검색
검색 팝업 닫기

Ex) Article Title, Author, Keywords

Article

Split Viewer

Research Paper

Curr. Opt. Photon. 2024; 8(5): 484-492

Published online October 25, 2024 https://doi.org/10.3807/COPP.2024.8.5.484

Copyright © Optical Society of Korea.

Design of an Asymmetric-custom-surface Imaging Optical System for Two-dimensional Temperature-field Measurement

Guanghai Liu1,2, Ming Gao1 , Jixiang Zhao1, Yang Chen1

1Institute of Optical Information Technology, School of Optoelectronic Engineering, Xi′an Technological University, Xi’an, Shaanxi 710021, China
2Sichuan Physcience Optics and Fine Mechanics Co., Ltd., Mianyang 621000, China

Corresponding author: *guanghailiu@163.com, ORCID 0009-0004-5624-3148

Received: June 5, 2024; Revised: August 20, 2024; Accepted: August 26, 2204

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

In response to the difficulty of synchronously obtaining multiwavelength images for fast two-dimensional (2D) temperature measurement, a multispectral framing imaging optical system is designed, based on the segmented-aperture imaging method and asymmetric surface shape. The system adopts a common-aperture four-channel array structure to synchronously collect multiwavelength temperaturefield images. To solve the problem of asymmetric aberration caused by being off-axis, a model of the relationship between incident and outgoing rays is established to calculate the asymmetric custom surface. The designed focal length of the optical system is 80 mm, the F-number is 1:3.8, and the operating wavelength range is 0.48–0.65 μm. The system is divided into four channels, corresponding to wavelengths of 0.48, 0.55, 0.58, and 0.65 μm respectively. The modulation transfer function value of a single channel lens is higher than 0.6 in the full field of view at 35 lp/mm. The experimental results show that the asymmetric-custom-surface imaging system can capture clear multiwavelength images of a temperature field. The framing imaging system can capture clear images of multiwavelength temperature fields, with high consistency in images of different wavelengths. The designed optical system can provide reliable multiwavelength image data for 2D temperature-field measurement.

Keywords: 2D temperature measurement, Asymmetric surface shape, Segmented aperture imaging

OCIS codes: (080.3620) Lens system design; (080.4225) Nonspherical lens design; (110.4190) Multiple imaging; (120.6780) Temperature

In the subjects of combustion- and explosion-fields reconstruction, turbine-blade inspection, and engine-temperature analysis and detection [14], temperature fields feature characteristics such as rapid changes, requirements for high measurement accuracy, and significantly nonuniform temperature distributions [58]. These factors drive the development of technology toward high-precision two-dimensional (2D) temperature measurement [913]. In 2016, Dagel et al. [14] designed a four-color imaging pyrometer using a prism and four detectors, achieving temperature measurement with ultralarge dynamic range, from 900 to 3,800 K. However, the device is complex and high precision is required for the spectroscopic system, as even minor deviations in components can significantly impact its accuracy. In 2021, Cao [15] established a colorimetric light-field temperature-measurement system based on lens arrays. Through calibration experiments on the spectral-radiance brightness of light-field blackbodies, they derived a fitting relationship between the spectral-radiance brightness of the light-field temperature-measurement system and the grayscale values of the images. However, the imaging range of the lens array is extremely small, making it difficult to measure the entire temperature field. In 2021 Li et al. [16], aiming to meet the needs of ultrafast phenomena such as explosions and high-voltage discharges, developed a full-optical spatial segmented-aperture imaging system, using diffractive optical elements and narrowband filters. This system can achieve 16-segment aperture imaging in a 4 × 4 array across different wavelength bands, with a modulation transfer function (MTF) of 0.991 at a resolution of 35 lp/mm. However, the processing of diffractive elements is complex, and the diffraction efficiency decreases significantly at noncentral wavelengths.

The most feasible approach for 2D temperature measurement currently is multispectral segmented-aperture thermometry. The core device of this technology is the multiwavelength segmented-aperture imaging camera. Compared to traditional cameras, it divides the camera’s focal plane into multiple images corresponding to different wavelength channels. Through segmented apertures, it can capture multispectral images in real time, and then quickly reconstruct the 2D temperature-field distribution by combining radiation curve fitting.

Therefore, this article proposes a transient 2D temperature-field image-acquisition system based on aperture segmentation and asymmetric custom surface profiles. Aperture segmentation divides the focal plane into regions, to simultaneously acquire multiwavelength temperature images while ensuring consistency of information. The asymmetric custom surface profile has complete freedom in the meridional and sagittal directions, enabling the focusing of off-axis light rays and improving the imaging quality of the 2D temperature-measurement optical system. The segmented-aperture custom-surface-profile imaging system proposed in this paper can provide a technical approach for the acquisition of critical information in 2D temperature measurement.

After segmenting the aperture of the optical system, there is a deviation between the optical axes of the main subaperture system and the common aperture system, resulting in asymmetric light beams incident upon the subaperture and causing inconsistent image aberrations in different fields of view along different directions, as shown in Fig. 1. Analysis is conducted using vector aberration theory. Based on the third-order aberration polynomials and the influence of tilted or eccentric elements on aberrations, the vector expression for the third-order wavefront aberration generated on the nth surface of a tilted or eccentric optical system can be obtained as follows [17, 18]:

Figure 1.Schematic diagram of asymmetric aberrations: (a) Causes of asymmetric aberrations, (b) asymmetric aberrations in symmetric subaperture optical groups, and (c) correction of asymmetric aberrations in asymmetric optical groups.

Wi=W040i(rr)2+W131iHSirrr          +W222iHSir2          ×W220iHSiHSirr          +W313iHSiHSiHSir,

where W is the aberration coefficient, and W040, W131, W222, W220, and W313 are the aberration coefficients of the spherical aberration, coma aberration, field curvature, astigmatism, and distortion respectively. H and r represent the vector forms of the normalized field point and aperture point at the entrance pupil of the system when there is no tilt or eccentricity, and Si denotes the deviation of the aberration field center. To address the inconsistencies in the system’s aberrations in the y-direction, this paper proposes the method of incorporating asymmetric custom surface profiles into the system, which utilizes surface profiles without rotational symmetry to correct the inconsistencies in the system’s aberrations in the y-direction.

To efficiently design asymmetric surface profiles, a model of the relationship between incident and exiting light rays is established. The incident light rays are considered as input variables, while the optical system can be viewed as a set of modulation functions. When both are known, the output variables and exiting light rays can be solved for. Similarly, if the input and output variables are known, the modulation function (or in this case the optical system’s surface-profile parameters) can be solved for in reverse. In the implementation of this paper, the incident light ray’s parameters can be calculated from the front-end common-aperture optical group, and the exiting light ray’s parameters can be determined based on the requirements of the segmented image-plane positions and the ideal imaging conditions of the approximate light rays. Through the established coordinate relationship between the incident and exiting light rays, the required asymmetric surface profile can be solved for.

2.1. Calculation of Incident Light Rays

2.1.1. Calculation of the Common-aperture Light Ray

Since the asymmetry of the light beam has a clearly directional nature, only the y-section direction is selected for analysis in the calculation. Using the theory of geometric optics, the calculation of the common-aperture optical path employs the formula for calculating the actual optical path on a per-surface basis:

sinIC=LCrCrCsinUCsinIC=n nsinICUC=UC+ICICLC=rC+rCsinICsinUC.

In the formulae above, IC and IC represent respectively the incidence angle and refraction angle of the light ray in the common-aperture optical group for the first surface, LC and LC represent respectively the incidence angle and refraction angle of the light ray in the common-aperture optical group for the second surface, rC is the curvature radius of the refracting surface, n and n′ are the refractive indices for the object side and image side respectively, and UC and UC are the object-side and image-side aperture angles of the light ray in the common-aperture optical group.

Assuming that the common-aperture system has m surfaces, the light ray’s parameters for the next surface can be obtained through the ray-tracing formula:

L2C=L1Cd1C,L3C=L2Cd2C,...,LmC=LmCdmCU2C=U1C,U3C=U2C,...,UmC=UmCn2C=n1C,n3C=n2C,...,nmC=nmC,

where diC represents the separation of the ith refracting surface in the common-aperture optical group.

2.1.2. The Coordinates of the Light Ray Exiting the Common-aperture Optical Group

Taking the vertex of the common-aperture refracting surface as the origin, and given that the curvature of the refracting surface is rmC, the coordinates (xmC, ymC) of the light ray exiting the common-aperture optical group are calculated as:

xmC2+ymC2=rmC2ymC=tanUmC×xmC+LmCtanUmC.

2.1.3. Coordinate Transformation from Common Aperture to Subaperture

Assuming that the offsets of the subaperture optical axis from the common-aperture optical axis in the x- and y-directions are Δx and Δy respectively, and that the separation between the last surface m of the common-aperture optical group and the subaperture is dmC, the coordinates (x1S, y1S) on the first surface of the subaperture optical group can be calculated as:

x1S=xmCΔxy1S=ymCΔydmC×tanUmCL1S=LmCdmCU1S=UmC.

2.2. Calculation of the Exiting Light Ray’s Coordinates

2.2.1. 2×2 Image-plane Segmentation

In the x and y directions, the detector sizes are set as LDX and LDY respectively, and the subaperture image-plane sizes are LISX and LISY. In the x direction, the center spacing is ∆LXC and the edge spacing is ∆LXE. In the y direction, the center spacing is ∆LYC and the edge spacing is ∆LYE.

LDX=2LISX+ΔLXC+2ΔLXELDY=2LISY+ΔLYC+2ΔLYE.

2.2.2. Calculation of the Ideal Point’s Coordinates

The ideal imaging position is calculated using the ideal imaging formula. Assuming a tolerance of δ relative to the ideal imaging position, a combined focal length of comb(fC, fS) for the common aperture and subaperture, a field of view angle of comb(fC, fS)in the y-direction, and an ideal imaging position of (xI, yI), the imaging range of the exiting light ray from the subaperture optical group on the image plane should satisfy:

xI=tanωCx×combfC,fSyI=tanωCy×combfC,fSxkS<xI±δykS<yI±δ.

2.3. Calculation of the Surface Profile

2.3.1. Asymmetric Wassermann-Wolf Surface Profile

By using the modified asymmetric Wassermann-Wolf formula, a model for incident and emergent light rays is established. From the known incident light ray, the coordinates of the emergent light ray are solved for, to calculate the asymmetric surface profile coordinates (xS, yS, zS):

zi=xkSnk1cosθxk1nk+1cosθxks+yksnk1cosθyk1nkscosθyksnk1cosθxk1+nkscosθxks.

In the formula above, nk is the refractive index, and cosθxk, 3cosθyk are the angles between the x- and y-direction vectors and the normal vector respectively.

2.3.2. Fitting the Surface Profile

Next, we select the aperture and field of view, calculate the surface profile’s coordinates, and perform fitting on the discrete coordinates.

The asymmetric custom surface design process and the relationship between incident and exiting light are shown in Fig. 2.

Figure 2.Asymmetric custom surface design flow and the relationship between incident and outgoing.

3.1. Parameters and Design Results for the Segmented-aperture Imaging System

The segmented-aperture imaging optical system comprises a common-aperture optical group and a subaperture optical group. An asymmetric surface is added to the last surface of the subaperture optical group, to correct the asymmetric aberrations introduced by off-axis imaging. The performance specifications of the segmented-aperture imaging system are shown in Table 1.

TABLE 1 System parameters

ParametricTarget
Wave Band (μm)0.48–0.65
Focal Length (mm)80
Image Number4
Hight of Image (mm)6
Imaging Interval (mm)6
F/#4


After inputting the calculated asymmetric surface profile into the optical-design software and performing simple optimization, the final system’s structure is obtained, as shown in Fig. 3. The system utilizes a common aperture to ensure imaging of the same target after aperture division, and it is characterized by a small number of lenses, compact size, and light weight.

Figure 3.Structural diagram of the segmented-aperture imaging system.

3.2. Image-quality Analysis

Figure 4 shows the asymmetric custom surface profile of the segmented-aperture imaging system. Figure 5 presents scatter plots for the symmetric and asymmetric subaperture optical groups, as can be seen from the figure, after adding the asymmetric custom surface, the size of the light spot converges, and the defocus of the convergence point is improved. Figure 6 depicts the MTF graph for the segmented-aperture imaging system. It can be observed that in the wavelength band of 0.48–0.65 μm, at the Nyquist frequency of 35 lp/mm the on-axis point is higher than 0.7, and the off-axis point is higher than 0.6. Figure 7 shows the system’s spot diagram, revealing that the root-mean-square value for the blur spot in the visible-light band is a maximum of 5.9 μm, indicating that the system’s imaging quality is close to the diffraction limit. Figure 8 displays the image-plane irradiance map after aperture division, demonstrating that the image irradiance remains consistent across the entire field of view, without the issue of vignetting after aperture division.

Figure 4.Asymmetric surface profile of the subaperture.

Figure 5.Scatter plots for (a) the symmetric subaperture optical group, and (b) the asymmetric subaperture optical group.

Figure 6.Modulation transfer function (MTF) diagram for the imaging system.

Figure 7.Spot diagram for the imaging system.

Figure 8.Relative-illuminance diagram for the imaging system.

Figure 9 shows the processed segmented-aperture imaging system, which consists of a common-aperture optical group used to image a target. The four-channel segmented-aperture system splits the image of the same target into four separate images, forming them on four designated regions of the detector. At the end of the segmented-aperture system are optical filters to capture images of the target at different wavelengths, providing multiwavelength data for 2D temperature measurement.

Figure 9.Photographs of the segmented-aperture imaging system.

Figure 10 illustrates image acquisition with the segmented-aperture system, and Fig. 11 shows the image of the resolution target captured by the segmented-aperture optical system. From Fig. 11, it can be seen that the segmented-aperture imaging system can achieve clear imaging at multiple wavelengths.

Figure 10.Image acquisition with the segmented-aperture imaging system.

Figure 11.Image of the resolution target captured by the segmented-aperture optical system.

Figure 12 displays the results of image acquisition. Figure 12(a) shows the plasma source, and Figs. 12(b)12(f) shows images of plasma source at different timess. It can be observed that the developed segmented aperture imaging system is capable of synchronously obtaining clear multi-wavelength images of the flame.

Figure 12.Temperature field images of plasma source.

To acquire 2D temperature-field information with high precision, a segmented-aperture imaging system based on asymmetric surface profiles and aperture-division technology is proposed. This system is capable of simultaneously acquiring multiwavelength information of the temperature field. To address the asymmetric aberrations caused by the off-axis positioning of the subapertures, an input-output ray-relationship model is established, and a custom surface profile is fitted to compensate for the asymmetric aberrations. The designed segmented-aperture imaging lens has a focal length of 80 mm, relative aperture of 4, and the capability of four subimages (corresponding to wavelengths of 0.48, 0.55, 0.58, and 0.65 μm) for the four subapertures. Results for the design indicate that the imaging quality of the system is close to the diffraction limit across the entire field of view, and the asymmetric aberrations are well-corrected. Upon testing the developed segmented-aperture imaging system, the experimental results show that the system can simultaneously acquire multiwavelength images of the temperature field with high image clarity and uniform illumination, making it suitable for data acquisition in 2D temperature-field measurement.

Data underlying the results presented in this paper are not publicly available at the time of publication, but maybe obtained from the authors upon reasonable request.

  1. E. M. Vuelban, F. Girard, M. Battuello, P. Nemeček, M. Maniur, P. Pavlásek, and T. Paans, “Radiometric techniques for emissivity and temperature measurements for industrial applications,” Int. J. Thermophys. 36, 1545-1568 (2015).
    CrossRef
  2. F. Girard, M. Battuello, and M. Florio, “Multiwavelength thermometry at high temperature: Why it is advantageous to work in the ultraviolet,” Int. J. Thermophys. 35, 1401-1413 (2014).
    CrossRef
  3. W. Zhang, Q. Sun, S. Hao, J. Geng, and C. Lv, “Experimental study on the variation of physical and mechanical properties of rock after high temperature treatment,” Appl. Therm. Eng. 98, 1297-1304 (2016).
    CrossRef
  4. A. Araújo, “Analysis of multi-band pyrometry for emissivity and temperature measurements of gray surfaces at ambient temperature,” Infrared Phys. Technol. 76, 365-374 (2016).
    CrossRef
  5. H. Liu, S. Zheng, H. Zhou, and C. Qi, “Measurement of distributions of temperature and wavelength-dependent emissivity of a laminar diffusion flame using hyper-spectral imaging technique,” Meas. Sci. Technol. 27, 025201 (2016).
    CrossRef
  6. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, "Nodal aberration theory applied to freeform surfaces," in Internation Optical Design Conference (Optica Publishing Group, 2014), p. paper. ITh2A.
    CrossRef
  7. A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
    Pubmed KoreaMed CrossRef
  8. D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using freeform surfaces,” Opt. Eng. 57, 101704 (2018).
    CrossRef
  9. J. C. Miñano, P. Benítez, and B. Narasimhan, “Freeform aplanatic systems as a limiting case of SMS,” Opt. Express 24, 13173-13178 (2016).
    Pubmed CrossRef
  10. T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light: Sci. Appl. 6, e17081 (2017).
    Pubmed KoreaMed CrossRef
  11. G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55, 1303-1308 (2006).
    CrossRef
  12. J. M. Densmore, B. E. Homan, M. M. Biss, and K. L. McNesby, “High-speed two-camera imaging pyrometer for mapping fireball temperatures,” Appl. Opt. 50, 6267-6271 (2011).
    Pubmed CrossRef
  13. E. R. Wainwright, S. W. Dean, S. V. Lakshman, T. P. Weihs, and J. L. Gottfried, “Evaluating compositional effects on the laser-induced combustion and shock velocities of Al/Zr-based composite fuels,” Combust. Flame 213, 357-368 (2020).
    CrossRef
  14. D. J. Dagel, G. D. Grossetete, D. O. MacCallum, and S. P. Korey, “Four-color imaging pyrometer for mapping temperatures of laser-based metal processes,” Proc. SPIE 9861, 986103 (2016).
    CrossRef
  15. J. Cao, “Research on colorimetric temperature measurement method based on light field camera,” Ph. D. Thesis, Xi'an University of Electronic Science and Technology, China (2021).
  16. Y. Li, L. Zhou, Z. Li, R. Shi, X. Wang, and S. Yang, “All optical framing imaging technology based on diffractive optical elements,” Acta Opt. Sin. 41, 0232001 (2021).
    CrossRef
  17. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” J. Opt. Express 22, 26585-26606 (2014).
    CrossRef
  18. J.-B. Volatier and G. Druart, “Differential method for freeform optics applied to two-mirror off-axis telescope design,” Opt. Lett. 44, 1174-1177 (2019).
    Pubmed CrossRef

Article

Research Paper

Curr. Opt. Photon. 2024; 8(5): 484-492

Published online October 25, 2024 https://doi.org/10.3807/COPP.2024.8.5.484

Copyright © Optical Society of Korea.

Design of an Asymmetric-custom-surface Imaging Optical System for Two-dimensional Temperature-field Measurement

Guanghai Liu1,2, Ming Gao1 , Jixiang Zhao1, Yang Chen1

1Institute of Optical Information Technology, School of Optoelectronic Engineering, Xi′an Technological University, Xi’an, Shaanxi 710021, China
2Sichuan Physcience Optics and Fine Mechanics Co., Ltd., Mianyang 621000, China

Correspondence to:*guanghailiu@163.com, ORCID 0009-0004-5624-3148

Received: June 5, 2024; Revised: August 20, 2024; Accepted: August 26, 2204

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In response to the difficulty of synchronously obtaining multiwavelength images for fast two-dimensional (2D) temperature measurement, a multispectral framing imaging optical system is designed, based on the segmented-aperture imaging method and asymmetric surface shape. The system adopts a common-aperture four-channel array structure to synchronously collect multiwavelength temperaturefield images. To solve the problem of asymmetric aberration caused by being off-axis, a model of the relationship between incident and outgoing rays is established to calculate the asymmetric custom surface. The designed focal length of the optical system is 80 mm, the F-number is 1:3.8, and the operating wavelength range is 0.48–0.65 μm. The system is divided into four channels, corresponding to wavelengths of 0.48, 0.55, 0.58, and 0.65 μm respectively. The modulation transfer function value of a single channel lens is higher than 0.6 in the full field of view at 35 lp/mm. The experimental results show that the asymmetric-custom-surface imaging system can capture clear multiwavelength images of a temperature field. The framing imaging system can capture clear images of multiwavelength temperature fields, with high consistency in images of different wavelengths. The designed optical system can provide reliable multiwavelength image data for 2D temperature-field measurement.

Keywords: 2D temperature measurement, Asymmetric surface shape, Segmented aperture imaging

I. INTRODUCTION

In the subjects of combustion- and explosion-fields reconstruction, turbine-blade inspection, and engine-temperature analysis and detection [14], temperature fields feature characteristics such as rapid changes, requirements for high measurement accuracy, and significantly nonuniform temperature distributions [58]. These factors drive the development of technology toward high-precision two-dimensional (2D) temperature measurement [913]. In 2016, Dagel et al. [14] designed a four-color imaging pyrometer using a prism and four detectors, achieving temperature measurement with ultralarge dynamic range, from 900 to 3,800 K. However, the device is complex and high precision is required for the spectroscopic system, as even minor deviations in components can significantly impact its accuracy. In 2021, Cao [15] established a colorimetric light-field temperature-measurement system based on lens arrays. Through calibration experiments on the spectral-radiance brightness of light-field blackbodies, they derived a fitting relationship between the spectral-radiance brightness of the light-field temperature-measurement system and the grayscale values of the images. However, the imaging range of the lens array is extremely small, making it difficult to measure the entire temperature field. In 2021 Li et al. [16], aiming to meet the needs of ultrafast phenomena such as explosions and high-voltage discharges, developed a full-optical spatial segmented-aperture imaging system, using diffractive optical elements and narrowband filters. This system can achieve 16-segment aperture imaging in a 4 × 4 array across different wavelength bands, with a modulation transfer function (MTF) of 0.991 at a resolution of 35 lp/mm. However, the processing of diffractive elements is complex, and the diffraction efficiency decreases significantly at noncentral wavelengths.

The most feasible approach for 2D temperature measurement currently is multispectral segmented-aperture thermometry. The core device of this technology is the multiwavelength segmented-aperture imaging camera. Compared to traditional cameras, it divides the camera’s focal plane into multiple images corresponding to different wavelength channels. Through segmented apertures, it can capture multispectral images in real time, and then quickly reconstruct the 2D temperature-field distribution by combining radiation curve fitting.

Therefore, this article proposes a transient 2D temperature-field image-acquisition system based on aperture segmentation and asymmetric custom surface profiles. Aperture segmentation divides the focal plane into regions, to simultaneously acquire multiwavelength temperature images while ensuring consistency of information. The asymmetric custom surface profile has complete freedom in the meridional and sagittal directions, enabling the focusing of off-axis light rays and improving the imaging quality of the 2D temperature-measurement optical system. The segmented-aperture custom-surface-profile imaging system proposed in this paper can provide a technical approach for the acquisition of critical information in 2D temperature measurement.

II. Principle of the Asymmetric Surface Profiles

After segmenting the aperture of the optical system, there is a deviation between the optical axes of the main subaperture system and the common aperture system, resulting in asymmetric light beams incident upon the subaperture and causing inconsistent image aberrations in different fields of view along different directions, as shown in Fig. 1. Analysis is conducted using vector aberration theory. Based on the third-order aberration polynomials and the influence of tilted or eccentric elements on aberrations, the vector expression for the third-order wavefront aberration generated on the nth surface of a tilted or eccentric optical system can be obtained as follows [17, 18]:

Figure 1. Schematic diagram of asymmetric aberrations: (a) Causes of asymmetric aberrations, (b) asymmetric aberrations in symmetric subaperture optical groups, and (c) correction of asymmetric aberrations in asymmetric optical groups.

Wi=W040i(rr)2+W131iHSirrr          +W222iHSir2          ×W220iHSiHSirr          +W313iHSiHSiHSir,

where W is the aberration coefficient, and W040, W131, W222, W220, and W313 are the aberration coefficients of the spherical aberration, coma aberration, field curvature, astigmatism, and distortion respectively. H and r represent the vector forms of the normalized field point and aperture point at the entrance pupil of the system when there is no tilt or eccentricity, and Si denotes the deviation of the aberration field center. To address the inconsistencies in the system’s aberrations in the y-direction, this paper proposes the method of incorporating asymmetric custom surface profiles into the system, which utilizes surface profiles without rotational symmetry to correct the inconsistencies in the system’s aberrations in the y-direction.

To efficiently design asymmetric surface profiles, a model of the relationship between incident and exiting light rays is established. The incident light rays are considered as input variables, while the optical system can be viewed as a set of modulation functions. When both are known, the output variables and exiting light rays can be solved for. Similarly, if the input and output variables are known, the modulation function (or in this case the optical system’s surface-profile parameters) can be solved for in reverse. In the implementation of this paper, the incident light ray’s parameters can be calculated from the front-end common-aperture optical group, and the exiting light ray’s parameters can be determined based on the requirements of the segmented image-plane positions and the ideal imaging conditions of the approximate light rays. Through the established coordinate relationship between the incident and exiting light rays, the required asymmetric surface profile can be solved for.

2.1. Calculation of Incident Light Rays

2.1.1. Calculation of the Common-aperture Light Ray

Since the asymmetry of the light beam has a clearly directional nature, only the y-section direction is selected for analysis in the calculation. Using the theory of geometric optics, the calculation of the common-aperture optical path employs the formula for calculating the actual optical path on a per-surface basis:

sinIC=LCrCrCsinUCsinIC=n nsinICUC=UC+ICICLC=rC+rCsinICsinUC.

In the formulae above, IC and IC represent respectively the incidence angle and refraction angle of the light ray in the common-aperture optical group for the first surface, LC and LC represent respectively the incidence angle and refraction angle of the light ray in the common-aperture optical group for the second surface, rC is the curvature radius of the refracting surface, n and n′ are the refractive indices for the object side and image side respectively, and UC and UC are the object-side and image-side aperture angles of the light ray in the common-aperture optical group.

Assuming that the common-aperture system has m surfaces, the light ray’s parameters for the next surface can be obtained through the ray-tracing formula:

L2C=L1Cd1C,L3C=L2Cd2C,...,LmC=LmCdmCU2C=U1C,U3C=U2C,...,UmC=UmCn2C=n1C,n3C=n2C,...,nmC=nmC,

where diC represents the separation of the ith refracting surface in the common-aperture optical group.

2.1.2. The Coordinates of the Light Ray Exiting the Common-aperture Optical Group

Taking the vertex of the common-aperture refracting surface as the origin, and given that the curvature of the refracting surface is rmC, the coordinates (xmC, ymC) of the light ray exiting the common-aperture optical group are calculated as:

xmC2+ymC2=rmC2ymC=tanUmC×xmC+LmCtanUmC.

2.1.3. Coordinate Transformation from Common Aperture to Subaperture

Assuming that the offsets of the subaperture optical axis from the common-aperture optical axis in the x- and y-directions are Δx and Δy respectively, and that the separation between the last surface m of the common-aperture optical group and the subaperture is dmC, the coordinates (x1S, y1S) on the first surface of the subaperture optical group can be calculated as:

x1S=xmCΔxy1S=ymCΔydmC×tanUmCL1S=LmCdmCU1S=UmC.

2.2. Calculation of the Exiting Light Ray’s Coordinates

2.2.1. 2×2 Image-plane Segmentation

In the x and y directions, the detector sizes are set as LDX and LDY respectively, and the subaperture image-plane sizes are LISX and LISY. In the x direction, the center spacing is ∆LXC and the edge spacing is ∆LXE. In the y direction, the center spacing is ∆LYC and the edge spacing is ∆LYE.

LDX=2LISX+ΔLXC+2ΔLXELDY=2LISY+ΔLYC+2ΔLYE.

2.2.2. Calculation of the Ideal Point’s Coordinates

The ideal imaging position is calculated using the ideal imaging formula. Assuming a tolerance of δ relative to the ideal imaging position, a combined focal length of comb(fC, fS) for the common aperture and subaperture, a field of view angle of comb(fC, fS)in the y-direction, and an ideal imaging position of (xI, yI), the imaging range of the exiting light ray from the subaperture optical group on the image plane should satisfy:

xI=tanωCx×combfC,fSyI=tanωCy×combfC,fSxkS<xI±δykS<yI±δ.

2.3. Calculation of the Surface Profile

2.3.1. Asymmetric Wassermann-Wolf Surface Profile

By using the modified asymmetric Wassermann-Wolf formula, a model for incident and emergent light rays is established. From the known incident light ray, the coordinates of the emergent light ray are solved for, to calculate the asymmetric surface profile coordinates (xS, yS, zS):

zi=xkSnk1cosθxk1nk+1cosθxks+yksnk1cosθyk1nkscosθyksnk1cosθxk1+nkscosθxks.

In the formula above, nk is the refractive index, and cosθxk, 3cosθyk are the angles between the x- and y-direction vectors and the normal vector respectively.

2.3.2. Fitting the Surface Profile

Next, we select the aperture and field of view, calculate the surface profile’s coordinates, and perform fitting on the discrete coordinates.

The asymmetric custom surface design process and the relationship between incident and exiting light are shown in Fig. 2.

Figure 2. Asymmetric custom surface design flow and the relationship between incident and outgoing.

III. Results of System Design

3.1. Parameters and Design Results for the Segmented-aperture Imaging System

The segmented-aperture imaging optical system comprises a common-aperture optical group and a subaperture optical group. An asymmetric surface is added to the last surface of the subaperture optical group, to correct the asymmetric aberrations introduced by off-axis imaging. The performance specifications of the segmented-aperture imaging system are shown in Table 1.

TABLE 1. System parameters.

ParametricTarget
Wave Band (μm)0.48–0.65
Focal Length (mm)80
Image Number4
Hight of Image (mm)6
Imaging Interval (mm)6
F/#4


After inputting the calculated asymmetric surface profile into the optical-design software and performing simple optimization, the final system’s structure is obtained, as shown in Fig. 3. The system utilizes a common aperture to ensure imaging of the same target after aperture division, and it is characterized by a small number of lenses, compact size, and light weight.

Figure 3. Structural diagram of the segmented-aperture imaging system.

3.2. Image-quality Analysis

Figure 4 shows the asymmetric custom surface profile of the segmented-aperture imaging system. Figure 5 presents scatter plots for the symmetric and asymmetric subaperture optical groups, as can be seen from the figure, after adding the asymmetric custom surface, the size of the light spot converges, and the defocus of the convergence point is improved. Figure 6 depicts the MTF graph for the segmented-aperture imaging system. It can be observed that in the wavelength band of 0.48–0.65 μm, at the Nyquist frequency of 35 lp/mm the on-axis point is higher than 0.7, and the off-axis point is higher than 0.6. Figure 7 shows the system’s spot diagram, revealing that the root-mean-square value for the blur spot in the visible-light band is a maximum of 5.9 μm, indicating that the system’s imaging quality is close to the diffraction limit. Figure 8 displays the image-plane irradiance map after aperture division, demonstrating that the image irradiance remains consistent across the entire field of view, without the issue of vignetting after aperture division.

Figure 4. Asymmetric surface profile of the subaperture.

Figure 5. Scatter plots for (a) the symmetric subaperture optical group, and (b) the asymmetric subaperture optical group.

Figure 6. Modulation transfer function (MTF) diagram for the imaging system.

Figure 7. Spot diagram for the imaging system.

Figure 8. Relative-illuminance diagram for the imaging system.

IV. Testing of the Segmented-Aperture Imaging System

Figure 9 shows the processed segmented-aperture imaging system, which consists of a common-aperture optical group used to image a target. The four-channel segmented-aperture system splits the image of the same target into four separate images, forming them on four designated regions of the detector. At the end of the segmented-aperture system are optical filters to capture images of the target at different wavelengths, providing multiwavelength data for 2D temperature measurement.

Figure 9. Photographs of the segmented-aperture imaging system.

Figure 10 illustrates image acquisition with the segmented-aperture system, and Fig. 11 shows the image of the resolution target captured by the segmented-aperture optical system. From Fig. 11, it can be seen that the segmented-aperture imaging system can achieve clear imaging at multiple wavelengths.

Figure 10. Image acquisition with the segmented-aperture imaging system.

Figure 11. Image of the resolution target captured by the segmented-aperture optical system.

Figure 12 displays the results of image acquisition. Figure 12(a) shows the plasma source, and Figs. 12(b)12(f) shows images of plasma source at different timess. It can be observed that the developed segmented aperture imaging system is capable of synchronously obtaining clear multi-wavelength images of the flame.

Figure 12. Temperature field images of plasma source.

V. Conclusion

To acquire 2D temperature-field information with high precision, a segmented-aperture imaging system based on asymmetric surface profiles and aperture-division technology is proposed. This system is capable of simultaneously acquiring multiwavelength information of the temperature field. To address the asymmetric aberrations caused by the off-axis positioning of the subapertures, an input-output ray-relationship model is established, and a custom surface profile is fitted to compensate for the asymmetric aberrations. The designed segmented-aperture imaging lens has a focal length of 80 mm, relative aperture of 4, and the capability of four subimages (corresponding to wavelengths of 0.48, 0.55, 0.58, and 0.65 μm) for the four subapertures. Results for the design indicate that the imaging quality of the system is close to the diffraction limit across the entire field of view, and the asymmetric aberrations are well-corrected. Upon testing the developed segmented-aperture imaging system, the experimental results show that the system can simultaneously acquire multiwavelength images of the temperature field with high image clarity and uniform illumination, making it suitable for data acquisition in 2D temperature-field measurement.

FUNDING

This study is supported by the Shaanxi Provincial Department of Science and Technology (Grant No. 2024GX YBXM-041).

DISCLOSURES

The authors declare no conflicts of interest.

DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but maybe obtained from the authors upon reasonable request.

Fig 1.

Figure 1.Schematic diagram of asymmetric aberrations: (a) Causes of asymmetric aberrations, (b) asymmetric aberrations in symmetric subaperture optical groups, and (c) correction of asymmetric aberrations in asymmetric optical groups.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 2.

Figure 2.Asymmetric custom surface design flow and the relationship between incident and outgoing.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 3.

Figure 3.Structural diagram of the segmented-aperture imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 4.

Figure 4.Asymmetric surface profile of the subaperture.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 5.

Figure 5.Scatter plots for (a) the symmetric subaperture optical group, and (b) the asymmetric subaperture optical group.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 6.

Figure 6.Modulation transfer function (MTF) diagram for the imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 7.

Figure 7.Spot diagram for the imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 8.

Figure 8.Relative-illuminance diagram for the imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 9.

Figure 9.Photographs of the segmented-aperture imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 10.

Figure 10.Image acquisition with the segmented-aperture imaging system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 11.

Figure 11.Image of the resolution target captured by the segmented-aperture optical system.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

Fig 12.

Figure 12.Temperature field images of plasma source.
Current Optics and Photonics 2024; 8: 484-492https://doi.org/10.3807/COPP.2024.8.5.484

TABLE 1 System parameters

ParametricTarget
Wave Band (μm)0.48–0.65
Focal Length (mm)80
Image Number4
Hight of Image (mm)6
Imaging Interval (mm)6
F/#4

References

  1. E. M. Vuelban, F. Girard, M. Battuello, P. Nemeček, M. Maniur, P. Pavlásek, and T. Paans, “Radiometric techniques for emissivity and temperature measurements for industrial applications,” Int. J. Thermophys. 36, 1545-1568 (2015).
    CrossRef
  2. F. Girard, M. Battuello, and M. Florio, “Multiwavelength thermometry at high temperature: Why it is advantageous to work in the ultraviolet,” Int. J. Thermophys. 35, 1401-1413 (2014).
    CrossRef
  3. W. Zhang, Q. Sun, S. Hao, J. Geng, and C. Lv, “Experimental study on the variation of physical and mechanical properties of rock after high temperature treatment,” Appl. Therm. Eng. 98, 1297-1304 (2016).
    CrossRef
  4. A. Araújo, “Analysis of multi-band pyrometry for emissivity and temperature measurements of gray surfaces at ambient temperature,” Infrared Phys. Technol. 76, 365-374 (2016).
    CrossRef
  5. H. Liu, S. Zheng, H. Zhou, and C. Qi, “Measurement of distributions of temperature and wavelength-dependent emissivity of a laminar diffusion flame using hyper-spectral imaging technique,” Meas. Sci. Technol. 27, 025201 (2016).
    CrossRef
  6. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, "Nodal aberration theory applied to freeform surfaces," in Internation Optical Design Conference (Optica Publishing Group, 2014), p. paper. ITh2A.
    CrossRef
  7. A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
    Pubmed KoreaMed CrossRef
  8. D. Reshidko and J. Sasian, “Method for the design of nonaxially symmetric optical systems using freeform surfaces,” Opt. Eng. 57, 101704 (2018).
    CrossRef
  9. J. C. Miñano, P. Benítez, and B. Narasimhan, “Freeform aplanatic systems as a limiting case of SMS,” Opt. Express 24, 13173-13178 (2016).
    Pubmed CrossRef
  10. T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light: Sci. Appl. 6, e17081 (2017).
    Pubmed KoreaMed CrossRef
  11. G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55, 1303-1308 (2006).
    CrossRef
  12. J. M. Densmore, B. E. Homan, M. M. Biss, and K. L. McNesby, “High-speed two-camera imaging pyrometer for mapping fireball temperatures,” Appl. Opt. 50, 6267-6271 (2011).
    Pubmed CrossRef
  13. E. R. Wainwright, S. W. Dean, S. V. Lakshman, T. P. Weihs, and J. L. Gottfried, “Evaluating compositional effects on the laser-induced combustion and shock velocities of Al/Zr-based composite fuels,” Combust. Flame 213, 357-368 (2020).
    CrossRef
  14. D. J. Dagel, G. D. Grossetete, D. O. MacCallum, and S. P. Korey, “Four-color imaging pyrometer for mapping temperatures of laser-based metal processes,” Proc. SPIE 9861, 986103 (2016).
    CrossRef
  15. J. Cao, “Research on colorimetric temperature measurement method based on light field camera,” Ph. D. Thesis, Xi'an University of Electronic Science and Technology, China (2021).
  16. Y. Li, L. Zhou, Z. Li, R. Shi, X. Wang, and S. Yang, “All optical framing imaging technology based on diffractive optical elements,” Acta Opt. Sin. 41, 0232001 (2021).
    CrossRef
  17. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” J. Opt. Express 22, 26585-26606 (2014).
    CrossRef
  18. J.-B. Volatier and G. Druart, “Differential method for freeform optics applied to two-mirror off-axis telescope design,” Opt. Lett. 44, 1174-1177 (2019).
    Pubmed CrossRef
Optical Society of Korea

Current Optics
and Photonics


Min-Kyo Seo,
Editor-in-chief

Share this article on :

  • line