Mold design and pre-compensation of precision molding for diffractive optical elements

ZHANG Yunlong; JIAO Mingyin; WANG Zhibin; ZHANG Feng; ZHANG Zheng

doi:10.5768/JAO202243.0405002

Journal of Applied Optics > 2022 > 43(4): 760-765. > DOI: 10.5768/JAO202243.0405002

ZHANG Yunlong, JIAO Mingyin, WANG Zhibin, ZHANG Feng, ZHANG Zheng. Mold design and pre-compensation of precision molding for diffractive optical elements[J]. Journal of Applied Optics, 2022, 43(4): 760-765. DOI: 10.5768/JAO202243.0405002

Citation:

PDF (2800 KB)

Mold design and pre-compensation of precision molding for diffractive optical elements

Xi'an Institute of Applied Optics, Xi'an 710065, China

More Information

Received Date: December 23, 2021
Revised Date: February 27, 2022
Available Online: May 13, 2022

Graphical Abstract

Abstract

Abstract

The diffractive optical elements (DOE) have great advantages in correcting chromatic aberration compared with spherical and aspheric optical selements, especially in the field of infrared optics, the application of DOE can further increase the design freedom of optical systems. With the further expansion of infrared optics market, the conventional single point diamond turning technology of diffraction optics is difficult to meet the large-scale demands, so the precision molding technology has become the key technology to solve the above problems. The mold design is one of the key points of precision molding. In order to reduce the mold design cycle, the pre-design and pre-correction of mold were carried out by using the finite element simulation method, and then the mold was processed. The single-station precision molding machine was adapted for precision molding test of designed molds. The test results show that, with the reasonable process parameters, the PV value of the surface shape accuracy of DOE can reach 0.56 μm, the position error is less than 0.011 mm, and the height error of the band is less than 0.12 μm, which verifies the effectiveness of the simulation pre-compensation in the design of diffractive optical molds.
- diffractive optical elements,
- precision molding,
- mold design,
- chalcogenide glass

FullText(HTML)

0. Introduction

With the continuous development of infrared optical systems in the fields of military affairs and national defense, a single waveband infrared imaging system can no longer satisfy the requirements of detective system. Dual-band focal plane array and dual infrared optical system enable simultaneous imaging onto the same detector in two spectral wavebands^[1-3]. In order to prevent the change of ambient environmental temperature from affecting the performance of the infrared optical system, it is generally required to realize athermalization within a certain temperature range. It is difficult to obtain good imaging quality, and hard to achieve athermalization because the optical materials that can be used for the infrared dual-band optical system are very limited. Diffractive optical elements (DOEs) can provide some degree of freedom in infrared optical system due to its special negative dispersion and thermal expansion properties^[4-5]. The diffraction efficiency of single-layer DOEs or harmonic diffractive elements (HDEs) drops rapidly as the wavelength deviates from the design wavelength. The working waveband of the optical system with DOEs is narrow as the modulation transfer function is proportional to the diffraction efficiency of DOEs^[6]. Accompanied with the appearance of multi-layer DOEs (MLDOEs) which can achieve a high diffraction efficiency over a wide spectral range, the optical systems working in wide waveband are studied a lot^[7-9].

A refractive-diffractive hybrid infrared optical system working at 8 μm~12 μm is designed, which can realize athermalization over the temperature range from -40 ℃to 60 ℃ in Ref. [10]. An uncooled optical system working at 3 μm~5 μm and 8 μm~12 μm dual infrared waveband is designed, which can realize athermalization over the temperature range from -50 ℃ to 60 ℃ in Ref. [11]. All the above designed optical system is uncooled. A four-channel cooled infrared dual-band optical system working at 3.5 μm~4.8 μm and 7.8 μm~9.8 μm is designed in Ref.[12], each optical system of imaging channel is designed to be double imaging configuration, and the structure of this optical system is complicated.

Based on the special properties of DOEs, a cooled infrared dual-band optical system with double-layer DOEs is designed in this paper. The working waveband is the mid-wave infrared (MWIR) 3.7 μm~4.8 μm and the long-wave infrared (LWIR) 7.9 μm~9.5 μm. The cooled focal plane array is 320×256 and the pixel pitch is 30 μm. The designed optical system realizes athermalization over the temperature range from -55℃ to 71℃. The polychromatic integral diffraction efficiency (PIDE) of double-layer DOEs is above 99.15% over the whole working wavebands. The comprehensive PIDE of the double-layer DOEs are 99.81% and 97.36% for the MWIR and LWIR waveband, respectively.

1. Theoretical diffraction efficiency of MLDOEs

Diffraction efficiency is an important parameter for evaluating DOEs and refractive-diffractive hybrid optical system with DOEs. The magnitude of diffraction efficiency determines the possibility of application and the working waveband of the DOEs. MLDOEs, composed of N HDEs with different dispersion materials. The general formula of phase retardation of MLDOEs as a function of incident angle is ^[13-14]

$\phi \left( \lambda \right) = \sum\limits_{i = 1}^N {\frac{{{d_i}\left[ {{n_{ij}}\left( \lambda \right)\cos {\theta _{ij}} - {n_{it}}\left( \lambda \right)\cos {\theta _{it}}} \right]}}{\lambda }} ,$

(1)

where d_i is the designed microstructure height of the ith HDEs, n_ij(λ) and n_it(λ) are the refractive index of the incident medium and emergent medium of the ith HDEs at the wavelength of λ respectively, θ_ijand θ_it are the incident and emergent angles of the ith HDEs. After a mathematical derivation, the relationship of diffraction efficiency of MLDOEs and incidence angle is expressed as

${n_m} = \sin {c^2}\left\{ {m - \sum\limits_{i = 1}^n {\frac{{{d_i}\left[ {\sqrt {n_{i,j}^2\left( \lambda \right) - {{\left( {{n_{1j}}\left( \lambda \right)\sin {\theta _{1j}}} \right)}^2}} - \sqrt {n_{i,t}^2\left( \lambda \right) - {{\left( {{n_{1j}}\left( \lambda \right)\sin {\theta _{1j}}} \right)}^2}} } \right]}}{\lambda }} } \right\}$

(2)

where sin c(x)=sin(πx)/(πx), m is the diffraction order. The PIDE of the mth diffraction order is

${{\bar \eta }_m}\left( \lambda \right) = \frac{1}{{{\lambda _{\max }} - {\lambda _{\min }}}}\int_{{\lambda _{\min }}}^{{\lambda _{\max }}} {\sin {c^2}} \left\{ {m - \sum\limits_{i = 1}^N {\frac{{{d_i}\left[ {\sqrt {n_{i,j}^2(\lambda ) - {{\left( {{n_{1j}}(\lambda )\sin {\theta _{1j}}} \right)}^2}} - \sqrt {n_{i,t}^2(\lambda ) - {{\left( {{n_{1j}}(\lambda )\sin {\theta _{1j}}} \right)}^2}} } \right]}}{\lambda }} } \right\}{\rm{d}}\lambda$

(3)

where λ_min and λ_max are respectively the minimum wavelength and maximum wavelength for the working waveband, and all the wavelengths are considered to be equally weighted. For MLDOEs working within a range of incident angle, the comprehensive PIDE is

${{\bar \eta }_{mc}}(\theta ) = \frac{1}{{{\theta _{\max }} - {\theta _{\min }}}}\int_{{\theta _{\min }}}^{{\theta _{\max }}} {{{\bar \eta }_m}} {\rm{d}}\theta$

(4)

where θ_minand θ_max are the minimum and maximum incident angles, respectively. According to Eq. (4), the comprehensive PIDE of MLDOEs working within a range of incident angle is calculated. When the imaging optical system with MLDOEs working with a few separate field of views, for example, the zoom system, the comprehensive PIDE is expressed as

$\begin{array}{l} {{\bar \eta }_{{\rm{m}}c}}(\theta ) = \frac{{{\omega _1}}}{{{\theta _{1\max }} - {\theta _{1\min }}}}\int_{{\theta _{1\min }}}^{{\theta _{ lmax }}} {{{\bar \eta }_m}} {\rm{d}}\theta + \frac{{{\omega _2}}}{{{\theta _{2\max }} - {\theta _{2\min }}}}\mathop \smallint \nolimits_{{\theta _{2\min }}}^{{\theta _{2\max }}} \\ {{\bar \eta }_{\rm{m}}}{\rm{d}}\theta + \cdots + \frac{{{\omega _K}}}{{{\theta _{K\max }} - {\theta _{K\min }}}}\int_{{\theta _{k\min }}}^{{\theta _{K\max }}} {{{\bar \eta }_m}} {\rm{d}}\theta \end{array}$

(5)

where θ_iminand θ_imax are the minimum and maximum incident angles respectively for the ith field of view, ω_i is the weight factor for the ith field of view, K stands for the number of field of view. If the imaging quality of the hybrid refractive-diffractive optical system is analyzed equally for each field of view, the weight factor for every field of view is equal, namely, ω₁=ω₂=…=ω_k=1/K.

2. Design of infrared dual-band optical system

For the infrared dual-band imaging optical system working within the MWIR 3.7 μm~4.8 μm and LWIR 7.7 μm~9.5 μm, it is demanded to satisfy three equations, the focal power distribution equation, achromatic equation and athermalized equation, to realize athermalization and achromatism simultaneously for the two wavebands. The three equations are

$\sum\limits_{i \to 1}^n {{h_i}} {\phi _i} = \phi$

(6)

$\Delta f_b^T = {\left( {\frac{1}{{{h_1}\phi }}} \right)^2}\sum {\left( {h_i^2{\omega _i}{\phi _i}} \right)} = 0$

(7)

$\Delta f_b^T = {\left( {\frac{1}{{{h_1}\phi }}} \right)^2}\sum {\left( {h_i^2{\chi _i}{\phi _i}} \right)} = {\alpha _h}L$

(8)

where h_i is the incident height of the first paraxial ray on the ith lens, Φ_i is the focal power of the ith lens; Φ is the total focal power of the optical system; f_b is the back focal length (BFL) of the optical system; ω_i is the dispersion factor of the ith lens, which is the relative change of focal power due to dispersion, and equal to the inverse of the Abbe number of the optical material ^[15]; x_i is the thermal expansion coefficient of the ith lens; α_h is the linear expansion coefficient of the total system; L is the length of the mechanical structure.

2.1 Athermal design of infrared dual-band optical system with double-layer DOEs

Based on the unique achromatic and athermalized properties of DOEs, an infrared dual-band optical system with double-layer DOEs is designed working within the two wavebands of 3.7 μm~4.8 μm and 7.7 μm~9.5μm. The focal length is demanded to be 200 mm, based on the configuration of Petzval objective, the structure of the designed infrared dual-band optical system is secondary imaging configuration as shown in Fig. 1, with only six lenses, three infrared optical materials, Ge, ZnSe and ZnS. The front group of the optical system are three separated lenses, and the rear group are double-layer DOEs and one single lens. F # is 2. The cooled focal plane array is 320×256 and the pixel pitch is 30 μm. The field of view is ±1.76°.

Figure 1. Structure of infrared dual-band optical system

DownLoad: Full-Size Img PowerPoint

2.2 Performance of designed optical system

The modulation transfer function (MTF) curves of MWIR and LWIR of the optical system at 20 ℃ are shown in Fig. 2 (a) and (b), respectively. The MTF is higher than 0.70 and 0.55 at the frequency of 17 lp/mm for MWIR and LWIR. The MTF curves of MWIR and LWIR of the optical system at -55 ℃ and 71℃ are shown in Fig. 3. Table 1 shows the minimum MTF for MWIR and LWIR at some different temperatures. The MTF is higher than 0.66 and 0.54 at the frequency of 17 lp/mm for MWIR and LWIR, with the imaging quality close to the diffraction limit. The designed infrared dual-band optical system realizes athermalization within the temperature range of -55℃~71℃.

Figure 2. MTF curves of MWIR and LWIR at 20 ℃

DownLoad: Full-Size Img PowerPoint

Figure 3. MTF curves of MWIR and LWIR at -55℃ and 71℃

DownLoad: Full-Size Img PowerPoint

Table 1. Minumum MTF at different temperatures

Temperature/℃	-55	-29.8	-4.6	20	45.9	71
MTF_MW	0.74	0.74	0.72	0.70	0.68	0.66
MTF_LW	0.54	0.56	0.56	0.55	0.54	0.54

| Show Table

DownLoad: CSV

The RMS radius of MWIR and LWIR are respectively 11.503 μm and 8.332 μm at 20℃ as shown is Fig. 4(a) and (b), both less than the pixel size 30 μm. For different field of view, the RMS radius of the full field of view is the maximum. Table. 2 is the RMS radius of the full field of view at some different temperatures. The maximum RMS radiuses are less than 11.702 μm and 9.021 μm for the MWIR and LWIR waveband, respectively, which are both smaller than the pixel size 30 μm.

Figure 4. Spot diagram of MWIR and LWIR at 20 ℃

DownLoad: Full-Size Img PowerPoint

Table 2. RMS radius of the full field at some different temperatures

Temperature/℃	-55	-29.8	-4.6	20	45.9	71
RMS radius of MWIR/μm	9.694	10.459	11.095	11.503	11.702	11.702
RMS radius of LWIR/μm	9.021	8.532	8.388	8.332	8.248	8.105

| Show Table

DownLoad: CSV

Table 3 shows the wavefront errors at some different temperatures. The maximum wavefront error is 0.191 7λ at 71℃ for the MWIR waveband, and 0.132 8λ at 71℃ for the LWIR waveband, both smaller than 0.25λ, so the image quality is great.

Table 3. Wavefront error at some different temperatures

Temperature/℃	-55	-29.8	-4.6	20	45.9	71
Wavefront error of MWIR/λ	0.0986	0.0724	0.0738	0.0958	0.1367	0.1917
Wavefront error of LWIR/λ	0.0935	0.0797	0.0793	0.0891	0.1077	0.1328

| Show Table

DownLoad: CSV

The focus depths of the designed optical system are ±33.6 μm and ±71.2 μm for the MWIR and LWIR waveband, respectively. The defocus at different temperatures is compared to that at 20℃, as shown in Table. 4. The maximal defocus from the temperature range from -55℃ to 71℃ are 10.48 μm and 9.79 μm respectively for the MWIR and LWIR waveband, the maximal defocus is less than focus depth.

Table 4. Defocus of designed optical system at different temperatures

Temperature/℃	-55	-29.8	-4.6	20	45.9	71
Defocus_MW /μm	3.20	-1.14	- 1.94	0	4.33	10.48
Defocus_LW /μm	4.14	-0.05	-1.61	0	3.99	9.79

| Show Table

DownLoad: CSV

3. Diffraction efficiency of double-layer DOEs

The substrate materials of the double-layer DOEs are ZnSe and ZnS. The relationship of PIDE and wavelength for the double-layer DOEs is shown in Fig. 5. The PIDE of the double-layer DOEs over the whole working waveband is above 99.15%^[16], which can be widely used in infrared dual-band optical system. The incident angle upon the diffractive surface is within the range of 0°~5.19°. Assuming the weight factor for every field of view is equal, the comprehensive PIDE of the double-layer DOEs are 99.81% and 97.36% for the MWIR and LWIR waveband, respectively.

Figure 5. PIDE of double-layer DOEs

DownLoad: Full-Size Img PowerPoint

4. Conclusion

The analysis model of comprehensive PIDE for MLDOEs working within a range of incident angle is established. MLDOEs can achieve a high diffraction efficiency over a wide waveband, an infrared dual-band optical system with double-layer DOEs working at 3.7 μm~4.8 μm and 7.7 μm~9.5 μm dual infrared waveband is designed. The cooled focal plane array is 320×256 and the pixel pitch is 30 μm. The maximal RMS radius of the designed optical system is less than 11.702 μm, the wavefront error is smaller than 0.191 7λ, and the absolution of maximal defocus is less than 10.48 μm. The designed optical system realizes athermalization over the temperature range from -55℃ to 71℃. The PIDE of double-layer DOEs is above 99.15% over the whole working wavebands. The incident angle upon the diffractive surface is within the range of 0°~5.19°. Assuming the weight factor for every field of view is equal, the comprehensive PIDE of the double-layer DOEs are 99.81% and 97.36% for the MWIR and LWIR waveband, respectively. The optical system can be applied to infrared dual-band detection system and has broad application prospect in the infrared thermal imaging system in military and defense fields.

References (15)

References

[1]	ZHANG Yunlong, WANG Zhibin, ZHANG Feng, et al. Processing and error compensation of diffractive optical element[C]//7th International symposium on advanced optical manufacturing and testing technologies. USA: SPIE, 2006, 9280: 92800G.
[2]	张峰, 汪志斌, 张云龙, 等. 衍射光学元件车削补偿技术的研究[J]. 应用光学,2014,35(6):1058-1062. ZHANG Feng, WANG Zhibin, ZHANG Yunlong, et al. Diamond turning compensation techniques of diffractive optical elements[J]. Journal of Applied Optics,2014,35(6):1058-1062.
[3]	林常规, 郭小勇, 王先锋, 等. As₂Se₃硫系玻璃非球面镜片的精密模压成型[J]. 红外与激光工程,2019,8(7):0742002-1-7. LIN Changgui, GUO Xiaoyong, WANG Xianfeng, et al. Precision molding of As₂Se₃ chalcogenide glass aspheric lens[J]. Infrared and Laser Engineering,2019,8(7):0742002-1-7.
[4]	汪志斌, 李军琪, 张峰, 等. 硫系红外玻璃精密模压模具有限元仿真设计[J]. 光电工程, 2016, 43(5): 53-58. WANG Zhibin, LI Junqi, ZHANG Feng, et al. The design of mold with simulation for chalcogenide glass precision molding[J]. Opto-Electronic Engineering, 2016, 43(5): 53-58.
[5]	ZHANG Y, LIANG R, SPIRES O J, et al. Precision glass molding of diffractive optical elements with high surface quality[J]. Opt. Lett.,2020,45(23):6438-6441. doi: 10.1364/OL.406195
[6]	YI A Y, CHEN Y, KLOCKE F. , et al. A high volume precision compression molding process of glass diffractive optics by use of a micromachined fused silica wafer mold and low Tg optical glass[J]. Journal of Micromechanics and Microengineering,2006,16(10):2000-2005. doi: 10.1088/0960-1317/16/10/012
[7]	ZHOU T, ZHU Z, LIU X, et al. A review of the precision glass molding of chalcogenide glass (ChG) for infrared optics[J]. Micromachines, 2018, 9(7): 337.
[8]	KLOCKE F, DAMBON O, LIU G, et al. Analysis of wear of fused silica moulding using glassy carbon moulds[J]. Production Engineering,2016,10(4):367-374.
[9]	ZHANG Y, ZHOU W, SPIRES O, et al. Precision glass molding for diffractive optics[C]. USA: OSA Technical Digest, 2020.
[10]	PRATER K, DUKWEN J, SCHARF T, et al. Micro-structuring of glassy carbon for precision glass molding of binary diffractive optical elements[J]. Optical Materials Express,2016,6(11):3407-3416. doi: 10.1364/OME.6.003407
[11]	LIU Y, XING Y, FU H, et al. Deformation analysis of the glass preform in the progress of precision glass molding for fabricating chalcogenide glass diffractive optics with the finite element method[J]. Micromachines,2021,12(12):1543. doi: 10.3390/mi12121543
[12]	HAMBLEN D P. Diffractive optics: the gradial zone lens[J]. Optics Letters,1994,19(21):1687-1689. doi: 10.1364/OL.19.001687
[13]	ZHANG Yunlong, WANG Zhibin, ZHANG Feng, et al. Research on molding of chalcogenide glass diffractive optical element [C]. USA: SPIE, 2022.
[14]	MADAPUSI S, KIM N H, TOMHE Y. Predictive molding of precision glass optics[J]. SAE International Journal of Materials and Manufacturing,2009,2(1):494-501. doi: 10.4271/2009-01-1199
[15]	ZHANG L, LIU W. Precision glass molding: Toward an optimal fabrication of optical lenses[J]. Front. Mech. Eng.,2017(12):3-17.

[1]	ZHANG Jiyan, LIN Haifeng, HUANG Zhangchao. Compact large relative aperture long wavelength infrared athermalization optical system with chalcogenide glasses[J]. Journal of Applied Optics, 2021, 42(5): 790-795. DOI: 10.5768/JAO202142.0501005
[2]	WANG Xiaobo, WANG Xi, LIU Guangkang, XIA Shuce, FU Mingliang, HAO Xinjian, CAO Qiankun. Design of athermal and lightweight optical system based on long-wave infrared detector[J]. Journal of Applied Optics, 2021, 42(3): 429-435. DOI: 10.5768/JAO202142.0301009
[3]	Li Jie, Qiu Yafeng, Qian Yunsheng, Qian Xin. Design and research of glass fiber making system based on MCP[J]. Journal of Applied Optics, 2018, 39(1): 112-116. DOI: 10.5768/JAO201839.0105001
[4]	MA Bo-tao, PEI Chun-yan, Li Xiao-chun. Modified formula of environmental conditions in precision measurement of optical glass refractive index[J]. Journal of Applied Optics, 2012, 33(5): 936-939.
[5]	LIU Jun-han, YAN De-quan, ZHOU Yang. High precision glass drilling technology[J]. Journal of Applied Optics, 2009, 30(2): 309-312.
[6]	ZHANG Bao-an, CHEN He-ming, ZHU Jian-qiang. Quality control in large-aperture laser glass optical processing[J]. Journal of Applied Optics, 2009, 30(1): 96-100.
[7]	REN Shu-feng, XU Xing-lei, ZHANG Yun-hai, WU Fu-quan. Design of parallel beam-splitting Nicol prism with combination of Iceland spar and glass[J]. Journal of Applied Optics, 2007, 28(3): 297-300.
[8]	WANG Yao-xiang. Development and Applications of Optical Glasses[J]. Journal of Applied Optics, 2005, 26(5): 61-066.
[9]	HUANG Hai, BU Sheng-li. Research on Faraday Effect in Magneto-optic Glass[J]. Journal of Applied Optics, 2004, 25(4): 14-17.
[10]	GU Tong-zhao, ZHU Mao-hua, CAO Wang-he. Study on Radiative Lifetimes of Rare Earth Ions in Tellurite Glasses[J]. Journal of Applied Optics, 2004, 25(3): 9-10.

Cited By

Cited by

Periodical cited type(1)

丁一飞, 王永红, 胡悦, 黄安琪, 但西佐. 样本块匹配光栅投影阶梯标定方法. 中国测试. 2016(08): 7-12 .

Other cited types(2)

Figures(7) / Tables(4)

Get Citation

PDF

XML

Article views (590) PDF downloads (70) Cited by(3)

Turn off MathJax

Article Contents

Abstract

0. Introduction

1. Theoretical diffraction efficiency of MLDOEs

2. Design of infrared dual-band optical system

3. Diffraction efficiency of double-layer DOEs

4. Conclusion

References

Mold design and pre-compensation of precision molding for diffractive optical elements