Open Access
Add to BibSonomy
Abstract
In this study, we provide and validate an enhanced dispersion-encoded full-range spectral interferometry that offers improved measurement accuracy for samples characterized by significant depth, inclination, and roughness. Due to the low intensity of the optical signal in these samples, the optical signal is easy to be overwhelmed by the disturbance terms, demanding a more precise phase compensation. To address this issue, the direct current is removed by subtracting the envelope of the interference spectrum, allowing the weak signal near zero optical delay can be identified. Besides, considering the unwrapped phase error caused by the spectrometer aberrations, only the data with good phase continuity are preserved, which improves the accuracy of phase compensation. Using the proposed technique, the depth measurement range of the system is extended from 6 mm to 12 mm, while achieving an axial measurement precision of 2.5µm. In addition, the full-depth images of a ceramic standard step block and a 3D-printed sample are measured. It shows that our system exhibits superior adaptation to complex surfaces compared to the laser line profiler.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spectral-domain interferometry, also referred to as low coherence interferometry or optical coherence tomography (OCT), is a three-dimensional imaging technique that offers the benefits of non-destructive detection and high resolution [1]. This technique can retrieve parameters such as the geometric path difference of the interferometer or the thickness and group refractive index of the material by performing a Fourier analysis of the interference spectrum. However, since the detector can only collect the real part of the complex spectrum, the Fourier-transformed image of the collected spectrum will be symmetric with zero optical delay, which makes the mirror image artifact and the real signal cannot be distinguished. To avoid such signal aliasing, conventional spectral interferometry only uses half of the available measurement range [2].
There are two main types of techniques that have been developed to address this problem: (1) the phase modulation method, and (2) the dispersion-encoded full-range technique. The phase modulation method obtains the complex spectrum by introducing multiple phase shifts in the single-point measurement to remove the mirror signal. The hardware solutions include moving the reference mirror with PZT [3–5], moving grating method [6], imaging spectrometer [7], acoustic-optic modulation [8], electro-optic modulation [9], etc. Another method for introducing a phase shift between consecutive A-scans is to decenter the galvanometer's scanning pivot point [2,10,11]. The above schemes require the phase stability of the measurement spectrum, so the damping system is highly required. The dispersion-encoded full-range technique is simple in principle [12–17], requires only one measurement for a single location, and is not affected by phase fluctuations caused by environmental vibrations [18]. By introducing a large dispersion mismatch between the reference and the sample arm, the signal and the mirror image carry nonlinear phase terms of opposite signs, respectively. Then the nonlinear phase is compensated in one direction, allowing the sharpened signal to be distinguished from the blurred mirror image, thereby utilizing both the positive and negative spatial domains. Many scholars have carried out research on this technology. S. Witte et al. developed a full-field Fourier domain optical coherence tomography system using dispersion-encoded technology, which can record images of 2.5 × 0.2 mm at a depth resolution of 3µm [13]. Hofer et al. designed a dispersion-encoded full-range OCT with a depth measuring range of 2746µm and an axial resolution of 3µm using a 30 mm thick SF11 block [14].
In industrial testing, damping devices and phase shifting devices will increase the cost of the system, while the dispersion encoded technique is more suitable because of its simple principle and better vibration resistance. Reichold et al. proposed a hyperspectral profilometer employing a pinhole array with a system depth measurement range of 0.825 mm, allowing a measurement inclination of 33.3 mrad and a measurement accuracy of 6 nm [19]. Taudt et al. demonstrated a dispersion-encoded profiler that achieves an axial resolution of 0.1 nm over a measurement range of 80µm [20]. However, there are few studies on the topography measurement of the rough-surface and large-angle workpieces with a depth of more than 10 mm. Considering that the interference signals of the samples with rough surfaces and large dip angles are usually extremely weak [21–23], the accurate extraction of the dispersion phase and the suppression of disturbance term still need to be solved.
In this study, we aim to achieve micrometer-accuracy topography for samples with large inclinations, rough surfaces and a depth range of more than 10 mm. We proposed an improved dispersion-encoded full-range spectral interferometry, selected a suitable dispersion glass block, and achieved a range doubling for a system with a measurement range of 6 mm. Considering that the weak interference signal is easily submerged by the disturbance term and the phase compensation is inaccurate, an improved dispersion phase extraction method and a direct current(DC) removal method are proposed. In the improved dispersion phase extraction method, the aberrations of the spectrometer are taken into account [24], and the continuity of the unwrapped phase is evaluated to avoid the influence of spectral data in the large aberration region on the dispersion phase extraction results. Before the standard numerical dispersion compensation routine, a step of DC removal in the spectral domain is carried out. In previous studies, DC is mostly removed by setting the intensity at zero optical delay to 0 in the spatial domain [13], but the DC spreading still exists. We remove the DC component in the spectral domain, thereby suppressing the DC spreading in the spatial domain and revealing the weak signals near the zero optical delay. The full-range images of a ceramic standard step block and a metal 3D-printed sample were obtained using our spectral interferometry system combined with the improved dispersion encoded full-range algorithm. The measurement results were compared with those of a commercial line laser profiler.
2. Theories and methods
2.1 Basic principles of dispersion encoded OCT
The interference spectrum acquired by the spectral domain optical coherence tomography (SD-OCT) system can be expressed as,
Usually, the DC term and autocorrelation term are removed during data processing, without loss of generality, set ${a_R} = 1$, then Eq. (1) can be expressed as:
Numerical dispersion compensation is performed by multiplying Eq. (2) by ${e^{ - i{\varphi _n}(k)}}$, and then the inverse Fourier transform of the compensated result yields the information in the spatial domain,
2.2 DC removal in the spectral domain suppresses DC spreading
For the interference spectrum collected in the actual system, it is difficult to completely remove the DC component. Considering that the samples measured in this paper are single-layer samples and the internal reflection of the system is negligible, the autocorrelation signal can be ignored. Considering that the DC component is not negligible, and ${a_R} = 1$, then Eq. (1) can be approximated as,
To study the influence of DC component spreading, the dispersion compensation is temporarily not performed here, and the spatial domain information is obtained by direct inverse Fourier transform of Eq. (5),
In Eq. (6), the DC term $\Gamma (z) \otimes \delta (z)$ has a certain spreading. If the DC term is large enough, there will be a DC component spreading to drown out the nearby weak signals. In previous studies, the method of setting the value of the transformed spectrum at $z = 0$ to zero is mostly used to remove DC [13], which cannot completely remove the spreading of the DC component. The DC removal method proposed in this paper eliminates the DC component from the spectral domain, so that not only the intensity of zero optical delay is suppressed, but also the DC component spreading is reduced. The processing steps are as follows:
- 1. Find the local maximum ${I_{peak}}({k_i})$ and the local minimum ${I_{valley}}({k_j})$ of the interference spectrum, as well as their locations ${k_i}$ and ${k_j}$.
- 2. Compute the upper envelope ${I_{peak}}(k)$ and lower envelope ${I_{valley}}(k)$ by extrapolation fitting and mean filtering of ${I_{peak}}({k_i})$ and ${I_{valley}}({k_j})$, respectively.
- 3. Compute the DC component and the DC removed spectrum according to the following equations, ${I_{dc}}(k) = [{I_{peak}}(k) + {I_{valley}}(k)]/2$, ${I_{dc\_{remove}}}(k) = I(k) - {I_{dc}}(k)$.
Using the parameters of the spectrometer (Cobra-S 800, Wasatch Photonics, Inc.) and the light source (SLD830S-A20W, Thorlabs, Inc.) employed in this study, we designed a numerical simulation to confirm the effectiveness of the proposed DC removal method. In the simulation, the discrete wavenumber is $k = [2\pi /0.813,\ldots ,2\pi /0.870]$µm−1, and the number of sampling points is 2048, $a({z_0}) = 0.01$, ${z_0} = 4$ pix. Ignoring the dispersion mismatch and setting ${\varphi _n}(k) = 0$, Eq. (5) can be written as follows:
Fig. 1. Results of DC removal processing. (a) Interference spectrum without DC removal; (b) Interference spectrum with DC removal; (c) Transformation spectrum without DC removal; (d) Transformation spectrum processed by conventional and improved DC removal methods respectively.
This study aims to achieve full-range measurement using the dispersion encoded technology, so the pixels near $z = 0$ are needed for measurement. Due to the extremely small sample reflection coefficient and the DC spreading caused by the asymmetric light source power spectrum, the conventional DC removal method has great limitations. In contrast, the improved DC removal method enables the weak signal near the 0 frequency to be resolved, which better meets our measurement requirements.
2.3 Effect of spectrometer aberrations on the unwrapping phase
A key step in the dispersion encoded technique is to measure the nonlinear phase introduced by the dispersion mismatch of the system. The experimental measurement process of the nonlinear phase is phase unwrapping of the interference spectrum, then polynomial fitting of the unwrapping phase, and then extracting the nonlinear term. However, phase unwrapping of the interference spectrum is affected by the optical aberration of the spectrometer, which increases the polynomial fitting error of the unwrapping phase and leads to the error of the nonlinear phase. This issue is explained in detail in the Supplement 1. Here, we only present the experimental results of this conclusion. We used three spectrometers of the same model (Cobra-S 800, Wasatch Photonics, Inc.) to collect the same interference light, phase unwraps the interference spectrum, and perform polynomial fitting analysis. Figure 2(a) shows the wavelength calibration curves of the three spectrometers. Figure 2(b) shows the polynomial fitting error of the unwrapping phase obtained by the three spectrometers. The error at the edge pixel is larger because the interference fringe in this region is less than one period, which leads to the error of phase unwrapping. Since the same interference spectrum is processed and the algorithm parameters used are consistent, it can be considered that the data difference in the middle region in Fig. 2(b) is only from the spectrometers themselves. That is to say, the aberrations of the spectrometer do reduce the phase unwrapping accuracy of the interference spectrum.
Fig. 2. Parameters and data fitting errors of the three spectrometers. (a) Calibration curves of the three spectrometers; (b) Polynomial fitting errors of unwrapping phase for three spectrometers.
To solve this problem, we propose an improved dispersion phase extraction algorithm, which only uses the data of the pixels in the region that are less affected by spectrometer aberration for phase extraction. The specific processing steps are as follows:
- 1. The phase unwrapping of the interference spectrum $I(k)$ is carried out, and the unwrapped phase ${\varphi _0}(k)$ is obtained.
- 2. The second-order derivative of the unwrapped phase $\frac{{{\partial ^2}{\varphi _0}(k)}}{{\partial {k^2}}}$ is used to characterize the acceleration of the phase change, and the region with a smaller $|\frac{{{\partial ^2}{\varphi _0}(k)}}{{\partial {k^2}}}|$ is considered to be less affected by spectrometer aberration.
- 3. Compare $|\frac{{{\partial ^2}{\varphi _0}(k)}}{{\partial {k^2}}}|$ with a given threshold T, and cut out the largest continuous sequence $\{ {\varphi _0}({k_m}),{\varphi _0}({k_{m + 1}}),\ldots ,{\varphi _0}({k_n})\} $ satisfying $|\frac{{{\partial ^2}{\varphi _0}(k)}}{{\partial {k^2}}}|< \textrm{T}$.
- 4. Polynomial fitting is performed on the sequence to extract the nonlinear term, which is the nonlinear phase ${\varphi _n}(k)$ caused by the dispersion mismatch of the two arms.
2.4 Improved dispersion-encoded full-range processing algorithm
The flowchart of the improved full-range dispersion encoded algorithm is shown in Fig. 3, which includes two parts: the depth coordinate extraction and the phase compensation factor calculation. The former is on the left side, and the steps are as follows. 1. The interference spectrum $I(k,{x_j},{y_j})$ of any certain point $({x_j},{y_j})$ is obtained by scanning the sample. 2. The interference spectrum without the DC component ${I_{\textrm{dc}\_{remove}}}(k,{x_j},{y_j})$ is obtained by using the DC removal method. 3. ${I_{{\textrm{dc}}\_{remove}}}(k,{x_j},{y_j})$ is multiplied by ${e^{ - i{\varphi _n}(k)}}$ for dispersion compensation, and then inverse Fourier transform is performed to obtain the spatial domain information. 4. The sub-pixel precision optical delay $Z({x_j},{y_j})$ corresponding to the sample at the point $({x_j},{y_j})$ is obtained using the energy centrobaric correction method(ECCM) [25]. The right side of Fig. 3 shows the calculation steps of the phase compensation factor. 1. The interference spectrum $I({k_0})$ is obtained from the plane mirror sample. 2. The interference spectrum without the DC component ${I_{{\textrm{dc}}\_{remove}\_{0}}}({k_0})$ is obtained by the proposed DC removal method. 3. The dispersion phase ${\varphi _n}(k)$ is obtained by using the improved dispersion phase extraction algorithm.
3. Experimental setup
Since the content of simulation analysis involves the structure and specific parameters of the experimental system, the experimental system is first introduced here. Figure 4 shows the schematic diagram of the experimental system. A superluminescent diode (SLD830S-A20W, Thorlabs, Inc.) is used as the light source with a central wavelength of 830 nm and a 3 dB bandwidth of 55 nm. The output light is divided into two paths by a fiber coupler, for the reference arm and the sample arm. The reference light is reflected by the mirror. The sample light is scanned on the sample surface by a two-dimensional galvanometer and a scanning lens ($f = 54mm$). The designed dispersion glass block is placed behind the collimator 2 of the sample arm, thus introducing a large dispersion to the system. The reflected light from the reference arm and the sample arm are combined by a fiber coupler and interfered. The interference spectrum is collected by a 2048-pixel spectrometer (Cobra-S 800, Wasatch Photonics, Inc.) with a wavelength resolution of 0.03 nm. The lateral resolution of the measurement system is 15µm, the spatial discrete resolution determined by the spectrometer is 6.2µm, and the half-range measurement depth is 6291.2µm.
Fig. 4. Schematic diagram of the system. L1 is an achromatic lens, L2 is the collimator lens and L3 is the focusing lens, DG is a dispersion glass block made of HZF73, and FC is a 50/50 fiber coupler.
4. Simulation
4.1 Accurate solution of the dispersion phase
In reality, the dispersion mismatch of the system comes from the fiber, lens, glass block, etc. However, the residual dispersion mismatch in the system excluding dispersive glass is small and it is difficult to obtain a theoretical value. Here, we only analyze the dispersion phase introduced by the glass block and evaluate the accuracy of the phase extraction algorithm by comparing the difference between the measured value and the theoretical value.
For the proposed system setup, the phase introduced by the dispersion glass can be written as follows:
where d is the thickness of the dispersion glass, $n(k)$ is the refractive index of the dispersion glass, and k is the wave number. Notice that the dispersion phase can be polynomially fitted and expanded as follows:We built an almost dispersion-balanced interferometer and installed a 21 mm thick HZF73 glass block in one arm. The nonlinear phase introduced by the glass block was measured experimentally and compared with the simulation. We measure the interference spectrum at four different locations 20 times each and use the data to calculate the dispersion phase. During data processing, it was noted that the repeatability of the dispersion phase obtained by different fitting orders was different. We evaluated the stability of the nonlinear phase and the broadened signal obtained through polynomial fitting of orders 2, 3, and 4, as well as the deviation from the simulation. The results are shown in Fig. 5. Standard deviation (SD) and root mean square error (RMSE) are calculated by the following formula respectively:
Fig. 5. SD and RMSE of nonlinear phase and broadened signal measured from a 21 mm thick HZF73 block. (a) SD curves of the nonlinear phase with different order fitting; (b) RMSE curves of the nonlinear phase compared with the simulation values for different order fitting; (c) SD curves of broadened signal with different order fitting; (d) RMSE curves of the broadened signal compared with the simulation results for different order fitting.
4.2 Selection of suitable dispersion glass blocks
According to Eq. (8), to increase the nonlinear phase caused by dispersion, it is necessary to increase the thickness of the glass block or choose a material with large dispersion. Based on the small Abbe number ${v_d}$, several common glass materials are selected: HZF73, SF11, ZnSe, and FDS16-W. Table 1 shows the Abbe numbers of these materials and the chromatic dispersion at 840 nm.
Table 1. Optical constants of selected materials
Table 1 indicates that, from largest to smallest, the chromaticity dispersion of the four materials at 840 nm is ZnSe, FDS16-W, HZF73, and SF11, and the values of ${v_d}$ are consistent with this. In addition, the HZF73 material was selected because of its nontoxicity and accessibility. Subsequently, glass blocks with thicknesses of 15 mm, 21 mm, and 27 mm were manufactured. Figure 6 shows the dispersion introduced by three different thickness dispersion blocks measured experimentally. Figure 6(a) shows the dispersion spreading caused by three glass blocks, and Fig. 6(b) shows the spatial domain signals of the same optical delay after dispersion compensation for the corresponding three levels of dispersion. The signals are normalized by the peak amplitudes of the genuine signal. Under 15 mm, 21 mm, and 27 mm thick dispersive blocks, the conjugate suppression ratio (the ratio of signal peak intensity to mirror peak intensity) of dispersion compensation is 9.05 dB, 11.15 dB, and 12.2 dB, respectively. Figure 7 illustrates the effect of coating on the measured spectrum. It can be seen that the coating enhances the light intensity of the sample arm, while the coating has little effect on the spectrum shape of the sample arm due to the flat transmittance property of HZF73 near 840 nm. In conclusion, when dealing with samples characterized by significant inclination angles and rough surfaces, it is advisable to go for a 27 mm thick coated HZF73 dispersion block. This option offers a better mirror image suppression effect and a stronger signal intensity.
Fig. 6. Experimentally measured dispersion of different thicknesses of HZF73. (a) The dispersion spreading of different thicknesses of HZF73; (b) The suppression of mirror peaks of different thicknesses of HZF73.
Fig. 7. Interference spectrum, the spectrum of the reference arm and sample arm. (a) Measurements using an uncoated dispersion block; (b) Measurements using a coated dispersion block.
5. Results and discussion
5.1 Measurement results of step blocks
To verify the proposed full-range measurement method, the ceramic step standard block was measured using the lab-built measurement system. The sample provided steps with specified heights, and the six steps were denoted as #1, #2, #3, #4, #5, and #6, and their nominal heights were 4, 6, 8, 14, 12, and 10 mm, respectively, as shown in Fig. 8(a). We performed a series of measurements on this sample, covering the area of 13 × 2mm2. We performed a series of filtering and correction processes on the original data. Firstly, the static outlier filtering algorithm is applied, the number of neighboring points is 6, and the standard deviation coefficient is 1. Then the distortion is removed by measuring a flat mirror, and finally, the tilt correction is performed. The final result is shown in Fig. 8(c). Figure 8(b) shows the measurement results obtained without using the full-range method. Since the first three steps and the last three steps are respectively on different sides of 0 optical delay, the mirror image of the first three steps and the real signal of the last three steps are obtained during the half-range measurement. In Fig. 8(c), using the proposed full-range method, the real signals of all steps can be acquired and the morphology of the sample is correctly reconstructed.
Fig. 8. Height measurement results of the step block. (a) Physical photograph; (b) Results measured without the full-range method; (c) Results measured with the full-range method.
In order to evaluate the accuracy of the proposed measurement method, the height profile of the step block is analyzed. As shown in Fig. 9(a), the height contour is extracted along the x direction at the center of the steps, and the result is shown in Fig. 9(b). The mean height and standard deviation(SD) of each step on the contour line were recorded (note that the wrong data due to edge effects were avoided when selecting the data, such as the data points in the green rectangle in Fig. 9(b)). As a comparison, the same measurements were performed using a commercial line laser profilometer (LJ-X8080, Keyence, Inc.). Figure 10 shows the measurement error comparison between the experimental system and the commercial sensor in four profile lines. The mean absolute error (MAE) was used to characterize the deviation between the measurement results and the quoted values, and the formula was $\textrm{MAE} = \sum\nolimits_{i = 1}^N {|{{\widehat y}_i} - {y_0}|} /N$, where ${y_i}$ is the measured height of a point on a single step, and ${y_0}$ is the quoted value, N is the number of the data. In Fig. 10, we annotate the MAE and SD of some step measurement results in the form of (MAE,SD). The results show that the maximum MAE of the step height measured by the experimental system is 18.8µm, and the maximum SD of the step height is 2.5µm, while the maximum MAE of the step height measured by the commercial profiler is 18.3µm, and the maximum SD of the step height is 4µm. It can be considered that the accuracy of the experimental system for measuring the ceramic step standard block is close to that of the commercial profilometer. The reason that the measurement results of commercial sensors and our system differ from the quoted values may be due to errors associated with different measurement principles. The quoted values are measured using a contact measuring instrument. The commercial sensor is based on the laser triangulation principle, and the results of height measurements contain nonlinear errors. Our system's measurement errors are primarily caused by the distortion of the galvanometric scanner. In addition, it is noted that the SD of steps #1, #2 and #3 measured by our system are much smaller than that of steps #4, #5 and #6, and are also smaller than that measured by the commercial profiler. This difference also comes from the galvanometer scanning mechanism. The measured optical signal intensity varies with the scanning angles, and the distortion at different fields of view and heights also differs (although the image plane distortion has been initially corrected by using a plane mirror).
Fig. 9. Height measurement results of the ceramic step standard block. (a) Three-dimensional morphology measurement results of the ceramic standard step block after outlier filtering and tilt correction, and the filtering parameters are 1 standard deviation and 6 adjacent points (red arrows indicate the position and direction of the profile line measurement); (b) The profile line at the central position of the step (the data points in the green rectangle are error points caused by edge effects).
Fig. 10. Errors of each step height measurement of ceramic step standard block. (a), (b), (c) and (d) are measurements taken at each of the four profile lines.
5.2 MATLAB logo sample measurement results
To evaluate the measurement performance of the proposed measurement method on samples with large inclination angles and rough surfaces, a MATLAB logo sample of 13 mm long by 13 mm wide by 15 mm high was fabricated using a metal 3D printing device (Flight 403P, Farsoon Technologies, Inc.). The sample is shown in Fig. 11.
Fig. 11. The MATLAB logo 3D morphology. (a) 3D data model; (b) 3D metal print sample (length 13 mm width 13 mm height 15 mm, rectangular step height 5 mm).
The sample is measured using the half-range processing and the proposed improved dispersion encoded full-range method, respectively. After filtering processing, and tilt correction, the final 3D reconstruction result is obtained as shown in Fig. 12. Figure 12(a) shows the reconstruction result obtained without using the full-range method, since only half of the spatial domain is adopted, the mirrored signal of the tip part is extracted, and thus appears as a pit. Figure 12(b) shows the reconstruction results obtained using the proposed improved full-range method, where the real signal of the tip part of the sample is enhanced and extracted, thus a correct 3D shape can be obtained.
Fig. 12. The reconstruction result of measurements of the MATLAB logo sample. (a) The reconstruction result without the full-range method; (b) The reconstruction result with the full-range method.
Notice that the missing points in Fig. 12 are the error points removed by outlier filtering. Due to the roughness of the sample and the large surface inclination, the detection light returned from the surface is usually weak, and the signals measured in the tip, depression and other areas are even weaker, so it is extremely difficult to extract reliable signals. This problem originates from the sample surface properties, but the system combined with the proposed improved full-range method still shows superior resistance. The proportion of valid data points in the measured points reaches 93.4%, which is enough to meet the needs of 3D reconstruction. In addition, the sample was measured using a commercial line laser profiler (LJ-X8080, Keyence, Inc.), and the result is shown in Fig. 13(b). The line laser profiler is based on the laser triangulation method, where there is an angle between the illumination light path and the detection light path [26]. The concave surface of the sample has a large amount of missing data due to occlusion (the red rectangular area in Fig. 13(b) is the missing data). In contrast, the system we built, combined with the proposed improved full-range method, shows better adaptability for such samples with rough surfaces and large inclination angles. As shown in Fig. 13(c), the concave surface data of the sample is complete, and the measured 3D topography is basically consistent with the data model in Fig. 13(a).
Fig. 13. The MATLAB logo sample measurements as well as simulated contours. (a) Data simulation results; (b) LJ-X8080 measurement results; (c) Experimental system measurement results.
6. Conclusion
This paper proposes an improved dispersion-encoded full-range interferometry, which is enhanced for measurement scenarios involving large dip angles, rough surfaces and weak signals. Finally, the spectral interference system achieved a measuring range of 12 mm, and the ceramic step block's measurement standard deviation was 2.5µm. Considering that the DC component spreading will drown the weak signal near 0 optical delay, a modified DC removal method is proposed, which significantly suppresses the DC component spreading. Given that the optical aberrations in the spectrometer are unavoidable, we propose a more accurate method for extracting the dispersion phase. By employing the proposed measurement method, it is possible to achieve satisfactory measurement accuracy even when dealing with samples characterized by rough surfaces and significant inclination angles. Experiments indicate that the measurement performance of the experimental system for the above samples is better than that of the commercial line laser profiler. In addition, although only the surface profile of the workpiece is measured in this paper, the system is entirely capable of measuring multi-layer samples when combined with the iterative dispersion encoded algorithm. See Table 2 in Appendix for a list of acronyms and abbreviations.
Appendix
Table 2. Acronyms and Abbreviations
Funding
National Key Research and Development Program of China (2022YFB3206003).
Acknowledgments
The authors would like to thank Wuhan Jingce Electronics Corporation for providing a test environment and test method discussion. We thank Keyence Corporation for providing sample testing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. X. Ge, S. Chen, S. Chen, et al., “High Resolution Optical Coherence Tomography,” J. Lightwave Technol. 39(12), 3824–3835 (2021). [CrossRef]
2. B. Baumann, M. Pircher, E. Götzinger, et al., “Full range complex spectral domain optical coherence tomography without additional phase shifters,” Opt. Express 15(20), 13375–13387 (2007). [CrossRef]
3. B. Fang, S. Zhong, Q. Zhang, et al., “Full-Range Line-Field Optical Coherence Tomography for High-Accuracy Measurements of Optical Lens,” IEEE Trans. Instrum. Meas. 69(9), 7180–7190 (2020). [CrossRef]
4. R. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90(5), 054103 (2007). [CrossRef]
5. Y. Yasuno, S. Makita, T. Endo, et al., “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef]
6. B. Huang, P. Bu, X. Wang, et al., “Full-range parallel Fourier-domain optical coherence tomography using a spatial carrier frequency,” Appl. Opt. 52(5), 958–965 (2013). [CrossRef]
7. S. Makita, Y. Yasuno, T. Endo, et al., “One-shot-phase-shifting full-range Fourier domain optical coherence tomography by reference wavefront tilting,” SPIE BiOS (SPIE, 2005), Vol. 5690.
8. A. H. Bachmann, R. A. Leitgeb, and T. Lasser, “Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution,” Opt. Express 14(4), 1487–1496 (2006). [CrossRef]
9. J. Zhang, J. S. Nelson, and Z. Chen, “Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator,” Opt. Lett. 30(2), 147–149 (2005). [CrossRef]
10. Y. Huang, Z. Qiao, J. Chen, et al., “Full-range optical coherence refraction tomography,” Opt. Lett. 47(4), 894–897 (2022). [CrossRef]
11. L. An and R. K. Wang, “Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography,” Opt. Lett. 32(23), 3423–3425 (2007). [CrossRef]
12. B. Hofer, B. Považay, B. Hermann, et al., “Dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express 17(1), 7–24 (2009). [CrossRef]
13. S. Witte, M. Baclayon, E. J. G. Peterman, et al., “Single-shot two-dimensional full-range optical coherence tomography achieved by dispersion control,” Opt. Express 17(14), 11335–11349 (2009). [CrossRef]
14. B. Hofer, B. Považay, A. Unterhuber, et al., “Fast dispersion encoded full range optical coherence tomography for retinal imaging at 800 nm and 1060 nm,” Opt. Express 18(5), 4898–4919 (2010). [CrossRef]
15. F. Köttig, P. Cimalla, M. Gärtner, et al., “An advanced algorithm for dispersion encoded full range frequency domain optical coherence tomography,” Opt. Express 20(22), 24925–24948 (2012). [CrossRef]
16. J. H. Mason, M. E. Davies, and P. O. Bagnaninchi, “Blur resolved OCT: full-range interferometric synthetic aperture microscopy through dispersion encoding,” Opt. Express 28(3), 3879–3894 (2020). [CrossRef]
17. A. Canales-Benavides, J. Zavislan, and P. S. Carney, “Suppression of the conjugate signal for broadband computed imaging via synthetic phase modulation,” J. Opt. Soc. Am. A 39(12), C203–C213 (2022). [CrossRef]
18. L. Yi, L. Sun, X. Ming, et al., “Full-depth spectral domain optical coherence tomography technology insensitive to phase disturbance,” Biomed. Opt. Express 9(10), 5071–5083 (2018). [CrossRef]
19. T. V. Reichold, P. D. Ruiz, and J. M. Huntley, “2500-Channel single-shot areal profilometer using hyperspectral interferometry with a pinhole array,” Opt. Lasers Eng. 122, 37–48 (2019). [CrossRef]
20. C. Taudt, B. Nelsen, T. Baselt, et al., “High-dynamic-range areal profilometry using an imaging, dispersion-encoded low-coherence interferometer,” Opt. Express 28(12), 17320–17333 (2020). [CrossRef]
21. C. Pang, D. Wu, H. Shi, et al., “Photon-counting laser interferometer for absolute distance measurement on rough surface,” Rev. Sci. Instrum. 90(8), 083101 (2019). [CrossRef]
22. T. Onoe, S. Takahashi, K. Takamasu, et al., “Non-contact precision profile measurement to rough-surface objects with optical frequency combs,” Meas. Sci. Technol. 27(12), 124002 (2016). [CrossRef]
23. N. N. Phan, H. H. Le, D. C. Duong, et al., “Measurement of nanoscale displacements using a Mirau white-light interference microscope and an inclined flat surface,” Opt. Eng. 58(6), 064106 (2019). [CrossRef]
24. A. Scheeline, “How to Design a Spectrometer,” Appl. Spectrosc. 71(10), 2237–2252 (2017). [CrossRef]
25. G. Yan, K. Yang, W. Li, et al., “Metrological performance analysis of optical coherent tomography,” Measurement 189, 110437 (2022). [CrossRef]
26. W. Pan, D. Zhang, C. Liang, et al., A high-precision laser displacement measurement system, Applied Optics and Photonics China 2021 (SPIE, 2021), Vol. 12065.
