct reference beam generated from the main beam splitter. Therefore, before reaching the diffraction grating, where it was diffracted at different angles, the beam followed the same trajectory. This made the sensor less susceptible to environmental impact, as the path length discrepancies were minimized to at least one-third of the length of the preceding arrangement. Measurement of the interferogram pattern resulting from the interference between the zero- and first-order diffraction beams was conducted to analyze the surface profile. In the Michelson interferometer arrangement, the reference beam was the zero-order beam that reflected off the grating forms, while the measurement beam was the first-order beam that reflected off the diffraction grating forms. Moreover, a reflecting mirror was incorporated in the zero-order beam, while the first-order beam was propagated via the dispersive probe across the sample. The diffraction grating caused the angular dispersion of the 8.3-mm wide broadband SLD beam in the dispersive probe. An objective lens (LSM02-BB) with 18-mm effective focal length was subsequently employed for collimation and concentration of the dispersed light on the specimen under test. The general diffraction grating equation can be shown as follows:

(13)$$m\lambda = d\,(\sin \alpha + \sin \,\beta ),$$

where $d$ is the diffraction grating period, ${m}$ is the integer value, and $ \lambda $ is the wavelength of the light source (incident light). $ \beta ,\alpha $ are the diffracted and incident angles, respectively, shown in Fig. 4.

Fig. 4. Diffraction gratings orders (first and zeroth orders).

Download Full Size | PDF

Hence, the phase can be introduced at every single point on the specimen being tested by the reflected light. When the SLD broadband light was dispersed upon the specimen by a first-order beam through spatial scanning (i.e., the lateral scanning range), direction $x$ can be expressed as in Fig. 5. Therefore, the surface scanning range ($ S $) can be defined as per the following equation:

(14)$$S = f\frac{{\Delta \lambda }}{{d\,\cos \,\beta }}.$$

The surface interrogation is gathered from the phase signal detection. The diffraction grating generates a first order that can be represented as a scanning range based on the objective lens. Therefore, $ f $ is the focal length of the objective scanning lens, $ \beta $ is the diffraction angle, $d$ is the number of grooves per millimeter (1200 L/mm), and finally, $ \Delta \lambda $ is the light source broadband (25 nm). The same parameters have been set with this configuration, such as the SLD center wavelength of 825 nm with the same value of angular dispersion (0.042 rad/nm), with the incident angle being ${2^\circ}$ and diffraction angle being ${73.55^\circ}$. Consequently, the scan range is approximately linear and corresponds to the wavelength scan range. Figure 6 presents the interferogram pattern recorded by spectrometer for the sample under test (1 µm-step height).

Fig. 5. Snapshot dispersive probe interferometry sensor and sample mapping information showing positions’ wavelength distribution of the specimen under test.

Download Full Size | PDF

Fig. 6. Interferogram pattern of the snapshot spatial dispersive interferometry sensor showing two spikes for sample.

Download Full Size | PDF

4. EXPERIMENTAL RESULTS AND DISCUSSION

The step-height sample can be simulated to drive and produce a complete simulation for the snapshot interferometry sensor, as shown in Fig. 7(a). Figure 7(b) illustrates the calculations for step-height range, which spans from more than 200 nm to 1 µm. Though the surface measurement analyses can only produce partial data for the samples, they are still useful indicators, particularly regarding online approaches. Considering the snapshot spatial dispersive interferometry sensor outcome results, it is possible to approximate these results similar to that in real-time operation. This type of simulated process is highly valuable for this application. For example, it is useful when applying the vertical measurement range that must be phase-altered according to the sample being tested [see Fig. 7(b)]. To retrieve the sample information from fringe patterns, Eq. (1) represents the best option for calculating sample characterizations. For this investigation, 16 fringe patterns were used to determine the carrier frequency of the boundary for the interference. This translates to six fringes per sample. In terms of defining the terms for the changing sign of the phase for interference fringe casting, the behavior and responses are largely the same, and a step-height position may be inferred. The snapshot dispersive optical sensor output result is improved to overcoming system limitations ($ \lambda /4 $) at any point of the sample under investigation by phase-changing at this point of measurement.

Fig. 7. General simulations outcome for (a) step-height sample; (b) fringes intensity pattern.

Download Full Size | PDF

The outcome of this work shows that the wrapping phase is a good observation for this experiment. As discussed in Fig. 8(a), the FTP method is effective for demodulating the fringe patterns. This is a necessary part of isolating and identifying the phase within a targeted wavelength. When a smooth sample surface is analyzed using interferometric methods, discontinuous height samples within the targeted objects may be generated.

Fig. 8. (a) Fourier transform frequency domain outcome; (b) unwrapping phase and step height.

Download Full Size | PDF

Fig. 9. Step-height and surface profile images. (a) ROBERT-511-single groove, $d = 1\,\,\unicode{x00B5}{\rm m}$ and $w = 100\,\,\unicode{x00B5}{\rm m}$; (b) and (c) surface scanning profiles for the specimen measurement using a Taylor Hobson CCI 3000 instrument.

Download Full Size | PDF

Fig. 10. Step-height measurement for ROBERT-511-single-groove sample using synthetic wavelength approach based on snapshot dispersive optical.

Download Full Size | PDF

Fig. 11. Step-height repeatability histogram for 100 measuerements for (a) diamond-turned multistep sample; (b) ROBERT-511-single groove, $d = 1\,\unicode{x00B5}{\rm m}$ and $w = 100\,\unicode{x00B5}{\rm m}$.

Download Full Size | PDF

Essentially, the phase-unwrapping process or system is possible because the discrete derivatives of the “unpacked” phase are revealed. Adjacent pixel variations are generated if these discrepancies are smaller in absolute value compared to the total step height of the surface profile [refer to Fig. 8(b)]. Therefore, this methodology was selected because it fulfils the conditions necessary for a successful embedded metrology analysis. The outcomes of the work indicate a strong relationship between the first and last wavelength phases. As a result, it may be argued that this represents a viable derivation for the expanded vertical range. Thus, the investigation can be considered a success, as its primary purpose was to simulate variations in vertical measurement range using a snapshot of spatial dispersive interferometry sensor parameters. Practically, the same SDSCI sensor configuration parameters have been used to measure 1 µm step-height sample. The ROBERT-511-single groove ($d = 1\,\,\unicode{x00B5}{\rm m}$ and $w = 100\,\unicode{x00B5}{\rm m}$) was measured with the new approach application snapshot dispersive interferometer sensor. Figure 9 shows the sample surface profiles of the specimen measured using a Taylor Hobson CCI 3000 instrument (UK) and by using surface inspection software (Surfstand, University of Huddersfield, Huddersfield, UK). The step AB is indicated in the surface profile for step height [see Figs. 9(b) and 9(c)].

The results were calculated using a new approach based on the synthetic wavelength, which provided good results that ensured the expansion of a wide vertical range of snapshot dispersive optical interferometry sensor capabilities to measure various samples beyond the sensor measurement limitation $ \lambda /4 $. The outcome results of the new approach are depicted in Fig. 10.

To identify important parameters for the optical inspection instruments, repeatability is an essential parameter to be determined. Two samples have been measured in the same environmental conditions and similar optical sensor configuration. Figures 11(a) and 11(b) show the histogram for 100 measurements’ repeatability for a diamond-turned multistep sample (step height 600 nm) and ROBERT-511-single groove samples, respectively. The snapshot dispersive optical interferometry sensor demonstrated that measurement repeatability using a synthetic wavelength approach has been improved to 20 nm. The boundary of repeatability measurements is 2 standard deviations (${2}\sigma $). The deviation error of step-height measurement of using the new signal processing approach is approximately 19 µm compared to the Taylor Hobson CCI 3000 noncontact profilometer instrument.

A summary of results using FTP and synthetic wavelength approaches is presented in Table 1.

Table 1. Comparison between FTP and New Synthetic Wavelength Approaches

View Table

5. CONCLUSION

A new synthetic wavelength method is suggested to ensure the snapshot dispersive optical interferometry sensor is able to extend a vertical range measurement of the sample. The results of the experiment showed clear evidence that the snapshot sensor successfully expanded vertical range measurement. The experimental results shows that the synthetic wavelength approach sufficiently validated the value of the dispersive optical sensor used for this research. With the synthetic wavelength method for support, surface calculations are significantly faster, had a compact design, and were more accurate with a greater scope; these are important requirements for embedded metrology systems.

This report was divided into two clear sections. The first discussed the mechanisms of the dispersive optical sensor and why it was a valuable tool. It also outlined key variables such as system resolution, the scanning objective lens, diffraction grating, and the rate of spectrometer resolution. The impact of all these variables on surface measurements was then considered and evaluated. The second part discussed the spatial dispersive interferometry measurement that used a synthetic wavelength method; though it was largely successful, it did have some weaknesses. For example, the FTP approach is less suitable for surface profiles showing a high-frequency content in the lateral dimension. It is often difficult to generate precise measurements because of the difficulty, and even impossibility, of isolating the imposed carrier fringes; this needs further investigation. The step-height repeatability in the sensor has been demonstrated with a good improvement degree of repeatability range from 22 to 20 nm compared to the previous measurement method.

Funding

Ministry of Higher Education and Scientific Research; Engineering and Physical Sciences Research Council (EP/P006930/1).

Acknowledgment

The authors gratefully acknowledge the Department of Laser and Optoelectronics Engineering Department at the University of Technology, MOHESR, Iraq for funding this work as well as the UK’s EPSRC funding for the Future Metrology Hub.

REFERENCES

1. S. Ghodrati, S. G. Kandi, and M. Mohseni, “Nondestructive, fast, and cost-effective image processing method for roughness measurement of randomly rough metallic surfaces,” J. Opt. Soc. Am. A 35, 998–1013 (2018). [CrossRef]

2. G. Samta, “Measurement and evaluation of surface roughness based on optic system using image processing and artificial neural network,” Int. J. Adv. Manuf. Technol. 73, 353–364 (2014). [CrossRef]

3. K. Kitagawa, “Single-shot surface profiling by multiwavelength interferometry without carrier fringe introduction,” J. Electron. Imaging 21, 021107 (2012). [CrossRef]

4. E. Gadelmawla, “Estimation of surface roughness for turning operations using image texture features,” Proc. Inst. Mech. Eng. Part B 225, 1281–1292 (2011). [CrossRef]

5. S. Ghodrati, M. Mohseni, and S. G. Kandi, “Application of image edge detection methods for precise estimation of the standard surface roughness parameters: polypropylene/ethylene-propylene-diene-monomer blend as a case study,” Measurement 138, 80–90 (2019). [CrossRef]

6. P. Sarma, L. Karunamoorthy, and K. Palanikumar, “Surface roughness parameters evaluation in machining GFRP composites by PCD tool using digital image processing,” J. Reinf. Plast. Compos. 28, 1567–1585 (2009). [CrossRef]

7. S. Ghodrati, S. G. Kandi, and M. Mohseni, “How accurately do different computer-based texture characterization methods predict material surface coarseness? A guideline for effective online inspection,” J. Opt. Soc. Am. A 35, 712–725 (2018). [CrossRef]

8. R. S. Lu and G. Y. Tian, “On-line measurement of surface roughness by laser light scattering,” Meas. Sci. Technol. 17, 1496–1502 (2006). [CrossRef]

9. K. Wang, H. Martin, and X. Jiang, “Actively stabilized optical fiber interferometry technique for online/in-process surface measurement,” Rev. Sci. Instrum. 79, 023109 (2008). [CrossRef]

10. B. Dhanasekar and B. Ramamoorthy, “Restoration of blurred images for surface roughness evaluation using machine vision,” Tribol. Int. 43, 268–276 (2010). [CrossRef]

11. G. A. Al-Kindi and B. Shirinzadeh, “Feasibility assessment of vision-based surface roughness parameters acquisition for different types of machined specimens,” Image Vis. Comput. 27, 444–458 (2009). [CrossRef]

12. Z. Sárosi, W. Knapp, A. Kunz, and K. Wegener, “Detection of surface defects on sheet metal parts by using one-shot deflectometry in the infrared range,” in Infrared Camera Applications Conference (ETH Zurich, IWF, 2010), pp. 243–254.

13. E. Papastathopoulos, K. Körner, and W. Osten, “Chromatic confocal spectral interferometry,” Appl. Opt. 45, 8244–8252 (2006). [CrossRef]

14. P. C. Lin, P.-C. Sun, L. Zhu, and Y. Fainman, “Single-shot depth-section imaging through chromatic slit-scan confocal microscopy,” Appl. Opt. 37, 6764–6770 (1998). [CrossRef]

15. I. Dancus, S. T. Popescu, and A. Petris, “Single shot interferometric method for measuring the nonlinear refractive index,” Opt. Express 21, 31303–31308 (2013). [CrossRef]

16. Y. Guo, Y. Wang, and M. Jin, “Improvement of measurement range of optical fiber displacement sensor based on neutral network,” Optik 125, 126–129 (2014). [CrossRef]

17. H. Rahman, H. Rahim, H. Ahmad, M. Yasin, R. Apsari, and S. W. Harun, “Fiber optic displacement sensor for imaging of tooth surface roughness,” Measurement 46, 546–551 (2013). [CrossRef]

18. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861–6868 (2005). [CrossRef]

19. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001). [CrossRef]

20. K. Kitagawa, Single-Shot Interferometry without Carrier Fringe Introduction (SPIE, 2012).

21. D. French, C. Dorrer, and I. Jovanovic, “Two-beam SPIDER for dual-pulse single-shot characterization,” Opt. Lett. 34, 3415–3417 (2009). [CrossRef]

22. R. Su, Y. Wang, J. Coupland, and R. Leach, “On tilt and curvature dependent errors and the calibration of coherence scanning interferometry,” Opt. Express 25, 3297–3310 (2017). [CrossRef]

23. Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984). [CrossRef]

24. C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1, 103 (1992). [CrossRef]

25. M. Sugiyama, H. Ogawa, K. Kitagawa, and K. Suzuki, “Single-shot surface profiling by local model fitting,” Appl. Opt. 45, 7999–8005 (2006). [CrossRef]

26. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983). [CrossRef]

27. M. A. Hassan, H. Martin, and X. Jiang, “Surface profile measurement using spatially dispersed short coherence interferometry,” Surf. Topography 2, 024001 (2014). [CrossRef]

28. M. A. Hassan, H. Martin, and X. Jiang, “Development of a spatially dispersed short-coherence interferometry sensor using diffraction grating orders,” Appl. Opt. 56, 6391–6397 (2017). [CrossRef]

29. P. De Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991). [CrossRef]

30. R. Dändliker, R. Thalmann, and D. Prongué, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988). [CrossRef]

Sample Measurement Type	SDSCI Layout	Measurement Method	Repeatability (nm)
Diamond turned multistep (step height 600 nm)	new compact layout	FPP	22
ROBERT-511-single groove ( $d = 1 µ m$ )	new compact layout	synthetic wavelength	20

Synthetic wavelength to increase the snapshot optical sensor’s elevated vertical measurement ranges

Abstract

1. INTRODUCTION

2. PRINCIPLE OF OPERATION

3. EXPERIMENTAL SETUP

4. EXPERIMENTAL RESULTS AND DISCUSSION

5. CONCLUSION

Funding

Acknowledgment

REFERENCES

Cited By

Figures (11)

Tables (1)

Equations (14)

Applied Optics