Abstract
The dataset describes the mechanism of suppressing the background noise of the divided-aperture differential confocal Raman microscopy system and the range of tilting angles that the system can handle. On the basis of the confocal microscopy (CM), the divided-aperture confocal microscopy divided the pupil plane of the objective lens into the illumination pupil and collection pupil. Compared with the CM, the divided-aperture confocal microscopy only changes the pupil parameters, according to the partially coherent imaging theory, we simulate and analyze the axial response curves of the divided-aperture confocal system and the traditional confocal system. We also simulated the differential confocal response curve at different tilting angles and get the data for the applicability of the differential confocal response curve to see if there is a single zero-crossing point or a good linearity near the zero-crossing point. The goodness-of-fit (GOF) is used to evaluate the accuracy of linear fitting, and can be used as a simple measure method of linearity. And the closer the GOF value is to 1, the higher fitting accuracy is. Through simulation analysis, we can have a better understanding of the advances of divided-aperture differential confocal Raman microscopy.
Keywords: Suppressing background noise, Tilting angles, Divided-aperture differential confocal Raman microscopy, Axial response curves, Goodness-of-fit (GOF)
Specifications Table
| Subject | Optics |
| Specific subject area | In-situ high-precision surface topographic and Raman mapping by divided-aperture differential confocal Raman microscopy |
| Type of data | Table, Graph, Figure |
| How data were acquired | Divided-aperture differential confocal Raman microscope (DADCRM): A semiconductor continuous-wave 532 nm laser (SambaTM 150, Cobolt, Sweden) was used as the laser source. An objective (100 ×, NA = 0.9, MPlanFLN, Olympus, Japan) with a custom-built aperture was installed in a high-precision piezoelectric actuator (P-725.4CD, Physik Instrumente, Germany). |
| Data format | Analyzed |
| Parameters for data collection | Laser power:10mW environment temperature:20±2 °C environment humidity:45±2% |
| Description of data collection | The axial response curve of the divided-aperture differential confocal microscope system under the influence of background noise is simulated and compared with the axial response curve of the confocal microscope system under the same conditions. The goodness-of-fit (GOF) is used to measure the imaging capability of the divided-aperture differential confocal microscopy system. When the sample has a tilt of 0–25°, the GOF of the system is simulated to obtain the imaging ability of the system under different sample tilt angles. |
| Data source location | Institution: Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology City/Town/Region: Beijing Country: China |
| Data accessibility | Repository name: Mendeley Data Data identification number: DOI:10.17632/rmdgkcyd2n.3 Direct URL to data: https://data.mendeley.com/datasets/rmdgkcyd2n/3 |
| Related research article | Zhang R, Wu H, Y Su, et al. In-situ high-precision surface topographic and Raman mapping by divided-aperture differential confocal Raman microscopy[J]. Applied Surface Science, 2021, 546:149061. DOI:10.1016/j.apsusc.2021.149061 Wu H, Zhao W, Su Y, et al. Divided-aperture confocal Brillouin microscopy for simultaneous high-precision topographic and mechanical mapping[J]. Optics Express, 2020, 28(21):31821. DOI:10.1364/OE.405458 |
Value of the Data
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This data set will be benefitial for understanding the mechanism of suppressing background noise of divided-aperture differential confocal Raman microscopy system, it will be useful to improve the imaging capability of optical system including Lidar sensor.
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This data set can be used as a reference for researchers in the field of microoptics and spectroscopy to optimize measurement techniques in the presence of stray light and the inclination of the sample.
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In the development and performance optimization of laser confocal Raman or photoluminescence microspectral detection system, the axial intensity response curve and goodness of fit (GOF) method can be used to quantitatively study the improvement of anti scattering noise of the system and the measurement range of sample tilt angle.
1. Data Description
The code used to generate the figures and table 1 is available on Mendeley dataset: https://doi.org/10.1016/j.apsusc.2021.149061.
1.1. The ability to resist background noise of the divided-aperture confocal microscopy
Full width at half maximum (FWHM) of the axial response curve is an important index to measure the axial resolution of the system.
It can be seen from Fig. 1 that the full width at half maximum (FWHM) of the axial response curve of the divided-aperture confocal microscopy is smaller, and the axial response curve of the divided-aperture confocal microscopy decreases faster under defocusing conditions.
Fig. 1.
The axial response curves between confocal microscopy and divided-aperture confocal microscopy (a) uniform coordinates (b) logarithmic coordinates.
1.2. The influence of different tilting angles of sample
When the sample tilts at the angle ξ as shown in Fig. 2. IA and IB are the light intensity signals obtained by the two virtual pinholes A and B. Idiff is the differential confocal response curve. IA, IB and Idiff will be covered in more detail in 2.2.
Fig. 2.
The schematic diagram of tilted sample.
The goodness-of-fit (GOF) is often used to evaluate the accuracy of linear fitting, and can be used as a simple measure of linearity [1,2] The values of GOF at different tilting angles ξ can be obtained as shown in Table 1. From Fig. 3(a)-(b) and Table 1, it can be seen that when the tilting angle changes to 19°, the linearity around the zero-crossing of the differential confocal response curve Idiff is still good, and the GOF is 0.9994, and there is still a relatively good monotonicity of the Idiff curve near the zero-crossing. However, when the tilting angle ξ increases, the Idiff no longer has a unique zero crossing, and the normalized IA and IB signals are obviously asymmetric, and the GOF is poor.
Table 1.
GOF with different ξ.
| ξ | 0° | 1° | 3° | 5° | 7° | 9° | 11° |
| GOF | 0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9998 | 0.9997 | 0.9996 |
| ξ | 13° | 15° | 17° | 19° | 21° | 23° | 25° |
| GOF | 0.9995 | 0.9994 | 0.9994 | 0.9994 | 0.9896 | 0.8815 | 0.7789 |
Fig. 3.
(a) The normalized IA (blue solid line), normalized IB (green solid line) and differential confocal response curve Idiff (red solid line) with different ξ, respectively; The x-axis represents the axial normalized coordinate u, and the y-axis represents the normalized intensity response. (b) The differential confocal response curve Idiff with different ξ.
2. Experimental Design, Materials and Methods
2.1. Suppressing the background noise
In optical systems, optimization the point spread function (PSF) can be used to improve the axial resolution and the ability to resist the interference of background noise. In the divided-aperture system, illuminated light path and collected light path are symmetrical about the optical axis of the objective, As shown in Fig. 4(a). The PSF of the illuminated light path at the focal plane is represented by the green ellipse, and the PSF of the collected light path is represented by the blue ellipse. The two PSFs have the same shape and are symmetrical about the optical axis of the objective, as shown in Fig. 4(b). The divided-aperture differential confocal system is provided with an illumination aperture and a collection aperture on the aperture surface of the objective lens, and the light beam passes through the illumination aperture and the collection aperture to form an illumination light path and a collection light path respectively. The illumination PSF hi(vx, vy, u) and the collection PSF hc(vx, vy, u) only coincide on the focal plane of the system. Since the PSF of the divided-aperture system is the product of the illumination PSF and the collected PSF, the PSF of the divided-aperture system is shown in Fig. 4(c), The divided-aperture system compresses the width of the PSF in the Z-axial direction, so that the divided-aperture system can improve the axial resolution and resist the interference of background noise.
Fig. 4.
(a) The structure diagram of the divided-aperture system. S1 and S2 are the illumination pupil and collection pupil respectively; (b) the PSFs of the illuminated light path and the collected light path; (c) the PSF of the divided-aperture system.
Compared with the confocal microscopy, the divided-aperture confocal microscopy only changes the pupil parameters, according to the partially coherent imaging theory [3], the PSF and intensity of the divided-aperture confocal microscopy can be expressed as [4]
| (1) |
Here, vp is the normalized radius of the detection area expressed as vp=2πRsinαd/λ; R is the radius of the virtual pinhole; sinαd is the numerical aperture of the detection objective;λ is the laser wavelength (vx, vy, u) are the normalized optical coordinates of (x, y, z) expressed as (vx, vy) = 2π(x, y)sinαo/λ and u = 8πzsin2(αo/2)/λ; sinαo is the numerical aperture of the objective; ρ and θ are the normalized polar coordinates in the pupil plane of the objective; ρ and θ are the normalized polar coordinates in the pupil plane of the objective; r and φ are the normalized polar coordinates in the detection plane; and S1 and S2 are the illumination pupil and collection pupil respectively. Pi (ρ, θ, u) is the defocus pupil function of S1, Pc (ρ, θ, u) is the defocus pupil function of S2. The axial response curve shown in Fig. 1 can be obtained by Eq. (1).
2.2. Simulation analysis of the influence of different tilting angles
We did intensity simulation analysis of the influence of different tilting angles and found this system is applicable in the range of 0-19° for tilting angles [5], [6]. When the sample tilts at the angle ξ as shown in Fig. 2. As is shown in Fig. 5, in the divided-aperture differential confocal system, the reflected light spot is detected by the CCD. As the sample moves axially, the spot on the CCD moves laterally. Two virtual pinholes A and B are set by software along the xd axis and symmetric about the yd axis, and the normalized offset of these two virtual pinholes is vM. Therefore, two light intensity responses IA and IB can be obtained by the virtual pinholes A and B respectively.
Fig. 5.
Installation diagram.
The light intensity signals IA and IB obtained by the two virtual pinholes IA and IB can be expressed as
| (2) |
where, hi(vx, vy, u) and hc(vx, vy, u, vM, r, φ) are the amplitude point spread functions of the illumination optical path and the collection optical path, respectively
| (3) |
Here, Pi(ρ, θ, u) is the defocus pupil function of the illumination optical path; Pc(ρ, θ, u) is the defocus pupil function of the collection optical path; (vx, vy, u) are the normalized optical coordinates of (x, y, z) expressed as (vx, vy) = 2π(x, y)sinαo/λ and u = 8πzsin2(αo/2)/λ; vp is the normalized radius of the virtual pinhole expressed as vp = 2πRsinαo/λ; R is the radius of the circular virtual pinhole; vM is the lateral normalized off-axis offset of the circular virtual pinhole expressed as vM = 2πMsinαo/λ; M is the lateral off-axis offset of the virtual pinhole; λ is the laser wavelength; sinαo is the numerical aperture of the objective; ρ and θ are the normalized polar coordinates in the pupil plane of the objective; r and φ are the normalized polar coordinates in the detection plane; and S1 and S2 are the illumination pupil and collection pupil respectively. The differential confocal response curve Idiff is obtained by
| (4) |
We simulated the differential confocal response curve Idiff at different tilting angles ξ, and the simulation results are shown in Figs. 2(b)-(c). We study the applicability of the differential confocal response curve Idiff to see if there is a single zero-crossing point or a good linearity near the zero-crossing point. The goodness-of-fit (GOF) is often used to evaluate the accuracy of linear fitting, and can be used as a simple measure of linearity [2,3]. The expression of GOF is as follows:
| (5) |
where yi is the intensity of the ith sampling point in the selected curve, is the average intensity of all sampling points, and ŷi is the intensity of the fitting line corresponding to the ith sampling point. And the closer the GOF value is to 1, the higher fitting accuracy is. The axial response curve Idiff cannot be process by linear fitting when GOF is below 0.999.
Ethics Statement
This work has not involved any use of human subjects and animal experiments.
CRediT Author Statement
Yunhao Su: Conceptualization, Methodology, Writing - review & editing; Ruirui Zhang: Data curation, Writing - original draft; Hanxu Wu: Conceptualization, Resources, Formal Analysis; Lirong Qiu: Methodology, Validation, Supervision; He Ni: Software, Validation; Ke-Mi Xu: Writing - review & Editing; Weiqian Zhao: Conceptualization, Methodology, Visualization, Investigation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships which have or could be perceived to have influenced the work reported in this article.
Acknowledgments
This work was supported by National Natural Science Foundation of China (NSFC) (61827826, 51825501), the Fundamental Research Funds for the Central Universities (2020CX02002), Science and technology funding program for innovative talents of Beijing University of Technology (2019CX01020) and Zhejiang Lab (No. 2020MC0AE01).
Contributor Information
Lirong Qiu, Email: qiugrass@126.com.
Ke-Mi Xu, Email: xukemi@bit.edu.cn.
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